The bearing fault diagnosis of petrochemical rotating machinery faces the problems of large data volume, weak fault feature signal strength and susceptibility to noise interference. To solve these problems, current research presents a combined ICEEMDAN-wavelet threshold joint noise reduction, mutual dimensionless metrics and MPGA-SVM approach for rotating machinery bearing fault diagnosis. Firstly, we propose an improved joint noise-reduction method of an Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and wavelet thresholding. Moreover, the noise-reduced data are processed by mutual dimensionless processing to construct a mutual dimensionless index sensitive to bearing fault features and complete the fault feature extraction of the bearing signals. Furthermore, we design experiments on faulty bearings of multistage centrifugal fans in petrochemical rotating machinery and processed the input data set according to ICEEMDAN-wavelet threshold joint noise reduction and mutual dimensionless indexes for later validation of the model and algorithm. Finally, a support vector machine model used to effectively identify the bearing failures, and a multi-population genetic algorithm, is studied to optimize the relevant parameters of the support vector machine. The powerful global parallel search capability of the multigroup genetic algorithm is used to search for the penalty factor c and kernel parameter r that affect the classification performance of the support vector machine. The global optimal solutions of c and r are found in a short time to construct a multigroup genetic algorithm-support vector machine bearing fault diagnosis and identification model. The proposed model is verified to have 95.3% accuracy for the bearing fault diagnosis, and the training time is 11.1608 s, while the traditional GA-SVM has only 89.875% accuracy and the training time is 17.4612 s. Meanwhile, to exclude the influence of experimental data on the specificity of our method, the experimental validation of the Western Reserve University bearing failure open-source dataset was added, and the results showed that the accuracy could reach 97.1% with a training time of 14.2735 s, thus proving that the method proposed in our paper can achieve good results in practical applications.