基于自适应无迹卡尔曼滤波算法的非线性系统估计  

Adaptive unscented Kalman filter for nonlinear structural identification

作　　者：仝运佳 谢丽宇[1] 薛松涛[1,2] 唐和生[1] TONG Yunjia;XIE Liyu;XUE Songtao;TANG Hesheng(Department of Disaster Mitigation for Structures,Tongji University,Shanghai 200092,China;Department of Architecture,Tohoku Institute of Technology,Sendai 982-8577,Japan)

机构地区：[1]同济大学结构防灾减灾工程系,上海200092 [2]日本东北工业大学工学部建筑学科,日本仙台982-8577

出　　处：《建筑结构学报》2023年第1期182-191,224,共11页Journal of Building Structures

基　　金：政府间国际科技创新合作重点专项(2021YFE0112200);上海市自然科学基金(20ZR1461800)。

摘　　要：采用无迹卡尔曼滤波算法在线识别非线性系统参数和进行状态估计时,要求全部外部激励已知,而大多情况下结构外部激励特别是强震甚至未知激励难以直接量测。为解决上述问题,提出并推导了只需结构输出响应,即可实时估计结构状态、未知参数和未知外部激励力的自适应无迹卡尔曼滤波算法。该自适应无迹卡尔曼滤波算法能够自动递推估计观测噪声的协方差,可以有效避免系统估计受限于不当选取的测量噪声初始值。同时,引入最小二乘法估计未知外部激励力。为验证所提出的自适应无迹卡尔曼滤波算法的可行性,以及其对于多种强非线性系统的适用性,选取两种典型的非线性系统包括一个3自由度Bouc-Wen滞回非线性结构和一个Duffing型剪切梁结构进行数值模拟分析。并对一单自由度非线性能量阱进行振动台试验研究,估计未知激励力。由识别结果和实际观测值的良好一致性,以及参数的识别精度表明:在有限的响应测量条件下,提出的自适应无迹卡尔曼滤波算法能够有效地实时追踪非线性系统的状态、估计未知参数以及非线性系统的未知外部激励力。With the premise of external excitations to be known, unscented Kalman filter algorithms can be effectively used for on-line tracking parameter variation and performing states estimation of nonlinear systems. However, in most case, external forces are unreachable or difficult to measure. In this paper, an adaptive unscented Kalman filter was proposed to simultaneously identify structural parameters, structural states and forcing input under the condition of unknown excitation history. The adaptive unscented Kalman filter algorithm can automatically and recursively estimate the covariance of the observation noise, a case which can effectively avoid the limitation of improperly selected initial value of the measurement noise in system estimation. The least squares method was introduced to estimate the unknown external excitation force. To further validate the effectiveness and robust of the proposed approach, numerical simulation and experimental analysis were performed, including a three-story hysteretic shear-beam building with a Bouc-Wen model, a nonlinear Duffing-type shear-beam structure analysis, a nonlinear energy sink experimental analysis. Numerical simulation verification and experimental validation examples illustrate that the developed adaptive unscented Kalman filter algorithm is capable of tracking the variations of structural parameters, states, as well as unknown excitation forces.

关 键 词：非线性结构 无迹卡尔曼滤波 自适应追踪 未知力估计 

分 类 号：TU317.9[建筑科学—结构工程]