力学学报 ›› 2018, Vol. 50 ›› Issue (3): 677-687.doi: 10.6052/0459-1879-18-014

• 生物、工程及交叉力学 • 上一篇    下一篇

预测结构性能退化的混合粒子滤波方法

关雪雪, 陈建桥*, 郑瑶辰*, 张晓生   

  1. 华中科技大学力学系,武汉 430074;
    工程结构分析与安全评定湖北省重点实验室,武汉 430074
  • 收稿日期:2018-01-08 出版日期:2018-05-15 发布日期:2018-06-11
  • 通讯作者: 陈建桥,教授,主要研究方向:结构可靠性分析等. E-mail:jqchen@mail.hust.edu.cn;郑瑶辰,博士研究生,主要研究方向:结构优化设计. E-mail:zyc276565153@126.com
  • 基金资助:
    国家自然科学基金资助项目(11572134).

A COMBINED PARTICLE FILTER METHOD FOR PREDICTING STRUCTURAL PERFORMANCE DEGRADATION

Guan Xuexue, Chen Jianqiao*, Zheng Yaochen*, Zhang Xiaosheng   

  1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;
    Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China
  • Received:2018-01-08 Online:2018-05-15 Published:2018-06-11

摘要: 由于载荷,环境以及材料内部因素的作用,结构的性能一般随时间而逐渐退化. 为了评估结构服役期间的状态,常采用随机变量模型来描述结构性能的退化规律. 即,采用含不确定性模型参数的物理模型来逼近结构响应特性. 利用同类型结构的先知数据集信息可确定模型参数的先验分布. 结合结构服役期间的检测信息和贝叶斯原理,对模型参数进行更新,从而提高物理模型的准确性. 本文提出一种混合粒子滤波方法(particle filter-differential evolution adaptive Metropolis,PF-DREAM)用于模型更新,即:在确定参数先验分布时,采用证据理论(Dempster-shafer theory, DST)初始化模型参数;结合差分进化自适应 Metropolis 算法(differential evolution adaptive Metropolis, DREAM)和粒子滤波(particle filter, PF)算法,来计算更新公式中的复杂的高维积分. 相比于传统的 PF 算法,混合 PF-DREAM 方法可以有效提高样本粒子的多样性,解决重采样算法中粒子多样性匮乏的问题,从而得到更加合理的物理模型. 为了证明该方法的有效性,将提出的方法分别应用于电池性能退化和裂纹扩展规律预测. 算例表明采用本文提出的模型参数确定方法,使得物理模型更加合理,性能预测更加准确. 用于更新的数据越多,模型参数的分散性越小. 本文方法应用于高维问题或隐式函数问题时,计算原理和步骤不发生改变,但函数评价次数和计算时间会随之增大.

关键词: 贝叶斯原理|证据理论|粒子滤波|差分进化自适应Metropolis算法

Abstract: Structural performances will degrade with time due to the influence of loading, environmental and material factors. To assess the status of a structure in service, the structural deterioration process is usually described through physical models with uncertain model parameters. Prior distributions of model parameters are often determined by using the data collected from similar structures. To improve the accuracy of the model, Bayesian inference incorporated with available data is often used to update the distribution of the parameters. In this work, an effective Bayesian method PF-DREAM is proposed. In this approach, firstly, the mixing combination rule of the Dempster-shafer theory (DST) is utilized to get the prior distribution. Thereafter, for evaluating the complicated multidimensional integral in the Bayesian inference formula and obtaining the posterior distribution, a differential evolution adaptive Metropolis (DREAM) approach integrated with the particle filter (PF) is developed. As compared with the original PF method, the proposed PF-DREAM method can enhance the sample particles' diversity and improve the quality of the model. To illustrate the efficiency and accuracy of the proposed method, a lithium-ion battery problem and a fatigue crack propagation problem are presented. Results demonstrated that the proposed method can provide more accurate results in parameters updating as well as response prediction. As more data is incorporated, the model's variance becomes smaller, and the predicted mean trajectory is more reliable in terms of the actual deteriorate curves. It is pointed out that PF-DREAM method can be applied to high-dimensional problems and implicit function problems with the same algorithm presented in this paper, only accompanying more iteration numbers and greater computational load for obtaining convergent results.

Key words: Bayesian inference|Dempster-shafer theory|particle filter|differential evolution adaptive Metropolis

中图分类号: 

  • O346.2