Mitsuru MURASE and Izuru TAKEWAKI, Reliability-based design optimization for building-connecting inertial-mass damper, J. Struct. Constr. Eng., AIJ, Vol. 88, #805, 437-446, Mar., 2023 (in Japanese, but see fig.1). Abstract. Here is the full paper.
Bachy E., Jaboviste K., Sadoulet-Reboul E., Peyret N., Chevallier G., Arnould C., and Collard E., 2022, Investigations on the performance and the robustness of a metabsorber designed for structural vibration mitigation, Mechanical Systems and Signal Processing, Volume 170, Article number 108830. DOI 10.1016/j.ymssp.2022.108830. Abstract.
Antoine Ajenjo, Emmanuel Ardillon, Vincent Chabridon, Bertrand Iooss, Scott Cogan, Emeline Sadoulet-Reboul, 2022, An info-gap framework for robustness assessment of epistemic uncertainty models in hybrid structural reliability analysis, Structural Safety, Vol. 96, May 2022, 102196. Abstract.
R. Viala, S. Le Conte, S. Vaiedelich, S. Cogan and Y. Ben-Haim, 2022, Playability of a 1734 Guarneri cello: Info-gap robustness analysis of uncertainty, Model Validation and Uncertainty Quantification, vol. 3, pp.67-72, Part of the Conference Proceedings of the Society for Experimental Mechanics Series. Abstract.
Xiang Li, Xibing Li, Zilong Zhou, Yonghua Su and Wengui Cao, 2021, A non-probabilistic information-gap approach to rock tunnel reliability assessment under severe uncertainty, Computers and Geotechnics, 132 (1-2): 103940. DOI: 10.1016/j.compgeo.2020.103940. Abstract.
Zahra Marvi and Bahare Kiumarsi, 2021, Robust satisficing cooperative control barrier functions for multirobots systems using information‐gap theory, International Journal of Robust and Nonlinear Control, December 2021, DOI: 10.1002/rnc.5914. Abstract.
Kohei Fujita, Ryota Wataya and Izuru Takewaki, 2021, Robust optimal damper placement of nonlinear oil dampers with uncertainty using critical double impulse, Frontiers in Built Environment, 7, art. no. 744973, 20 August 2021, https://doi.org/10.3389/fbuil.2021.744973. Abstract.
Jie Liu, Zhongbo Yu, Dequan Zhang, Hao Liu and Xu Han, 2021, Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation, June 2021, International Journal of Mechanics and Materials in Design, DOI: 10.1007/s10999-021-09551-z. Abstract.
Erfeng Zhao and Chengqing Wu, 2021, Long-term safety assessment of large-scale arch dam based on non-probabilistic reliability analysis, Structures, 32 298-312. Abstract.
Kuczkowiak, A., Cogan, S., Ouisse, M., Foltête, E, Corus, M., 2020, Experimental validation of an info-gap uncertainty model for a robustness analysis of structural responses, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, Vol. 6, #3, 1 September 2020, article number 030905. Abstract.
Kyoichiro Kondo and Izuru Takewaki, 2019, Simultaneous approach to critical fault rupture slip distribution and optimal damper placement for resilient building design, Frontiers in Built Environment, 24 October 2019, https://doi.org/10.3389/fbuil.2019.00126. Abstract.
Asl, M.E., Niezrecki, C., Sherwood, J. and Avitabile, P., 2019, Scaling and structural similarity under uncertainty, Conference Proceedings of the Society for Experimental Mechanics Series, Volume 3, 2019, pp.167-174. 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018. Abstract.
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.
Koki Makita, Kyoichiro Kondo and Izuru Takewaki, 2019, Finite Difference Method-Based Critical Ground Motion and Robustness Evaluation for Long-Period Building Structures Under Uncertainty in Fault Rupture, Front. Built Environ. Abstract.https://doi.org/10.3389/fbuil.2019.00002.
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.
Yoshihiro Kanno, Shinnosuke Fujita and Yakov Ben-Haim, 2017, Structural Design for earthquake resilience: Info-gap management of uncertainty, Structural Safety, vol. 69, pp.23-33. 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.
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.
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.
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
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.
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.
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.
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.
Robustness; Structural safety; Semidefinite program; Quasiconvex optimization; Data uncertainty.
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.
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.
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.
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.
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.
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.
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.
Finite element analysis; Mechanical latch; Robust design; Uncertainty quantification.
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.
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.
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.
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.
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.
Izuru Takewaki, 2013, Towards narrowing unexpected issues in future earthquakes: A review, Advances in Structural Engineering, 16(5): 931-946.
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.
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.
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.
Foundation pile; Info-Gap theory; Karst; Pile foundations; Robust reliability index; Stability of karst roof; Uncertainty analysis
Yoshihiro Kanno, 2012, Worst scenario detection in limit analysis of trusses against deficiency of structural components, Engineering Structures, 42: 33-42.
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.
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.
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.
Decision making; Eco-design; Function Impact Method; Info-gap decision theory; Life Cycle Analysis
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.
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.
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.
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.
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.
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.
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.
Info-gap; Lack of knowledge; Robustness; Sensor placement; Uncertainty
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.
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.
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.
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.
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
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.
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.
Kaihong Wang, 2005, Vibration Analysis of Cracked Composite Bending-torsion Beams for Damage Diagnosis, PhD thesis, Virginia Tech.
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.
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.
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.
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.
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.