Tikhonov正则化在运行工况传递路径分析的应用
Tikhonov Regularization for Operational Transfer Path Analysis

针对传统运行工况传递路径分析(operational transfer path analysis，简称OTPA)存在的不足，通过理论和试验分析，提出基于Tikhonov正则化方法的OTPA反问题模型。首先，分析Tikhonov正则化方法的理论优势，给出Tikhonov正则化参数选择的依据，同时调节电机转速获得不同运行工况数据，利用奇异值分解方法研究壳体结构的振动传递路径，分析传统OTPA算法总贡献量误差及路径贡献量估计精度；其次，分析运行工况数据是否满足Picard条件，提出基于Tikhonov正则化方法的OTPA算法，并分析Tikhonov正则化参数对所提出算法的影响。分析结果表明，所提出的方法显著减小了总贡献量和路径贡献量误差以及路径误判现象。该研究可为振动噪声监控与减振降噪提供理论依据。
To overcome the shortcomings of the traditional operational transfer path analysis (OTPA), this paper proposes a novel OTPA model for inverse problems based on Tikhonov regularization through theoretical and experimental analysis. First, we analyzed the theoretical advantages of Tikhonov regularization and provided the basic criteria for determining Tikhonov regularization parameters. We obtained operational data according to changing rotational speeds of the motors and studied the vibration transfer paths of the shell structure by singular value decomposition. Furthermore, we analyzed the errors of total contributions and path contributions for traditional OTPA. Next, we proposed a novel OTPA method based on Tikhonov regularization with Picard conditions and analyzd the effects of regularization parameters. Finally, the comparative study results showed that the proposed method reduced the errors of total contributions, path contributions, and path misjudgment. This study thus provides theoretical references for the monitoring, reduction and control of vibration and noise.