Evidence-Based Multidisciplinary Design Optimization with the Active Global Kriging Model

This article presents an approach that combines the active global Kriging method and multidisciplinary strategy to investigate the problem of evidence-based multidisciplinary design optimization. The global Kriging model is constructed by introducing a so-called learning function and using actively selected samples in the entire optimization space. With the Kriging model, the plausibility, Pl, of failure is obtained with evidence theory. The multidisciplinary feasible and collaborative optimization strategies of multidisciplinary design optimization are combined with the evidence-based reliability analysis. Numerical examples are provided to illustrate the efficiency and accuracy of the proposed method. The numerical results show that the proposed algorithm is effective and valuable, which is valuable in engineering application.

[1]  Li-Ping He,et al.  Possibility and evidence theory-based design optimization: an overview , 2008, Kybernetes.

[2]  Lei Li,et al.  Reliability based multidisciplinary design optimization of cooling turbine blade considering uncertainty data statistics , 2018, Structural and Multidisciplinary Optimization.

[3]  Rehan Haider,et al.  Creep Life Estimation of Low Pressure Reaction Turbine Blade , 2014 .

[4]  Erik Kjeang,et al.  Modification of DIRECT for high-dimensional design problems , 2014 .

[5]  Liang Gao,et al.  An Efficient Method for Structural Reliability Analysis Using Evidence Theory , 2014, 2014 IEEE 17th International Conference on Computational Science and Engineering.

[6]  Xiaoqian Chen,et al.  A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory , 2013 .

[7]  Yongshou Liu,et al.  Structural reliability analysis under evidence theory using the active learning kriging model , 2017 .

[8]  Ramana V. Grandhi,et al.  Uncertainty Quantification of Structural Response Using Evidence Theory , 2002 .

[9]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[10]  A. Sudjianto,et al.  Reliability-Based Design With the Mixture of Random and Interval Variables , 2005, DAC 2003.

[11]  Cheng Lin,et al.  An intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method , 2018 .

[12]  Yang Gao,et al.  Fault Tree Interval Analysis of Complex Systems Based on Universal Grey Operation , 2019, Complex..

[13]  John E. Renaud,et al.  Uncertainty quantification using evidence theory in multidisciplinary design optimization , 2004, Reliab. Eng. Syst. Saf..

[14]  Liang Gao,et al.  An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression , 2015 .

[15]  Michel van Tooren,et al.  Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles , 2011 .

[16]  Yu Liu,et al.  Reliability-Based Multidisciplinary Design Optimization Using Subset Simulation Analysis and Its Application in the Hydraulic Transmission Mechanism Design , 2014 .

[17]  E. Zio,et al.  Measuring reliability under epistemic uncertainty: Review on non-probabilistic reliability metrics , 2016 .

[18]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[19]  Kalyanmoy Deb,et al.  An EA-based approach to design optimization using evidence theory , 2011, GECCO '11.

[20]  Chong Wang,et al.  Evidence theory-based reliability optimization design using polynomial chaos expansion , 2018, Computer Methods in Applied Mechanics and Engineering.

[21]  Hong-Zhong Huang,et al.  An approach to system reliability analysis with fuzzy random variables , 2012 .

[22]  C. Jiang,et al.  A decoupling approach for evidence-theory-based reliability design optimization , 2017 .

[23]  Jun Zhou,et al.  Design under Uncertainty using a Combination of Evidence Theory and a Bayesian Approach , 2008 .

[24]  Xue Han,et al.  First and second order approximate reliability analysis methods using evidence theory , 2015, Reliab. Eng. Syst. Saf..

[25]  Jay D. Johnson,et al.  A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory , 2007 .

[26]  Kyung K. Choi,et al.  Reliability-based design optimization for crashworthiness of vehicle side impact , 2004 .

[27]  Philipp Limbourg,et al.  Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints , 2010, Reliab. Eng. Syst. Saf..

[28]  Masoud Rais-Rohani,et al.  Optimization of structures under material parameter uncertainty using evidence theory , 2013 .

[29]  Jun Zhou,et al.  A Design Optimization Method Using Evidence Theory , 2005, DAC 2005.

[30]  Sankaran Mahadevan,et al.  Reliability-based design optimization of multidisciplinary system under aleatory and epistemic uncertainty , 2016, Structural and Multidisciplinary Optimization.

[31]  Geoffrey T. Parks,et al.  Review of improved Monte Carlo methods in uncertainty-based design optimization for aerospace vehicles , 2016 .

[32]  Hong-Zhong Huang,et al.  Fatigue Life Prediction of Fan Blade Using Nominal Stress Method and Cumulative Fatigue Damage Theory , 2020 .

[33]  Xu Han,et al.  A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty , 2013 .

[34]  Liang Gao,et al.  An improved two-stage framework of evidence-based design optimization , 2018 .

[35]  Diego A. Alvarez,et al.  On the calculation of the bounds of probability of events using infinite random sets , 2006, Int. J. Approx. Reason..

[36]  Vladik Kreinovich,et al.  Convergence properties of an interval probabilistic approach to system reliability estimation , 2005, Int. J. Gen. Syst..

[37]  Nic Wilson The combination of belief: When and how fast? , 1992, Int. J. Approx. Reason..

[38]  Xue Han,et al.  Comparative study of metamodeling techniques for reliability analysis using evidence theory , 2012, Adv. Eng. Softw..

[39]  Yi Gao,et al.  Unified reliability analysis by active learning Kriging model combining with Random‐set based Monte Carlo simulation method , 2016 .

[40]  Lei Li,et al.  Hybrid reliability-based multidisciplinary design optimization with random and interval variables , 2017 .

[41]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[42]  V. Kreinovich,et al.  Monte-Carlo methods make Dempster-Shafer formalism feasible , 1994 .