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首页> 外文期刊>Mechanical systems and signal processing >Stochastic model updating utilizing Bayesian approach and Gaussian process model
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Stochastic model updating utilizing Bayesian approach and Gaussian process model

机译：利用贝叶斯方法和高斯过程模型的随机模型更新

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摘要

Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
机译：随机模型更新（SMU）已越来越多地用于根据响应变异性来量化结构参数不确定性。用于参数不确定性量化的SMU是指逆不确定性量化（IUQ）的问题，这是一项艰巨的任务。通过优化解决的逆问题通常带来梯度计算，病态和非唯一性的问题。而且，响应中存在的不确定性使反问题变得更加复杂。在这项研究中，贝叶斯方法在SMU中用于参数不确定性量化。贝叶斯方法对IUQ问题的突出优势在于它可以直接解决IUQ问题，从而避免了以前的问题。但是，当贝叶斯方法应用于以高分辨率有限元模型（FEM）建模的工程结构时，其计算量仍然很大，因为用于贝叶斯推理的常用马尔可夫链蒙特卡洛（MCMC）方法需要大量的模型运算保证收敛。在此，我们从两个方面降低了计算成本。一方面，快速运行的高斯过程模型（GPM）用于近似耗时的高分辨率FEM。另一方面，采用结合了局部自适应策略和全局自适应策略的延迟拒绝自适应大都会（DRAM）算法的高级MCMC方法用于贝叶斯推理。此外，我们建议在参数选择中使用强大的基于方差的全局灵敏度分析（GSA），以从校准参数中排除非影响性参数，从而产生降阶模型，从而进一步减轻计算负担。提出了一个模拟铝板和一个现实世界中复杂的斜拉人行桥，以说明所提出的框架并验证其可行性。

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