BiEntropiGram: A Novel Time-Frequency Entropy Map for Rotating Machines Incipient Fault Diagnosis

Abstract Diagnosing incipient faults in rotating machinery is crucial for reducing maintenance costs and preventingthe occurrence of other faults. Accurately extracting fault-related features from vibrationaltime series is fundamental to early fault detection. Entropy has emerged as a robust metric for quantifyingcomplexity in time series; however, entropy-based feature extraction methods often requireparameter tuning and tend to overlook frequency-domain features. This paper introduces BiEntropi-Gram, a novel time-frequency entropy mapping technique synthesizing information from both thetime and frequency domains into a 2D image representation. In this framework, time-domain featuresare extracted using Time Shift Multi-Scale Attention Entropy (TSMAtE), while frequency-domainfeatures are derived through Time Shift Multi-Scale Spectral Entropy (TSMSpE). Noise analysisis employed to determine the optimal number of time scales and the ideal time series length tooptimize performance. Analytical studies with various noise types further demonstrate the superiorperformance of BiEntropiGram compared to features extracted solely via TSMAtE or TSMSpE. Theproposed fault diagnosis system utilizes an optimized convolutional neural network (CNN) coupledwith the Bees Algorithm (BA)—termed BACNN—to refine feature selection and classify faults usingan optimized support vector machine (SVM). The efficacy of BiEntropiGram is validated across fivepublicly available datasets, achieving 100% diagnostic accuracy on three datasets with faults of varyingseverity. Furthermore, BiEntropiGram outperforms traditional methods, including the Morlet andMexican Hat Continuous Wavelet Transforms (CWTs) and Short-Time Fourier Transform (STFT).These results confirm the effectiveness of the proposed BiEntropiGram-based fault diagnosis approachfor the diagnosis of incipient faults in rotating machinery.