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Resampling method for reliability-based design optimization based on thermodynamic integration and parallel tempering

机译：基于热力学集成和并联回火的基于可靠性的设计优化的重采样方法

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摘要

In this paper, a fully decoupled simulation method is proposed for reliability-based design optimization (RBDO) based on thermodynamic integration and parallel tempering (TIPT). We show that the failure probability function and its gradient can be obtained simultane-ously with once generalized reliability analysis, and thus the RBDO problem is converted to the traditional optimization problem efficiently. Firstly, the design parameters are deemed as uniformly distributed random variables, and an auxiliary probability density function (PDF) of random design variables is constructed to cover its whole parameter space. Then, based on thermodynamic integration, the estimation of failure probability is con-verted to a series of simple integration problems with smooth integrand, and they are esti-mated by running multiple Markov chains using the so-called parallel tempering method. Finally, importance sampling (IS) is used to estimate the failure probability function and its gradient, and the IS samples are obtained by resampling from the existing Markov chains without extra computation. The proposed method is tested with severa benchmarks, and the results show that it provides robust solution for problems with various nonlinear con-straints compared to other popular methods, include double-loop Monte Carlo simulation (MCS), Quantile MCS, sequential optimization and reliability assessment, performance measure approach and reliability index approach.
机译：本文基于热力学积分和并联回火（TIPT），提出了一种基于可靠性的设计优化（RBDO）的完全解耦模拟方法。我们表明，一旦广泛性可靠性分析，可以同时获得故障概率函数及其梯度，从而有效地将RBDO问题转换为传统优化问题。首先，设计参数被认为是均匀分布的随机变量，并且构造随机设计变量的辅助概率密度函数（PDF）以覆盖其整个参数空间。然后，基于热力学集成，将失效概率的估计与光滑的整合性的一系列简单的集成问题相连，并且通过使用所谓的并行回火方法运行多个马尔可夫链来进行esti-mated。最后，重要的采样（IS）用于估计失败概率函数及其梯度，并且通过从现有的马尔可夫链重新采样而没有额外计算来获得该样本。该方法用Severa基准测试，结果表明，与其他流行方法相比，它为各种非线性配置的问题提供了强大的解决方案，包括双环蒙特卡罗模拟（MCS），定量MCS，顺序优化和可靠性评估，绩效措施方法和可靠性指标方法。

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  • 来源
    《Mechanical systems and signal processing》 |2021年第7期|107630.1-107630.15|共15页
  • 作者

    Kai Cheng; Zhenzhou Lu; Sinan Xiao; Xiaobo Zhang; Sergey Oladyshkin; Wolfgang Nowak;

  • 作者单位

    School of Aeronautics Northwestern Polytechnical University. Xi'an 710072 PR China Department of Stochastic Simulation and Safety Research for Hydrosystems (IWS/LS3) University of Stuttgart Pfaffenwaldring 5a Stuttgart 70569 Germany;

    School of Aeronautics Northwestern Polytechnical University. Xi'an 710072 PR China;

    Department of Stochastic Simulation and Safety Research for Hydrosystems (IWS/LS3) University of Stuttgart Pfaffenwaldring 5a Stuttgart 70569 Germany Institute of Bio- and Ceosciences (IBG-3): Agrosphere Forschungszentrum Jiilich GmbH Julich Germany;

    School of Aeronautics Northwestern Polytechnical University. Xi'an 710072 PR China;

    Department of Stochastic Simulation and Safety Research for Hydrosystems (IWS/LS3) University of Stuttgart Pfaffenwaldring 5a Stuttgart 70569 Germany;

    Department of Stochastic Simulation and Safety Research for Hydrosystems (IWS/LS3) University of Stuttgart Pfaffenwaldring 5a Stuttgart 70569 Germany;

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  • 正文语种 eng
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  • 关键词

    Reliability-based design optimization; Resampling; Thermodynamic integration; Parallel tempering;

    机译：基于可靠性的设计优化;重新采样;热力学集成;并行回火;

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