Variational mode decomposition: mode determination method for rotating machinery diagnosis

Variational mode decomposition (VMD) is a modern decomposition method used for many engineering monitoring and diagnosis recently, which replaced traditional empirical mode decomposition (EMD) method. However, the performance of VMD method specifically depends on the parameter that need to pre-determine for VMD method especially the mode number. This paper proposed a mode determination method using signal difference average (SDA) to determine the mode number for the VMD method by taking the advantages of similarities concept between sum of variational mode functions (VMFs) and the input signals. Online high-speed gear and bearing fault data were used to validate the performance of the proposed method. The diagnosis result using frequency spectrum has been compared with traditional EMD method and the proposed method has been proved to be able to provide an accurate number of mode for the VMD method effectively for rotating machinery applications

Gearbox fault diagnosis based on VMD-MSE and adaboost classifier

Accurate and efficient fault diagnosis is of great importance for gearbox. This study proposed a fault diagnosis based on variational mode decomposition (VMD) – multiscale entropy (MSE) and adaboost algorithm. First, the VMD is employed to decompose the raw signal in time-frequency domain. Then, MSE is computed to generate the feature vectors. Finally, the classifier based on adaboost is training and several weak classifiers form a strong classifier to realize the fault diagnosis. The feasibility and accuracy of the method is validated by the data from the Prognostics and Health Management Society for the 2009 data challenge competition

Vibration-based Fault Diagnostics in Wind Turbine Gearboxes Using Machine Learning

A significantly increased production of wind energy offers a path to achieve the goals of green energy policies in the United States and other countries. However, failures in wind turbines and specifically their gearboxes are higher due to their operation in unpredictable wind conditions that result in downtime and losses. Early detection of faults in wind turbines will greatly increase their reliability and commercial feasibility. Recently, data-driven fault diagnosis techniques based on deep learning have gained significant attention due to their powerful feature learning capabilities. Nonetheless, diagnosing faults in wind turbines operating under varying conditions poses a major challenge. Signal components unrelated to faults and high levels of noise obscure the signature generated by early-stage damage. To address this issue, we propose an innovative fault diagnosis framework that utilizes deep learning and leverages cyclostationary analysis of sensor data. By generating cyclic spectral coherence maps from the sensor data, we can emphasize fault-related signatures. These 2D color map representations are then used to train convolutional neural networks capable of detecting even minor faults and early-stage damages. The proposed method is evaluated using test data obtained from multibody dynamic simulations conducted under various operating conditions. The benchmark test cases, inspired by an NREL study, are successfully detected using our approach. To further enhance the accuracy of the model, subsequent studies employ Convolutional Neural Networks with Local Interpretable Model-Agnostic Explanations (LIME). This approach aids in interpreting classifier predictions and developing an interpretable classifier by focusing on a subset range of cyclic spectral coherence maps that carry the unique fault signatures. This improvement contributes to better accuracy, especially in scenarios involving multiple faults in the gearbox that need to be identified. Moreover, to address the challenge of applying this framework in practical settings, where standard deep learning techniques tend to provide inaccurate predictions for unseen faults or unusual operating conditions, we investigate fault diagnostics using a Bayesian convolutional neural network. This approach incorporates uncertainty bounds into prediction results, reducing overconfident misclassifications. The results demonstrate the effectiveness of the Bayesian approach in fault diagnosis, offering valuable implications for condition monitoring in other rotating machinery applications

A Machine Learning Approach for Gearbox System Fault Diagnosis

This study proposes a fully automated gearbox fault diagnosis approach that does not require knowledge about the specific gearbox construction and its load. The proposed approach is based on evaluating an adaptive filter's prediction error. The obtained prediction error's standard deviation is further processed with a support-vector machine to classify the gearbox's condition. The proposed method was cross-validated on a public dataset, segmented into 1760 test samples, against two other reference methods. The accuracy achieved by the proposed method was better than the accuracies of the reference methods. The accuracy of the proposed method was on average 9% higher compared to both reference methods for different support vector settings

Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA)

This paper discusses the possible observation of an integrated gear tooth crack analysis procedure that employs the combined approach of variable mode decomposition (VMD) and time synchronous averaging (TSA) based on the coupled electromechanical gearbox (CEMG) system. This paper also incorporates the modified Lagrangian formulation to model the CEMG system by considering Rayleigh's dissipative potential. An analytical improved time-varying mesh stiffness (IAM-TVMS) with different levels of gear tooth crack depts is also incorporated into the CEMG system to inspect the influence of cracks on the system's dynamic behavior. Dynamic responses of the CEMG system with different tooth crack levels have been used for further investigations. For the first time, the integrated approach of variable mode decomposition (VMD) and time-synchronous averaging (TSA) has been presented to analyze the dynamic behaviour of CEMG systems at the different gear tooth cracks have been experienced as non-stationary and complex vibration signals with noise. Based on the integrated approach of VMD-TSA, two types of nonlinear features, i.e., Lyapunov Exponent (LE) and Correlation Dimension (CD), were calculated to predict the level of chaotic vibration and complexity of the CEMG system at the different levels of gear tooth cracks. Also, the LE and CD are used as chaotic behaviour features to predict the gear tooth crack propagation level. The results of the proposed approach show significant improvements in the gear tooth crack analysis based on the chaotic features. Also, this is one of the first attempts to study the CEMG system using chaotic features based on the combined approach of VMD-TSA.Comment: 17 pages, 36 figures, 6th Joint International Conference on Multibody System Dynamics and the 10th Asian Conference on Multibody Dynamics 202

Application of variational mode decomposition in vibration analysis of machine components

Monitoring and diagnosis of machinery in maintenance are often undertaken using vibration analysis. The machine vibration signal is invariably complex and diverse, and thus useful information and features are difficult to extract. Variational mode decomposition (VMD) is a recent signal processing method that able to extract some of important features from machine vibration signal. The performance of the VMD method depends on the selection of its input parameters, especially the mode number and balancing parameter (also known as quadratic penalty term). However, the current VMD method is still using a manual effort to extract the input parameters where it subjects to interpretation of experienced experts. Hence, machine diagnosis becomes time consuming and prone to error. The aim of this research was to propose an automated parameter selection method for selecting the VMD input parameters. The proposed method consisted of two-stage selections where the first stage selection was used to select the initial mode number and the second stage selection was used to select the optimized mode number and balancing parameter. A new machine diagnosis approach was developed, named as VMD Differential Evolution Algorithm (VMDEA)-Extreme Learning Machine (ELM). Vibration signal datasets were then reconstructed using VMDEA and the multi-domain features consisted of time-domain, frequency-domain and multi-scale fuzzy entropy were extracted. It was demonstrated that the VMDEA method was able to reduce the computational time about 14% to 53% as compared to VMD-Genetic Algorithm (GA), VMD-Particle Swarm Optimization (PSO) and VMD-Differential Evolution (DE) approaches for bearing, shaft and gear. It also exhibited a better convergence with about two to nine less iterations as compared to VMD-GA, VMD-PSO and VMD-DE for bearing, shaft and gear. The VMDEA-ELM was able to illustrate higher classification accuracy about 11% to 20% than Empirical Mode Decomposition (EMD)-ELM, Ensemble EMD (EEMD)-ELM and Complimentary EEMD (CEEMD)-ELM for bearing shaft and gear. The bearing datasets from Case Western Reserve University were tested with VMDEA-ELM model and compared with Support Vector Machine (SVM)-Dempster-Shafer (DS), EEMD Optimal Mode Multi-scale Fuzzy Entropy Fault Diagnosis (EOMSMFD), Wavelet Packet Transform (WPT)-Local Characteristic-scale Decomposition (LCD)- ELM, and Arctangent S-shaped PSO least square support vector machine (ATSWPLM) models in term of its classification accuracy. The VMDEA-ELM model demonstrates better diagnosis accuracy with small differences between 2% to 4% as compared to EOMSMFD and WPT-LCD-ELM but less diagnosis accuracy in the range of 4% to 5% as compared to SVM-DS and ATSWPLM. The diagnosis approach VMDEA-ELM was also able to provide faster classification performance about 6 40 times faster than Back Propagation Neural Network (BPNN) and Support Vector Machine (SVM). This study provides an improved solution in determining an optimized VMD parameters by using VMDEA. It also demonstrates a more accurate and effective diagnostic approach for machine maintenance using VMDEA-ELM

Leak location based on PDS-VMD of leakage-induced vibration signal under low SNR in water-supply pipelines

Leak location in water-supply pipelines is of great significance in order to preserve water resources and reduce economic losses. Cross-correlation (CC) based leak location is a popular and effective method in water-supply pipelines (WSP). However, with a decrease of signal to noise ratio (SNR), the errors of time-delay estimation (TDE) based on CC will become larger making it almost impossible to determine a leakage position. Hence, this work proposes leak location based on a combination of phase difference spectrum and variational mode decomposition (PDS-VMD) of leakage-induced vibration signal under low SNR for WSP. Firstly, the leakage-induced vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, where the characteristic frequency band is determined by PDS of cross spectrum of two leakage signals. Then, the energy ratio of leakage signal in characteristic frequency band serves as a guideline to select effective IMF components from the decomposed IMFs. Finally, the selective IMFs are reconstituted into a new signal which can be used to determine a leak position using CC based TDE. In order to verify the effectiveness of the proposed leak location algorithm, the method based on PDS-VMD is compared with that using CC, combination of CC coefficient and VMD (CCC-VMD) using both simulation and experiment. The simulation and experimental results demonstrate that the proposed PDS-VMD method is more suitable for leak location in WSP, which provides immunity to both broadband and narrow band noise under low SNR. © 2020 IEEE