基于扩展卡尔曼滤波和初等变换的结构参数和荷载识别研究

Parameters and loads identification basing on extended Kalman filter and elementary transformation

扩展卡尔曼滤波(extend Kalman filter,EKF)是一种能有效识别结构参数的时域方法,但经典的EKF需要已知外激励信息。在实际工程中,由于受各种条件限制,往往难以有效获取作用于结构的外激励信息,这大大限制了此类EKF算法的工程应用。为克服这一局限性,提出一种基于EKF的未知激励下的结构参数识别方法。通过初等行变换矩阵,变换观测方程,消除未知外激励在观测方程中的影响。利用状态方程获取先验估计,并基于变换后的观测方程,进一步获取结构状态的后验估计,从而实现结构参数的有效识别。同时,基于当前时间步的系统状态和观测信息,识别作用于结构的未知外激励。通过剪切框架结构模型和平面桁架2个数值算例,验证该方法的有效性。此外,通过进一步识别未知激励作用下含有Dahl模型的非线性结构,验证该方法在非线性系统参数识别中的可行性。研究结果表明,在考虑部分响应观测和噪声影响下,该方法能有效地对线性和非线性结构的参数及未知外激励进行识别。

The extend Kalman filter(EKF)can provide a promising way for the identification of structural parameters in the time domain.As well-known,the external excitation is required in the classic EKF algorithm.However,in many practical situations,it is not easy to obtain the input information,which significantly hinder the application of this method.To circumvent this limitation,an EKF-based approach was proposed for identifying structural parameters under unknown inputs.By using the elementary transformation matrix,the observation equation was divided into two parts and the influence of the unknown inputs can be eliminated.The prior state estimates can be obtained using the state equation.Then,based on the revised observation equation,the posteriori state estimates can be calculated.Finally,the unknown loads are identified on the basis of these estimated structural states.The effectiveness of the proposed approach was numerically validated via a shear building model and a planar truss structure.Moreover,a building structure equipped with Dahl model was also considered.Results show that by using partial observations the proposed approach can effectively identify the parameters of linear and nonlinear structures and the unknown inputs applied to them.