Structural optimization considering dynamic reliability constraints via probability density evolution method and change of probability measure

The present paper presents a framework for solving dynamic reliability–based design optimization (DRBDO) problems. The proposed approach is based on a sequential approximate programming technique, where the solution of the original design problem is obtained by converting it into a sequence of sub-optimization problems with a simple explicit algebraic structure. The technique is combined with the probability density evolution method (PDEM) for the purpose of estimating the reliability and/or the failure probability at the different designs in an efficient manner. The change of probability measure (COM), a strategy based on the Radon-Nikodym derivative, is employed to estimate the sensitivity information required by the optimization scheme. Based on this strategy, the sensitivity information can be obtained without any additional function evaluation. Thus, the numerical efforts associated with the reliability assessment and sensitivity analysis can be considerably reduced. The results of the numerical examples indicate that the proposed method is an effective and efficient tool for solving a class of DRBDO problems.

[1]  Jie Li,et al.  An efficient new PDEM-COM based approach for time-variant reliability assessment of structures with monotonically deteriorating materials , 2020 .

[2]  Jia Wang,et al.  Reliability analysis and reliability-based optimal design of linear structures subjected to stochastic excitations , 2014 .

[3]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..

[4]  Meng-Gang Yang,et al.  An experimental study on using MR damper to mitigate longitudinal seismic response of a suspension bridge , 2011 .

[5]  Hector A. Jensen,et al.  Structural optimization of uncertain dynamical systems considering mixed-design variables , 2011 .

[6]  Jianbing Chen,et al.  The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters , 2007 .

[7]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[8]  Jianbing Chen,et al.  A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters , 2016 .

[9]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[10]  Zhao Jing,et al.  A reliability-based optimization method using sequential surrogate model and Monte Carlo simulation , 2018, Structural and Multidisciplinary Optimization.

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

[12]  Peter Wriggers,et al.  Reliability-based optimization of trusses with random parameters under dynamic loads , 2011 .

[13]  Seymour M.J. Spence,et al.  Optimization of uncertain structures subject to stochastic wind loads under system-level first excursion constraints: A data-driven approach , 2018, Computers & Structures.

[14]  Alexandros A. Taflanidis,et al.  Reliability-based optimal design of linear dynamical systems under stochastic stationary excitation and model uncertainty , 2010 .

[15]  Jianbing Chen,et al.  Stochastic Dynamics of Structures , 2009 .

[16]  B. Ellingwood,et al.  Directional methods for structural reliability analysis , 2000 .

[17]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[18]  James L. Beck,et al.  Global optimization using the asymptotically independent Markov sampling method , 2013 .

[19]  Jianbing Chen,et al.  Error estimate of point selection in uncertainty quantification of nonlinear structures involving multiple nonuniformly distributed parameters , 2019, International Journal for Numerical Methods in Engineering.

[20]  Jianbing Chen,et al.  Probability density evolution method for dynamic response analysis of structures with uncertain parameters , 2004 .

[21]  J. Beck,et al.  Stochastic Subset Optimization for optimal reliability problems , 2008 .

[22]  B. Prasad.  Explicit constraint approximation forms in structural optimization Part 1: Analyses and projections , 1983 .

[23]  Jie Li,et al.  An ensemble evolution numerical method for solving generalized density evolution equation , 2017 .

[24]  L. Watson,et al.  An inverse-measure-based unilevel architecture for reliability-based design optimization , 2007 .

[25]  Lei Jiang,et al.  A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization , 2008 .

[26]  Jianbing Chen,et al.  Dynamic response and reliability analysis of non-linear stochastic structures , 2005 .

[27]  Bruno Sudret,et al.  Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework , 2019, Structural and Multidisciplinary Optimization.

[28]  Teng Fang,et al.  Time-Variant Reliability-Based Design Optimization Using an Equivalent Most Probable Point , 2019, IEEE Transactions on Reliability.

[29]  V. Papadopoulos,et al.  A Galerkin-based formulation of the probability density evolution method for general stochastic finite element systems , 2016, Computational Mechanics.

[30]  G. Cheng,et al.  A sequential approximate programming strategy for reliability-based structural optimization , 2006 .

[31]  Jianbing Chen,et al.  The principle of preservation of probability and the generalized density evolution equation , 2008 .

[32]  Gerhart I. Schuëller,et al.  Efficient strategies for reliability-based optimization involving non-linear, dynamical structures , 2011 .

[33]  Jianbing Chen,et al.  A global sensitivity index based on Fréchet derivative and its efficient numerical analysis , 2020 .

[34]  André T. Beck,et al.  A stochastic gradient approach for the reliability maximization of passively controlled structures , 2019, Engineering Structures.

[35]  M. Valdebenito,et al.  On the use of a class of interior point algorithms in stochastic structural optimization , 2013 .

[36]  Kamran Behdinan,et al.  Particle swarm approach for structural design optimization , 2007 .

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

[38]  J. Barthelemy,et al.  Two point exponential approximation method for structural optimization , 1990 .

[39]  F. Ikhouane,et al.  Systems with Hysteresis: Analysis, Identification and Control Using the Bouc-Wen Model , 2007 .

[40]  Dixiong Yang,et al.  Reliability analysis of structures with complex limit state functions using probability density evolution method , 2014 .

[41]  Fayal Ikhouane,et al.  Systems with Hysteresis , 2007 .

[42]  M. Beer,et al.  Approximate fuzzy analysis of linear structural systems applying intervening variables , 2016 .

[43]  Jianbing Chen,et al.  Advances of the probability density evolution method for nonlinear stochastic systems , 2012 .

[44]  W. M. Jenkins,et al.  Towards structural optimization via the genetic algorithm , 1991 .

[45]  Peter Wriggers,et al.  Structural dynamic optimal design based on dynamic reliability , 2011 .

[46]  M. Valdebenito,et al.  Reliability-based optimization of stochastic systems using line search , 2009 .

[47]  Jianbing Chen,et al.  Improving Point Selection in Cubature by a New Discrepancy , 2013, SIAM J. Sci. Comput..

[48]  Helmut J. Pradlwarter,et al.  Reliability of MDOF-systems with hysteretic devices , 1998 .

[49]  André T. Beck,et al.  A comparison of deterministic‚ reliability-based and risk-based structural optimization under uncertainty , 2012 .

[50]  Rüdiger Rackwitz,et al.  Two basic problems in reliability-based structural optimization , 1997, Math. Methods Oper. Res..

[51]  Zhen Hu,et al.  Reliability-based design optimization under stationary stochastic process loads , 2016 .

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

[53]  Zhiqiang Wan,et al.  A compatible probabilistic framework for quantification of simultaneous aleatory and epistemic uncertainty of basic parameters of structures by synthesizing the change of measure and change of random variables , 2019, Structural Safety.

[54]  Lfp Pascal Etman,et al.  Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations , 2009 .

[55]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[56]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[57]  Wilson H. Tang,et al.  Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering , 2006 .

[58]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[59]  Luciano Lamberti,et al.  An efficient simulated annealing algorithm for design optimization of truss structures , 2008 .