Engineering Analysis and Design

Engineering systems entail uncertainties of many sorts: loads, material properties, environmental conditions, etc. Info-gap theory has been applied in many analyses of design, safety and reliability.

• Questions or comments on info-gap theory? Contact me at yakov@technion.ac.il
• Yakov Ben-Haim, 2006, Info-gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, London.
  • Chapter 3: Robustness and Opportuneness.
    • Section 3.2.1: Engineering design: Cantilever.
    • Section 3.2.2: Structural reliability.
    • Section 3.2.3: Structural reliability with uncertain probability.
  • Chapter 5: Antagonistic and Sympathetic Immunities.
    • Section 5.3: Vibrating Mechanical Contact.
  • Chapter 7: Value of Information.
    • Section 7.3 Uncertain loads on a cantilever.
    • Section 7.4 Cantilever: Simple and complex info-gap models.
  • Chapter 8: Learning.
    • Section 8.2: Info-gap supervision of a classifier.
    • Section 8.3: Acoustic noise.
       
• Yakov Ben-Haim, 2005, Info-gap Decision Theory For Engineering Design. Or: Why `Good’ is Preferable to `Best’, appearing as chapter 11 in Engineering Design Reliability Handbook, Edited by Efstratios Nikolaidis, Dan M.Ghiocel and Surendra Singhal, CRC Press, Boca Raton. Pre-print.
   
• K.Jaboviste, E.Sadoulet-Reboul, N.Peyret, C.Arnould, E.Collard, G.Chevallier, 2019, On the compromise between performance and robustness for viscoelastic damped structures, Mechanical Systems and Signal Processing, 119: 65-80. Abstract.
   
• Koki Makita, Kyoichiro Kondo and Izuru Takewaki, 2018, Critical ground motion for resilient building design considering uncertainty of fault rupture slip, Front. Built Environ., 07 November 2018, doi.org/10.3389/fbuil.2018.00064. Abstract.
   
• Yakov Ben-Haim, 2018, Cascading failures: A preliminary info-gap analysis, presented at an International Workshop on Cascading Disasters: Theory, Methods and Empirics, Technion, 28-29.11.2018. Working draft.
   
• Seyed-Ehsan Razavi, Ali Esmaeel Nezhad, Hani Mavalizadeh, Fatima Raeisi, Abdollah Ahmadi, 2018, Robust hydrothermal unit commitment: A mixed-integer linear framework, Energy, vol. 165, pp. 593-602. Abstract.
   
• Maryam Soltani, Reza Kerachian, Mohammad reza Nikoo, Hamideh Noory, 2018, Planning for agricultural return flow allocation: Application of info-gap decision theory and a nonlinear CVaR-based optimization model, Environmental Science and Pollution Research, DOI: 10.1007/s11356-018-2544-7. Abstract.
   
• Koki Makita, Mitsuru Murase, Kyoichiro Kondo and Izuru Takewaki, 2018, Robustness evaluation of base-isolation building-connection hybrid controlled building structures considering uncertainties in deep ground, Frontiers in Built Environment, 4:16. DOI 10.3389/fbuil.2018.00016. Abstract.
   
• Deping Ke , Feifan Shen, C. Y. Chung , Chen Zhang , Jian Xu , and Yuanzhang Sun, 2018, Application of information gap decision theory to the design of robust wide-area power system stabilizers considering uncertainties of wind power, IEEE Transactions on Sustainable Energy, vol. 9, no. 2, April 2018, pp.805-817. Abstract.
   
• Yakov Ben-Haim, 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin.
   
• Yakov Ben-Haim, 2017, Does a better model yield a better argument? An info-gap analysis, Proceedings of the Royal Society, A, 5 April 2017. Abstract. Pre-publication version. Link to PRSA site. Summarized on Phys.org here.
   
• Yoshihiro Kanno, Shinnosuke Fujita and Yakov Ben-Haim, 2018, Structural Design for earthquake resilience: Info-gap management of uncertainty, Structural Safety, to appear. Pre-publication version.
   
• Yoshihiro Kanno, Keisuke Yasuda, Kohei Fujita, Izuru Takewaki, 2017, Robustness of SDOF elastoplastic structure subjected to double-impulse input under simultaneous uncertainties of yield deformation and stiffness, International Journal of Non–Linear Mechanics, 91: 151-162. Abstract.
   
• Platz, R and Goetz, B., 2017, Non-probabilistic uncertainty evaluation in the concept phase for airplane landing gear design, Proceedings of the Society for Experimental Mechanics, Volume 3 Part F2, 2017, Pages 161–169, 35th IMAC Conference and Exposition on Structural Dynamics, 2017; Garden Grove; United States; 30.1–2.2.2016. Abstract.
   
• Farkhondeh Jabari, Sayyad Nojavan, Behnam Mohammadi-ivatloo, Hadi Ghaebi and Hasan Mehrjerdi, 2018, Risk-constrained scheduling of solar Stirling engine based industrial continuous heat treatment furnace, Applied Thermal Engineering, Vol.128, #5, pp.940-955. Abstract.
   
• Sayyad Nojavan, Majid Majidi, Kazem Zare, 2017, Performance improvement of a battery/PV/fuel cell/grid hybrid energy system considering load uncertainty modeling using IGDT, Energy Conversion and Management, Volume 147, #1 pp.29-39. Abstract.
   
• Sayyad Nojavan, Majid Majidi, Kazem Zare, 2017, Risk-based optimal performance of a PV/fuel cell/battery/grid hybrid energy system using information gap decision theory in the presence of demand response program, Intl Journal of Hydrogen Energy, to appear. Abstract.
   
• Yakov Ben-Haim, 2016, Innovation Dilemmas, Design Optimization, and Info-Gaps, 34th International Modal Analysis Conference (34th IMAC), 25-28.1.2016, Orlando, Florida, appearing as chapter 15 in Model Validation and Uncertainty Quantification, Volume 3, Proceedings of the 34th IMAC, Springer. Pre-print.
   
• Ahmed E. Al-Juaidi and Tarek Hegazy, 2017, Conflict resolution for Sacramento-San-Joaquin delta with stability and sensitivity analyses using the graph model, British Journal of Mathematics & Computer Science, vol. 20 (5): 1-10, DOI: 10.9734/BJMCS/2017/31225. Abstract.
   
• Ahmed E. M. Al-Juaidi, 2017, Decision support system analysis with the graph model on non-cooperative generic water resource conflicts, International Journal of Engineering & Technology, 6 (4): 145-153. Abstract.
   
• Ahmed E. Al-Juaidi, 2017, Decision support system with multi-criteria, stability, and uncertainty analysis for resolving the municipal infrastructure conflict in the city of Jeddah, Journal of King Saud University – Engineering Sciences, to appear. Abstract.
   
• Ali Mehdizadeh, Navid Taghizadegan, Javad Salehi, 2018, Risk-based energy management of renewable-based microgrid using information gap decision theory in the presence of peak load management, Applied Energy, 211: 617-630. Abstract.
   
• Morteza Aien, Ali Hajebrahimi, Mahmud Fotuhi-Firuzabad, 2016, A comprehensive review on uncertainty modeling techniques in power system studies. Renewable and Sustainable Energy Reviews, 57: 1077-1089.
  
  Abstract

  Abstract

  As a direct consequence of power systems restructuring on one hand and unprecedented renewable energy utilization on the other, the uncertainties of power systems are getting more and more attention. This fact intensifies the difficulty of decision making in the power system context; therefore, the uncertainty analysis of the system performance seems necessary. Generally, uncertainties in any engineering system study can be represented probabilistically or possibilistically. When sufficient historical data of the system variables is not available, a probability density function (PDF) might not be defined, they must be represented in another manner i.e. using possibilistic theory. When some of the system uncertain variables are probabilistic and some are possibilistic, neither the conventional pure probabilistic nor pure possibilistic methods can be implemented. Hence, a combined solution is needed. This paper gives a complete review on uncertainty modeling approaches for power system studies making sense about the strengths and weakness of these methods. This work may be used in order to select the most appropriate method for each application.

  Author keywords

  Decision making, Probabilistic uncertainty modeling, Possibilistic uncertainty modeling, Uncertain power system studies, Joint possibilisticג€“probabilistic uncertainty modeling
  

• Wei-Chih Lin, Yu-Pin Lin, and Yung-Chieh Wang, 2016, A decision-making approach for delineating sites which are potentially contaminated by heavy metals via joint simulation, Environmental Pollution, 211: 98-110.
  
  Abstract

  Abstract

  This work develops a new approach for delineating sites that are contaminated by multiple soil heavy metals and applies it to a case study. First a number of contaminant sample data are transformed into multiple spatially un-correlated factors using Uniformly Weighted Exhaustive Diagonalization with Gauss iterations (U-WEDGE). Sequential Gaussian simulation (sGs) is then used to generate sets of realizations of each resultant factor. These are then transformed into sets of sGs contaminant distribution realizations, which are then used to analyze the local and spatial (global) uncertainties in the distribution and concentration of contaminants via joint simulation. Finally, Info-Gap Decision Theory (IGDT) is used to consider different monitoring and or remediation regimes based on the analysis of contaminant realization spatial uncertainty. In our case study each heavy metal contaminant was considered individually and together with all other heavy metals; as the number of heavy metals considered increased, higher critical proportion values of local probability were chosen to obtain a low global uncertainty (to provide high reliability). Info-Gap Decision Theory (IGDT) yielded the most appropriate critical proportion values which minimized information loss in terms of specific goals. When the false negative rate is set to zero, meaning that it is necessary to monitor all potentially polluted areas, the corresponding false positive rates are at least 63%, 65%, 66%, 68%, 70%, and 78% to yield robustness levels of 0.50, 0.60, 0.70, 0.80, 0.90, and 1.00 respectively. However, when the false negative rate tolerance threshold is raised to 50%, the false positive rate tolerance which yields robustness levels of 0.50, 0.60, 0.70, 0.80, 0.90 and 1.00 drop to 12%, 14%, 15%, 18%, 20%, and 39%. The case study demonstrates the effectiveness of the developed approach at making robust decisions concerning the delineation of sites contaminated by multiple heavy metals.

  keywords

  Decision-making, Robustness, Contaminated sites, Conditional simulation, Uncertainty, Heavy metals, Soil, GIS.
  

• Ghodsi, S.H.,  Kerachian, R.,  Estalaki, S.M.,  Nikoo, M.R.,  Zahmatkesh, Z., 2016, Developing a stochastic conflict resolution model for urban runoff quality management: Application of info-gap and bargaining theories, Journal of Hydrology, Vol. 533: 200-212.
  
  Abstract

  Abstract

  In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.

  Keywords:

  Bargaining theory; Info-gap theory; Low Impact Development (LID); SWMM; Uncertainty analysis; Urban runoff.
  

• Yakov Ben-Haim, 2015, Info-gap theory: An intuitive overview for engineering design and reliability assessment, ESREL 2015, European Safety and Reliability Conference, 7-10.9.2015, Zurich, Switzerland. Pre-print.
   
• Yakov Ben-Haim, Xavier Irias and Roberts McMullin, 2015, Managing technological and economic uncertainties in design of long-term infrastructure projects: An info-gap approach, 25th CIRP Design Conference, Procedia CIRP, 36 pp. 59-63, Haifa, Israel. Pre-print.
   
• Mohammad Sadegh Javadi, Amjad Anvari-Moghaddam and Josep M. Guerrero, 2017, Robust energy hub management using information gap decision theory, Annual Conference of the IEEE Industrial Electronics Society (IECON 2017), Beijing. Abstract.
   
• Alireza Soroudi, Pouria Maghouli, Andrew Keane, 2017, Resiliency oriented integration of distributed series reactors in transmission networks, IET Generation Transmission & Distribution. Abstract.
   
• Abbas Rabiee, Saman Nikkhah and Alireza Soroudi, 2018, Information Gap Decision Theory to Deal with Long-term Wind Energy Planning Considering Voltage Stability Energy, Volume 147, Pages 451-463. Abstract.
   
   
• Alireza Soroudi, Abbas Rabiee and Andrew Keane, 2017, Information gap decision theory approach to deal with wind power uncertainty in unit commitment, Electric Power Systems Research, 145: 137-148. Abstract.
   
   
• Alison O’Connell, Alireza Soroudi and Andrew Keane, 2016, Distribution network operation under uncertainty using information gap decision theory, Transactions on Smart Grid, to appear.
  
  Abstract

  Abstract

  The presence of uncertain parameters in electrical power systems presents an ongoing problem for system operators and other stakeholders when it comes to making decisions. Determining the most appropriate dispatch schedule or system configuration relies heavily on forecasts for a number of parameters such as demand, generator availability and more recently weather. These uncertain parameters present an even more compelling problem at the distribution level, as these networks are inherently unbalanced, and need to be represented as such for certain tasks. The work in this paper presents an information gap decision theory based three-phase optimal power flow. Assuming that the demand is uncertain, the aim is to provide optimal and robust tap setting and switch decisions over a 24-hour period, while ensuring that the network is operated safely, and that losses are kept within an acceptable range. The formulation is tested on a section of realistic low voltage distribution network with switches and tap changers present.

  Index terms

  Load flow, optimisation, power distribution, smart grids, three-phase electric power, uncertainty.
  

• Murphy, C.; Soroudi, A.; Keane, A., 2015, Information gap decision theory-based congestion and voltage management in the presence of uncertain wind power, IEEE Transactions on Sustainable Energy, DOI: 10.1109/TSTE.2015.2497544
  
  Abstract

  Abstract

  The supply of electrical energy is being increasingly sourced from renewable generation. The variability and uncertainty of renewable generation, compared to a dispatchable plant, is a significant dissimilarity of concern to the traditionally reliable and robust power system. This change is driving the power system towards a more flexible entity that carries greater amounts of reserve. For congestion management purposes it is of benefit to know the probable and possible renewable generation dispatch, but to what extent will these variations effect the management of congestion on the system? Reactive power generation from wind generators and demand response flexibility are the decision variables here in a risk averse multi-period AC optimal power flow (OPF) seeking to manage congestion on distribution systems. Information Gap Decision Theory is used to address the variability and uncertainty of renewable generation. In addition, this work considers the natural benefits to the congestion on a system from the over estimation of wind forecast; providing an opportunistic schedule for both demand response nodes and reactive power provision from distributed generation.
  

• Rabiee, A.; Soroudi, A.; Keane, A., 2015, Information gap decision theory based OPF with HVDC connected wind farms,IEEE Transactions on Power Systems, vol.30, no.6, pp.3396-3406, DOI: 10.1109/TPWRS.2014.2377201
  
  Abstract

  Abstract

  A method for solving the optimal power flow (OPF) problem including HVDC connected offshore wind farms is presented in this paper. Different factors have been considered in the proposed method, namely, voltage source converter (VSC-HVDC) and line-commutated converter high-voltage DC (LCC-HVDC) link constraints, doubly fed induction generators’ (DFIGs) capability curve as well as the uncertainties of wind power generation. Information gap decision theory (IGDT) is utilized for handling the uncertainties associated with the volatility of wind power generation. It is computationally efficient and does not require the probability density function of wind speed. The proposed decision-making framework finds the optimal decision variables in a way that they remain robust against the considered uncertainties. To illustrate the effectiveness of the proposed approach, it is applied on the IEEE 118-bus system. The obtained results validate the applicability of the proposed IGDT-based OPF model for optimal operation of AC/DC power systems with high penetration of offshore wind farms.
  

• P Maghouli, A Soroudi, A Keane, 2015, Robust computational framework for mid-term techno-economical assessment of energy storage, IET Generation, Transmission & Distribution, http://dx.doi.org/10.1049/iet-gtd.2015.0453
  
  Abstract

  Abstract

  Rapid expansion and integration of wind energy is restrained due to transmission capacity constraints and conventional generation technologies limited operational flexibility in today’s power systems. Energy storage is an attractive option to integrate and utilise more renewable energy without major and timely upgrade of existing transmission infrastructure. Moreover, it can be considered as a means for differing the reinforcement plans. The evaluation of energy storage deployment projects is a challenging task due to severe uncertainty of wind power generation. In this study, a robust techno-economic framework is proposed for energy storage evaluation based on information gap decision theory for handling wind generation uncertainty. The total social cost of the system including conventional generators’ fuel and pollution cost and wind power curtailment cost is optimised considering generators operational constraints and transmission system capacity limitations based on the DC model of the power grid. The effect of storage devices on system performance is evaluated taking into account wind power uncertainty. The proposed method is conducted on the modified IEEE reliability test system and the modified IEEE-118-bus test system to assess its applicability and performance in mid-term robust evaluation of energy storage implementation plans.
  

• Tianyang Zhao, Jianhua Zhang, and Peng Wang, 2016, Flexible active distribution system management considering interaction with transmission networks using information-gap decision theory, Canadian Society for Electrical Engineering (CSEE) Journal of Power and Energy Systems, vol. 2, no. 4, pp.76-86. Abstract.
   
• A. Soroudi, A. Keane, 2015, Risk averse energy hub management considering plug-in electric vehicles using information gap decision theory, in S. Rajakaruna, F. Shahnia, A. Ghosh, eds., Plug in Electric Vehicles in Smart Grids, Springer, Singapore, pp. 107-127,
  
  Abstract

  Abstract

  The energy hub is defined as the multi-input multi-output energy converter. It usually consists of various converters like thermal generators, combined heat and power (CHP), renewable energies and energy storage devices. The plug-in electric vehicles as energy storage devices can bring various flexibilities to energy hub management problem. These flexibilities include emission reduction, cost reduction, controlling financial risks, mitigating volatility of power output in renewable energy resources, active demand side management and ancillary service provision. In this chapter a comprehensive risk hedging model for energy hub management is proposed. The focus is placed on minimizing both the energy procurement cost and financial risks in energy hub. For controlling the undesired effects of the uncertainties, the Information gap decision theory (IGDT) technique is used as the risk management tool. The proposed model is formulated as a mixed integer linear programming (MILP) problem and solved using General Algebraic Modeling System (GAMS). An illustrative example is analyzed to demonstrate the applicability of the proposed method.
  

• Kendra Van Buren, Jack Reilly, Kyle Neal, Harry Edwards, François Hemez, 2016, Guaranteeing robustness of structural condition monitoring to environmental variability, Journal of Sound and Vibration, available online 14 October 2016.
  
  Abstract

  Abstract

  Advances in sensor deployment and computational modeling have allowed significant strides to be recently made in the field of Structural Health Monitoring (SHM). One widely used SHM strategy is to perform a vibration analysis where a model of the structure’s pristine (undamaged) condition is compared with vibration response data collected from the physical structure. Discrepancies between model predictions and monitoring data can be interpreted as structural damage. Unfortunately, multiple sources of uncertainty must also be considered in the analysis, including environmental variability, unknown model functional forms, and unknown values of model parameters. Not accounting for these sources of uncertainty can lead to false-positives or false-negatives in the structural condition assessment. To manage the uncertainty, we propose a robust SHM methodology that combines three technologies. A time series algorithm is trained using “baseline” data to predict the vibration response, compare predictions to actual measurements collected on a potentially damaged structure, and calculate a user-defined damage indicator. The second technology handles the uncertainty present in the problem. An analysis of robustness is performed to propagate this uncertainty through the time series algorithm and obtain the corresponding bounds of variation of the damage indicator. The uncertainty description and robustness analysis are both inspired by the theory of info-gap decision-making. Lastly, an appropriate “size” of the uncertainty space is determined through physical experiments performed in laboratory conditions. Our hypothesis is that examining how the uncertainty space changes throughout time might lead to superior diagnostics of structural damage as compared to only monitoring the damage indicator. This methodology is applied to a portal frame structure to assess if the strategy holds promise for robust SHM.

  Keywords

  Structural health monitoring, Time series modeling, Uncertainty quantification
  

• Kendra L. Van Buren and François M. Hemez, 2016, Achieving robust design through statistical effect screening, Int. J. Numer. Meth. Engng, 105 (5) pp. 351-371. DOI: 10.1002/nme.4981
  
  Abstract

  Abstract

  This work proposes a method for statistical effect screening to identify design parameters of a numerical simulation that are influential to performance while simultaneously being robust to epistemic uncertainty introduced by calibration variables. Design parameters are controlled by the analyst, but the optimal design is often uncertain, while calibration variables are introduced by modeling choices.We argue that uncertainty introduced by design parameters and calibration variables should be treated differently, despite potential interactions between the two sets. Herein, a robustness criterion is embedded in our effect screening to guarantee the influence of design parameters, irrespective of values used for calibration variables. The Morris screening method is utilized to explore the design space, while robustness to uncertainty is quantified in the context of info-gap decision theory. The proposed method is applied to the National Aeronautics and Space Administration Multidisciplinary Uncertainty Quantification Challenge Problem, which is a blackbox code for aeronautic flight guidance that requires 35 input parameters. The application demonstrates that a large number of variables can be handled without formulating simplifying assumptions about the potential coupling between calibration variables and design parameters. Because of the computational efficiency of the Morris screening method, we conclude that the analysis can be applied to even larger-dimensional problems.

  keywords

  sensitivity analysis; effect screening; robust design; uncertainty quantification; optimization
  

• Van Buren, K. and Hemez, F., 2015, Robust-optimal design using multifidelity models, Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 3, 2015, Article A28, pp.199-205. 2014 Annual Conference on Experimental and Applied Mechanics, Greenville, SC, 2-5 June 2014.
  
  Abstract

  Abstract

  Applications in engineering analysis and design have benefited from the use of numerical models to supplement or replace the costly design-build-test paradigm. Previous work has acknowledged that design optimization should not only consider the performance of the model, but also be as insensitive as possible, or robust, to sources of uncertainty that are used to define the simulation. Clearly, evaluating robustness to sources of uncertainty can be computationally expensive, due to the number of iterations required at every step of the optimization. Multifidelity techniques have been introduced to mitigate this computational expense by taking advantage of fast-running lower-fidelity models or emulators. Herein, to achieve robust design, we argue that it is more effective to reduce the total range of variation in model performance rather than to reduce the standard deviation of model performances due to uncertainty in calibration variables of the model. We utilize a multifidelity approach to apply this paradigm to a sub-problem of the NASA Uncertainty Quantification Challenge problem, which is a high-dimensional and nonlinear MATLAB-based code used to simulate dynamics of remotely operated aircraft developed at NASA Langley. This method demonstrates an alternative and computationally efficient approach to robust design. ֲ© The Society for Experimental Mechanics, Inc. 2015.

  Author keywords

  Info-gap; Metamodels; Multi-fidelity optimization; Robust design; Uncertainty
  

• Jonathan D. Herman,  Patrick M. Reed, Ph.D., Harrison B. Zeff, and Gregory W. Characklis, 2015, How should robustness be defined for water systems planning under change? Journal of Water Resources Planning and Management, vol. 141, issue 10. Abstract.
   
• Jonatan Zischg, Mariana L. R. Goncalves, Taneha Kuzniecow Bacchin, Guenther Leonhardt, Maria Viklander, Arjan van Timmeren, Wolfgang Rauch and Robert Sitzenfrei, 2017, Info-Gap robustness pathway method for transitioning of urban drainage systems under deep uncertainties, Water Science & Technology, 76(5): 1272-1281. Abstract.
    
• Yakov Ben-Haim, 2012, Doing Our Best: Optimization and the Management of Risk, Risk Analysis, 32(8): 1326-1332. Pre-print, The published version, The definitive version.
  
  Abstract

  Abstract

  Tools and concepts of optimization are widespread in decision-making, design and planning. There is a moral imperative to ‘do our best’. Optimization underlies theories in physics and biology, and economic theories often presume that economic agents are optimizers. We argue that, in decisions under uncertainty, what should be optimized is robustness rather than performance. We discuss the equity premium puzzle from financial economics, and explain that the puzzle can be resolved by using the strategy of satisficing rather than optimizing. We discuss design of critical technological infrastructure, showing that satisficing of performance requirements – rather than optimizing them – is a preferable design concept. We explore the need for disaster recovery capability and its methodological dilemma. The disparate domains – economics and engineering – illuminate different aspects of the challenge of uncertainty and of the significance of robust-satisficing.

  keywords

  optimizing, satisficing, robustness, uncertainty, info-gap, financial investment, equity premium puzzle, technological infrastructure, moral hazard, disaster recovery
  

• Yakov Ben-Haim, 2012, Why risk analysis is difficult, and some thoughts on how to proceed, Risk Analysis,32(10): 1638-1646. Pre-print,  Published version, The definitive version
  
  Abstract

  Abstract

  Risk analysis is challenged in three ways by uncertainty. Our understanding of the world and its uncertainties is evolving; indeterminism is an inherent part of the open universe in which we live; and learning from experience involves untestable assumptions. We discuss several concepts of robustness as tools for responding to these epistemological challenges. The use of models is justified, even though they are known to err. A concept of robustness is illustrated in choosing between a conventional technology and an innovative, promising, but more uncertain technology. We explain that non-probabilistic robust decisions are sometimes good probabilistic bets. Info-gap and worst-case concepts of robustness are compared. Finally, we examine the exploitation of favorable but uncertain opportunities and its relation to robust decision making.

  Keywords:

  robustness, uncertainty, info-gap theory, satisficing, optimizing
  

• Yiping Li, Jianwen Chen, and Ling Feng, Dealing with uncertainty: A survey of theories and practices, IEEE Transactions on Knowledge and Data Engineering, vol.25, issue 11, November 2013, pages 2463-2482.
  
  Abstract

  Abstract

  Uncertainty accompanies our life processes and covers almost all fields of scientific studies. Two general categories of uncertainty, namely, aleatory uncertainty and epistemic uncertainty, exist in the world. While aleatory uncertainty refers to the inherent randomness in nature, derived from natural variability of the physical world (e.g., random show of a flipped coin), epistemic uncertainty origins from human’s lack of knowledge of the physical world, as well as ability of measuring and modeling the physical world (e.g., computation of the distance between two cities). Different kinds of uncertainty call for different handling methods. Aggarwal, Yu, Sarma, and Zhang et al. have made good surveys on uncertain database management based on the probability theory. This paper reviews multidisciplinary uncertainty processing activities in diverse fields. Beyond the dominant probability theory and fuzzy theory, we also review information-gap theory and recently derived uncertainty theory. Practices of these uncertainty handling theories in the domains of economics, engineering, ecology, and information sciences are also described. It is our hope that this study could provide insights to the database community on how uncertainty is managed in other disciplines, and further challenge and inspire database researchers to develop more advanced data management techniques and tools to cope with a variety of uncertainty issues in the real world.

  keywords

  Uncertainty management, probability theory, Dempster-Shafer theory, fuzzy theory, info-gap theory, probabilistic database, fuzzy database
  

• Xavier Irias, Robustness: Strategies for Utility Management in Conditions of Uncertainty, Source, vol.26, #2, pp.20-23, Spring 2012. Online version.
• D.V. Cicala and X. Irias, 2014, Utilizing info-gap decision theory to improve pipeline reliability: A case study,Pipelines 2014: From Underground to the Forefront of Innovation and Sustainability, Portland, 3-6 August 2014, pp.1749-1760.
  
  Abstract

  Abstract

  Info-gap decision theory, a tool for evaluating severe uncertainty, can be of tremendous value for managing risk and assessing the vulnerability of water conveyance systems in areas of high seismicity. In those areas, significant consequences can result from decisions made with a profound lack of information, such as the uncertainty of seismic loading, unknown performance of pipelines and other infrastructure, unknown costs to repair seismic damage, and unknown societal impacts from downtime following an event. Info-gap is a tool for making good decisions with very little information and recognizes up front that our best projections of the future may be wrong. Thus, rather than seeking a solution that is optimal for that projection, info-gap seeks a solution that works reasonably well for all plausible conditions. In other words, info-gap seeks solutions that are robust in the face of uncertainty. EBMUD is currently using info-gap to gain insight into possible solutions for providing reliable water service to an island community within its service area. The island, containing about 75,000 customers, is particularly vulnerable to water supply disruption from earthquakes, because it has no water storage on the island and is entirely dependent on four potentially fragile water transmission mains under the waterway for its day-to-day water supply. Info-gap analysis is being used to evaluate competing tunneling strategies for supplying water to the island. Horizontal directional drilling and microtunneling alternatives are being evaluated for their ability to survive a major earthquake and for speed of repair should they be damaged by an earthquake. The analysis considers not only the expected results for each alternative but also the worst-case performance of each alternative under varying levels of uncertainty. Thus, the info-gap model is a tool for evaluating the level of reliability each mitigation buys, even in the face of significant uncertainty. This analysis is improving the quality of the planning process, because it can identify strategies that ensure minimal disruption of water supply following a major earthquake, even if the earthquake and resulting damage fail to conform to our expectations. The model results prompt discussion regarding how much mitigation is desired, or expected to be reliable enough, even in the face of great uncertainty regarding the damage. Results of the study are presented, including a discussion of how info-gap model results complemented existing tools for comparing alternative strategies and how info-gap improves our ability to quantify our tolerance for uncertainty. © 2014 American Society of Civil Engineers.

  keywords

   

  Engineering controlled terms:

  Decision theory; Directional drilling; Earthquakes; Pipelines; Repair; Risk management; Structural analysis; Sustainable development; Uncertainty analysis; Water supply; Horizontal directional drilling; Info-gap decision theories; Planning process; Societal impacts; Supply disruption; Water conveyance; Water transmission mains; Worst-case performance

   

  Engineering main heading:

  Quality control
  

• David Hambling, 2012, Self-Defense for the Self-Driving Car, Popular Mechanics, Online version.
  
  Selection from article

  Selection

  :”One of [David] Mascarenas’s projects makes robots less predictable and reduces their vulnerability to ambush. If you know a driverless delivery truck always goes down the same deserted street at 6:14 am, you can get there first. Mascarenas addressed this using a technique known as info-gap decision theory. This allows the robot to weigh the risk of any particular route with the possible benefits. … Crucially, the process is unpredictable: The machine will not always take the same route twice, and would-be ambushers can’t anticipate where it will be.”
  

• Yoshihiro Kanno and Yakov Ben-Haim, 2011, Redundancy and Robustness, Or, When is Redundancy Redundant? ASCE Journal of Structural Engineering, 137(9): 935-945. Pre-print.
   
• Yoshihiro Kanno, 2012, Worst scenario detection in limit analysis of trusses against deficiency of structural components, Engineering Structures, 42: 33-42.
  
  Abstract

  Abstract

  This paper addresses the plastic limit analysis of a truss with some deficient structural components. Given the upper bound for the number of deficient members, we consider uncertainty in the locations of deficient members, i.e., the set of deficient members is not specified in advance. Then we attempt to find the worst scenario of deficiency, in which the limit load factor attains the minimum value. We formulate this combinatorial optimization problem as a mixed integer linear programming problem and solve it by using an algorithm with guaranteed global convergence. The deficient structural components in the worst scenario are regarded as key elements which cause the largest degradation of structural performance. Numerical examples illustrate that the set of key elements, as well as the collapse mode in the worst scenario, depends on the number of deficient structural components.

  Keywords:

  Robustness, Uncertainty, Structural degradation, Structural integrity, Plastic limit analysis, Integer optimization
  

• Yakov Ben-Haim and Francois Hemez, 2012, Robustness, Fidelity and Prediction-Looseness of Models,Proceedings of the Royal Society, A, 468: 227-244. Pre-print.
   
• Yakov Ben-Haim, 2011, When is non-probabilistic robustness a good probabilistic bet? Working paper.
   
• Yakov Ben-Haim, 2014, Robust satisficing and the probability of survival, Intl. J. of Systems Science, 45(1): 3-19, appearing on-line 9 May 2012. Online preview.
   
• S.Gareth Pierce, Yakov Ben-Haim, Keith Worden, Graeme Manson, 2006, Evaluation of neural network robust reliability using information-gap theory, IEEE Transactions on Neural Networks, vol.17, No.6, pp.1349-1361.
   
• Y. Kanno and I. Takewaki, Robustness analysis of trusses with separable load and structural uncertainties,International Journal of Solids and Structures, Volume 43, Issue 9, May 2006, pp.2646-2669.
  
  Abstract

  Abstract

  This paper discusses evaluation techniques of the robustness function of trusses, which is regarded as one of measures of structural robustness, under the uncertainties of member stiffnesses and external forces. By using quadratic embedding of the uncertainty and the S-procedure, we formulate a quasiconvex optimization problem which provides lower bounds of the robustness functions. A bisection method is proposed, where we solve a finite number of semidefinite programming problems in order to obtain a global optimal solution to the proposed quasiconvex optimization problem. The lower bounds of the robustness functions are computed for various trusses under several uncertainty circumstances.

  Keywords:

  Robustness; Structural safety; Semidefinite program; Quasiconvex optimization; Data uncertainty.
  

• Miriam Zacksenhouse, Simona Nemets, Miikhail A Lebedev and Miguel A Nicolelis, 2009, Robust Satisficing Linear Regression: performance/robustness trade-off and consistency criterion, Mechanical Systems and Signal Processing, vol.23, pp.1954-1964.
  
  Abstract

  Abstract

  Linear regression quantifies the linear relationship between paired sets of input and output observations. The well known least-squares regression optimizes the performance criterion defined by the residual error, but is highly sensitive to uncertainties or perturbations in the observations. Robust least-squares algorithms have been developed to optimize the worst case performance for a given limit on the level of uncertainty, but they are applicable only when that limit is known. Herein, we present a robust-satisficing approach that maximizes the robustness to uncertainties in the observations, while satisficing a critical sub-optimal level of performance. The method emphasizes the trade-off between performance and robustness, which are inversely correlated. To resolve the resulting trade-off we introduce a new criterion, which assesses the consistency between the observations and the linear model. The proposed criterion determines a unique robust-satisficing regression and reveals the underlying level of uncertainty in the observations with only weak assumptions. These algorithms are demonstrated for the challenging application of linear regression to neural decoding for brain-machine interfaces. The model-consistent robust-satisfying regression provides superior performance for new observations under both similar and different conditions. Keywords: Linear regression, Robust regression, Regularization, Information-gap, Uncertainties, Brain machine interface.

• Sisso, Itay, Tal Shima, and Yakov Ben-Haim, 2010, Info-gap approach to multi agent search under severe uncertainty, IEEE Transactions on Robotics, vol. 26, issue 6, pp.1032-1041. Pre-print.
   
• Navid Rezaei, Abdollah Ahmadi, A.H. Khazali and Josep M. Guerrero, 2018, Energy and Frequency Hierarchical Management System Using Information Gap Decision Theory for Islanded Microgrids, IEEE Transactions on Industrial Electronics. DOI 10.1109/TIE.2018.2798616   Abstract.
   
• Jian Zhao ; Can Wan ; Zhao Xu ; Jianhui Wang, 2017, Risk-based day-ahead scheduling of electric vehicle aggregator using information gap decision theory, IEEE Transactions on Smart Grid, vol. 8(4): 1609-1618, July 2017. Abstract.
   
• Si, T.-Q.,  Su, Y.-H.,  Xiao, W., 2017, Robust reliability analysis of support surrounding rock based on Info-gap theory, Yantu Lixue/Rock and Soil Mechanics, Volume 38, Issue 3, 10 March 2017, Pages 827-832 and 910. Abstract.
   
• Ji, X. and  Niu, Y., 2016, Robust strategy planning for UAV with LTL specifications, 35th Chinese Control Conference, CCC, 27-29 July 2016, Chengdu; China, Article number 7553803, Pages 2890-2895.
  
  Abstract

  Abstract

  This paper presents a high level strategy planning framework for the UAV, in which the strategy planning problem under uncertain conditions is abstracted into Markov Decision Processes with uncertain parameters, and the mission requirements are specified using Linear Temporal Logic Language. The objective is to compute a robust satisfying policy to maximize the robustness to the uncertainty while satisfying the desired requirements of system performance or the mission specification. The info-gap decision model is used to describe the uncertain parameters of MDP, i.e., the transition probability, and thus we propose a new model as Info-gap based MDPs (IMDPs). The LTL formula of mission specifications is converted to Deterministic Rabin Automaton (DRA). A product IMDP is constructed by combing the IMDP with DRA in the form of Cartesian product. Based on robust dynamic programming, we propose a robust satisfying policy generation algorithm to solve the product IMDP. An example of UAV high level strategy planning is given to verify our algorithm and the resulting policy can maximize the robustness while satisfying the mission specifications.

  Author keywords

  Info-gap decision; Linear Temporal Logic; Markov Decision Process; Robust satisfying policy
  

• Xiaoting Ji, Yifeng Niu and Lincheng Shen, 2016, Robust satisficing decision making for unmanned aerial vehicle complex missions under severe uncertainty, PLoS One, 11(11): e0166448. doi:10.1371/journal.pone.0166448. Abstract.
   
• Aurélien Hot, Thomas Weisser and Scott Cogan, 2017, An info-gap application to robust design of a prestressed space structure under epistemic uncertainties, Mechanical Systems and Signal Processing, 91: 1-9. Abstract.
   
• Maugan, F.,  Cogan, S.,  Foltête, E.,  Hot, A., 2016, Robust sensor and exciter design for linear structures, 34th IMAC, A Conference and Exposition on Structural Dynamics, Orlando; 25-28 January 2016.
  
  Abstract

  Abstract

  A wide variety of model-based modal test design methodologies have been developed over the past two decades using a non-validated baseline model of the structure of interest. Due to the presence of lack of knowledge, this process can lead to less than optimal distributions of sensors and exciters due to the discrepancy between the model and the prototype behaviors. More recent strategies take into account statistical variability in model parameters but the results depend strongly on the hypothesized distributions. This paper provides a decision making tool using a robust satisficing approach that provides a better understanding of the trade-off between the performance of the test design and its robustness to model form errors and associated imprecisions. The latter will be represented as an info-gap model and the proposed methodology seeks a sensor and exciter distribution that will satisfy a given design performance while tolerating a specified degree of modeling error. The evolution of this performance for increasing horizons of uncertainty is an important information for the test planner in choosing the total number of sensors. The methodology will be illustrated on an academic but practically useful example under severe uncertainty.

  Author keywords

  Info-gap; Lack of knowledge; Robustness; Sensor placement; Uncertainty.
  

• Edwards, H.,  Neal, K.,  Reilly, J.,  Van Buren, K.,  Hemez, F., 2016, Making structural condition diagnostics robust to environmental variability, 34th IMAC, A Conference and Exposition on Structural Dynamics, Orlando; 25-28 January 2016.
  
  Abstract

  Abstract

  Advances in sensor deployment and computational modeling have allowed significant strides to be made recently in the field of Structural Health Monitoring (SHM). One widely used SHM technique is to perform a vibration analysis where a model of the structure’s pristine (undamaged) condition is compared with vibration response data collected from the physical structure. Discrepancies between model predictions and monitoring data can be interpreted as structural damage. Unfortunately, multiple sources of uncertainty must also be considered in the analysis, including environmental variability and unknown values for model parameters. Not accounting for uncertainty in the analysis can lead to false-positives or false-negatives in the assessment of the structural condition. To manage the aforementioned uncertainty, we propose a robust- SHM methodology that combines three technologies. A time series algorithm is trained using “baseline” data to predict the vibration response, compare predictions to actual measurements collected on a potentially damaged structure, and calculate a user-defined damage indicator. The second technology handles the uncertainty present in the problem. An analysis of robustness is performed to propagate this uncertainty through the time series algorithm and obtain the corresponding bounds of variation of the damage indicator. The uncertainty description and robustness analysis are both inspired by the theory of info-gap decision-making. Lastly, an appropriate “size” of the uncertainty space is determined through physical experiments performed in laboratory conditions. Our hypothesis is that examining how the uncertainty space changes in time might lead to superior diagnostics of structural damage as compared to only monitoring the damage indicator. This methodology is applied to a portal frame structure to assess if the strategy holds promise for robust SHM.

  Author keywords

  Robustness; Structural health monitoring; Time series modeling; Uncertainty.
  

• Hemez, F.,  Van Buren, K., 2016, Designing a mechanical latch for robust performance, 34th IMAC, A Conference and Exposition on Structural Dynamics, Orlando; 25-28 January 2016.
  
  Abstract

  Abstract

  Advances in computational sciences in the past three decades, such as those embodied by the finite element method, have made it possible to perform design and analysis using numerical simulations. While they offer undeniable benefits for rapid prototyping and can shorten the design-test-optimize cycle, numerical simulations also introduce assumptions and various sources of uncertainty. Examples are modeling assumptions proposed to represent a nonlinear material behavior, energy dissipation mechanisms and environmental conditions, in addition to numerical effects such as truncation error, mesh adaptation and artificial dissipation. Given these sources of uncertainty, what is the best way to support a design decision using simulations? We propose that an effective simulation-based design hinges on the ability to establish the robustness of its performance to assumptions and sources of uncertainty. Robustness means that exploring the uncertainty space that characterizes the simulation should not violate the performance requirement. The theory of information-gap (“info-gap”) for decision-making under severe uncertainty is applied to assess the robustness of two competing designs. The application is the dynamic stress performance of a mechanical latch for a consumer electronics product. The results are that the variant design only yields 10% improvement in robustness to uncertainty while requiring 44% more material for manufacturing. The analysis provides a rigorous rationale to decide that the variant design is not viable.

  Author keywords

  Finite element analysis; Mechanical latch; Robust design; Uncertainty quantification.
  

• Piegat, A.,  Tomaszewska, K., 2013, Decision-Making under uncertainty using Info-Gap Theory and a new multi-dimensional RDM interval arithmetic, Przeglad Elektrotechniczny, R. 89 NR 8/2013. Abstract.
    
• Piegat, A.,  Tomaszewska, K., 2015, Assessment of fertilizer nitrogen requirement of sugar beetroot using info-gap theory, Lecture Notes in Artificial Intelligence, (Subseries of Lecture Notes in Computer Science) Volume 9120, 2015, Pages 448-459, 14th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2015. Abstract.
     
• Lépine, P.,  Cogan, S.,  Foltête, E.,  Parent, M.-O., 2016, Robust model calibration using determinist and stochastic performance metrics, 34th IMAC, A Conference and Exposition on Structural Dynamics, Orlando; 25-28 January 2016.
  
  Abstract

  Abstract

  The aeronautics industry has benefited from the use of numerical models to supplement or replace the costly design-build-test paradigm. These models are often calibrated using experimental data to obtain optimal fidelity-to-data but compensating effects between calibration parameters can complicate the model selection process due to the non-uniqueness of the solution. One way to reduce this ambiguity is to include a robustness requirement to the selection criteria. In this study, the info-gap decision theory is used to represent the lack of knowledge resulting from compensating effects and a robustness analysis is performed to investigate the impact of uncertainty on both deterministic and stochastic fidelity metrics. The proposed methodology is illustrated on an academic example representing the dynamic response of a composite turbine blade.

  Author keywords

  Info-gap approach; Model calibration; Performance metric; Robust solution; Uncertainty.
  

• Yoshihiro Kanno and Izuru Takewaki, 2016, Robustness analysis of elastoplastic structure subjected to double impulse, Journal of Sound and Vibration, vol. 383 pp. 309-323.
  
  Abstract

  Abstract

  The double impulse has extensively been used to evaluate the critical response of an elastoplastic structure against a pulse-type input, including near-fault earthquake ground motions. In this paper, we propose a robustness assessment method for elastoplastic single-degree-of-freedom structures subjected to the double impulse input. Uncertainties in the initial velocity of the input, as well as the natural frequency and the strength of the structure, are considered. As fundamental properties of the structural robustness, we show monotonicity of the robustness measure with respect to the natural frequency. In contrast, we show that robustness is not necessarily improved even if the structural strength is increased. Moreover, the robustness preference between two structures with different values of structural strength can possibly reverse when the performance requirement is changed.

  Author keywords

  Impulse, Elastoplastic response, Info-gap model, Near-fault ground motion, Robustness, Uncertainty
  

• Liu, G.,  Li, K.,  Wang, X.,  Li, L.-L., 2016, Damage detection based on info-gap approach, Gongcheng Lixue/Engineering Mechanics, Volume 33, 1 June 2016, Pages 257-261.
  
  Abstract

  Abstract

  A novel Information-gap-based (Info-gap) damage detection method for uncertainty quantification is proposed in this study. The modal shapes of structures are selected as damage indices, and the uncertainty level of these indices caused by measurement errors and modal identification are described by Info-gap model. The decision function is defined as the distance of modal shape between health and unknown condition of structures, and then the solution of this function is translated into an optimization problem. The results from a numerical simulation and lab-scale structure show that the location and severity of damage can be successfully identified.

  Author keywords

  Damage detection; Distance function; Info-gap theory; Optimization; Uncertainty.

  Indexed keywords

  Optimization; Uncertainty analysis; Decision functions; Distance functions; Info-gap; Modal identification; Novel information; Optimization problems; Uncertainty; Uncertainty quantifications; Damage detection
  

• T. Roach, Z. Kapelan, R. Ledbetter and M. Ledbetter, 2016, Comparison of robust optimization and info-gap methods for water resource management under deep uncertainty, Journal of Water Resources Planning and Management, 142: 9,  art. no. 08217002.
  
  Abstract

  Abstract

  This paper evaluates two established decision-making methods and analyzes their performance and suitability within a water resources management (WRM) problem. The methods under assessment are info-gap (IG) decision theory and robust optimization (RO). The methods have been selected primarily to investigate a contrasting local versus global method of assessing water system robustness to deep uncertainty, but also to compare a robustness model approach (IG) with a robustness algorithm approach (RO), whereby the former selects and analyzes a set of prespecified strategies and the latter uses optimization algorithms to automatically generate and evaluate solutions. The study presents a novel area-based method for IG robustness modeling and assesses the applicability of utilizing the future flows climate change projections in scenario generation for water resource adaptation planning. The methods were applied to a case study resembling the Sussex North Water Resource Zone in England, assessing their applicability at improving a risk-based WRM problem and highlighting the strengths and weaknesses of each method at selecting suitable adaptation strategies under climate change and future demand uncertainties. Pareto sets of robustness to cost are produced for both methods and highlight RO as producing the lower cost strategies for the full range of varying target robustness levels. IG produced the more expensive Pareto strategies due to its more selective and stringent robustness analysis, resulting from the more complex scenario ordering process.

  Keywords

  Algorithms; Climate change; Decision making; Decision theory; Optimization; Risk assessment; Uncertainty analysis; Water management; Adaptation strategies; Algorithm approaches; Climate change projections; Decision-making method; Optimization algorithms; Robustness analysis; Water resources management; Waterresource management
  

• Tom Roach, Zoran Kapelan and Ralph Ledbetter, 2015, Comparison of info-gap and robust optimisation methods for integrated water resource management under severe uncertainty, Procedia Engineering, 119 (2015) 874-883, 13th Computer Control for Water Industry Conference, CCWI 2015.
  
  Abstract

  Abstract

  This paper evaluates two established decision making methods and analyses their performance and suitability within an Integrated Water Resource Management (IWRM) problem. The methods under comparison are Info-Gap decision theory (IG) and Robust Optimisation (RO), with particular regard to two key issues: (a) a local vs global measure of water supply robustness and (b) a pre-specified vs optimisation method of generating intervention strategies. Solutions are compared with plans proposed from current industry practice especially in regard to employing a longer planning horizon. The results reveal the impact of using alternative methodologies and analysis parameters on the final intervention strategies selected.

  Keywords

  Water resources planning, decision making methods, climate change uncertainity, robust optimisation, info-gap decision theory
  

• Tang, H.-S.,  Fan, D.-W.,  Li, D.-W.,  Xue, S.-T., 2015, Info-gap decision for the robust seismic design optimization of structures, Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences, 42(5): pp.21-28.
  
  Abstract

  Abstract

  Seismic design for buildings is usually subject to various uncertainties, often severe, which have the potential to undermine engineering decisions. It is crucial that these uncertainties be accounted for in seismic design. We formulated a performance-based seismic design model that takes into account uncertainty in the seismic design spectrum of the αmax and Tg. We used info-gap theory for satisfying the critical performance requirements, while at the same time maximized the robustness to uncertainty through nested optimization. The design implications of this robust-satisfying approach were demonstrated with a three-span six-floor steel frame design example. It is shown that design preferences depend upon the performance requirements considering the trade-off between robustness to uncertainty. Also, the result reveals that the proposed method provides a novel tool for the performance-based seismic reliability design under the lack of knowledge.

  Keywords

  Info-Gap theory; Robust; Seismic design; Uncertainty
  

• Garrison Stevens,  Kendra Van Buren, Elizabeth Wheeler and Sez Atamturktur, 2015, Evaluating the fidelity and robustness of calibrated numerical model predictions, Engineering Computations, 32(3): 621-642.
  
  Abstract

  Abstract

  Purpose: Numerical models are being increasingly relied upon to evaluate wind turbine performance by simulating phenomena that are infeasible to measure experimentally. These numerical models, however, require a large number of input parameters that often need to be calibrated against available experiments. Owing to the unavoidable scarcity of experiments and inherent uncertainties in measurements, this calibration process may yield non-unique solutions, i.e. multiple sets of parameters may reproduce the available experiments with similar fidelity. The purpose of this paper is to study the trade-off between fidelity to measurements and the robustness of this fidelity to uncertainty in calibrated input parameters.

  Design/methodology/approach: Here, fidelity is defined as the ability of the model to reproduce measurements and robustness is defined as the allowable variation in the input parameters with which the model maintains a predefined level of threshold fidelity. These two vital attributes of model predictiveness are evaluated in the development of a simplified finite element beam model of the CX-100 wind turbine blade.

  Findings: Findings of this study show that calibrating the input parameters of a numerical model with the sole objective of improving fidelity to available measurements degrades the robustness of model predictions at both tested and untested settings. A more optimal model may be obtained by calibration methods considering both fidelity and robustness. Multi-criteria Decision Making further confirms the conclusion that the optimal model performance is achieved by maintaining a balance between fidelity and robustness during calibration.

  Originality/value: Current methods for model calibration focus solely on fidelity while the authors focus on the trade-off between fidelity and robustness.

  Keywords Uncertainty quantification, Validation, Experimental modal analysis, Prediction accuracy, Self-consistency, Test-analysis correlation
  

• Yakov Ben-Haim, Miriam Zacksenhouse, Ronit Eshel, Raphael Levi, Avi Fuerst and Wayne Bentley, 2014, Failure detection with likelihood ratio tests and uncertain probabilities: An info-gap application, Mechanical Systems and Signal Processing, vol. 48, pp.1-14. Pre-print.
   
• Atamturktur, S., Liu, Z., Cogan, S., Juang, H., 2015, Calibration of imprecise and inaccurate numerical models considering fidelity and robustness: a multi-objective optimization-based approach, Structural and Multidisciplinary Optimization, 51 (3) pp. 659-671.
  
  Abstract

  Abstract

  Traditionally, model calibration is formulated as a single objective problem, where fidelity to measurements is maximized by adjusting model parameters. In such a formulation however, the model with best fidelity merely represents an optimum compromise between various forms of errors and uncertainties and thus, multiple calibrated models can be found to demonstrate comparable fidelity producing non-unique solutions. To alleviate this problem, the authors formulate model calibration as a multi-objective problem with two distinct objectives: fidelity and robustness. Herein, robustness is defined as the maximum allowable uncertainty in calibrating model parameters with which the model continues to yield acceptable agreement with measurements. The proposed approach is demonstrated through the calibration of a finite element model of a steel moment resisting frame.

  Author keywords

  Experiment-based model validation; Info-gap decision theory; Info-gap uncertainty model; Nondominated sorting genetic algorithm; Prediction looseness; Self-consistency
  

• Atamturktur, S., Stevens, G., Cheng, Y., 2015, Clustered parameters of calibrated models when considering both fidelity and robustness, Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 3, 2015, Article A30, pp.215-224. 2014 Annual Conference on Experimental and Applied Mechanics, Greenville, SC, 2-5 June 2014.
  
  Abstract

  Abstract

  In computer modeling, errors and uncertainties inevitably arise due to the mathematical idealization of physical processes stemming from insufficient knowledge regarding accurate model forms as well as the precise values of input parameters. While these errors and uncertainties are quantifiable, compensations between them can lead to multiple model forms and input parameter sets exhibiting a similar level of agreement with available experimental observations. Such nonuniqueness makes the selection of a single, best computer model (i.e. model form and values for its associate parameters) unjustifiable. Therefore, it becomes necessary to evaluate model performance based not only on the fidelity of the predictions to available experiments but also on a model’s ability to sustain such fidelity given the incompleteness of knowledge regarding the model itself, such an ability will herein be referred to as robustness. In this paper, the authors present a multiobjective approach to model calibration that accounts for not only the model’s fidelity to experiments but also its robustness to incomplete knowledge. With two conflicting objectives, the multi-objective model calibration results in a family of nondominated solutions exhibiting varying levels of fidelity and robustness effectively forming a Pareto front. The Pareto front solutions can be grouped depending on their nature of compromise between the two objectives, which can in turn help determine clusters in the parameter domain. The knowledge of these clusters can shed light on the nature of compensations as well as aid in the inference of uncertain input parameters. To demonstrate the feasibility and application of this new approach, we consider the computer model of a structural steel frame with uncertain connection stiffness parameters under static loading conditions. © The Society for Experimental Mechanics, Inc. 2015.

  Author keywords

  Info-gap decision theory; K-means clustering; Model calibration; Multi-objective optimization; Non-dominated sorting genetic algorithm (NSGA-II)
  

• M. Pasquali, C.J. Stull and C.R. Farrar, 2015, Info-gap robustness of an input signal optimization algorithm for damage detection, Mechanical Systems and Signal Processing, vol.50-51: 1-10.
  
  Abstract

  Highlights

  • IGDT is used to assess the robustness of an optimal input signal designing technique.
  • The case of uncertainty affecting the parameters of a 2-DOF system is analyzed.
  • It can be critical when affecting the masses or the linear stiffnesses values.
  • Small influence is due to changes in the nonlinear stiffnesses or the damping ratios.
  • The analyzed algorithm has shown to be robust to variations in the damage level.

  Abstract

  Info-Gap Decision Theory is adopted to assess the robustness of a technique aimed at identifying the optimal excitation signal to be used for active sensing approaches to damage detection. Here the term “active sensing” refers to procedures where a known input is applied to the structure to enhance the damage detection process. Given limited system response measurements and ever-present physical limits on the level of excitation, the ultimate goal of the mentioned technique is to improve the detectability of damage by increasing the difference between measured outputs of the undamaged and damaged systems. In particular, a two degree-of-freedom mass–spring–damper system characterized by the presence of a nonlinear stiffness is considered. Uncertainty is introduced to the system in the form of deviations of its parameters (mass, stiffness, damping ratio) from their nominal values. Variations in the performance of the mentioned technique are then evaluated both in terms of changes in the estimated difference between the responses of the damaged and undamaged systems and in terms of deviations of the identified optimal input signal from its nominal estimation. Finally, plots of the performances of the analyzed algorithm for different levels of uncertainty are obtained, enabling a clear evaluation of the risks connected with designing excitation signals for damage detection, when the parameters that dictate system behavior (e.g. stiffness, mass) are poorly characterized or improperly modeled.

  Keywords

  Info-Gap Decision Theory; Uncertainty; Structural health monitoring; Optimization
  

• Yakov Ben-Haim, 2012, Modeling and design of a Hertzian contact: An info-gap approach, Journal of Strain Analysis for Engineering Design, 47(3): 153-162. Pre-print.
• Izuru Takewaki, 2013, Toward greater building earthquake resilience using concept of critical excitation: A review, Sustainable Cities and Society, 9: 39-53, http://dx.doi.org/10.1016/j.scs.2013.02.001
  
  Abstract

  Abstract

  The words of ‘unexpected issue’ and ‘earthquake resilience’ are frequently used after the 2011 off the Pacific coast of Tohoku earthquake which occurred March 11, 2011. Although the unexpected issues are hard to include in the structural design stage of civil structures, those certainly decrease the earthquake resilience of those civil structures. Once these unexpected issues are taken into account in the structural design, those issues become expected issues. However these repetitions of cycles, i.e. experiences of unexpected issues during earthquakes and incorporation into design codes, never resolve the essential problems in structural earthquake engineering. In this paper, a historical review is made on the development of critical excitation methods as worst-scenario analysis and some possibilities of application of this concept to upgrading of building earthquake resilience are discussed.

  Keywords

  Earthquake resilience; Critical excitation method; Uncertainty analysis; Robustness; Redundancy; Earthquake engineering
  

• Izuru Takewaki, 2013, Towards narrowing unexpected issues in future earthquakes: A review, Advances in Structural Engineering, 16(5): 931-946.
  
  Abstract

  Abstract

  When we encounter a devastating earthquake disaster, we have upgraded the earthquake resistant design codes in the long history of earthquake structural engineering. However the repetition of this action does never resolve the essential problem. This is because building structures and input ground motions have various complex uncertainties and unexpected phenomena often occur. The 2011 off the Pacific coast of Tohoku earthquake also provided some unexpected phenomena. This review paper discusses how to narrow unexpected issues in future earthquakes by referring to several concepts. Critical excitation methods, info-gap theories for uncertainty representation and interval analysis methods are the principal concepts.

  Keywords

  critical excitation method; earthquake resilience; earthquake resistant design; info-gap uncertainty model; interval analysis; worst case analysis
  

• Alireza Soroudi and Turaj Amraee, 2013, Decision making under uncertainty in energy systems: State of the art, Renewable and Sustainable Energy Reviews, 28: 376-384.
  
  Abstract

  Abstract

  The energy system studies include a wide range of issues from short term (e.g. real-time, hourly, daily and weekly operating decisions) to long term horizons (e.g. planning or policy making). The decision making chain is fed by input parameters which are usually subject to uncertainties. The art of dealing with uncertainties has been developed in various directions and has recently become a focal point of interest. In this paper, a new standard classification of uncertainty modeling techniques for decision making process is proposed. These methods are introduced and compared along with demonstrating their strengths and weaknesses. The promising lines of future researches are explored in the shadow of a comprehensive overview of the past and present applications. The possibility of using the novel concept of Z-numbers is introduced for the first time.

  Keywords

  Fuzzy arithmetic, Info-gap decision theory, Probabilistic modeling, Robust optimization, Interval based analysis, Z-number
  

• Korteling, B., Dessai, S., Kapelan, Z., 2012, Using information-gap decision theory for water resources planning under severe uncertainty, Water Resources Management, 27 (4): 1149-1172.
  
  Abstract

  Abstract

  Water resource managers are required to develop comprehensive water resources plans based on severely uncertain information of the effects of climate change on local hydrology and future socio-economic changes on localised demand. In England and Wales, current water resources planning methodologies include a headroom estimation process separate from water resource simulation modelling. This process quantifies uncertainty based on only one point of an assumed range of deviations from the expected climate and projected demand 25 years into the future. This paper utilises an integrated method based on Information-Gap decision theory to quantitatively assess the robustness of various supply side and demand side management options over a broad range of plausible futures. Findings show that beyond the uncertainty range explored with the headroom method, a preference reversal can occur, i.e. some management options that underperform at lower uncertainties, outperform at higher levels of uncertainty. This study also shows that when 50% or more of the population adopts demand side management, efficiency related measures and innovative options such as rainwater collection can perform equally well or better than some supply side options The additional use of Multi-Criteria Decision Analysis shifts the focus away from reservoir expansion options, that perform best in regards to water availability, to combined strategies that include innovative demand side management actions of rainwater collection and greywater reuse as well efficiency measures and additional regional transfers. This paper illustrates how an Information-Gap based approach can offer a comprehensive picture of potential supply/demand futures and a rich variety of information to support adaptive management of water systems under severe uncertainty.

  Keywords

  Climate change; Demand management; Info-Gap; Planning; Uncertainty; Water resources.
  

• Mascareñas, D., Stull, C., Farrar, C., 2012, Development of an info-gap-based path planner to enable nondeterministic low-observability mobile sensor nodes, Proceedings of SPIE – The International Society for Optical Engineering. Vol. 8387, 2012, Article number 838719.
  
  Abstract

  Abstract

  Mobile sensor nodes are an ideal solution for efficiently collecting measurements for a variety of applications. Mobile sensor nodes offer a particular advantage when measurements must be made in hazardous and/or adversarial environments. When mobile sensor nodes must operate in hostile environments, it would be advantageous for them to be able to avoid undesired interactions with hostile elements. It is also of interest for the mobile sensor node to maintain low-observability in order to avoid detection by hostile elements. Conventional path-planning strategies typically attempt to plan a path by optimizing some performance metric. The problem with this approach in an adversarial environment is that it may be relatively simple for a hostile element to anticipate the mobile sensor node’s actions (i.e. optimal paths are also often predictable paths). Such information could then be leveraged to exploit the mobile sensor node. Furthermore, dynamic adversarial environments are typically characterized by high-uncertainty and highcomplexity that can make synthesizing paths featuring adequate performance very difficult. The goal of this work is to develop a path-planner anchored in info-gap decision theory, capable of generating non-deterministic paths that satisfy predetermined performance requirements in the face of uncertainty surrounding the actions of the hostile element(s) and/or the environment. This type of path-planner will inherently make use of the time-tested security technique of varying paths and changing routines while taking into account the current state estimate of the environment and the uncertainties associated with it.

  © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

  Keywords

  anti-tamper; anti-theft; cyber-physical security; ground robot; info-gap decision theory; mobile sensor nodes; robotics; unmanned systems
  

• Jim W. Hall, Robert J. Lempert, Klaus Keller, Andrew Hackbarth, Christophe Mijere, and David J. McInerney, 2012, Robust Climate Policies Under Uncertainty: A Comparison of Robust Decision Making and Info-Gap Methods, Risk Analysis, 32 (10): 1657-1672.
  
  Abstract

  Keywords

  Abrupt change; climate change; deep uncertainty; info-gap; robust decision making

  Abstract

  This study compares two widely used approaches for robustness analysis of decision problems: the info-gap method originally developed by Ben-Haim and the robust decision making (RDM) approach originally developed by Lempert, Popper, and Bankes. The study uses each approach to evaluate alternative paths for climate-altering greenhouse gas emissions given the potential for nonlinear threshold responses in the climate system, significant uncertainty about such a threshold response and a variety of other key parameters, as well as the ability to learn about any threshold responses over time. Info-gap and RDM share many similarities. Both represent uncertainty as sets of multiple plausible futures, and both seek to identify robust strategies whose performance is insensitive to uncertainties. Yet they also exhibit important differences, as they arrange their analyses in different orders, treat losses and gains in different ways, and take different approaches to imprecise probabilistic information. The study finds that the two approaches reach similar but not identical policy recommendations and that their differing attributes raise important questions about their appropriate roles in decision support applications. The comparison not only improves understanding of these specific methods, it also suggests some broader insights into robustness approaches and a framework for comparing them.
  

• Christopher J. Stull and François M. Hemez, 2012, On the Use of Info-gap Decision Theory to Choose From Among Models of Varying Complexity, ICOSSAR2013. Abstract.
   
• Christopher J. Stull, François M. Hemez and Charles R. Farrar, 2012, On assessing the robustness of structural health monitoring technologies, Structural Health Monitoring, Abstract.
   
•  Tania Mirer and Yakov Ben-Haim, 2010, Reliability Assessment of Explosive Material Based on Penalty Tests: An Info-Gap Approach, Proceedings of the Institution of Mechanical Engineers, Part O, Journal of Risk and Reliability, vol. 224(4), pp.346-355. Pre-print.
• Abstract

  Abstract

  A method is developed for experimental assessment of reliability of a system with a stringent safety requirement: explosive material. The focus is on analysis and management of both statistical variability of measurements and non-probabilistic uncertainty in probability distributions (distributional uncertainty). Info-gap theory is used to model the distributional uncertainty in the pdf of the threshold for actuation of the explosive material. The quantitative analysis and the qualitative judgments which accompany the certification of safety are studied. A proposition is proven asserting that the info-gap robustness function, for the class of problems examined, is independent of the experimental design over virtually all of its range.
  

• Matthew Grasinger, Daniel O’Malley, Velimir Vesselinov, and Satish Karra, 2016, Decision analysis for robust CO2 injection: Application of Bayesian-Information-Gap Decision Theory, International Journal of Greenhouse Gas Control, 49: 73-80. Abstract.
   
• O’Malley, D. and Vesselinov, V.V., 2014, Groundwater remediation using the information gap decision theory,Water Resources Research,  50(1): 246-256.
  
  Abstract

  Abstract

  One of the challenges in the design and selection of remediation activities for subsurface contamination is dealing with manifold uncertainties. A scientifically defensible decision process demands consideration of the uncertainties involved. A nonprobabilistic approach based on information gap (info-gap) decision theory is employed to study the robustness of alternative remediation activities. This approach incorporates both parametric and nonparametric (conceptual) uncertainty in predicting contaminant concentrations that are effected by natural processes and the remediation activities. Two remedial scenarios are explored to demonstrate the applicability of the info-gap approach to decision making related to groundwater remediation.

  Keywords

  Decision theory; Groundwater remediation; Uncertainty analysis
  

• Dylan R. Harp, Philip H. Stauffer, Daniel O’Malley, Zunsheng Jiao, Evan P. Egenolf, Terry A. Miller, Daniella Martinez, Kelsey A. Hunter, Richard S. Middleton, Jeffrey M. Bielicki, Rajesh Pawar, 2017, Development of robust pressure management strategies for geologic CO2 sequestration, International Journal of Greenhouse Gas Control, vol. 64, September 2017, Pages 43-59. Abstract.
   
• Dylan R. Harp and Velimir V. Vesselinov, 2013, Contaminant remediation decision analysis using information gap theoy, Stochastic Environmental Research and Risk Assessment,27(1) pp.159-168. Abstract and full paper.
   
• O’Malley, D. and Vesselinov, V.V., 2016, Bayesian-information-gap decision theory with an application to CO2 sequestration, Water Resources Research, vol. 49, pp.73-80. DOI: 10.1002/2015WR017413. The full paper.
  
  Abstract

  Abstract

  Decisions related to subsurface engineering problems such as groundwater management, fossil fuel production, and geologic carbon sequestration are frequently challenging because of an overabundance of uncertainties (related to conceptualizations, parameters, observations, etc.). Because of the importance of these problems to agriculture, energy, and the climate (respectively), good decisions that are scientifically defensible must be made despite the uncertainties. We describe a general approach to making decisions for challenging problems such as these in the presence of severe uncertainties that combines probabilistic and nonprobabilistic methods. The approach uses Bayesian sampling to assess parametric uncertainty and Information-Gap Decision Theory (IGDT) to address model inadequacy. The combined approach also resolves an issue that frequently arises when applying Bayesian methods to real-world engineering problems related to the enumeration of possible outcomes. In the case of zero nonprobabilistic uncertainty, the method reduces to a Bayesian method. To illustrate the approach, we apply it to a site-selection decision for geologic CO2 sequestration.
  

• Cao, W. , Li, Y., Zhai, Y., 2013, Active analysis method for stability of karst roof under foundation pile based on info-gap theory, Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, 32(2): 393-400.
  
  Abstract

  Abstract

  Aiming at the inability to obtain enough information to describe the random distribution of uncertain variables accurately, the Information-Gap theory which is abbreviated as Info-Gap theory is adopted. Firstly, a robust reliability model for uncertainty analysis of stability about karst roof under foundation pile is established based on the research about the method to measure the uncertainty degree of uncertain variables and to determine the allowable change range of these uncertain variables on the condition that the structural performance can satisfy the intended function. Secondly, according to the existing limit equilibrium analysis method on safety factor of karst roof under foundation pile under different failure modes, a response output model to the stabilization and security function of karst roof is set up; then the calculation method of the robust reliability index is brought forward by interval combination algorithm; so an uncertainty analysis method for the stability of karst roof under foundation pile based on Info-Gap theory is put forward. It not only has lower requirement for the message amount of engineering data but also can not know the random distribution shape of uncertain variables; and it is a supplement and improvement for the existing relative research. What’s more, because these uncertain variables are divided into design variables and design parameters in this method to achieve the dynamic analysis of allowable uncertain degree of design parameters under different design variables; thus, the method proposed has the function of not only passive reply but also active disposal. Finally, the rationality and feasibility of the method are verified by analysis of practical engineering example.

  Keywords

  Foundation pile; Info-Gap theory; Karst; Pile foundations; Robust reliability index; Stability of karst roof; Uncertainty analysis
  

• Yuanfu Tang, Jianqiao Chen and Junhong Wei, 2012, A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty, ASME Journal of Mechanical Design, January 2012, Vol. 134.
  
  Abstract

  Abstract

  In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

  Keywords

  epistemic uncertainty, info-gap models, feasible robustness index, sequential algorithm, shifting factor, reliabilitybased robust design optimization
  

• Chen, J., Tang, Y., Wei, J. and Ge, R., 2012, Reliability robust design of structures under incomplete information, Yingyong Lixue Xuebao/Chinese Journal of Applied Mechanics, Volume 29(4): 404-409.
  
  Abstract

  Abstract

  This paper first discusses the reliability-based design optimization (RDO) of structures under the mixture of random, interval and fuzzy variables. The sequential single-loop optimization method is applied for RDO with different combinations of uncertaities. Info-gap models are used to represent errors between “true” values and design results. A sequential algorithm for the robust reliability design is presented. Example 1 shows that the fuzzy reliability design can offer conservative result. The results of example 2 show there are different robust optimal solutions when the robustness index takes different values. When alpha_t is greater than 0.2, the robust optimal solution does not exist. After 1291 times computation of the objective function, the optimal result can be obtained by using the sequential algorithm for the robust reliability design, while 8107 times computation are needed by the conventional optimum algorithm.

  Keywords

  Incomplete information; Info-gap model; Possibility-based design; Reliability-based design; Robust design optimization
  

• Plucinski, M., 2012, Application of the information-gap theory for evaluation of nearest neighbours method robustness to data uncertainty. Electrical Review, Vol. 88, Issue 10B, 2012, pp.272-275.
  
  Abstract

  Abstract

  The paper describes a new method based on the information-gap theory which enables an evaluation of worst case error predictions of the kNN method in the presence of a specified level of uncertainty in the data. There are presented concepts of a robustness and an opportunity of the kNN model and calculations of these concepts were performed for a simple 1-D data set and next, for a more complicated 6-D data set. In both cases the method worked correctly and enabled evaluation of the robustness and the opportunity for a given lowest acceptable quality rc or a windfall quality rw. The method enabled also choosing of the most robust kNN model for a given level of an uncertainty alpha.

  Keywords

  Data uncertainty; Function approximation; Information-gap theory; k-nearest neighbours method; Local regression
  

• Wang, F. , Zhang, J., Wang, X., Wang, C., and Liu, Z., 2012, A non-probabilistic reliability analysis on uncertainties systems, Proceedings of IEEE 2012 Prognostics and System Health Management Conference,Article number 6228861.
  
  Abstract

  Abstract

  This paper is concerned with the non-probabilistic methods to deal with uncertainties problems. First, this paper analyzes the difference between non-probabilistic reliability methods and traditional probabilistic reliability methods, which makes the comparative analysis on aspects of the application scope of methods, the use of processes and the complexity of employment. Second, this paper introduces the basic concept of the convex model, as the interval model, the ellipsoid model and the multidimensional ellipsoid model are briefly presented. Third, this paper analyzes the use of information gap model of uncertainty, including the basic application of the model and the way to use. Finally, numerical example is given to illustrate the validity and efficiency of non-probabilistic reliability method. The example used herein is reliability analysis of fatigue strength of turbine blade, but it is also an important reference of other types of uncertainties systems. Compared with the probability approach, the non-probabilistic information gap model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters, and whereby makes the reliability analysis very convenient and economical.

  Keywords

  information gap model of uncertainty; non-probabilistic reliability method; the convex model
  

• Ramanujan, D., Bernstein, W.Z., Zhao, F., Ramani, K., 2011, Addressing uncertainties within product redesign for sustainability: A function based framework, Proceedings of the ASME Design Engineering Technical Conference, Volume 9, 28-31 August 2011, Washington, DC, pp.1057-1064.
  
  Abstract

  Abstract

  The Function Impact Method (FIM) is a semi-quantitative eco-design methodology that is targeted specifically towards the early stages of the design process. The FIM allows a designer to predict the environmental impacts associated with a new functional embodiment by extrapolating knowledge from Life cycle assessment (LCA) of similar existing designs. LCA however, is associated with substantial sources of uncertainty. Furthermore, the FIM uses a subjective weighting scheme for representing function-structure affinities. In the authors’ previous work, a Monte-Carlo variation analysis was used to estimate sensitivity of the input data and select the preferred redesign strategy. This paper proposes a method to formalize the input uncertainties in the FIM by modeling the uncertainties present in the results of the LCA’s and the involved function-structure affinities using Info-gap decision theory. The desirability of redesigning a particular function based on the magnitude of its function-connectivity and eco-impact is estimated, and a decision making methodology based on robust satisficing is discussed. This method is applied for making robust redesign decisions with regards to re-designing a pneumatic impact wrench for sustainability.

  Keywords

  Decision making; Eco-design; Function Impact Method; Info-gap decision theory; Life Cycle Analysis
  

• Zhang, J., 2011, Newsboy problem under Knightian uncertainty, 8th International Conference on Service Systems and Service Management, ICSSSM’11, Tianjin, China, 25-27 June 2011.
  
  Abstract

  Abstract

  In this paper, we consider newsboy problem under Knightian uncertainty. That is, we assume that the uncertainty of demand is Knightian uncertainty. We use info-gap uncertainty to model the uncertainty of the demand. The objective is to study the robustness of the optimal policy. We first assume that the price is exogenous and then the price is determined endogenously and is a decision variable. We study the optimal policies for the inventory control system with and without price setting under Knightian uncertainty and their robustness. We show that the relative robustness of the sole inventory system and the joint pricing and inventory control with multiplicative demand function to profit loss are the same and higher than that of the joint pricing and inventory control with additive demand function.

  Keywords

  Info-gap; Inventory control; Newsboy problem; Pricing
  

• Xu, R., Tang, H., and Xue, S., 2010, Structural robust design based on Info-Gap model, Modelling and Computation in Engineering – Proc Intl Conf Modelling and Computation in Engineering, CMCE 2010, Hong Kong, November 2010, Taylor and Francis, pp.67-71. ISBN: 978-041561516-7.
  
  Abstract

  Abstract

  A novel Info-Gap robust design concept to structural robust optimization under severe uncertainties is presented in this paper. This Info-Gap model is a non-probabilistic method for the problem considering severe uncertainties using the Info-Gap Decision Theory (IGDT). IGDT models the clustering of uncertain events in families of nested sets instead of assuming a probability structure, which only require the nominal estimate of uncertain parameters to be known before analysis or use in optimization. The heuristic algorithm is applied to the nested optimizations in IGDT and simulation results show that the proposed approach can solve complex problems effectively.
  

• Wu, D., Gao, W. , Li, G., Tangaramvong, S., Tin-Loi, F., 2015, Robust assessment of collapse resistance of structures under uncertain loads based on Info-Gap model, Computer Methods in Applied Mechanics and Engineering, 2015, Vol. 285, pp.208-227.
  
  Abstract

  Abstract

  The paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case, and the best limit in the other case of rigid perfectly-plastic structures subjected to uncertain-but-bounded applied loads using an Info-Gap model. The methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem, and vice versa for the best collapse load limit. The formulation for capturing the worst collapse load limit (robust worst case solution) takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm, whilst that for the best collapse load limit is a standard linear programming problem. The efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples.

  Keywords

  Linear programming; Load limits; Mathematical programming; Uncertainty analysis; Collapse resistance; Complementarity; Info-gap model; Limit analysis; Linear programming problem; Mathematical program with equilibrium constraints; Uncertain kinematics; Uncertainty; Rigid structures
  

• Maugan, F., Cogan, S., Foltete, E., Buffe, F. and Gaetan Kerschen, 2014, Robust Design of Notching Profiles Under Epistemic Model Uncertainties, Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014.
  
  Abstract

  Abstract

  The notching profile defines the loading conditions for satellite subsystem shake tests. Its model-based design is a critical issue in the space field and must be defined early in order to initiate as soon as possible discussions between launch authorities and subcontractors. This discussion revolves around the following dilemma: how conservative can the loading be and still be safe for the subsystem interfaces? Indeed, the significant lack of knowledge present in the non-validated model can result in overloading conditions. This paper will propose a global strategy for the model-based design of notching profiles which accounts for epistemic modeling uncertainties using an info-gap approach. The latter provides a generic framework for evaluating and comparing the performances of competing profile designs as well as addressing issues of lack of knowledge in both deterministic and probabilistic model parameters. The proposed methodologies will be illustrated on an academic test case.

  Keywords

  Notching, robustness, info-gap, uncertainty, lack of knowledge
  

• Maugan, F., Cogan, S., Foltête, E., Buffe, F., 2014, Robust design of notching profiles under epistemic model uncertainties,  26th International Conference on Noise and Vibration Engineering, ISMA 2014, Leuven, Belgium; 15-17 September 2014.
  
  Abstract

  Abstract

  Spacecraft mechanical tests aim at qualifying structures with respect to a launcher flight environment and investigating the finite element model (FEM) ability to correctly represent experimental measurements. An input spectrum is specified by the launcher authority to encompass flight events, but in order to avoid over testing in frequency bands with highly excited modes due to the presence of huge lack of knowledge in the non-validated model, it must be locally decreased. This model-based design is a critical issue in the space field and must be defined early in order to initiate as soon as possible discussions between launcher authorities and subcontractors. This discussion revolves around the following dilemma: how conservative can the loading be and still be safe for the subsystem interfaces? This paper will propose a global strategy for the model-based design of notching profiles which accounts for epistemic modeling uncertainties using an info-gap approach. The latter provides a generic framework for evaluating the performances of profile designs as well as addressing issues of lack of knowledge in this approach. The proposed methodologies will be illustrated on an academic test case, modeling the first and second longitudinal modes for a medium-size scientific satellite. Solutions will then be discussed in order to turn this methodology applicable on real industrial satellite structures.

• Maugan, F. Cogan, S. Foltête, E. Hot, A., 2015, Robust modal test design under epistemic model uncertainties, Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 3, 2015, Article A29, pp.207-214. 2014 Annual Conference on Experimental and Applied Mechanics, Greenville, SC, 2-5 June 2014.
  
  Abstract

  Abstract

  A wide variety of model-based modal test design methodologies have been developed over the past two decades using a non-validated baseline model of the structure of interest. Due to the presence of lack of knowledge, this process can lead to less than optimal distributions of sensors and exciters due to the discrepancy between the model and the prototype behaviors. More recent strategies take into account statistical variability in model parameters but the results depend strongly on the hypothesized distributions. This paper provides a decision making tool using a robust satisficing approach that provides a better understanding of the trade-off between the performance of the test design and its robustness to model form errors and associated imprecisions. The latter will be represented as an info-gap model and the proposed methodology seeks a sensor distribution that will satisfy a given design performance while tolerating a specified degree of modeling error. The evolution of this performance for increasing horizons of uncertainty is an important information for the test planner in choosing the total number of sensors. © The Society for Experimental Mechanics, Inc. 2015.

  Author keywords

  Info-gap; Lack of knowledge; Robustness; Sensor placement; Uncertainty
  

• Pereiro, D., Cogan, S., Sadoulet-Reboul, E., Martinez, F., Salgado, O., 2014, Wind turbine power train robust model calibration with load uncertainties, 26th International Conference on Noise and Vibration Engineering, ISMA 2014, Leuven, Belgium; 15-17 September 2014.
  
  Abstract

  Abstract

  The goal of this work is to propose a model calibration strategy for an industrial problem consisting in a MW class geared wind turbine power train subjected to uncertain loads. Lack of knowledge is commonplace in this kind of engineering system and a realistic model calibration cannot be performed without taking into account this type of uncertainty. The question at stake in this study is how to perform a robust predictive model of a dynamic system given that the excitations are poorly known. The uncertainty in the latter will be represented with an info-gap model. The tradeoff between fidelity to data and robustness to uncertainty is then investigated in order to maximize the robustness of the prediction error at a given horizon of uncertainty, a method is also proposed to increase confidence in model prediction for untested configurations. This methodology is illustrated on a simple academic model and on a more complex engineering system representing a wind turbine geared power train.

• Pereiro, D., Cogan, S., Sadoulet-Reboul, E. and Martinez, F., 2013, Robust model calibration with load uncertainties, 31st IMAC, A Conference on Structural Dynamics, Garden Grove, CA, 11-14 February 2013, vol. 5, pp.89-97.
  
  Abstract

  Abstract

  The goal of this work is to propose a model calibration strategy for an industrial problem consisting in a MW class geared wind turbine power train subjected to uncertain loads. Lack of knowledge is commonplace in this kind of engineering system and a realistic model calibration cannot be performed without taking into account this type of uncertainty. The question at stake in this study is how to perform a robust predictive model of a dynamic system given that the excitations are poorly known. The uncertainty in the latter will be represented with an info-gap model. The tradeoff between fidelity to data and robustness to uncertainty is then investigated in order to maximize the robustness of the prediction error at a given horizon of uncertainty. This methodology is illustrated on a simple academic model and on a more complex engineering system representing a wind turbine geared power train.

  Keywords

  Load uncertainty; Model fidelity; Model updating; Robust calibration; Transient analysis; Wind turbine.
  

• Aurélien Hot, Scott Cogan, Emmanuel Foltete, Gaetan Kerschen, Fabrice Buffe, Jérôme Buffe, Stéphanie Behar, 2012, Design of uncertain prestressed space structures: an Info-gap approach, Proceedings of the SEM IMAC XXX Conference, Jan. 30 – Feb. 2, 2012, Jacksonville, FL USA.
  
  Abstract

  Abstract

  Uncertainty quantification is an integral part of the model validation process and is important to take into account during the design of mechanical systems. Sources of uncertainty are diverse but generally fall into two categories: aleatory uncertainties due to random processes and epistemic uncertainty resulting from a lack of knowledge or erroneous assumptions.

  This work focuses on the impact of uncertain levels of prestress on the behavior of solar arrays in their stowed configuration. In this context, snubbers are inserted between two adjacent panels to maintain contact and absorb vibrations during launch. However, under high excitation loads, a loss of contact between the two panels may occur.

  This results in impacts that can cause extensive damages to fragile elements. In practice, the specific load configuration for which the separation of the two panels occurs is difficult to determine precisely since the exact level of prestress applied to the structure is unknown. An info-gap robustness analysis is applied to study the impact of this lack of knowledge on the prestress safety factor required to avoid loss of contact. The proposed methodology is illustrated using a simplified model of a solar array.

• Arkadeb Ghosal, Haibo Zeng, Marco Di Natale and Yakov Ben-Haim, Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters. Presented at Design, Automation & Test in Europe (DATE), Dreden, 8-12 March 2010, Dresden, Germany. pre-print
   
• Li, K.  and Z. Yang, Study on non-probabilistic structural reliability method based on info-gap decision theory,Jixie Qiangdu/Journal of Mechanical Strength, vol.35, issue 2, April 2013, pages 174-178.
  
  Abstract

  Abstract

  A dispersion parameter was proposed and introduced in the info-gap (information gap) model. The info-gap model introduced dispersion parameter has more applicability for structural reliability analysis. A general non-probabilistic structural reliability model was established by using the info-gap model introduced dispersion parameter to describe the uncertainties based on the info-gap decision theory. The non-probabilistic reliability index defined in the new model can be obtained by solving a nonlinear programming problem. The mathematical deduction shows the relationship of the non-probabilistic structural reliability method based on info-gap model and the traditional probabilistic structural reliability method, which also shows the consistency of the two methods.

  Keywords

  Dispersion parameter; Info-gap(information-gap) model; Non-probabilistic reliability; Reliability index
  

• Li, K., Z. Yang and Z. Zhou, Non-probabilistic structural reliability model introduced restrictions on set expansion, Jixie Qiangdu/Journal of Mechanical Strength, vol.35, issue 3, June 2013, pages 258-262.
  
  Abstract

  Abstract

  The difference of the dispersion style of the uncertainty quantities in the practical structural reliability problems was pointed out. The info-gap (information-gap) model with restriction was advanced by introducing a new parameter in the origin model. The new model could be degenerated into the origin model. The non-probabilistic structural reliability method with the info-gap model introducing restriction parameter could utilize the existing information thoroughly and estimate the structural reliability more reasonably. Comparing with the existing model the new non-probabilistic structural reliability model could reveal the influence of the restriction information on structural reliability. The numerical example shows that the non-probabilistic reliability index ignored the restriction of uncertainty quantities span would be too conservative.

  Keywords

  Info-gap(information-gap) model; Non-probabilistic reliability; Reliability index; Robust reliability; Set expansion
  

• Li, K., Yang, Z., Sun, W., 2011, Non-probabilistic structural reliability model based on ellipsoidal-bound model with nonlinear expansion, Applied Mechanics and Materials, Vol. 65, pp.264-267.
  
  Abstract

  Abstract

  Info-gap model is the foundation of the non-probabilistic reliability model. In this paper, ellipsoidal-bound model which is the most common Info-gap model has been updated by acquiring restriction information about uncertain quantities. The initial ellipsoidal-bound model can be degenerated from the updated model. A non-probabilistic structural reliability model based on the updated ellipsoidal-bound model was established. A non-probabilistic reliability index was proposed and the calculation method was also given. The example shows that the introduction of restriction information is valid, and the new non-probabilistic reliability model can reveal the influence of the span restriction of uncertain quantities on structural reliability.
  

• Kendra L. Van Buren and Francois M. Hemez, 2014, Robust decision making applied to the NASA multidisciplinary uncertainty quantification challenge problem, 16th AIAA Non-Deterministic Approaches Conference, National Harbor, MD, 13-17 January 2014.Full paper.
  
  Abstract

  Abstract

  This paper addresses the NASA Langley Multidisciplinary Uncertainty Quantification Challenge (MUQC) Problem, which is intended to pose challenges to the uncertainty quantification and robust design communities. The goals of the MUQC problem can be formulated into four main topics that are commonly encountered in the model development process: calibration, sensitivity analysis, uncertainty propagation, and robust design. Our analysis places a particular emphasis on the use of info-gap decision theory (IGDT) to address the goals of the MUQC problem. IGDT provides a convenient framework to treat epistemic uncertainty when using simulation models for decision-making. We utilize a robustness criterion, defined in the context of IGDT, to pursue calibration, uncertainty propagation, and robust design. Herein, our calibration utilizes IGDT to address the situation whereby traditional calibration techniques might result in non-unique results where different sets of calibration variables are able to replicate experiments with comparable fidelity. Uncertainty propagation is performed such that the worst-case and best-case performances of the model output are conditioned on the level of uncertainty that is permitted in the simulations. To pursue robust design, we utilize the robustness criterion to establish whether the amount of uncertainty tolerable in our optimized design is an improvement over the baseline design. We demonstrate that improving the robustness of the model requires different knowledge than improving performance of the model. The main conclusion is that IGDT provides a sound theoretical basis, and practical implementation, to meet the goals of the NASA MUQC problem without formulating simplifying assumptions.
  

• Kendra L. Van Buren, Sez Atamturktur, Francois M. Hemez, 2013, Model selection through robustness and fidelity criteria: Modeling the dynamics of the CX-100 wind turbine blade, Mechanical Systems and Signal Processing, 43 (1-2) pp. 246-259.
  
  Abstract

  Abstract

  Several plausible modeling strategies are available to develop numerical models for simulating the dynamics of wind turbine blades. While the modeling strategy is typically selected according to expert judgment, the “best” modeling approach is unknown to the model developer. Thus, comparing plausible modeling strategies through a systematic and rigorous approach becomes necessary. This manuscript departs from the conventional approach that selects the model with the highest fidelity-to-data; and instead explores the trade-off between fidelity of model predictions to experiments and robustness of model predictions to model imprecision and inexactness. Exploring robustness in addition to fidelity lends credibility to the model, ensuring model predictions can be trusted even when lack-of-knowledge in the modeling assumptions and/or input parameters result in unforeseen errors and uncertainties. This concept is demonstrated on the CX-100 wind turbine blade in an experimental configuration with large masses added to load the blade in bending during vibration testing. The finite element model of the blade is built with shell elements and validated against experimental evidence, while the large masses are modeled according to two different, but plausible strategies using (i) a combination of point-mass and spring elements, and (ii) solid elements. These two modeling strategies are evaluated considering both the fidelity of the natural frequency predictions against experiments, and the robustness of the predicted natural frequencies to uncertainties in the input parameters. By considering robustness during model selection, the authors determine the extent to which prediction accuracy deteriorates as the lack-of-knowledge increases. The findings suggest the model with solid elements offers a higher degree of fidelity-to-data and robustness to uncertainties, thus providing a superior modeling strategy than the model with point masses and stiffening springs.

  Keywords

  Info-Gap decision theory; Model selection; Wind turbine blade; Model complexity; Prediction; Test-analysis correlation

  Highlights

  • Model selection is formulated in the context of info-gap decision theory.
  • Competing finite element models of the CX-100 wind turbine blade are developed.
  • Results demonstrate the trade-offs of accuracy and uncertainty.
• Mollineaux, M.G., Van Buren, K.L., Hemez, F.M., Atamturktur, H.S., Simulating the Dynamics of the CX-100 Wind Turbine Blade: Part I, Model Development, Verification and Validation, American Society of Mechanical Engineers (ASME) Verification and Validation Symposium, Las Vegas, Nevada, May 2-4, 2012. Full paper.
   
• Van Buren, K.L., Mollineaux, M.G., Hemez, F.M., Atamturktur, H.S., Simulating the Dynamics of the CX-100 Wind Turbine Blade: Part II, Model Selection Using a Robustness Criterion, American Society of Mechanical Engineers (ASME) Verification and Validation Symposium, Las Vegas, Nevada, May 2-4, 2012. Full paper.
   
• Ashley Woods, Evgenii Matrosov, Julien J. Harou, 2011, Applying info-gap decision theory to water supply system planning: Application to the thames basin, Computer Control and the Water Industry (CCWI) Conference, Exeter, UK, Sept 2011. Pre-print.
   
• Matrosov, E.S., Woods, A.M., Harou, J.J., 2013, Robust decision making and info-gap decision theory for water resource system planning, Journal of Hydrology, 2013, 494: 43-58.
  
  Abstract

  Abstract

  Stationarity assumptions of linked human-water systems are frequently invalid given the difficult-to-predict changes affecting such systems. In this case water planning occurs under conditions of deep or severe uncertainty, where the statistical distributions of future conditions and events are poorly known. In such situations predictive system simulation models are typically run under different scenarios to evaluate the performance of future plans under different conditions. Given that there are many possible plans and many possible futures, which simulations will lead to the best designs? Robust Decision Making (RDM) and Info-Gap Decision Theory (IGDT) provide a structured approach to planning complex systems under such uncertainty. Both RDM and IGDT make repeated use of trusted simulation models to evaluate different plans under different future conditions. Both methods seek to identify robust rather than optimal decisions, where a robust decision works satisfactorily over a broad range of possible futures. IGDT efficiently charts system performance with robustness and opportuneness plots summarising system performance for different plans under the most dire and favourable sets of future conditions. RDM samples a wider range of dire, benign and opportune futures and offers a holistic assessment of the performance of different options. RDM also identifies through ‘scenario discovery’ which combinations of uncertain future stresses lead to system vulnerabilities. In our study we apply both frameworks to a water resource system planning problem: London’s water supply system expansion in the Thames basin, UK. The methods help identify which out of 20 proposed water supply infrastructure portfolios is the most robust given severely uncertain future hydrological inflows, water demands and energy prices. Multiple criteria of system performance are considered: service reliability, storage susceptibility, capital and operating cost, energy use and environmental flows. Initially the two decision frameworks lead to different recommendations. We show the methods are complementary and can be beneficially used together to better understand results and reveal how the particulars of each method can skew results towards particular future plans.

  Keywords

  Info-Gap Decision Theory (IGDT); Infrastructure planning; Robust Decision Making (RDM); Uncertainty; Water resources planning

• S. Chinnappen-Rimer and G.P. Hancke, 2011, Actor coordination using info-gap decision theory in wireless sensor and actor networks, International Journal of Sensor Networks, Vol. 10, #4, pp.177-191.
  
  Abstract

  Abstract

  Mobile, unmanned, power and resource-rich devices, called actors, deployed within a Wireless Sensor Network (WSN) application area, enable faster response times to events. Due to cost constraints, only a few actors can be placed within a WSN application area. Determining which actor or set of actors should respond to an event is important, because the correct decision will increase the event response time and reduce energy expenditure. Since the mobile actors are widely dispersed over the application area, the actors’ accurate location and energy details will not always be available. In this paper, we show that using info-gap decision theory to choose the correct actors to respond to an event when uncertainty about an actor’s location and/or energy exists ensures that the actors chosen can adequately respond to the event. The robustness of the decision choice of the set of actor(s) assigned to respond to an event means that all chosen actor(s) have sufficient energy to respond to the event in real time.

• Chinnappen-Rimer, S. and Hancke, G.P., 2009, Actor coordination in wireless sensor-actor networks, IEEE India Council Conference, INDICON 2009; Ahmedabad; 18-20 December 2009.
  
  Abstract

  Abstract

  Wireless Sensor Networks (WSN) depend on remote human interaction. This slows the real time response to an event. Certain applications require rapid response to events detected by sensor nodes. The use of actors in a WSN enhances the real time response of the whole network. The coordination of actors to sensed events is thus vital for the efficient operation of the network. The goal is to optimise coordination between actors to determine which actors respond to an event message. We provide a model to determine which actors respond to an event based on Info-gap Decision Theory. We show that it is possible to choose some correct actors out of a set when faced with severe uncertainty about the environment.

• Yakov Ben-Haim and Scott Cogan, 2009, Linear Bounds on an Uncertain Non-Linear Oscillator: An Info-Gap Approach, Proceedings of the IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties, St. Petersburg, Russia, 5-9 July 2009, pp.3-14. Pre-print.
• Duncan, S.J., Paredis, C.J.J. and Bras, B., 2007, Applying info-gap theory to remanufacturing process selection affected by severe uncertainty, Proceedings of IMECE2007, 2007 ASME International Mechanical Engineering Congress and Exposition, November 11-15, 2007, Seattle.
  
  Abstract

  Abstract

  In this article, Information-Gap Decision Theory (IGDT), an approach to robust decision making under severe uncertainty, is applied to decisions about a remanufacturing process. IGDT is useful when only a nominal estimate is available for an uncertain quantity; the amount that estimate differs from the quantity’s actual value is not known. The decision strategy in IGDT involves maximizing robustness to uncertainty of unknown size, while still guaranteeing no worse than some “good enough” critical level of performance, rather than optimal performance. The design scenario presented involves selecting the types of technologies and number of stations to be used in a remanufacturing process. The profitability of the process is affected by severe uncertainty in the demand for remanufactured parts. Because nothing is know about demand except an estimate based on a different product from a previous year, info-gap theory will be used to determine an appropriate tradeoff between performance and robustness to severe uncertainty. Which design is most preferred is seen to switch depending on choice of critical performance level. Implications of findings, as well as future research directions, are discussed.

• Neil D. Sims, Graeme Manson and Brian Mann, 2009, Fuzzy stability analysis of regenerative chatter in milling, Journal of Sound and Vibration, to appear.
   
• Manning, L.J., J.W. Hall, H.J. Fowler, C.G. Kilsby and C. Tebaldi, 2010, Using probabilistic climate change information from a multimodel ensemble for water resources assessment, Water Resources Research, VOL. 45, doi:10.1029/2007WR006674.
   
• Hine, Daniel and Jim W. Hall, 2010, Information gap analysis of flood model uncertainties and regional frequency analysis, Water Resources Research, vol. 46, issue 1, W01514, doi:10.1029/2008WR007620.
  
  Abstract

  Abstract

  Flood risk analysis is subject to often severe uncertainties, which can potentially undermine flood management decisions. This paper explores the use of information gap theory to analyze the sensitivity of flood management decisions to uncertainties in flood inundation models and flood frequency analysis. Information gap is a quantified nonprobabilistic theory of robustness. To analyze uncertainties in flood modeling, an energy-bounded information gap model is established and applied first to a simplified uniform channel and then to a more realistic 2-D flood model. Information gap theory is then applied to the estimation of flood discharges using regional frequency analysis. The use of an information gap model is motivated by the notion that hydrologically similar sites are clustered in the space of their L moments. The information gap model is constructed around a parametric statistical flood frequency analysis, resulting in a hybrid model of uncertainty in which natural variability is handled statistically while epistemic uncertainties are represented in the information gap model. The analysis is demonstrated for sites in the Trent catchment, United Kingdom. The analysis is extended to address ungauged catchments, which, because of the attendant uncertainties in flood frequency analysis, are particularly appropriate for information gap analysis. Finally, the information gap model of flood frequency is combined with the treatment of hydraulic model uncertainties in an example of how both sources of uncertainty can be accounted for using information gap theory in a flood risk management decision.

• Hall, J.W. and Harvey, H., 2009, Decision making under severe uncertainty for flood risk management: A case study of info-gap robustness analysis. Proc. Int. Conf. Science and Information Technologies for Sustainable Management of Aquatic Ecosystems, Concepcion, Chile, 12-16 January 2009.
   
• Harvey, D.Y., Worden, K., Todd, M.D., 2014, Robust evaluation of time series classification algorithms for structural health monitoring, Health Monitoring of Structural and Biological Systems 2014, San Diego, CA, 10-13 March 2014. Proceedings of SPIE – The International Society for Optical Engineering, Volume 9064, 2014, Article number 90640K.
  
  Abstract

  Abstract

  Structural health monitoring (SHM) systems provide real-time damage and performance information for civil, aerospace, and mechanical infrastructure through analysis of structural response measurements. The supervised learning methodology for data-driven SHM involves computation of low-dimensional, damage-sensitive features from raw measurement data that are then used in conjunction with machine learning algorithms to detect, classify, and quantify damage states. However, these systems often suffer from performance degradation in real-world applications due to varying operational and environmental conditions. Probabilistic approaches to robust SHM system design suffer from incomplete knowledge of all conditions a system will experience over its lifetime. Info-gap decision theory enables nonprobabilistic evaluation of the robustness of competing models and systems in a variety of decision making applications. Previous work employed info-gap models to handle feature uncertainty when selecting various components of a supervised learning system, namely features from a pre-selected family and classifiers. In this work, the info-gap framework is extended to robust feature design and classifier selection for general time series classification through an efficient, interval arithmetic implementation of an info-gap data model. Experimental results are presented for a damage type classification problem on a ball bearing in a rotating machine. The info-gap framework in conjunction with an evolutionary feature design system allows for fully automated design of a time series classifier to meet performance requirements under maximum allowable uncertainty. © 2014 SPIE.

  Author keywords

  Feature extraction; Info-gap decision theory; Robustness; Structural health monitoring; Time series classification
  

• S.G. Pierce, K. Worden and G. Manson, 2006, A novel information-gap technique to assess reliability of neural network-based damage detection Journal of Sound and Vibration, 293: Issues 1-2, pp.96-111.
   
• Miriam Zacksenhouse, Simona Nemets, Anna Yoffe, Yakov Ben-Haim, Mikhail Lebedev, Miguel Nicolelis, An info-gap approach to linear regression, 2006 IEEE International conference on Acoustics, Speech and Signal Processing, ICASSP 2006 May 14-19, 2006, Toulouse, France, Vol.3: 800-803.
   
• Gaetan Kerschen, Keith Worden, Alexander F. Vakakis and Jean-Claude Golinval, 2006, Past, present and future of nonlinear system identification in structural dynamics Mechanical Systems and Signal Processing,Volume 20, Issue 3, Pages 505-592.
   
• Chetwynd, D., Worden, K., Manson, G., 2006, An application of interval-valued neural networks to a regression problem, Proceedings of the Royal Society – Mathematical, Physical and Engineering Sciences, (Series A), 462 (2074) pp.3097-3114.
   
• Matsuda, Y. and Y. Kanno, 2008, Robustness analysis of structures based on plastic limit analysis with uncertain loads, Journal of Mechanics of Materials and Structures, vol.3, pp.213-242.
  
  Abstract

  Abstract

  This paper presents a method for computing an info-gap robustness function of structures, which is regarded as one measure of structural robustness, under uncertainties associated with the limit load factor. We assume that the external load in the plastic limit analysis is uncertain around its nominal value. Various uncertainties are considered for the live, dead, and reference disturbance loads based on the nonstochastic info-gap uncertainty model. Although the robustness function is originally defined by using the optimization problem with infinitely many constraints, we show that the robustness function is obtained as an optimal value of a linear programming (LP) problem. Hence, we can easily compute the info-gap robustness function associated with the limit load factor by solving an LP problem. As the second contribution, we show that the robust structural optimization problems of trusses and frames can also be reduced to LP problems. In numerical examples, the robustness functions, as well as the robust optimal designs, are computed for trusses and framed structures by solving LP problems.
  

• Y. Kanno and I. Takewaki, 2006, Sequential semidefinite program for maximum robustness design of structures under load uncertainty, Journal of Optimization Theory and Applications, vol.130, #2, pp.265-287.
   
• University of Newcastle upon Tyne and Halcrow. Early Conceptual Options, A framework for Uncertainty Analysis in TE2100, Environment Agency ECO Report R10X, June 2006, 42pp.
   
• Jim Hall and Dimitri Solomatine, 2008, A framework for uncertainty analysis in flood risk management decisions, International Journal of River Basin Management, Vol.6, No. 2, pp.85–98.
   
• D.J. Hine and J.W. Hall, Convex Analysis of Flood Inundation Model Uncertainties and Info-Gap Flood Management Decisions, ISSH – Stochastic Hydraulics 2005, 23 and 24 May 2005, Nijmegen, The Netherlands.
   
• Meir Tahan and Joseph Z. Ben-Asher, 2005, Modeling and analysis of integration processes for engineering systems, Systems Engineering, Vol. 8, No. 1, pp.62-77.
   
• Izuru Takewaki and Yakov Ben-Haim, 2005, Info-gap robust design with load and model uncertainties, Journal of Sound and Vibration, 288: 551-570.
   
• Izuru Takewaki and Yakov Ben-Haim, 2007, Info-gap robust design of passively controlled structures with load and model uncertainties, appearing in Structural Design Optimization Considering Uncertainties, Yiannis Tsompanakis, Nikkos D. Lagaros and Manolis Papadrakakis, editors. Taylor and Francis Publishers.
   
• Izuru Takewaki and Yakov Ben-Haim, 2005, Info-gap Robust Design with Load and Model Uncertainties, Journal of Sound and Vibration, 288: 551-570.Pre-print
  
  Abstract

  Abstract

  This paper develops a new structural design concept which incorporates uncertainties in both the load and the structural model parameters. Info-gap models of uncertainty are used to represent uncertainty in the power spectral density of the load and in parameters of the vibration model of the structure. It is demonstrated that any design which optimizes functional performance will also minimize the robustness to uncertainty. Since uncertainties are prevalent in many applications, this paper argues that it is necessary to satisfy critical performance requirements (rather than to optimize performance), and to maximize the robustness to uncertainty. The design implications of this robust-satisficing approach are demonstrated with several heuristic structural design examples. It is shown that design preferences depend upon performance requirements: preferences between designs can be reversed when performance requirements change. Also, we show that the info-gap robustness function provides an attractive tool for adjudicating between conflicting objectives in multi-criteria design.

  Keywords

  Earthquake excitation, building design, information-gap decision theory, uncertainty, robustness.
  

• Duncan, S.J., Aughenbaugh, J.M., Paredis, C.J.J., Bras, B. Considering the info-gap approach to robust decisions under severe uncertainty in the context of environmentally benign design, Proceedings of the ASME Design Engineering Technical Conference, 2006.
• Duncan, S.J., Bras, B. and Paredis, C.J.J., 2008, An approach to robust decision making under severe uncertainty in life cycle design, Int. J. Sustainable Design, Vol. 1, No. 1, pp.45-59.
• Duncan, S.J., Paredis, C.J.J., Bras, B., 2008, Applying info-gap theory to remanufacturing process selection affected by severe uncertainty, ASME International Mechanical Engineering Congress and Exposition, Proceedings Vol. 15, pp.293-300.
• D. Lim, Y. S. Ong, Y. Jin, B. Sendhoff, and B. S. Lee, 2006, Inverse Multi-objective Robust Evolutionary Design, Genetic Programming and Evolvable Machines Journal, Vol. 7, No. 4, pp. 383-404.
• P. Vinot, S. Cogan and V. Cipolla, 2005, A robust model-based test planning procedure Journal of Sound and Vibration, Volume 288, Issue 3, pp.571-585.
• Kaihong Wang, 2005, Vibration Analysis of Cracked Composite Bending-torsion Beams for Damage Diagnosis, PhD thesis, Virginia Tech.
• Francois M. Hemez and Yakov Ben-Haim, 2004, Info-gap robustness for the correlation of tests and simulations of a nonlinear transient, Mechanical Systems and Signal Processing, vol. 18, #6, pp.1443-1467.
• Yakov Ben-Haim, 2004, Uncertainty, probability and information-gaps, Reliability Engineering and System Safety, 85: 249-266. Pre-print. 
• Daniel Berleant, Karen Villaverde and Olga M. Koseheleva, 2008, Towards a more realistic representation of uncertainty: An approach motivated by Info-Gap Decision Theory, Fuzzy Information Processing Society, 2008. NAFIPS 2008. Annual Meeting of the North American Conference. DOI10.1109/NAFIPS.2008.4531297. Abstract.
• M.-P. Cheong, D. Berleant, and G. B. Shebl’e,Information Gap Decision Theory as a tool for Strategic Bidding in Competitive Electricity Markets, 8th International Conference on Probabilistic Methods Applied to Power Systems, Iowa State University, Ames, lowa, September 12-16,2004.
• Z.P. Qiu, P.C. Mueller and A. Frommer, 2004, The new nonprobabilistic criterion of failure for dynamical systems based on convex models, Mathematical and Computer Modelling, Vol. 40, Issues 1-2, pp.201-215.
• Pascal Vinot, Scott Cogan and Gerard Lallement, 2003, Approche non-probabiliste de fiabilite basee sur les modeles convexes: A non-probabilistic reliability approach based on convex models, Mecanique & Industries,Volume 4, Issue 1, January-February 2003, Pages 45-50.
• Attoh-Okine, N.O., 2002, Uncertainty analysis in structural number determination in flexible pavement design — A convex model approach, Construction and Building Materials, Volume 16, Issue 2, March 2002, Pages 67-71.
• Yakov Ben-Haim, 2001, Info-gap value of information in model up-dating, Mechanical Systems and Signal Processing, 15: 457-474.
• Yakov Ben-Haim, 1997, Robust reliability of structures, Advances in Applied Mechanics, vol. 33, pp.1-41.
• S. Ganzerli and C.P. Pantelides, Optimum structural design via convex model superposition, Comput Struct,74, \#6 (2000), pp. 639-647.
• C.P. Pantelides and B.C. Booth, Computer-aided design of optimal structures with uncertainty, Comput Struct,74, #3 (2000), pp. 293-307.
• S. Ganzerli and C.P. Pantelides, Load and resistance convex models for optimum design, Struct Optim, 174 (1999), pp. 259-268.
• C.P. Pantelides and S. Ganzerli, Design of trusses under uncertain loads using convex models, J Struc Eng ASCE, 124 (1998) (3), pp. 318-329.
• Yakov Ben-Haim and Scott Cogan, 1998, Usability of mathematical models in mechanical decision processes,Mechanical Systems and Signal Processing, 12(1): 121-134. Pre-print.
• Keith W. Hipel and Yakov Ben-Haim, 1999, Decision making in an uncertain world: Information-gap modelling in water resources management, IEEE Trans., Systems, Man and Cybernetics, Part C: Applications and Reviews, 29: 506-517. Pre-print.
• H.E. Lindberg, 1991, Dynamic response and buckling failure measures for structures with bounded and random imperfections, Trans ASME J Appl Mech, vol. 58, pp.1092–1094.
• H.E. Lindberg, 1992, An evaluation of convex modelling for multimode dynamic buckling, Trans ASME J Appl Mech, vol. 59, pp.929-936.
• H.E. Lindberg, 1992, Convex models for uncertain imperfection control in multimode dynamic buckling, Trans ASME J Appl Mech, vol. 59, pp.937-945.
• Yakov Ben-Haim and Isaac Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier, Amsterdam.
• Yakov Ben-Haim, 1985, The Assay of Spatially Random Material, Kluwer Academic Publishers, Dordrecht, Holland.
• Zhiping Qiu, Lihong Ma and Xiaojun Wang, 2006, Ellipsoidal-bound convex model for the non-linear buckling of a column with uncertain initial imperfection, International Journal of Non-Linear Mechanics, to appear.
• Yakov Ben-Haim, Genda Chen and T.T. Soong, 1996, Maximum Structural Response Using Convex Models, ASCE J. Engineering Mechanics, 122: 325-333.
• Yakov Ben-Haim, 1995, Convex models of uncertainty for small initial imperfections of non-linear structures,Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 75: 901-908.
• Yakov Ben-Haim, 1993, Convex models for uncertainty in radial pulse buckling of shells, ASME Journal of Applied Mechanics, 60: 683-688.
• Xiao-Ming Zhang and Han Ding, 2008, Design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model, Journal of Sound and Vibration, to appear.
• Chen, S.H., K.J. Guo and Y.D. Chen, 2004, A method for estimating upper and lower bounds of eigenvalues of closed-loop systems with uncertain parameters, Journal of Sound and Vibration, Vol.276, Issues 3-5, 22 September 2004, pp.527-539.
• Yakov Ben-Haim, 1998, Reliability of Vibrating Structures With Uncertain Inputs. Shock and Vibration Digest, 30: 106-113. Pre-print.
   
• Yakov Ben-Haim, A non-probabilistic concept of reliability, Structural Safety, 14:227-245 (1994). Link to a pre-print.