Maximal Overlap Discrete Wavelet Packet Transform Research Articles

A maximal overlap discrete wavelet packet transform coupled with an LSTM deep learning model for improving multilevel groundwater level forecasts

Developing precise groundwater level (GWL) forecast models is essential for the optimal usage of limited groundwater resources and sustainable planning and management of water resources. In this study, an improved forecasting accuracy for up to 3 weeks ahead of GWLs in Bangladesh was achieved by employing a coupled Long Short Term Memory (LSTM) network-based deep learning algorithm and Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) data preprocessing. The coupled LSTM-MODWPT model’s performance was compared with that of the LSTM model. For both standalone LSTM and LSTM-MODWPT models, the Random Forest feature selection approach was employed to select the ideal inputs from the candidate GWL lags. In the LSTM-MODWPT model, input GWL time series were decomposed using MODWPT. The ‘Fejér-Korovkin’ mother wavelet with a filter length of 18 was used to obtain a collection of scaling coefficients and wavelets for every single input time series. Model performance was assessed using five performance indices: Root Mean Squared Error; Scatter Index; Maximum Absolute Error; Median Absolute Deviation; and an a-20 index. The LSTM-MODWPT model outperformed standalone LSTM models for all time horizons in GWL forecasting. The percentage improvements in the forecasting accuracies were 36.28%, 32.97%, and 30.77%, respectively, for 1-, 2-, and 3-weeks ahead forecasts at the observation well GT3330001. Accordingly, the coupled LSTM-MODWPT model could potentially be used to enhance multiscale GWL forecasts. This research demonstrates that the coupled LSTM-MODWPT model could generate more precise GWL forecasts at the Bangladesh study site, with potential applications in other geographic locations globally.

De-noising of microwave reflectometry signal using maximal overlap discrete wavelet packet transform for plasma density measurement

For microwave reflectometry-based fusion plasma diagnostics, the acquired data is contaminated by the surrounding noise environment, making it difficult to measure the beat frequency accurately. Discrete wavelet and wavelet packet transforms are unsuitable as the former cannot decompose detailed coefficients, and the latter is a time-variant transform. This paper presents a correlation-based Maximal Overlap Discrete Wavelet Packet Transform (MODWPT), which decomposes the signal using different mother wavelet families. The suitable mother wavelet is chosen based on the metrics like signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), mean squared error (MSE), and mean absolute error (MAE). The data used for analysis is the stationary tokamak wall, for which the beat frequency and distance are measured. After rigorous analysis, it is found that sym12 outperforms with the following values 0.0493 (MSE), 0.1736 (MAE), 4.3334(SNR(dB)), 13.0634(PSNR(dB)) respectively. This technique can be extended to plasma scenarios for accurately measuring beat frequency and density profile.

Intelligent fault classification of air compressors using Harris hawks optimization and machine learning algorithms

Due to their complexity and often harsh working environment, air compressors are inevitably exposed to a variety of faults and defects during their operation. Thus, condition monitoring is critically required for early fault recognition and detection to avoid any type industrial failures. In this paper, an intelligent algorithm for reciprocating air compressor fault diagnosis is developed using real-time acoustic signals acquired from an air compressor with one healthy and seven different faulty states such as leakage inlet valve (LIV), leakage outlet valve (LOV), non-return valve (NRV), piston ring, flywheel, rider-belt and bearing defects. The proposed algorithm mainly consists of three steps: feature extraction, selection, and classification. For feature extraction, experimental acoustic signals are decomposed using maximal overlap discrete wavelet packet transform (MODWPT) by six levels into 64 wavelet coefficients (nodes). Thereafter, time domain features are calculated for each node to build each air compressor’s health state feature matrix. Each feature matrix dimension is reduced by selecting the most useful features using Harris hawks optimization (HHO) in the feature selection step. Finally, for feature classification, selected features are used as inputs for random forest (RF), ensemble tree (ET) and K-nearest neighbors (KNN) to detect, identify, and classify the compressor health states with high classification accuracy. Comparative studies with several feature extraction and selection methods prove the proposed approach’s efficiency in detecting, identifying, and classifying all air compressor faults.

An Intelligent Fault Diagnosis Scheme for Rotating Machinery Based on Supervised Domain Adaptation With Manifold Embedding

In rotating machinery fault diagnosis, domain adaptation (DA) transfer learning-based framework has been attracting great attentions to tackle the problem of inconsistent feature distribution and insufficient labeled fault feature data. However, most of the existing approaches mainly focus on either the cross-domain distribution alignment or manifold subspace learning, which faces two critical limitations: 1) it is hard to overcome the feature distortions when aligning the distribution in the original feature space and 2) subspace learning is insufficient to decrease the distribution divergence. To address the above limitations, this work proposes an intelligent fault diagnosis scheme based on supervised DA with manifold embedding and key features selection. It first applies maximal overlap discrete wavelet packet transform (MODWPT) to process the vibration signals and performs the statistical feature extraction. In order to ensure that the selected key features are conductive to domain adaption, the fault discriminative ability and domain invariance of the features are investigated based on the domain differences and Laplacian score. Then, it presents a new supervised domain adaption with manifold embedding for the distribution alignment in manifold subspace by taking the class information and neighboring relationships into account. Finally, an intra classifier is learned to predict the unlabeled target domain. The proposed fault diagnosis scheme is evaluated using a set of practical data sets of motor and bearing. The extensive experimental results demonstrate that it significantly outperforms the comparative models and achieves much more effective fault diagnosis under different working conditions.

Detection of Tram Wheel Faults Using MEMS-Based Sensors.

Micro-electromechanical-systems (MEMS) based sensors are used for monitoring the state of machines in condition-based maintenance tasks. This approach is applied at tram depots for the purpose of identifying faulty wheels on trams in order to eliminate defective trams at the entry or dispatch gates. The application of MEMS-based sensors for the detection of wheel faults is the focus of this study. A method for processing of the collected sensor data is developed. It is based on assessing the energy of vibrations at different frequency bands. Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) is used for obtaining a description of the sensor data. The task of finding the energy threshold for detecting faulty wheels, frequency band and parameters of MODWPT which most distinctly distinguish the wheels is the goal of the method. The weighted difference (DW) between the extreme values of energy in a frequency band for normal and faulty wheels is proposed as the measure of the ability to distinguish the wheels. The search for the solution is formulated as a discrete optimisation problem of maximising this measure. Both the simulation and experimental results indicate that faulty wheels have greater vibration energy than normal wheels. The properties of this approach are discussed and evaluated.

A Novel Based on the Log-Squared Envelope Harmonic Noise Ratio Fault Transient Feature Extraction Method

To counter the sensitivity of kurtosis for the random pulse, a novel periodic detection index based on the log-squared envelope harmonic noise ratio (LSEHNR) is constructed, and then, a novel LSEHNRgram feature extraction method is proposed by introducing the maximal overlap discrete wavelet packet transform (MODWPT). Firstly, MODWPT is used to decompose the frequency band of the signal and a series of subsignals are obtained from each stage of decomposition, which are called nodes. Secondly, autocorrelation of the log-squared envelope for each node at each level is computed; calculate the LSEHNR, simultaneously. Then, the LSEHNR values of all nodes are calculated and the node with the maximal of the LSEHNR value is selected for spectrum analysis. Finally, the square envelope spectrum (SES) analysis is performed on the in-band filtered signal to extract the transient characteristics of the rolling bearing fault. The experimental results indicate that the LSEHNRgram method can accurately detect the demodulation frequency band and enhance the fault features under the condition of the low noise-to-signal ratio (SNR). The effectiveness of the method is verified on numerical and experimental datasets by comparison with autogram, infogram, and fast kurtgram methods.

Maximal overlap discrete wavelet packet transforms and variants of neutrosophic cubic cross-entropy-based identification of rotor defects

The present study proposes a novel procedure for automated testimony of rotor defects through maximal overlap discrete wavelet packet transform (MODWPT) and the proposed neutrosophic cubic cross-entropy, fuzzy cross-entropy and single-valued neutrosophic cross-entropy (NCE) measures consecutively. Discrete wavelet transform is an efficient data decomposition technique, but the technical barrier with this technique is that it can decompose only low-frequency (approximate) signals and also it does not possess the shift invariance property. MODWPT possesses the shift invariance property and is highly capable of decomposing both approximate and detailed signals in time–frequency analysis. After the decomposition of raw signals through MODWPT, the lower and upper bounds of normalized energy readings of various rotor defect conditions (familiar and unfamiliar) are extracted and converted into the forms of fuzzy sets, single-valued neutrosophic sets and neutrosophic cubic sets respectively. The minimum neutrosophic cubic cross-entropy measure as well as fuzzy and single-valued NCE measure values between each rotor defect condition (familiar and unfamiliar) are computed and then utilized to identify various rotor defect conditions, such as parallel and angular misalignment of 7 Mils, rub, unbalance and defect-free respectively. The proposed variants of cross-entropy measure are intelligent in identifying the rotor defect conditions in comparison with the existing cosine similarity measure which exhibits unjustified and meaningless results during mathematical treatments.

A novel microgrid fault detection and classification method using maximal overlap discrete wavelet packet transform and an augmented Lagrangian particle swarm optimization-support vector machine

In this paper, an intelligent method for fault detection and classification for a microgrid (MG) was proposed. The idea was based on the combination of three computational tools: signal processing using the maximal overlap discrete wavelet packet transform (MODWPT), parameter optimization by the augmented Lagrangian particle swarm optimization (ALPSO), and machine learning using the support vector machine (SVM). The MODWPT was applied to preprocess half cycle of the post-fault current samples measured at both ends of feeders. The wavelet coefficients derived from the MODWPT were statistically evaluated using the mean, standard deviation, energy, skewness, kurtosis, logarithmic energy entropy, max, min, and Shannon entropy. These were the input feature datasets and were used to train the SVM classifier. The ALPSO was utilized to reduce the feature subsets and select the sensitive parameters of the SVM (i.e., penalty factor and the slack variable) to further improve the performance of the SVM. The intelligent relaying scheme was executed on a real-time digital simulator (RTDS) which is integrated with Matlab. The performance of SVM-based protection method is compared to several different protection models in terms of signal processing tools, optimization techniques used for selecting datasets and sensitive parameters, and classifiers under different operating conditions. Numerous operating conditions, including islanded or non-islanded operation modes and radial and or loop topologies introducing different characteristics of fault were included as the case studies for the proposed technique. A comprehensive evaluation study of the consortium for electric reliability technology solutions (CERTS) MG system and IEEE 34-bus confirms that the proposed protection scheme is accurate, fast, and robust to noisy measurements. In addition, the obtained results illustrate that the proposed method is superior to the recently published works in the literature.

The Detection of Motor Bearing Fault with Maximal Overlap Discrete Wavelet Packet Transform and Teager Energy Adaptive Spectral Kurtosis.

Motor bearings are one of the most critical components in rotating machinery. Envelope demodulation analysis has been widely used to demodulate bearing vibration signals to extract bearing defect frequency components but one of the main challenges is to accurately locate the major fault-induced frequency band with a high signal-to-noise ratio (SNR) for demodulation. Hence, an enhanced fault detection method combining the maximal overlap discrete wavelet packet transform (MODWPT) and the Teager energy adaptive spectral kurtosis (TEASK) denoising algorithms is proposed for identifying the weak periodic impulses. The Teager energy power spectrum (TEPS) defines the sparse representation of the filtered signals of the MODWPT in the frequency domain via the Teager energy operator (TEO); the TEASK helps determine the most informative frequency band for demodulation. The methodology is compared in terms of performance with the fast Kurtogram and the Autogram methods. The simulation and practical application examples have shown that the proposed MODWPT-TEASK method outperforms the above two methods in diagnosing defects of motor bearings.

Gearboxes fault detection under operation varying condition based on MODWPT, Ant colony optimization algorithm and Random Forest classifier

Gearboxes are massively utilized in nowadays industries due to their huge importance in power transmission; hence, their defects can heavily affect the machines performance. Therefore, many researchers are working on gearboxes fault detection and classification. However, most of the works are carried out under constant speed conditions, while gears usually operate under varying speed and torque conditions, making the task more challenging. In this paper, we propose a new method for gearboxes condition monitoring that is efficiently able to reveal the fault from the vibration signatures under varying operating condition. First, the vibration signal is processed with the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) to extract the AM-FM modes. Next, time domain features are calculated from each mode. Then the features set are reduced using the Ant colony optimization algorithm (ACO) by removing the redundant and unimportant parameters that may mislead the classification. Finally, an ensemble learning algorithm Random Forest (RF) is used to train a model able to classify the fault based on the selected features. The innovative aspect about this method is that, unlike other existing methods, ACO is able to optimize not only the features but also the parameters of the classifier in order to obtain the highest classification accuracy. The proposed method was tested on varying operating condition real dataset consisting of six different gearboxes. In the aim to prove the performance of our method, it had been compared to other conventional methods. The obtained results indicate its robustness, and its accuracy stability to handle the varying operating condition issue in gearboxes fault detection and classification with high efficiency.

A maximal overlap discrete wavelet packet transform integrated approach for rainfall forecasting – A case study in the Awash River Basin (Ethiopia)

This study introduces the maximal overlap discrete wavelet packet transform (MODWPT) for forecasting hydrological variables that exhibit change over multiple timescales (e.g., rainfall, streamflow). The advantage of the MODWPT over other recent wavelet decomposition methods (à trous algorithm (AT) and the maximal overlap discrete wavelet transform (MODWT)) is that it can extract finer scale information that may be important for improving forecast performance. Multiple wavelet decomposition methods (MODWPT, AT, MODWT) are integrated within the Wavelet Data-Driven Forecasting Framework (WDDFF), applied for forecasting monthly rainfall at six meteorological stations in the Awash River Basin (Ethiopia), and compared using eight statistical performance metrics. Results demonstrate that the MODWPT can be used to generate more accurate forecasts than the AT and MODWT for the majority of stations and performance metrics. Certain settings within the WDDFF (decomposition level, wavelet filter, input variable method, and data-driven model) lead to improved performance more often than others.

Forecasting Model of Silicon Content in Molten Iron Using Wavelet Decomposition and Artificial Neural Networks

Silicon content forecasting models have been requested by the operational team to anticipate necessary actions during the blast furnace operation when producing molten iron, to control the quality of the product and reduce costs. This paper proposed a new algorithm to perform the silicon content time series up to 8 h ahead, immediately after the molten iron chemical analysis is delivered by the laboratory. Due to the delay of the laboratory when delivering the silicon content measurement, the proposed algorithm considers a minimum useful forecasting horizon of 3 h ahead. In a first step, it decomposes the silicon content time series into different subseries using the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). Next, all subseries forecasts were determined through Nonlinear Autoregressive (NAR) networks, and finally, these forecasts were summed to furnish the long-term forecast of silicon content. Using data from a real industry, we showed that the prediction error was within an acceptable range according to the blast furnace technical team.

A prediction framework with time-frequency localization feature for detecting the onset of seismic events.

Onset detection of P-wave in seismic signals is of vital importance to seismologists because it is not only crucial to the development of early warning systems but it also aids in estimating the seismic source parameters. All the existing P-wave onset detection methods are based on a combination of statistical signal processing and time-series modeling ideas. However, these methods do not adequately accommodate some advanced ideas that exist in fault detection literature, especially those based on predictive analytics. When combined with a time-frequency (t-f) / temporal-spectral localization method, the effectiveness of such methods is enhanced significantly. This work proposes a novel real-time automatic P-wave detector and picker in the prediction framework with a time-frequency localization feature. The proposed approach brings a diverse set of capabilities in accurately detecting the P-wave onset, especially in low signal-to-noise ratio (SNR) conditions that all the existing methods fail to attain. The core idea is to monitor the difference in squared magnitudes of one-step-ahead predictions and measurements in the time-frequency bands with a statistically determined threshold. The proposed framework essentially accommodates any suitable prediction methodology and time-frequency transformation. We demonstrate the proposed framework by deploying auto-regressive integrated moving average (ARIMA) models for predictions and the well-known maximal overlap discrete wavelet packet transform (MODWPT) for the t-f projection of measurements. The ability and efficacy of the proposed method, especially in detecting P-waves embedded in low SNR measurements, is illustrated on a synthetic data set and 200 real-time data sets spanning four different geographical regions. A comparison with three prominently used detectors, namely, STA/LTA, AIC, and DWT-AIC, shows improved detection rate for low SNR events, better accuracy of detection and picking, decreased false alarm rate, and robustness to outliers in data. Specifically, the proposed method yields a detection rate of 89% and a false alarm rate of 11.11%, which are significantly better than those of existing methods.

New Gear Fault Diagnosis Method Based on MODWPT and Neural Network for Feature Extraction and Classification

Abstract Gear fault diagnosis using vibration signals has become the subject of intensive studies to detect any sudden failure. However, these signals exhibit nonlinear and nonstationary behaviors when the rotating machine operates under multiple working conditions. Furthermore, fault features extraction and classification of multiple gear states are always unsatisfactory and considered as a huge task. This is the main reason that motivates us to develop a new intelligent gear fault diagnosis method in order to automatically identify and classify several kinds of gear defects under different work conditions. So in this article, we propose a combination between the maximal overlap discrete wavelet packet transform (MODWPT), entropy indicator, and a multilayer perceptron (MLP) neural network as a new automatic fault diagnosis approach. MODWPT decomposes the data signal into several components using a uniform frequency bandwidth. Each decomposed component is selected to extract feature vector using entropy indicator. Finally, MLP provides a powerful automatic tool for identifying and classifying the aforementioned extracted features. Experimental vibration signals of healthy gear; gear with general surface wear; gear with chipped tooth in length; gear with chipped tooth in width; gear with missing tooth; and gear with tooth root crack are recorded under fifteen different work conditions to test the effectiveness of the suggested technique. Experimental results affirm that our proposed approach can successfully detect, identify, and classify the gear fault pattern in all cases.

Fault Diagnosis Scheme for Cross-Country Faults in Dual-Circuit Line With Emphasis on High-Impedance Fault Syndrome

In a power system network, transmission lines are exposed to atypical fault scenarios. The transmission line is the longest component in a power system and sometimes it passes through forest areas where the occurrence of cross-country faults (CCFs) associated with high-impedance fault (HIF) syndrome is more due to thunderstorms, cyclones, and poor vegetation management/tree trimming. Detection and classification of CCFs which are associated with HIF syndrome is the most challenging task. In this article, maximal overlap discrete wavelet packet transform (MODWPT) has been employed to extract the characteristics of the signals during CCF with HIF syndrome which are more complex and aperiodic/asymmetric/nonlinear. Thereafter, maximum change in wavelet packet energy of MODWPT coefficients of currents/voltages have been deliberated as unique features to design proposed fault diagnosis scheme for a dual-circuit transmission line. The efficacy of the proposed scheme has been investigated on the Chhattisgarh State Power Transmission Network. The proposed scheme is appraised with exclusive case studies such as switching of capacitor bank, switching of reactor string, switching of load/feeder, effect of power swing, nonlinear loads, lightly loading conditions, and measurement noise. The proposed scheme has been also validated on standard IEEE 13 bus distribution system with nonlinear loads to confirm its adaptability.

Spatial air quality index prediction model based on decomposition, adaptive boosting, and three-stage feature selection: A case study in China

Accurate prediction of air quality index (AQI) plays a vital role in pollution control and air quality warnings. Considering the strong spatial correlation of air pollutants, this study focuses on the spatial prediction of AQI and proposes a novel hybrid model combining decomposition, three-stage feature selection, and boosted extreme learning machine. The spatiotemporal features are gradually extracted in three stages, including spatial correlation analysis, mutuality, and binary grey wolf optimization (BGWO). Moreover, decomposition and ensemble methods are adopted to further enhance the robustness and accuracy of the model. Based on maximal overlap discrete wavelet packet transform (MODWPT), the original AQI series in target site is decomposed into eight subseries with different frequency bands to reduce the non-stationarity of time series. Outlier robust extreme learning machine (ORELM) serves as base predictor, and the adaptive boosting. MRT (Adabost.MRT) is adopted to combine several ORELMs to generate more robust forecasts. To comprehensively evaluate the proposed model, data collected from 1497 air quality monitoring sites in China are used, and six sites are randomly selected as prediction targets. The proposed model is compared with several baseline models and existing models. The results demonstrated that the proposed model significantly outperforms other models in all target sites. All components of the proposed hybrid model are proved to be indispensable to guarantee outstanding performance. The spatiotemporal data are reasonably taken into consideration, which provides improvement for air pollution prediction models.

A Fault Feature Extraction Method for the Fluid Pressure Signal of Hydraulic Pumps Based on Autogram

Center spring wear faults in hydraulic pumps can cause fluid pressure fluctuations at the outlet, and the fault feature information on fluctuations is often contaminated by different types of fluid flow interferences. Aiming to resolve the above problems, a fluid pressure signal method for hydraulic pumps based on Autogram was applied to extract the fault feature information. Firstly, maximal overlap discrete wavelet packet transform (MODWPT) was adopted to decompose the contaminated fault pressure signal of center spring wear. Secondly, based on the squared envelope of each node, three kinds of kurtosis of unbiased autocorrelation (AC) were computed in order to describe the fault feature information comprehensively. These are known as standard Autogram, upper Autogram and lower Autogram. Then a node corresponding to the biggest kurtosis value was selected as a data source for further spectrum analysis. Lastly, the data source was processed by threshold values, and then the fault could be diagnosed based on the fluid pressure signal.

An evolution-dependent multi-objective ensemble model of vanishing moment with adversarial auto-encoder for short-term wind speed forecasting in Xinjiang wind farm, China

Wind speed forecasting can enhance the safety and economy of wind energy integration and conversion. The characteristic of the wind speed evolves over time. In this paper, a novel evolution-dependent multi-objective ensemble model of vanishing moment is proposed to solve the above problem. The proposed model can assign time-varying ensemble weights to base predictors with the different vanishing moments, so as to achieve better forecasting performance. In this model, the deep Adversarial Auto-Encoder (AAE) is firstly utilized to convert the wind speed into a two-dimension Gaussian distribution feature space. The Bat Algorithm (BA) is applied to partition the feature space into several sectors. Each sector represents a cluster of wind speed. Outlier Robust Extreme Learning Machines (ORELMs) improved by Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) with the different vanishing moments are applied as base predictors, and the Multi-Objective Feasible Enhanced Particle Swarm Optimization (MOFEPSO) is used to obtain the best ensemble weights for each cluster. At last, the suitable ensemble model is applied for forecasting at each time. Four actual wind speed series collected from Xinjiang wind farm are used to verify the effectiveness of the proposed model. The experimental results indicate the proposed model outperforms other benchmark models.

Automated interpretable detection of myocardial infarction fusing energy entropy and morphological features

Background and objectiveThe 12 leads electrocardiogram (ECG) is an effective tool to diagnose myocardial infarction (MI) on account of its inexpensive, noninvasive and convenient. Many methodologies have been widely adopted to detect it. However, much existing method did not integrate with diagnostic logic of clinician and practical application. The aim of the paper is to provide an automated interpretable detection method of myocardial infarction. MethodsThe paper presents a novel method fusing energy entropy and morphological features for MI detection via 12 leads ECG. Specifically, ECG signals are firstly decomposed by maximal overlap discrete wavelet packet transform (MODWPT), then energy entropy is calculated from the decomposed coefficients as global features. Area, kurtosis coefficient, skewness coefficient and standard deviation extracted from QRS wave and ST-T segment of ECG beat are computed as local morphological features. Combining global features based on record and local features based on beat for single lead, all the 12 leads features are fused as the ultimate feature vector. What's more, different methods including principal component analysis (PCA), linear discriminant analysis (LDA) and locality preserving projection (LPP) are employed to reduce the computational complexity and redundant information. Meanwhile, principal component features are ranked by F-value. To evaluate the proposed method, PTB (Physikalisch-Technische Bundesanstalt) database and inter-patient paradigm are employed. ResultsCompared with different algorithms, support vector machine (SVM) using radial basis kernel function combined with 10-fold cross validation achieves the best average performance with accuracy of 99.81%, sensitivity of 99.56%, precision of 99.74% and F1 of 99.70% based on 18 features in the intra-patient paradigm. By contrast, the accuracy is 92.69% with only 22 features for the inter-patient paradigm. ConclusionsThe experimental results present a superior performance compared to the state-of-the-art method. Meanwhile, above approach has the characteristic of interpretability according with diagnostic logic and strategy of clinician and specific change of ECG for MI.

The FERgram: A rolling bearing compound fault diagnosis based on maximal overlap discrete wavelet packet transform and fault energy ratio

Compound fault features of the rolling bearing are difficult to separate and extract. To address this problem, the present paper proposed a diagnosis algorithm, namely FERgram, on the base of maximal overlap discrete wavelet packet transform (MODWPT) and fault energy ratio (FER). First, a group of frequency band signals are gained after MODWPT processing the initial vibration signal. Second, FER is chosen as the evaluation index, and then the FER values of each frequency band signal are calculated and used to generate FERgram. The frequency band signal with the maximum FER value containing plentiful fault information is chosen for envelope analysis. Finally, the fault type is determined by contrasting the prominent frequency component of the envelope spectrum with the fault feature frequency. The feasibility and superiority of the FERgram method are verified by four signals and four comparison methods. The results show that the FERgram method can effectively extract and accurately diagnose the compound fault of rolling bearing.