Topological Incremental Fast Fourier transform on time–frequency domain feature extraction for equipment fault diagnosis

Equipment fault diagnosis is crucial to ensure safe operation of industrial systems. The development of artificial intelligence has led to increasing applications of data-driven methods for fault diagnosis. However, such methods often require a large amount of labeled data for training and are tend to be sensitive to noise. To address these challenges, a novel model using topological data analysis (TDA)—-topological incremental fast Fourier transform(TIFF)—-for equipment fault diagnosis is proposed in this paper, leveraging the capability of TDA in extracting geometric features of dataset after continuous deformations of topology space. First, for time series signal of equipment operation, persistent homology fluctuating series is constructed by calculating the topological Wasserstein distance between two successive windows of the raw signal, which contains more condensed information on its fault pattern. Then, the time–frequency domain features of the raw signals are obtained by concatenating the frequency domain features derived from fast Fourier transformation and time domain features derived from statistical analysis on both of the persistent homology fluctuating and the raw signal series. Finally, a machine learning based equipment fault diagnosis framework is proposed. By feeding the time–frequency domain features extracted by TDA method, a model based on support vector machine(SVM) classifier after supervised training is established to give identification result for type of fault. The proposed method is tested on two publicly available datasets under different conditions and the results prove that it outperforms three state-of-the-art benchmarks in noisy settings and with few-shot.