基于PCE代理模型和贝叶斯优化的结构参数快速反演方法

Fast inversion method of structural parameters based on PCE surrogate model and Bayesian optimization

为保证工程结构的安全,根据实测资料进行反演分析,获取真实环境下的材料参数值具有重要价值.而现有的参数反演方法普遍存在计算效率与精度不可兼得的问题.本文利用小样本构建基于混沌多项式展开(polynomial chaos expansions,PCE)的高精度代理模型,并采用贝叶斯优化进行参数反演.新方法基于大型结构响应随机量化方法,充分利用复杂因素影响下结构响应随机特性,并依据贝叶斯后验更新方法,仅需要少量正向计算样本,便可高效、精确地进行大型结构的参数反演.某混凝土拱坝材料参数的反演算例表明,与基于贝叶斯优化算法直接进行迭代优化反演方法和基于Kriging代理模型的反演方法相比,本文所构建的方法具有优异的计算效率,适合于大型复杂结构问题的快速反演,为实际工程中在线反演和实时预测提供了新的发展维度.

To ensure the safety of engineering structures,conducting inversion analysis according to the measured data and obtaining the material parameter values in the real environment are vital.However,the existing parameter inversion methods have the problem that calculation efficiency and accuracy cannot be achieved simultaneously.In this paper,a high-precision surrogate model based on polynomial chaos expansions is constructed with small samples,and Bayesian optimization is used for parameter inversion.The new method is based on the random quantification method of large-scale structural response,which makes full use of the random characteristics of structural response under the influence of complex factors.According to the Bayesian posterior updating method,the parameter inversion of large-scale structure can be conducted efficiently and accurately with only a few forward calculation samples.The inversion example of material parameters of a concrete arch dam shows that compared with the iterative optimization inversion method based on the Bayesian optimization algorithm and the inversion method based on the Kriging surrogate model,the method constructed in this paper has excellent calculation efficiency and is suitable for rapid inversion of large and complex structural problems;moreover,it provides a new development dimension for online inversion and real-time prediction in actual engineering.