基于高斯过程潜在力模型的结构参数-荷载联合识别方法

Joint Structural Parameter-load Identification Method Based on Gaussian Process Latent Force Model

摘要:

提出一种基于高斯过程潜在力模型（Gaussian process latent force model，GPLFM）的结构参数?输入荷载?系统状态联合识别方法。将结构参数识别融入GPLFM的超参数优化过程，避免了额外的模型修正步骤，荷载识别精度显著优于主流贝叶斯滤波方法。未知荷载时程被建模为高斯过程，通过高斯过程回归向线性状态空间模型的转换，实现数值模型、测量数据、输入荷载先验信息的有机整合。采用贝叶斯滤波器估计输入荷载和系统状态，并将结构参数视为超参数，在高斯过程框架内基于能量函数和马尔科夫链蒙特卡罗（MCMC）采样技术对超参数进行优化，实现结构参数识别。通过10层剪切框架的数值模拟案例和3层框架的振动试验，以及与增广卡尔曼滤波器（AKF）和双重滤波器（DKF）的对比，验证了该方法在结构参数?输入荷载?系统状态识别上的有效性。

Abstract:

This study presents a joint identification method for structural parameters， input loads， and system states based on the Gaussian process latent force model （GPLFM）. The structural parameter identification is integrated into the hyperparameter optimization process of GPLFM， thereby avoiding additional model updating steps， and the load identification accuracy significantly outperforms that of mainstream Bayesian filtering methods. In the proposed method， the unknown load time history is first modeled as a Gaussian process. By converting the Gaussian process regression into a linear state-space model， the numerical model， measurement data， and prior information of input loads are organically integrated. A Bayesian filter is then employed to estimate input loads and system states， while structural parameters are treated as hyperparameters and optimized within the Gaussian process framework via an energy function and Markov Chain Monte Carlo （MCMC） sampling， thus achieving structural parameter identification. The effectiveness of the method in identifying structural parameters， input loads， and system states is validated through a numerical simulation of a 10-story shear frame， a vibration test on a 3-story frame， and comparisons with the augmented Kalman filter （AKF） and the dual Kalman filter （DKF）.