A Bayesian Structural Modal Updating Method Based on Sparse Grid and Ensemble Kalman Filter

IF 4.6 2区 工程技术 Q1 CONSTRUCTION & BUILDING TECHNOLOGY
Guangwei Lin, Yi Zhang, Enjian Cai, Min Luo, Jing Guo
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Abstract

This study presents a sparse grid interpolation and ensemble Kalman filter (EnKF)-based Markov Chain Monte Carlo (MCMC) method (SG-EnMCMC). Initiating with the formulation of a recursive equation for the state space vector, derived from the structural dynamic equation, this study adopts a dimensionality reduction strategy. This approach involves a separation of physical parameters and the state space vector. The acquisition of physical parameters is accomplished through sampling, utilizing sample moments to substitute population moments, thereby mitigating the need for computationally high-dimensional covariance matrix calculations. To further streamline the recursive equation of the state space vector, a sparse grid method is employed for interpolation. This step simplifies the process while ensuring superior accuracy compared to the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Subsequent to this, acceptance rates and the final parameter posterior distribution within the MCMC framework are derived. The efficiency of the proposed method is assessed through validation in two shaking table experiments.

Abstract Image

基于稀疏网格和集合卡尔曼滤波器的贝叶斯结构模态更新方法
本研究提出了一种基于稀疏网格插值和集合卡尔曼滤波器(EnKF)的马尔可夫链蒙特卡罗(MCMC)方法(SG-EnMCMC)。从结构动态方程导出的状态空间向量递归方程开始,本研究采用了降维策略。这种方法涉及物理参数和状态空间向量的分离。物理参数的获取是通过采样完成的,利用样本矩来替代总体矩,从而减少了计算高维协方差矩阵的需要。为了进一步简化状态空间向量的递归方程,采用了稀疏网格法进行插值。与扩展卡尔曼滤波器(EKF)和无符号卡尔曼滤波器(UKF)相比,这一步骤简化了过程,同时确保了更高的精度。随后,在 MCMC 框架内推导出接受率和最终参数后验分布。通过两个振动台实验的验证,对所提方法的效率进行了评估。
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来源期刊
Structural Control & Health Monitoring
Structural Control & Health Monitoring 工程技术-工程:土木
CiteScore
9.50
自引率
13.00%
发文量
234
审稿时长
8 months
期刊介绍: The Journal Structural Control and Health Monitoring encompasses all theoretical and technological aspects of structural control, structural health monitoring theory and smart materials and structures. The journal focuses on aerospace, civil, infrastructure and mechanical engineering applications. Original contributions based on analytical, computational and experimental methods are solicited in three main areas: monitoring, control, and smart materials and structures, covering subjects such as system identification, health monitoring, health diagnostics, multi-functional materials, signal processing, sensor technology, passive, active and semi active control schemes and implementations, shape memory alloys, piezoelectrics and mechatronics. Also of interest are actuator design, dynamic systems, dynamic stability, artificial intelligence tools, data acquisition, wireless communications, measurements, MEMS/NEMS sensors for local damage detection, optical fibre sensors for health monitoring, remote control of monitoring systems, sensor-logger combinations for mobile applications, corrosion sensors, scour indicators and experimental techniques.
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