基于复杂度追踪的模态参数识别方法对比研究

胡志祥, 黄磊, 郅伦海, 胡峰

振动与冲击 ›› 2024, Vol. 43 ›› Issue (15) : 22-31.

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PDF(3540 KB)
振动与冲击 ›› 2024, Vol. 43 ›› Issue (15) : 22-31.
论文

基于复杂度追踪的模态参数识别方法对比研究

  • 胡志祥,黄磊,郅伦海,胡峰
作者信息 +

Comparative study on modal parametric identification methods based on complexity pursuit

  • HU Zhixiang, HUANG Lei, ZHI Lunhai, HU Feng
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文章历史 +

摘要

复杂度追踪(Complexity Pursuit,CP)是求解振动信号盲源分离(Blind source separation,BSS)问题的一类经典方法。用复杂度追踪估计解混矩阵主要有基于源信号复杂度计算的梯度下降(Complexity Pursuit-Gradient Descent,CP-GD)算法和基于时间可预测度的广义特征值分解(Temporal Predictability-Generalized Eigenvalue Decomposition,TP-GED)算法。当前,这两种算法的关联性与算法性能尚缺乏研究,因此对这两种算法的等价性和计算性能进行了研究。首先,给出CP-GD和TP-GED两种算法的具体理论及算法流程;其次,利用二、三自由度振动系统直观地展示并对比解混向量对应的源信号复杂度及可预测度的变化规律;最后,通过对多工况下多自由度系统的模态参数识别算例,对比研究两种算法的精度及计算量。研究结果表明,在低阻尼比及高信噪比条件下,两种方法得到的解混矩阵是相同的;考虑到计算信号复杂度和梯度下降较为耗时,CP-GD算法计算代价要高于TP-GED算法。

Abstract

Complexity Pursuit (CP) is a classical method for blind source separation of vibration signals. Two main approaches for estimating the de-mixing matrix using Complexity Pursuit are Complexity Pursuit-Gradient Descent (CP-GD), based on the complexity calculation of source signals, and Temporal Predictability-Generalized Eigenvalue Decomposition (TP-GED), based on the temporal predictability. The equivalence and computational performance of these two algorithms were studied based on vibration simulation. Firstly, the specific theories and algorithm procedures of CP-GD and TP-GED algorithms were presented. Secondly, the variations of source signal complexity and predictability corresponding to the de-mixed vectors were intuitively demonstrated and compared using two- and three-degree-of-freedom vibration systems. Finally, the accuracy and computation cost of the two algorithms were compared through modal parameter identification examples with multiple operating conditions and multiple degrees of freedom. The research results show that under low damping ratio and high signal-to-noise ratio conditions, the de-mixing matrices obtained with both methods are the same. Considering the computational cost of calculating signal complexity and performing gradient descent, the CP-GD algorithm has a higher computational cost than the TP-GED algorithm.

关键词

盲源分离(BSS) / 模态参数识别 / 柯尔莫哥洛夫复杂度 / 时间可预测度 / 梯度下降 / 广义特征值分解

Key words

blind source separation(BSS) / modal parameter identification / kolmogoroff complexity / temporal predictability / gradient descent / generalized eigenvalue decomposition

引用本文

导出引用
胡志祥, 黄磊, 郅伦海, 胡峰. 基于复杂度追踪的模态参数识别方法对比研究[J]. 振动与冲击, 2024, 43(15): 22-31
HU Zhixiang, HUANG Lei, ZHI Lunhai, HU Feng. Comparative study on modal parametric identification methods based on complexity pursuit[J]. Journal of Vibration and Shock, 2024, 43(15): 22-31

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