With the continuous advancement of China's aerospace technology, especially in space development, the requirements for spacecraft simulation experiments are becoming increasingly stringent. Ultra-low temperature and high vacuum environments are essential for these tests. Among the key components, vacuum pumps play a crucial role in simulating the space environment. Their proper functioning is vital to ensure that the thermal vacuum test of the spacecraft is conducted accurately and effectively. Given the large number of aerospace bases and metallurgical industries in China, the demand for vacuum pumps is immense. Therefore, detecting pump failures not only ensures equipment safety but also brings significant social and economic benefits.
Traditional mechanical fault diagnosis methods often rely on Fourier transform, which is widely used in frequency domain analysis. However, it struggles with nonlinear and time-varying signals. In contrast, wavelet transform adapts its sampling step size based on frequency, offering better time resolution for high-frequency signals and frequency resolution for low-frequency ones. This makes it more suitable for processing complex signals.
Singular Value Decomposition (SVD) is an effective method for extracting signal features. The singular values obtained through SVD represent the intrinsic properties of the data, exhibiting strong stability and invariance. Studies have shown that by reconstructing the signal after applying SVD, noise can be effectively removed while preserving useful information. By constructing an attractor trajectory matrix and performing SVD, the random components of the signal can be eliminated, leaving only the meaningful part for denoising.
Support Vector Machine (SVM), a powerful machine learning technique, is widely used in pattern recognition. Based on statistical learning theory, SVM excels in handling high-dimensional, nonlinear, and small sample problems. This paper employs SVM for fault mode identification due to its robustness and accuracy.
In this study, we combine SVD and wavelet packet decomposition to extract fault features from vacuum pump signals. These features are then input into an SVM model to identify different fault conditions.
1. Singular Value Decomposition (SVD)
1.1 SVD Principle
For a given time series x(n) of length N, the phase space is reconstructed using a delay time Ï„, resulting in an attractor trajectory matrix A as described in [7].
1.2 Signal Denoising Using SVD
When analyzing a mixed signal, if the original signal is smooth, the rank r of the attractor trajectory matrix is less than min(L, M). If the signal contains noise, the rank remains at min(L, M). Research shows that singular values of smooth signals concentrate in the first k values, whereas noise signals distribute their singular values evenly. Thus, retaining the first k singular values and setting the rest to zero allows effective noise removal. The contribution rate Ï is defined as:
Ï = Σα_i / Σα_1 (i=1 to k)
It is generally accepted that when the contribution rate is ≥ 0.9, most of the useful signal is retained.
2. Wavelet Packet Decomposition (WPD)
Compared to traditional wavelet decomposition, WPD further decomposes high-frequency bands, enhancing time-frequency resolution and making it more applicable in signal processing.
3. Experimental System and Fault Feature Extraction
3.1 Data Collection
The system includes a host computer, NI acquisition card 6366, preamplifier, and PAC R3α sensor. With a sampling rate of up to 2 MS/s, it supports simultaneous 8-channel acquisition. Vibration signals were collected under normal and overload conditions at 100 kHz, with 5,000 points per set. A total of 130 samples were collected, with the first 60 used for training and the remaining 70 for testing.
3.2 Signal Feature Extraction
After data collection, the vibration signal was processed using SVD for denoising. The delay time Ï„ was determined via autocorrelation, and the embedded dimension was set to 200. After retaining 90% of the singular values, the signal was reconstructed. Subsequently, 7-layer WPD using db11 wavelet was applied, and energy from the first 8 frequency bands was extracted.
4. Pattern Recognition
SVM was used to classify the signals, where normal operation corresponds to output 1 and faults to -1. The results showed a classification accuracy of 98.57%, confirming the effectiveness of the proposed method.
5. Conclusion
By integrating SVD, WPD, and SVM, this study successfully identified vacuum pump faults with high accuracy. The method proves to be both effective and practical for real-world applications.
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