基于敏感性分析的协方差随机子空间方法参数优化

在工作模态分析中,结构模态的准确识别在包括结构健康监测在内的许多应用中至关重要。该文基于敏感性分析,研究了模型系统阶数N和Toeplitz矩阵行块数i在协方差驱动随机子空间法(covariance-driven stochastic subspace identification,SSI-Cov)中对模态识别结果的影响规律。结合一经典数值算例及藏式古城墙现场实测数据对SSI-Cov算法的参数优化进行了分析。根据奇异熵增量理论对系统阶数进行识别;利用Toeplitz矩阵或系统矩阵的条件数及识别结果的变异系数对Toeplitz矩阵行块数的选择进行研究,并给出参数取值建议。研究结果表明:Toeplitz矩阵或系统矩阵的条件数越小计算结果精度越高;识别频率、阻尼比的变异系数越小,对应的模态稳定图质量越好。通过奇异熵增量理论可准确识别结构的系统阶数,奇异熵增量的一阶灵敏度降至0时对应的阶数即为系统阶数N。Toeplitz矩阵行块数i的建议取值范围为2β~4β(β为采样频率与结构基频的比值)。基于该文提出的参数优化方法,能有效识别藏式古城墙的动力特性,包括频率、振型和阻尼比。

PARAMETER OPTIMIZATION OF COVARIANCE-DRIVEN STOCHASTIC SUBSPACE IDENTIFICATION METHOD BASED ON SENSITIVITY ANALYSIS

The accurate estimation of the modal properties of civil structures in operational modal analysis is critical in many applications, including structural health monitoring. Based on the sensitivity analysis, the model system order N and the number of block rows of the Toeplitz matrix i are investigated. The rules of their influence on the results of modal identification in covariance-driven stochastic subspace identification(SSI-Cov) are developed. The parameter optimization of SSI-Cov algorithm is analyzed based on a classical numerical example and the field measured data of the ancient Tibetan wall. The system order is identified through the theory of singular entropy increment. The recommended value of the number of block rows of Toeplitz matrix is proposed.The basis of the recommended value is the condition number of Toeplitz matrix or system matrix and the variation coefficient of the identification result. The research shows that: the smaller the condition number of the Toeplitz matrix or of the system matrix,the higher the accuracy of the calculation result,the smaller the coefficient of variation of the recognition frequency and damping ratio,and the better the quality of the corresponding modal stability diagram.The system order N of the structure can be accurately identified through the singular entropy increment theory.It is equal to the corresponding order when the first-order sensitivity of the singular entropy increment drops to zero.The suggested value of the number of block rows of the Toeplitz matrix i is between 2β and 4β,in which β is the ratio of the sampling frequency to the fundamental frequency.Based on the parameter optimization method proposed,the dynamic characteristics of the ancient Tibetan wall are effectively identified,including frequency,mode shape and damping ratio.