CS-SHAP: Extending SHAP to Cyclic-Spectral Domain for Better Interpretability of Intelligent Fault Diagnosis

TL;DR

This work tackles the interpretability gap in neural network–based intelligent fault diagnosis (IFD) by extending SHAP explanations to the cyclic-spectral (CS) domain. It derives a CS transform $\mathcal{Z}$ and its inverse to map deterministic signals into the CS space, enabling attribution over both carrier $f_c$ and modulation $f_m$ frequencies without altering the end-to-end model. The method, CS-SHAP, is model-agnostic and validated on simulation, CWRU bearing, and private gearbox datasets, showing clearer, more complete, and noise-robust explanations than time-domain or frequency-domain SHAP variants. The authors release open-source code to establish CS-SHAP as a benchmark for post-hoc interpretability in IFD and beyond, with potential applicability to other classification tasks.

Abstract

Neural networks (NNs), with their powerful nonlinear mapping and end-to-end capabilities, are widely applied in mechanical intelligent fault diagnosis (IFD). However, as typical black-box models, they pose challenges in understanding their decision basis and logic, limiting their deployment in high-reliability scenarios. Hence, various methods have been proposed to enhance the interpretability of IFD. Among these, post-hoc approaches can provide explanations without changing model architecture, preserving its flexibility and scalability. However, existing post-hoc methods often suffer from limitations in explanation forms. They either require preprocessing that disrupts the end-to-end nature or overlook fault mechanisms, leading to suboptimal explanations. To address these issues, we derived the cyclic-spectral (CS) transform and proposed the CS-SHAP by extending Shapley additive explanations (SHAP) to the CS domain. CS-SHAP can evaluate contributions from both carrier and modulation frequencies, aligning more closely with fault mechanisms and delivering clearer and more accurate explanations. Three datasets are utilized to validate the superior interpretability of CS-SHAP, ensuring its correctness, reproducibility, and practical performance. With open-source code and outstanding interpretability, CS-SHAP has the potential to be widely adopted and become the post-hoc interpretability benchmark in IFD, even in other classification tasks. The code is available on https://github.com/ChenQian0618/CS-SHAP.

Figures (21)

• Figure 1: The schematic diagram of the relationship between rotating machinery fault and vibration signal, and the characteristics and attribution results of vibration signal in different domains. Here, $f_c$ represents the carrier frequency, corresponding to the fault resonance frequency, while $f_m$ denotes the modulation frequency, corresponding to the fault excitation frequency. (a) A bearing with outer race fault, will generate impulses during each engagement periodically. (b) Time domain. (c) Frequency domain. (d) Envelope domain. (e) Time-frequency domain. (f) Cyclic-spectral (CS) domain.
• Figure 2: The processes of the CS transform and inverse CS transform.
• Figure 3: The illustration of SHAP attribution methods in time-domain and CS-domain. (a) The traditonal time-domain SHAP, whose result is the components with different timings. (b) The proposed CS-SHAP, whose result is the components with different spectral frequency and cyclic frequency.
• Figure 4: The flow chart of applying CS-SHAP for interpretability analysis.
• Figure 5: The representations of three classes in the simulation dataset. (a) Time domain. (b) Frequency domain.