基于Cholesky分解的改进的随机子空间法研究

基于数据的随机子空间法是计算精度较高的环境激励下结构模态参数辨识方法之一。该方法的缺点是当响应数据量很大时,对Hankel矩阵(Y矩阵)进行QR分解的计算效率不够理想。对YYT矩阵元素进行合理简化,再对YYT简化矩阵进行乔利斯基(Cholesky)分解。理论推导和算例分析结果均表明在不降低计算精度的同时,新方法的计算效率至少提高10倍。

Improved Stochastic Subspace Identification Based on Cholesky Factorization

Data-driven stochastic subspace identification is one of the most advanced methods for structural modal parameter identification under ambient excitation.However,direct QR decomposition of Hankel matrix(matrix Y) in dealing with huge information decreases the computational efficiency.In this paper,reasonable simplification was adopted to the multiplication of Hankel matrix and its transpose(matrix YYT),and Cholesky factorization of matrix YYT was proposed to replace the QR decomposition to obtain the low triangular matrix R.Theoretical derivation and identification results of numerical example show that the improved data-driven stochastic subspace identification increases computational efficiency remarkably at least 10 times while maintaining its original computational precision.