Detection of incipient rotor unbalance fault based on the RIME-VMD and modified-WKN

www.nature.com/scientificreports OPEN Detection of incipient rotor unbalance fault based on the RIME‑VMD and modified‑WKN Qian Wang 1,2*, Shuo Hu 1 & Xinya Wang 2 Due to the high incidence and inconspicuous initial characteristics of rotor unbalance faults, the detection of incipient unbalance faults is becoming a very challenging problem. In this paper, a new method of small rotor unbalance fault diagnosis based on RIME-VMD and modified wavelet kernel network (modified-WKN) is proposed. Firstly, in order to extract the small unbalance fault information from the vibration signals with low signal-to-noise ratio (SNR) more efficiently, the RIME algorithm is used to search for the optimal location of the penalty factor and decomposition layer in the variable mode decomposition (VMD). Secondly, the most relevant decomposition components to the small unbalance fault information are selected by using Pearson Correlation Coefficients and utilized to reconstruct the signal. Finally, the modified-WKN diagnostic model that is used for multi-sensor data fusion is constructed. The model can acquire features of vibration signals from multiple position sensors, which enhances the ability of the modified WKN diagnostic model to deal with incipient fault modes. Based on the experimental analysis of rotor unbalance fault datasets with different SNRs, it is verified that the detection performance of the proposed method is better than the traditional WKN and VMD-WKN methods. Specifically, the proposed method is more sensitive to the initial unbalance faults. As the core component of rotating machinery, the rotor system has been extensively applied in the aerospace, petrochemical, coal, and electricity industries1,2. The primary faults in the rotor system include rotor unbalance, misalignment, rub-impact, and o thers3. Among these, rotor unbalance is a significant cause of instability in rotor systems. In practical engineering, the early characteristics of rotor unbalance fault signals are relatively weak. Additionally, they are always accompanied by noise and other uncertainties, leading to even weaker features. Therefore, the rapid and accurate detection of initial rotor unbalance faults is a very challenging diagnostic problem and is also a crucial safeguard for the long-term safe and stable operation of rotating machinery systems. In the past few decades, the diagnosis methods for rotor faults can be divided into two c ategories4: one is time-frequency fault diagnosis methods, such as the wavelet transform, variational modal decomposition (VMD), and others5–7. The other is knowledge-based fault diagnostic methods, which includes support vector machines, expert systems, dynamic learning, and deep l earning8–11. Currently, deep learning-based fault diagnosis methods have become a research hotspot, and various advanced learning models (CNN, LSTM, DBN, AE, and others) are widely utilized in the field of rotor fault diagnosis12–17. Among these deep learning models, CNNs stand out for their exceptional performance in fault d iagnosis18. However, the CNN-based models are often considered as black boxes due to the lack of interpretability. With the advancement of learning methods, various approaches have been proposed to enhance interpretability. With the advancement of learning methods, various approaches have been proposed to enhance interpretability. Zilke et al.19 developed a novel scheme for neural network rule extraction based on decision trees to investigate the decision-making process. Grezmak et al.20 utilized layer-by-layer correlation propagation as an indicator to elucidate the key features learning process of CNN from time-frequency spectrum images. J ia21 employed a Neuron Activation Maximization algorithm to visualize the kernels of convolutional layers, aiming to comprehend the process of feature learning. Chen22 applied Gradient Class Activation Mapping to generate an attention model and explained the model by analyzing attention matters. Li et al.23 introduced an attention mechanism to assist 1 College of Electrical Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450000, China. 2IoT Equipment Research Institute, GL TECH Co., Ltd., Zhengzhou 450000, China. *email: wangqian@ zzuli.edu.cn Scientific Reports | (2024) 14:4683 | https://doi.org/10.1038/s41598-024-54984-z 1 Vol.:(0123456789) www.nature.com/scientificreports/ deep neural networks in focusing on critical data segments, and the learned fault diagnosis characteristics can be presented in a visualized manner. It should be noted that the rotor fault diagnosis signals are vibration data, and the above-mentioned methods are mainly suitable for processing two-dimensional image data. In order to solve this problem, Li et al.24 proposed an interpretable model known as the Wavelet-Kernel Network (WKN), which is suitable for dealing with the vibration fault signals. The wavelet transformation is employed in the first convolutional layer of CNN, and the physical significance of wavelet transformation is taken as the interpretability process. However, WKN is implemented based on a single sensor signal and cannot fully capture the fault information concealed within the noise in the rotor vibration signals. Inspired by the WKN method, this paper proposes a new rotor unbalance fault diagnosis method based on a RIME-VMD and modified-WKN. Firstly, to extract the initial unbalance fault information accurately under the condition of complex noises, the VMD decomposition algorithm is employed to decompose the vibration signals. In addition, the RIME algorithm25 is used to search for the optimal combination of penalty factor α and decomposition layer k of VMD. Secondly, the obtained optimal IMF components are selected by using the Pearson Correlation Coefficient (PCC), and the most relevant fault IMF components are used for the signal reconstruction. Thirdly, a new multi-head convolutional layer of the WKN is constructed to capture rotor unbalance fault information comprehensively based on the multiple vibration data from different positions in the rotor system. Additionally, this paper adopts multi-scale convolution to extract fault information of various scales in the fused features, which enhances the ability to perceive complex patterns. Finally, the diagnostic performance of the proposed method is illustrated based on the experimental analysis with varying SNRs. The results demonstrate that it is better than the traditional WKN method and the WKN combined with VMD (VMD-WKN) methods. Specifically, the proposed method is more sensitive to the initial unbalance faults. The main contributions of this article are shown as follows: 1) The most relevant unbalance fault IMF components are obtained according to the parameter-optimized VMD method, and the optimal combination of penalty factor α and number of decomposition layers k is automatically searched by embedding the RIME algorithm. 2) Different fro (...truncated)