This article focuses on the fault diagnosis of gears in nuclear power planetary gearboxes. In the presence of strong background noise, extracting impact characteristics from vibration signals is crucial for accurate fault diagnosis. The combination of Singular Value Decomposition (SVD) and S-transform is proposed, along with the assistance of MATLAB software, to handle noise and extract prominent fault information. Three singular value selection methods, namely the singular value median method, characteristic mean method, and singular value difference spectrum method, are employed to process the Hankel matrix constructed from the noisy signal. After reconstructing the signal to reduce noise, the S-transform is applied to obtain the time-frequency spectrogram, and the inverse S-transform is used to extract the impact characteristics. Experimental results on both simulated and actual fault signals demonstrate that the singular value difference spectrum method combined with S-transform yields the best results, providing valuable prior information for diagnosing gear-related faults in nuclear power planetary gearboxes.
1. Introduction
1.1 Background
Nuclear power plants rely on high-power gearboxes, especially planetary gearboxes, which are vital for the CRF system. The planetary gear system’s complexity and harsh working environment make it prone to faults such as broken teeth, wear, and pitting. These faults often lead to significant economic losses and safety risks due to production downtime. Fault signals are typically masked by strong background noise, necessitating effective noise reduction and feature extraction methods for accurate fault diagnosis.
1.2 Significance
The proposed method in this study combines SVD and S-transform to overcome the challenges in gear fault diagnosis. By accurately extracting impact characteristics, it enables early detection and prevention of gear failures, ensuring the reliable operation of nuclear power plants and reducing maintenance costs.
1.3 Objectives
The main objective is to develop a reliable and efficient fault diagnosis method for nuclear power planetary gearbox gears. This involves evaluating the performance of different singular value selection methods in combination with S-transform for impact feature extraction and providing a practical solution for real-world applications.
2. Singular Value Decomposition (SVD)
2.1 Principle
SVD is a powerful tool for analyzing matrices. For a real matrix , it can be decomposed as , where and are orthogonal matrices, and is a diagonal matrix containing the singular values . The energy decomposability of signals and noise is utilized in SVD-based noise reduction, where the matrix constructed from the noisy signal is decomposed, and only the characteristic singular values are retained to reconstruct the signal.
2.2 Hankel Matrix Construction
The discrete signal is used to construct a Hankel matrix . The choice of matrix dimensions and depends on the signal length , with the aim of maximizing the separation of signal and noise components.
2.3 Singular Value Selection Methods
2.3.1 Singular Value Median Method
The median of the singular values is calculated, and those smaller than the median are set to zero. This method is simple but may not always accurately capture the signal characteristics.
| Method | Description | Advantage | Disadvantage |
|---|---|---|---|
| Singular Value Median Method | Calculate median, set smaller values to zero | Simple | May lose some signal details |
2.3.2 Characteristic Mean Method
The mean of the eigenvalues (square roots of singular values) is computed, and singular values corresponding to eigenvalues smaller than the mean are discarded. This method takes into account the overall distribution of eigenvalues.
| Method | Description | Advantage | Disadvantage |
|---|---|---|---|
| Characteristic Mean Method | Compute mean of eigenvalues, discard small values | Considers eigenvalue distribution | Sensitive to noise |
2.3.3 Singular Value Difference Spectrum Method
The difference between consecutive singular values is calculated to form a difference spectrum. The peak point where the monotonicity changes is used as the threshold for selecting singular values. This method is more effective in capturing the signal’s impact characteristics.
| Method | Description | Advantage | Disadvantage |
|---|---|---|---|
| Singular Value Difference Spectrum Method | Use difference spectrum peak as threshold | Good at extracting impact features | Complex calculation |
3. S-transform
3.1 Definition and Properties
The S-transform is a time-frequency analysis method that converts a one-dimensional time-domain signal into a two-dimensional time-frequency domain signal. It is defined as and has the advantage of being invertible. It overcomes the limitations of short-time Fourier transform and Wigner-Ville distribution and is less sensitive to the choice of mother wavelet in wavelet transform.
3.2 Discrete S-transform
For practical implementation, the S-transform can be rewritten in terms of the frequency-domain signal as , which enables efficient computation using the fast Fourier transform.
4. Impact Feature Extraction Using SVD and S-transform
4.1 Flowchart
The process begins with the construction of the Hankel matrix from the noisy gear fault signal. Then, SVD is applied using one of the three singular value selection methods. The reconstructed signal is obtained and subjected to S-transform for time-frequency analysis. Finally, the inverse S-transform is used to extract the impact characteristics.
4.2 Simulation Signal Analysis
A simulation signal is constructed to mimic the impact characteristics of a faulty gear. It consists of exponentially decaying sinusoidal impulses with added Gaussian white noise. The performance of the three singular value selection methods in combination with S-transform is evaluated using SNR and RMSE as metrics.
| Method | SNR | RMSE | Impact Feature Extraction |
|---|---|---|---|
| Singular Value Median Method | -5.57040 | 1.92590 | Partial extraction, distorted |
| Characteristic Mean Method | -0.74512 | 1.55470 | Some extraction, less distorted |
| Singular Value Difference Spectrum Method | 5.22200 | 0.56759 | Complete extraction, slight distortion |
4.3 Experimental Results and Analysis
4.3.1 Test Setup
The experimental setup includes a PCB-356A32 three-axis acceleration sensor, NI Cdaq-9189 data acquisition card chassis, NI 9232 data acquisition card, and a scaled test bench for high-power nuclear power gearboxes. The test bench consists of input and output components, a vertical planetary gearbox, a right-angle reduction gearbox, a coupling, and a variable frequency motor.
4.3.2 Data Processing
The sampling frequency is set to 20 kHz with 1000 sampling points. The fault feature frequency of the sun gear is calculated based on the gear parameters. The Hankel matrix is constructed from the measured vibration acceleration signal of the sun gear, and SVD is performed. The performance of the singular value selection methods is evaluated based on the extracted impact characteristics.
| Method | Impact Feature Detection | Frequency Consistency |
|---|---|---|
| Singular Value Median Method | No | – |
| Characteristic Mean Method | No | – |
| Singular Value Difference Spectrum Method | Yes | Consistent with calculated frequency |
5. Conclusion
In this study, the combination of SVD and S-transform is proven to be an effective approach for extracting impact characteristics from gear fault signals in nuclear power planetary gearboxes. The singular value difference spectrum method outperforms the other two methods in both simulation and experimental scenarios. The proposed method provides a reliable solution for gear fault diagnosis, enabling timely maintenance and ensuring the safe and efficient operation of nuclear power plants. Future research can focus on further optimizing the algorithm and applying it to other types of gear systems.
