基于Sigma点全局迭代参数卡尔曼滤波的折线型本构模型参数识别

PARAMETER IDENTIFICATION OF BROKEN LINE CONSTITUTIVE MODEL BASED ON SIGMA POINT GLOBAL ITERATION PARAMETRIC KALMAN FILTER

折线型本构模型控制参数少,物理意义明确,但其数学表达式复杂因而识别困难。针对折线型本构模型的参数识别,提出基于Sigma点变换的全局迭代参数卡尔曼滤波算法。所提方法以待识别参数作为状态向量,降低状态向量维度,减少计算量;基于Sigma点卡尔曼滤波避免求解雅克比(Jacobian)矩阵,实现非连续型函数本构模型的参数识别;通过设定目标函数进行全局迭代,以获得最优解。由于非线性系统下一时刻响应与历史路径有关,量测更新时由初始时刻计算到当前时刻。最后,在地震荷载下,将隔震支座系统简化为单自由度双线性模型,将桥墩简化为单自由度Takeda模型,根据该文所提出的方法理念,分别基于无迹卡尔曼滤波(unscented Kalman filter,UKF)、容积卡尔曼滤波(cubature Kalman filter,CKF)和球面单纯形径向容积正交卡尔曼滤波(spherical simplex-radial cubature quadrature Kalman filter,SSRCQKF)采样规则识别折线型本构模型参数。结果表明所提方法能够准确识别非线性参数,同时具有较强的鲁棒性,不同滤波器收敛过程及结果也有所差异。

The broken line constitutive model has few control parameters and clear physical meaning, but its mathematical expression is complex. Thusly, it is difficult to identify. Aiming at the parameter identification of the broken line constitutive model, a global iteration parametric Kalman filter algorithm based on Sigma point transform is proposed. The method proposed takes the parameters to be identified as the state vector to reduce the dimension of the state vector and the amount of calculation. Based on Sigma point Kalman filter, the Jacobian matrix is avoided, and the parameter identification of a discontinuous function constitutive model is realized. By setting the objective function for a global iteration, the optimal solution can be obtained. Because the next time response of the nonlinear system is related to the historical path, the measurement update is calculated from the initial time to the current time. Finally, under seismic loading, the isolated bearing system is simplified as a single degree of freedom with a bilinear model, and the pier is simplified as a single degree of freedom with a Takeda model. According to the method proposed, the broken line constitutive model parameters are identified based on different sampling rules, such as unscented Kalman filter (UKF), cubature Kalman filter (CKF) and spherical simplex-radial cubature quadrature Kalman filter (SSRCQKF). The results demonstrate that the method proposed can accurately identify the nonlinear parameters and has strong robustness. The convergence process and results of different filters are also different.