The monitoring of mechanical equipment systems contains an increasing number of complex content, expanding from traditional time, and frequency information to three-dimensional data of the time, space, and frequency information, and even higher-dimensional data containing subjects, experimental conditions. For high-dimensional data analysis, traditional decomposition methods such as Hilbert transform, fast Fourier transformation, and Gabor transformation not only lose the integrity of the data, but also increase the amount of calculation and introduce a lot of redundant information. The phenomenon of feature coupling, aliasing, and redundancy between the mechanical multi-source data signals will cause the inaccuracy of the evaluation, diagnosis, and prediction of industrial production operation status. The analysis of the three-way tensor composed of channel, frequency, and time is called parallel factor analysis (PARAFAC). The properties between the parallel factor analysis results and the input signals are studied through simulation experiments. Parallel factor analysis is used to decompose the third-order tensor composed of channel-time-frequency after continuous wavelet transformation of vibration signal into channel, time, and frequency characteristics. Multi-scale parallel factor analysis successfully extracted non-linear multi-dimensional dynamic fault characteristics by generating the spatial, spectral, time-domain signal loading value and three-dimensional fault characteristic expression. In order to verify the effectiveness of the space, frequency, and time domain signal loading values of the fault characteristic factors generated by the centrifugal pump system after parallel factor analysis, the characteristic factors obtained after parallel factor analysis are used as the SPRT test sequence for identification and verification. The results indicate that the method proposed in this article improves the measurement accuracy and intelligence of mechanical fault detection.

机械设备系统的监测包含越来越多的复杂内容，从传统的时间、频率信息扩展到时间、空间、频率信息的三维数据，甚至包含主体、实验条件的更高维数据。对于高维数据分析，传统的Hilbert变换、快速傅立叶变换、Gabor变换等分解方法不仅失去了数据的完整性，而且增加了计算量，引入了大量冗余信息。机械多源数据信号之间存在特征耦合、混叠、冗余等现象，会导致对工业生产运行状态的评价、诊断和预测的不准确。由通道、频率和时间组成的三向张量的分析称为并行因子分析（PARAFAC）。通过仿真实验研究了并行因子分析结果与输入信号之间的性质。并行因子分析用于将振动信号连续小波变换后由通道-时间-频率组成的三阶张量分解为通道、时间和频率特性。多尺度并行因子分析通过生成空间、频谱、时域信号载荷值和三维故障特征表达式，成功提取非线性多维动态故障特征。为了验证空间、频率的有效性，离心泵系统产生的故障特征因子经并行因子分析后的时域信号载荷值，将并行因子分析后得到的特征因子作为SPRT测试序列进行识别验证。结果表明，本文提出的方法提高了机械故障检测的测量精度和智能化程度。