Nikolaos I. Ioakimidis, 2023, Application of the method of quantifier elimination to Ben-Haim’s info-gap decision theory (IGDT) under the presence of both horizon-of-uncertainty-related and ordinary interval uncertain variables, Technical Report No. TR-2023-Q22, University of Patras. DOI: 10.13140/RG.2.2.29885.44006. Abstract.
Yakov Ben-Haim, 2022, Inferring extreme values from measured averages under deep uncertainty, ASME Journal of Verification, Validation and Uncertainty Quantification, June 2022, vol. 7, pp.021002-1 to 021002-12. Abstract.
Nikolaos I. Ioakimidis, 2022, An application of Ben-Haim’s info-gap decision theory (IGDT) to Todinov’s method of algebraic inequalities by employing the method of quantifier elimination, Technical Report, October 2022, DOI: 10.13140/RG.2.2.30031.36000. Abstract.
Erdem Acar, Gamze Bayrak, Yongsu Jung, Ikjin Lee, Palaniappan Ramu and Suja Shree Ravichandran, 2021, Modeling, analysis, and optimization under uncertainties: a review. Structural and Multidisciplinary Optimization, https://doi.org/10.1007/s00158-021-03026-7. Abstract.
Muriel C. Bonjean Stanton and Katy Roelich, 2021, Decision making under deep uncertainties: A review of the applicability of methods in practice, Technological Forecasting and Social Change, Volume 171, October 2021, 120939. Abstract.
Nikolaos I. Ioakimidis, 2022, Problems under uncertainty: quantifier elimination to universally–existentially (AE) quantified formulae related to two or more horizons of uncertainty, March 2022, DOI: 10.13140/RG.2.2.22282.34247. Abstract.
Nikolaos I. Ioakimidis, 2021, Quantifier elimination and quantifier-free formulae for universally–existentially (AE) quantified formulae in Ben-Haim’s info-gap model of uncertainty, Technical Report No. TR-2021-Q18, December, 2021, deposited to Nemertes and appeared online also at Nemertes. DOI: 10.13140/RG.2.2.32057.70246. Abstract.
Nikolaos I. Ioakimidis, 2021, Robust reliability under uncertainty conditions by using modified info-gap models with two to four horizons of uncertainty and quantifier elimination, September 2021, DOI: 10.13140/RG.2.2.35922.27844, Report number: TR-2021-Q17. Abstract.
Nikolaos I. Ioakimidis, 2021, Application of quantifier elimination to robust reliability under severe uncertainty conditions by using the info-gap decision theory (IGDT), Technical Report No. TR-2021-Q16, 31 pages, July 4, 2021, deposited to Nemertes and appeared online also at Nemertes. DOI: 10.13140/RG.2.2.22065.51041. Abstract.
Francois Hemez, 2020, Robust estimation of truncation-induced numerical uncertainty, Proceedings of the Society for Experimental Mechanics Series, IMAC, A Conference and Exposition on Structural Dynamics, Houston, 10 February 2020 through 13 February 2020, Code 245349, pp.223-232. Abstract.
Yakov Ben-Haim and Francois Hemez, 2020, Richardson Extrapolation: An Info-Gap Analysis of Numerical Uncertainty, ASME Journal of Verification, Validation and Uncertainty Quantification, vol.5, number 2, article 021004, pp.1-8. Abstract.
Yakov Ben-Haim, 2019, Cascading Failures in Hierarchical Networks with Unity of Command: An Info-Gap Analysis, International Journal of Disaster Risk Reduction, vol. 41: 101291. Abstract. Pre publicationpre-print.
Yakov Ben-Haim, 2019, Info-gap decision theory, in V.A.W.J. Marchau, W.E. Walker, P. Bloemen, and S.W. Popper (eds.), Decision Making Under Deep Uncertainty: From Theory to Practice, Springer. Linkto the open-access online version.
Navid Rezaei, Abdollah Ahmadi, Ali Esmaeel Nezhad and Amirhossein Khazali, 2019, Information-gap decision theory: Principles and fundamentals, chapter 2 in Behnam Mohammadi-ivatloo and Morteza Nazari-Heris, eds., 2019, Robust Optimal Planning and Operation of Electrical Energy Systems, Springer. DOI: 10.1007/978-3-030-04296-7_2. Abstract.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Info-gap approach; Model calibration; Performance metric; Robust solution; 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.
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.
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.
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.
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.
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.
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.
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.
Data uncertainty; Function approximation; Information-gap theory; k-nearest neighbours method; Local regression
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.
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.
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.
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.
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.
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
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.
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.
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.
Info-Gap decision theory; Model selection; Wind turbine blade; Model complexity; Prediction; Test-analysis correlation
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.
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.
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.
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.
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.
Feature extraction; Info-gap decision theory; Robustness; Structural health monitoring; Time series classification
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.
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.
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.
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.
Yakov Ben-Haim, 2001, Info-gap value of information in model up-dating, Mechanical Systems and Signal Processing, 15: 457-474.
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.
Yakov Ben-Haim, 1985, The Assay of Spatially Random Material, Kluwer Academic Publishers, Dordrecht, Holland.