Time–Frequency Dispersion Entropy Plane and its Application in Mechanical Fault Diagnosis

Fourier transform and entropy are two essential mathematical tools, and they have a fruitful role in system dynamics and machine learning research. In this paper, we propose a generalized composite multiscale amplitude dispersion entropy (GCMADE) and time–frequency dispersion entropy plane. GCMADE measures the complexity of the frequency domain of a time series and can approach the zero complexity of periodic sequences, unlike most other entropy methods. The time–frequency dispersion entropy plane further extracts time domain and frequency domain features of complex signals simultaneously through entropy. Its ability to measure the uncertainty of complex systems is analyzed by simulated data, and the results show that it can effectively distinguish between periodic sequences, chaotic sequences and stochastic processes. Finally, we introduce support vector machine (SVM) to perform mechanical fault diagnosis on five datasets. Compared with the other six algorithms, our method has significantly higher accuracy.