Optimized S-transform embedded time–frequency interpretable neural network for aero-engine fault diagnosis

Convolutional neural network (CNN) has attracted significant attention for its powerful capability in fault feature extraction, and has has found widespread applications in intelligent fault diagnosis of mechanical systems. Nevertheless, its limited interpretability and vulnerability to noise remain key challenges in both academic and industrial contexts. Motivated by the strong theoretical foundations and physical interpretability of traditional signal processing methods, this study aims to enhance the performance of CNN by integrating signal analysis theory. Given the non-stationary characteristics and high noise levels commonly observed in aero-engine vibration signals, conventional time–frequency analysis methods often fail to provide optimal representations. To address this limitation, a first-order frequency function with two adjustable parameters are introduced into the Gaussian window function of the original S-transform, deriving an optimized S-transform (OST) that exhibits improved window adaptability and enhanced time–frequency representation capability. Then, an OST embedded time–frequency interpretable neural network (OSTNN) is proposed for fault diagnosis in aero-engines without any predefined parameters. This design enables the transformation of standard first layer convolutional kernel in the CNN method into OST convolutional kernel, whose parameters are continuously adjusted during the training procedure. The proposed OSTNN framework not only effectively suppresses noise interference effectively but also enhances model interpretability through visualization of learned time–frequency feature distributions and analysis of overall amplitude-frequency response. Extensive experiments on three aero-engine datasets, covering typical bearing and rotor faults, demonstrated that the OSTNN method consistently outperforms surpasses eight state-of-the-art diagnostic approaches in terms of effectiveness, noise robustness, interpretability, imbalance, generalization, and few-shot learning capability.