基于改进PC-Kriging高保真代理模型的结构损伤识别方法

STRUCTURAL DAMAGE IDENTIFICATION METHOD UPON IMPROVED PC-KRIGING HIGH FIDELITY SURROGATE MODEL

  • 摘要: 针对基于贝叶斯模型的结构损伤识别方法在处理密集数值模型时计算量巨大的缺陷,该文提出了一种自适应稀疏混沌多项式展开(PCE)和克里金(Kriging)模型结合的高保真代理模型构建方法,并以此代理模型为基础,提出了一种新的结构损伤识别方法。首先,通过最小角回归算法自适应选择截断PCE最优展开项作为Kriging模型的趋势项,提升代理模型训练及预测效率,其中随机项通过高斯随机过程模拟;其次,以所构建的代理模型预测值代替有限元模型计算值,规避贝叶斯推断中反复调用有限元模型;然后,通过改进标准马尔可夫链蒙特卡罗方法得到不确定性参数的后验概率分布,以此判断结构损伤位置、程度及损伤概率;最后,通过两个数值算例分析,证明该文方法具备良好的鲁棒性,可应用于复杂环境下结构的损伤识别,且识别精度较高,为后续实现基于贝叶斯有限元模型修正的大型土木工程结构实时健康监测提供了一种有效手段。

     

    Abstract: Aiming at the huge computational load of the structural damage identification method based on Bayesian model in the face of dealing with an intensive numerical model, this study proposes a high fidelity surrogate model construction method combining adaptive sparse Polynomial Chaos Expansions(PCE) and Kriging model. Based on this surrogate model, a new structural damage identification method is proposed. Firstly, the Least-Angle Regression algorithm was used to adaptively select the truncated PCE optimal expansion item as the trend item of Kriging model to improve the training and prediction efficiency of the surrogate model. The random item is modeled by Gauss’s random process. Secondly, the calculated value of the finite element model is replaced by the predicted value of the surrogate model to avoid repeated calls to finite element models in Bayesian inference. Then, the modified MCMC method was used to obtain the posterior probability distribution of the uncertain parameters to determine the location, degree and damage probability of the structure. Finally, two numerical examples show that the method proposed has a good robustness and can be applied to structural damage identification in complex environments with high identification accuracy. It provides an effective method for real-time health monitoring of large-scale civil engineering structures based on Bayesian finite element model modification.

     

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