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TFN: An Interpretable Neural Network with Time-Frequency Transform Embedded for Intelligent Fault Diagnosis
Qian Chen, Xingjian Dong, Guowei Tu, Dong Wang, Baoxuan Zhao, Zhike Peng
TL;DR
CNN-based mechanical fault diagnosis is accurate but difficult to interpret, limiting confidence in high-reliability settings. The paper embeds physically meaningful time-frequency transforms into an adaptive TFconv preprocessing layer within TFN. Across three mechanical fault diagnosis experiments, TFN improves diagnostic performance while revealing frequency-focused prediction logic.
Problem
CNNs achieve strong fault-diagnosis performance, but their decision-making logic is unclear and existing interpretation methods are limited for 1D vibration signals.
Method
TFN embeds physically meaningful time-frequency transforms into a trainable TFconv preprocessing layer constrained by transform-derived kernel functions.
Results
Three mechanical fault diagnosis experiments verify TFN's diagnostic effectiveness and interpretability, including frequency-domain explanations of CNN prediction-making.
Takeaways & Limitations
The TFconv layer improves CNN-based fault diagnosis while exposing the frequency areas used for feature extraction and prediction.
Takeaways & Limitations
For TFN-Morlet, adaptive wavelet bandwidth blurs focusing frequency bands and produces inferior interpretability compared with TFN-STTF and TFN-Chirplet.
Abstract
from arXiv · showhide
Convolutional Neural Networks (CNNs) are widely used in fault diagnosis of mechanical systems due to their powerful feature extraction and classification capabilities. However, the CNN is a typical black-box model, and the mechanism of CNN's decision-making are not clear, which limits its application in high-reliability-required fault diagnosis scenarios. To tackle this issue, we propose a novel interpretable neural network termed as Time-Frequency Network (TFN), where the physically meaningful time-frequency transform (TFT) method is embedded into the traditional convolutional layer as an adaptive preprocessing layer. This preprocessing layer named as time-frequency convolutional (TFconv) layer, is constrained by a well-designed kernel function to extract fault-related time-frequency information. It not only improves the diagnostic performance but also reveals the logical foundation of the CNN prediction in the frequency domain. Different TFT methods correspond to different kernel functions of the TFconv layer. In this study, four typical TFT methods are considered to formulate the TFNs and their effectiveness and interpretability are proved through three mechanical fault diagnosis experiments. Experimental results also show that the proposed TFconv layer can be easily generalized to other CNNs with different depths. The code of TFN is available on https://github.com/ChenQian0618/TFN.
1 Introduction
Mechanical fault diagnosis needs accurate, physically grounded feature extraction, but conventional CNNs provide limited insight into their decisions. TFN embeds time-frequency transforms into an adaptive convolutional layer to improve diagnosis while exposing frequency-focused reasoning.
- Motivation: Data-driven diagnosis reduces reliance on expert-designed signal processing, which is difficult to deploy broadly in industrial scenarios.Traditional transforms can extract useful frequency or time-frequency features, but applying them requires substantial expertise and prior knowledge.
- Motivation: CNNs provide strong diagnostic performance but remain difficult to interpret, limiting their use in high-reliability applications.The paper specifically identifies mechanical systems such as aero engines as settings where decision credibility matters.
- Related work: Existing CNN interpretation methods are mainly designed for 2D images, while interpretability studies for 1D vibration-based fault diagnosis remain limited.Prior approaches include rule, semantic, attribution, and example-based explanations, with only a few applications to mechanical fault diagnosis.
- Proposed approach: The TFconv layer embeds physically meaningful time-frequency transforms into convolutional processing through constrained kernel functions.TFN uses this layer as a preprocessing stage before a backbone CNN, linking feature extraction to frequency-domain interpretation.
- Contributions: TFN combines improved diagnostic performance with frequency-response analysis that explains which frequencies support CNN feature extraction and prediction.The study also considers complex-valued kernels and distinguishes the approach from real-valued filter-based models.
- Contributions: The proposed TFconv layer is evaluated across three mechanical fault diagnosis experiments and can be generalized to CNNs with different depths.The authors additionally report advantages in convergence speed and few-shot scenarios.
2 Prilimilary
Time-frequency transforms represent non-stationary vibration signals through localized time-frequency information, while CNNs learn hierarchical features and classify signals through convolutional processing. The preliminary foundations describe both pipelines and their component operations.
- Time-Frequency Transform: Inner-product time-frequency transforms decompose vibration signals into time-frequency spectra using localized basis functions.The window position controls time localization, while the frequency parameter controls frequency focus.
- Time-Frequency Transform: The TFT process convolves a signal with complex window functions across time and frequency to build a complete spectrum.The resulting complex spectrum contains power and phase information; modulus operation isolates power information.
- Time-Frequency Transform: STFT, Chirplet Transform, and wavelet transform differ primarily in their inner-product window functions.Chirplet Transform adds frequency modulation for variable-speed conditions, whereas wavelets adapt time-frequency resolution through scaling and translation.
- Time-Frequency Transform: TFTs provide joint time-frequency information for non-stationary signals, supporting feature extraction in mechanical fault diagnosis.For rolling-bearing signals, the spectrum can reveal both vibration frequency and dual-impulse behavior.
- CNN: A 1D CNN combines convolutional, normalization, activation, pooling, and classification components to process vibration signals.The convolutional part extracts features, while fully connected layers and Softmax produce category probabilities.
- CNN: Each convolution kernel slides along the input signal, and multiple kernel outputs are concatenated into feature maps.The convolution operator produces channel-specific representations that subsequent CNN layers process.
- CNN: Pooling compresses extracted features through downsampling while retaining their main information.Maximum and average downsampling are given as examples of pooling operations.
- CNN: Batch normalization standardizes channel inputs, activation functions add nonlinearity, and cross-entropy measures classification discrepancy during training.The model is optimized through backpropagation with methods such as stochastic gradient descent.
3 Methodology
The TFconv layer embeds physically interpretable time-frequency transforms into convolution through constrained complex kernels whose trainable parameters adapt during learning. Combined with frequency-response analysis and a backbone CNN, it forms TFN, linking fault-related frequency selection to CNN predictions.
- TFconv structure: TFconv embeds time-frequency transforms into convolution by using a complex-valued kernel derived from an inner-product window function.Its real and imaginary kernels convolve with the input separately, and their outputs are combined into the final feature map.
- TFconv structure: The TFconv layer differs from traditional convolution through real-imaginary processing, function-constrained weights, and trainable kernel control parameters rather than unconstrained weights.The control parameters are updated through backpropagation during training.
- Kernel functions: Three typical transforms—STFT, Chirplet, and Morlet wavelet—provide corresponding kernels with distinct frequency controls and physical parameter limits.STFT adjusts center frequency, Chirplet additionally modulates bandwidth, and Morlet wavelet scales time-frequency properties.
- Interpretability: Frequency-response analysis interprets trained TFconv layers by identifying frequencies that pass more readily and therefore receive greater attention in prediction-making.Channel-wise responses are computed first and averaged into an overall amplitude-frequency response.
- Interpretability: Unlike traditional convolution, whose initialized channel responses are randomly distributed, TFconv produces clear frequency preferences controlled by its kernel function.The comparison uses channel-wise and overall frequency responses for traditional and TFconv layers.
- TFN architecture: TFN uses the interpretable TFconv layer as a preprocessing stage before a backbone CNN to extract fault-related time-frequency information from raw vibration signals.This combination is presented as the complete workflow for intelligent mechanical fault diagnosis.
4 Experiment
Across three mechanical fault-diagnosis datasets, TFN models achieved strong diagnostic performance and aligned their learned frequency responses with dataset information bands. TFN-Chirplet generally provided the closest physical correspondence, while channel count influenced accuracy and interpretability varied by kernel.
- Diagnostic performance: Increasing channel numbers generally improved TFN accuracy, with larger gains than other methods, because more channels extracted more time-frequency information.At 16 channels, TFN and other methods were similar; the advantage became significant as channel count increased.
- Diagnostic performance: The three TFN kernels had similar diagnostic performance overall, with STTF slightly better than Chirplet and Morlet in general.
- Interpretability: TFN-Chirplet’s O-FR matched all CWRU information bands without unrelated peaks, whereas TFN-STTF retained two high-frequency peaks outside those bands.Chirplet’s linear frequency modulation factor adjusts filtering bandwidth; STTF changes centering frequency but not bandwidth.
- Planetary gearbox: On the planetary gearbox dataset, TFN models achieved the best overall diagnostic performance, and 32 channels were sufficient to extract adequate time-frequency information.Increasing from 16 to 32 channels improved performance, whereas 64 and 128 channels produced no corresponding accuracy increase.
- Interpretability: Across the planetary gearbox and aerospace bearing analyses, TFN-Chirplet’s O-FRs corresponded more closely to the datasets’ information bands than TFN-STTF’s responses.STTF retained unrelated amplitude peaks, while Chirplet reduced or eliminated them through bandwidth adjustment.
5 Discussion
The discussion shows that TFNs differ from contrast models by producing adaptive time-frequency distributions through complex-valued kernels, while also offering faster convergence, stronger few-shot performance, and generalizability across CNN backbones.
- 5.1 Comparison with Contrast Models: TFNs use complex-valued kernels to produce adaptive time-frequency distributions, whereas contrast models use real-valued kernels equivalent to bandpass FIR filters producing filtered sub-signals.The TFconv output focuses on information bands associated with the training dataset.
- 5.1 Comparison with Contrast Models: Real-kernel outputs retain phase information and therefore differ from the time-frequency distributions produced by TFNs.The formula analysis attributes the difference to the additional phase component in real-kernel outputs.
- 5.2 Training Process and Training Time: TFNs converge faster than all other compared models, with TFN-Morlet performing best among the TFNs.The authors attribute this convergence advantage to extracting time-frequency features, and report consistency with diagnostic performance.
- 5.3 Few-shot Analysis: When only 5 samples per class are used, TFNs achieve close to 75% accuracy while other models remain below 65%, exceeding them by more than 10%.With 50 samples per class, TFNs approach 100% accuracy; at larger sample counts, the gap narrows to about 1–2%.
- 5.4 Generalizability: The TFconv layer significantly improves diagnostic accuracy across CNN backbones, with Morlet performing best, followed by STTF and then Chirplet.The results support applying TFconv layers with different-depth CNNs.
6 Conclusion
The paper proposes TFN, an interpretable CNN architecture that embeds a TFconv layer to extract fault-related time-frequency information and expose the frequency regions used for prediction. Across three mechanical fault-diagnosis experiments, TFN improves diagnostic performance, convergence, and few-shot behavior while generalizing across CNN depths.
- 6 Conclusion: The TFconv layer extracts fault-related time-frequency information and explains the frequency area on which TFN focuses when making predictions.It serves as the interpretable preprocessing layer of the Time-Frequency Network.
- 6 Conclusion: The TFconv layer greatly improves CNN diagnostic performance in mechanical fault-diagnosis tasks.The paper reports this conclusion across its experimental evaluations.
- 6 Conclusion: Kernel function and channel number strongly influence TFN performance, with a 64-channel STTF kernel achieving the overall optimum in accuracy and efficiency.This conclusion identifies both design choices as important determinants of TFN behavior.
- 6 Conclusion: TFN performs strongly in convergence-speed and few-shot scenarios and can be generalized to CNN models with different depths.The conclusion links these properties to the broader applicability of the proposed architecture.