An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization

Abstract To achieve an optimal design of complicated structures with stochastic parameters, the reliability-based design optimization (RBDO) usually needs to handle the nested double optimization loops, which results in unbearable computational cost. In this paper, a new active learning method for RBDO combining with Kriging metamodel and accelerated chaotic single loop approach (AK-ACSLA) is developed, in which the most probable learning function (MPLF) is proposed to search the most probable point instead of the limit state function in entire design space with an active learning behavior. To ensure the high efficiency, the system’s most probable learning function (SMPLF) is further constructed to solve the RBDO problem of series system with multiple probabilistic constraints, and then the ACSLA is proposed by taking full advantage of chaos feedback control methodology for guaranteeing the validity of AK-ACSLA. Nonlinear mathematical examples and complex RBDO engineering examples illustrate the high efficiency and accuracy of AK-ACSLA through comparison with both existing gradient-based methods and active learning methods.

[1]  Hao Hu,et al.  An adaptive hybrid approach for reliability-based design optimization , 2015 .

[2]  Zhen Hu,et al.  Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis , 2015 .

[3]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[4]  Alaa Chateauneuf,et al.  Benchmark study of numerical methods for reliability-based design optimization , 2010 .

[5]  Gyung-Jin Park,et al.  Single loop single vector approach using the conjugate gradient in reliability based design optimization , 2017 .

[6]  S. Marelli,et al.  An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis , 2017, Structural Safety.

[7]  Samy Missoum,et al.  A Sampling-Based Approach for Probabilistic Design with Random Fields , 2008 .

[8]  Dixiong Yang,et al.  Chaos control of performance measure approach for evaluation of probabilistic constraints , 2009 .

[9]  Gang Li,et al.  A hybrid chaos control approach of the performance measure functions for reliability-based design optimization , 2015 .

[10]  Seymour M.J. Spence,et al.  Large scale reliability-based design optimization of wind excited tall buildings , 2012 .

[11]  Nicolas Gayton,et al.  AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models , 2018, Structural Safety.

[12]  Manolis Papadrakakis,et al.  Reliability-based structural optimization using neural networks and Monte Carlo simulation , 2002 .

[13]  Gerhart I. Schuëller,et al.  A survey on approaches for reliability-based optimization , 2010 .

[14]  X. Shao,et al.  A local Kriging approximation method using MPP for reliability-based design optimization , 2016 .

[15]  Peng Hao,et al.  An efficient adaptive-loop method for non-probabilistic reliability-based design optimization , 2017 .

[16]  N. Strömberg.  Reliability-based design optimization using SORM and SQP , 2017, Structural and Multidisciplinary Optimization.

[17]  Chang Yong Song,et al.  Role of Conservative Moving Least Squares Methods in Reliability Based Design Optimization: A Mathematical Foundation , 2011 .

[18]  Zhen Hu,et al.  First order reliability method for time-variant problems using series expansions , 2015 .

[19]  Glaucio H. Paulino,et al.  Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications , 2010 .

[20]  Pingfeng Wang,et al.  A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design , 2013, DAC 2013.

[21]  Sankaran Mahadevan,et al.  Efficient Global Surrogate Modeling for Reliability-Based Design Optimization , 2013 .

[22]  Miguel Carrasco,et al.  A new method for reliability analysis and reliability-based design optimization , 2019 .

[23]  Chen Jiang,et al.  Iterative reliable design space approach for efficient reliability-based design optimization , 2019, Engineering with Computers.

[24]  Rafael H. Lopez,et al.  A general RBDO decoupling approach for different reliability analysis methods , 2016 .

[25]  Kyung K. Choi,et al.  Hybrid Analysis Method for Reliability-Based Design Optimization , 2003 .

[26]  George Stefanou,et al.  Stochastic finite element analysis of composite structures based on mesoscale random fields of material properties , 2017 .

[27]  Tae Hee Lee,et al.  A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling , 2008 .

[28]  Peng Hao,et al.  Enhanced single-loop method for efficient reliability-based design optimization with complex constraints , 2018 .

[29]  D. Pingel,et al.  Stability transformation: a tool to solve nonlinear problems , 2004 .

[30]  Bruno Sudret,et al.  Uncertainty propagation of p-boxes using sparse polynomial chaos expansions , 2016, J. Comput. Phys..

[31]  Gianluca Iaccarino,et al.  Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty , 2018, International Journal for Numerical Methods in Engineering.

[32]  T. Cho,et al.  Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method , 2011 .

[33]  David Gorsich,et al.  Confidence-based reliability assessment considering limited numbers of both input and output test data , 2018 .

[34]  Hongping Zhu,et al.  Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation , 2016 .

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

[36]  Kyung K. Choi,et al.  A new response surface methodology for reliability-based design optimization , 2004 .

[37]  Xinyu Geng,et al.  An efficient single-loop strategy for reliability-based multidisciplinary design optimization under non-probabilistic set theory , 2018 .

[38]  Liang Gao,et al.  Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis , 2020 .

[39]  Carlos Guedes Soares,et al.  Adaptive surrogate model with active refinement combining Kriging and a trust region method , 2017, Reliab. Eng. Syst. Saf..

[40]  A. Kareem,et al.  Reliability-based topology optimization of uncertain building systems subject to stochastic excitation , 2017 .

[41]  Manolis Papadrakakis,et al.  Accelerated subset simulation with neural networks for reliability analysis , 2012 .

[42]  Zissimos P. Mourelatos,et al.  A Single-Loop Approach for System Reliability-Based Design Optimization , 2006, DAC 2006.

[43]  Jia Guo,et al.  Sequential optimization and reliability assessment for multidisciplinary systems design , 2008 .

[44]  Christopher D. Eamon,et al.  Reliability-based design optimization of a vehicular live load model , 2018, Engineering Structures.

[45]  Zeng Meng,et al.  Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization , 2019, Computer Methods in Applied Mechanics and Engineering.

[46]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[47]  Bo Yu,et al.  An importance learning method for non-probabilistic reliability analysis and optimization , 2018, Structural and Multidisciplinary Optimization.

[48]  Nicolas Gayton,et al.  A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models , 2013, Reliab. Eng. Syst. Saf..

[49]  Leandro Fleck Fadel Miguel,et al.  Overcoming the drawbacks of the FORM using a full characterization method , 2015 .

[50]  Liang Gao,et al.  A local adaptive sampling method for reliability-based design optimization using Kriging model , 2014 .

[51]  Zeng Meng,et al.  Convergence control of single loop approach for reliability-based design optimization , 2018 .

[52]  Lei Wang,et al.  Multiscale reliability-based topology optimization methodology for truss-like microstructures with unknown-but-bounded uncertainties , 2018, Computer Methods in Applied Mechanics and Engineering.

[53]  Chen Jiang,et al.  An adaptive hybrid single-loop method for reliability-based design optimization using iterative control strategy , 2017 .