Adaptive dynamic mode decomposition and GA-SVM with application to fault classification of planetary bearing

Recently, planetary gearboxes have been widely used in helicopters, heavy trucks, ships, and other large and complex mechanical equipment because of their smooth transmission characteristics, small volume, and large reduction ratio. The planetary bearing, which plays a supporting role in the planetary gearbox, usually works in a worse environment but suffers from low speed and heavy load for a long time. Additionally, because of the strong noise generated by the interaction between gears during the operation of the planetary gearbox, the fault characteristics of planetary bearings are completely submerged in the background noise and are difficult to extract, which complicates classifying planetary-bearing faults accurately. Therefore, to effectively remove noise information from planetary-bearing signals, accurately extract fault information, and classify the fault types of planetary bearings, an adaptive dynamic mode decomposition (ADMD) and genetic algorithm and support vector machine (GA-SVM) with application to the fault classification of planetary bearing is proposed in this paper. The hard threshold selection of the traditional truncated rank cannot effectively process the time-domain vibration signals using the dynamic mode decomposition (DMD) method. Hence, this paper proposes improved grasshopper optimization algorithm (IGOA) to optimize the grasshopper optimization algorithm (GOA) by using dynamic weight and avoid the linear gradient mechanism, which cannot fully use the entire iterative process. Furthermore, IGOA can perform a global search to achieve the adaptive optimal parameter selection of the truncated rank. Besides, a new fitness function is defined that can effectively process the original time-domain signals. The traditional refined composite multiscale discrete entropy (RCMDE) is relatively dispersed, and it cannot characterize the features hidden in the signal better. Therefore, we normalize the RCMDE, forming the improved refined composite multiscale discrete entropy (IRCMDE). Then, the IRCMDE is calculated for the denoised signal, and a feature matrix is constructed to better mine the hidden features in the signal. Finally, GA is used to optimize the key parameters C and g of the SVM. The GA-SVM classification model is also constructed and applied to the bearing fault classification of the planetary gearbox, which can avoid the overfitting phenomenon in the training process and provide better generalization performance. Taking the planetary-bearing fault data in the planetary gearbox of Nanchang Hangkong University as the research object, the validity and practicability of the proposed method are verified, and the final classification result of the inner ring fault, outer ring fault, rolling body fault, and normal condition is 96.43%. In addition, this method can more accurately identify the fault types of planetary bearings and has better generalization ability than the empirical mode decomposition (EMD) signal processing method and the convolutional neural network (CNN) classification method.