Fault Impulse Inference and Cyclostationary Approximation: A feature-interpretable intelligent fault detection method for few-shot unsupervised domain adaptation

With the advancement of intelligent detection for rotating machinery, numerous domain adaptation methods have been devised to transfer detection knowledge from one source domain working condition to another target domain working condition, involving extensive transfer scenarios including labeled, few-shot labeled, and unlabeled target conditions. Yet, learning from sparsely labeled signals in the source domain working condition and transferring to unlabeled target conditions, termed few-shot unsupervised domain adaptation (FUDA), is closer to reality but almost unexplored. Diverging from the intuition of combining existing transfer and few-shot learning technologies, this paper pioneers a novel single learning principle focusing on the cyclostationary mechanism (CT) of fault signals. In its implementation, named cyclically enhanced cyclostationary variational autoencoder (CCTVAE), the CT principle motivates the encoder to infer domain-shared representations with fault impulses, and the decoder approximates the cyclostationary structure containing the clear fault and working condition information. Then, auxiliary samples for few-shot expansion are generated by adjusting cyclic parameters of the posterior distribution of representations. Experimentally, CCTVAE achieves commendable results on simulated and real fault datasets. Even for compound faults, domain-shared representations and generated auxiliary signals manifest interpretable fault-indicating spectral lines in the frequency domain, underscoring method reliability.