压电结构系统辨识中的幂迭代子空间跟踪方法

Power iteration subspace tracing algorithm for identification of piezoelectric smart structures

针对子空间辨识压电结构系统模型,利用广义能观矩阵列空间与观测矢量相关矩阵信号子空间一致的特征,提出采用幂迭代子空间跟踪方法,保证全局且按指数收敛到主子空间。为避免跟踪过程中与主子空间偏离误差的传递,采用多级分解,形成多级幂迭代子空间跟踪方法。将其与投影逼近子空间方法比较,仿真结果表明,能观矩阵夹角小,输出均方根误差小,能提高跟踪精度。并运用于实际模型中,验证其有效性。

For the subspace identification of piezoelectric smart structure model, the power iteration subspace tracing algorithm was presented to assure the global and exponential convergence to the principle subspace, based on the fact that the column space of the extended observability matrix is the same with the signal subspace of autocorrelation matrix of observation vectors. In order to avoid the error propagation of the principal subspace derivation in each iteration, the multistage power iteration decomposition was proposed. The simulation results, compared with those by the projection approximation subspace tracking method, show that the proposed method can achieve smaller angle between the estimation and the true extended observability matrix, lower root mean square error of output, and higher tracking precision. Finally, the application to the actual model was given to demonstrate the efficiency of the proposed algorithm.