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

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

Iterative variational mode decomposition and extreme learning machine for gearbox diagnosis based on vibration signals

Vibration-based monitoring and diagnosis provide an excellent and reliable monitoring strategies for maintaining and sustaining a million dollars of industrial assets. The signal processing method is one of the key elements in gearbox fault diagnosis for extracting most useful information from raw vibration signals. Variational mode decomposition (VMD) is one of the recent signal processing methods that helps to solve many limitations in traditional signal processing method. However, pre-determine the input parameters especially the mode number become a challenging task for using this method. Then, this study aims to propose an iterative approach for selecting the mode number for the VMD method by using the normalized mean value (NMV) plot. The NMV value is calculates based on the ratio of a summation of VMD modes and the input signals. The result shows that the proposed iterative VMD approach can select an accurate mode number for the VMD method. Then, the vibration signals decomposed into different VMD modes and used for gearbox fault diagnosis. Statistical features have been extracted from the selected VMD modes and pass into extreme learning machine (ELM) for fault classification. Iterative VMD-ELM provide significance improvement of about 20% higher accuracy in classification result as compared with EMD-ELM. Hence, this research study offers a new mean for gearbox diagnosis strategy

Multipoint Optimal Minimum Entropy Deconvolution Adjusted for Automatic Fault Diagnosis of Hoist Bearing

Multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) is a powerful method that can extract the periodic characteristics of signal effectively, but this method needs to evaluate the fault cycle a priori, and moreover, the results obtained in a complex environment are easily affected by noise. These drawbacks reduce the application of MOMEDA in engineering practice greatly. In order to avoid such problems, in this paper, we propose an adaptive fault diagnosis method composed of two parts: fault information integration and extracted feature evaluation. In the first part, a Teager energy spectrum amplitude factor (T-SAF) is proposed to select the intrinsic mode function (IMF) components decomposed by ensemble empirical mode decomposition (EEMD), and a combined mode function (CMF) is proposed to further reduce the mode mixing. In the second part, the particle swarm optimization (PSO) taking fractal dimension as the objective function is employed to choose the filter length of MOMEDA, and then the feature frequency is extracted by MOMEDA from the reconstructed signal. A cyclic recognition method is proposed to appraise the extracted feature frequency, and the evaluation system based on threshold and weight coefficient removes the wrong feature frequency. Finally, the feasibility of the method is verified by simulation data, experimental signals, and on-site signals. The results show that the proposed method can effectively identify the bearing state

Lifting load monitoring of mine hoist through vibration signal analysis with variational mode decomposition

Mine hoists play a crucial role in vertical-shaft transportation, and one of the main causes of their faults is abnormal lifting load. However, direct measurement of the load value is difficult. Further, the original structure must be destroyed for sensor installation. To facilitate efficient and accurate monitoring of the lifting load of mine hoist, this paper presents a novel condition-monitoring method based on variational mode decomposition (VMD) and support vector machine (SVM) through vibration signal analysis. First, traditional empirical mode decomposition (EMD) is used to analyze the vibration signal collected by an acceleration sensor, and the number of obtained intrinsic mode functions (IMFs) is employed to set the VMD mode number. Second, the obtained vibration signal is processed by the parameterized VMD, and the useful IMFs of VMD are selected through correlation analysis for feature extraction. Third, the obtained features are used to train an SVM model, and the trained SVM is used to monitor the mine-hoist lifting load. In this study, experiments on an operated mine hoist are also conducted to verify the reliability and validity of the proposed method. The experimental results show that the proposed method can accurately identify the considered lifting load conditions

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 rolling bearing fault diagnosis method based on VMD – multiscale fractal dimension/energy and optimized support vector machine

To achieve the goal of automated rolling bearing fault diagnosis, a variational mode decomposition (VMD) based diagnosis scheme was proposed. VMD was firstly used to decompose the vibration signals into a series of band-limited intrinsic mode functions (BLIMFs). Subsequently, the multiscale fractal dimension (MSFD) and multiscale energy (MSEN) of each BLIMF were calculated and combined together as features of the original vibration signals. In an attempt to accelerate the classification speed, one-way analysis of variance (ANOVA) test was adopted to extract significant features from the redundant features. Finally, those significant features were fed into the optimized support vector machine (SVM), which was optimized by the genetic algorithm (GA), for classification. Experimental results on the international public Case Western Reserve University bearing data indicate the effectiveness of the proposed method with a classification accuracy of 99.75 % for seven classes. Moreover, our approach also shows good anti-noise performance in different signal-to-noise ratios (SNRs)

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

Friction, Vibration and Dynamic Properties of Transmission System under Wear Progression

This reprint focuses on wear and fatigue analysis, the dynamic properties of coating surfaces in transmission systems, and non-destructive condition monitoring for the health management of transmission systems. Transmission systems play a vital role in various types of industrial structure, including wind turbines, vehicles, mining and material-handling equipment, offshore vessels, and aircrafts. Surface wear is an inevitable phenomenon during the service life of transmission systems (such as on gearboxes, bearings, and shafts), and wear propagation can reduce the durability of the contact coating surface. As a result, the performance of the transmission system can degrade significantly, which can cause sudden shutdown of the whole system and lead to unexpected economic loss and accidents. Therefore, to ensure adequate health management of the transmission system, it is necessary to investigate the friction, vibration, and dynamic properties of its contact coating surface and monitor its operating conditions