Maximal Overlap Discrete Wavelet Packet 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.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

Precise disturbance localization of long distance fiber interferometer vibration senor based on an improved time–frequency variation feature extraction scheme

Locating intrusions with high accuracy is crucial for prompting long distance distributed optical fiber vibration sensing systems to practical applications in engineering filed. To achieve the high measurement accuracy and real-time performance simultaneously, in this paper, an intensity-modulated ultra-long distance distributed optical fiber vibration sensing system using an asymmetric dual Mach-Zehnder interferometer is experimentally established. More importantly, a positioning approach based on an ameliorated time–frequency feature extraction scheme is proposed with both theoretically analysis and experimental demonstration. In particular, an endpoint detection algorithm based on differential operation is firstly utilized to rapidly and accurately locate the endpoints of the received vibration signals. Thus the large-band width signals can be successfully acquired by setting an approximate window. Then, the ameliorated time–frequency feature extraction scheme based on a maximal overlap discrete wavelet packet transform is applied to eliminate the asymmetry of the large-band width signals, as it could lead to an erroneous positioning result when directly using a cross-correlation time delay estimation algorithm. Finally, the vibration positions along the sensing fiber link of the established sensing system can be successfully demodulated with the help of the extracted time–frequency features. To validate the effectiveness of the proposed scheme, vibration positioning tests were conducted in a real perimeter security scenario. And the results show that a mean positioning error of 11.12 m and a mean processing time of 0.276 s have been realized in a sensing length of 101 km. Thus, it is believed that through continuous technological advancements and refine algorithm optimization, the long distance distributed optical fiber vibration sensor founded on the proposed positioning strategy is poised to play an important role in the practical engineering applications.

A new epileptic seizure prediction model based on maximal overlap discrete wavelet packet transform, homogeneity index, and machine learning using ECG signals

Epilepsy, a complex pathology with various etiological origins, is characterized by producing hyperexcitability in the brain, which can have multiple disruptive symptoms. It impacts about 40 million people worldwide, of which 20 to 30% have chronic and intractable seizures. Each seizure can create hazardous situations for patients resulting from fractures, burns, submersion accidents, and soft-tissue injuries. Therefore, a method capable of predicting a seizure with sufficient window time before its onset is highly desirable because it will allow the patient to locate a safe place or take appropriate precautionary actions. In this article, a novel method is presented through adroit integration of maximal overlap wavelet packet transform, homogeneity index, and a K-Nearest Neighbors classifier to predict an epileptic event twenty minutes before its onset using electrocardiogram (ECG) signals. The method's effectiveness for predicting an epileptic seizure is verified by employing a database provided by the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH), which includes seven patients with ten epileptic seizures. The results show that the proposed method effectively predicts an epileptic seizure 20 min prior to its onset with an accuracy of 93.25%.

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.

A New Cross-Domain Bearing Fault Diagnosis Framework Based on Transferable Features and Manifold Embedded Discriminative Distribution Adaption Under Class Imbalance

Cross-domain fault diagnosis based on transfer learning has been popularly developed to overcome inconsistent data distribution-caused degradation of diagnostic performance. However, the existing methods are typically suffering from a class imbalance of domains and lacking sufficient fault data because it is difficult to obtain the real industrial data of machinery under fault conditions. To address these problems, this work proposes a new cross-domain bearing diagnosis framework based on transferable features and manifold embedded discriminative distribution adaption. First, it applies the maximal overlap discrete wavelet packet transform to process the vibration data and extract different statistics-based features. Then, to enhance the domain adaptation performance, it designs a transferability evaluation based on the adjusted rand index and maximum mean discrepancy to quantify the fault discriminability and domain invariance of the features. After that, it proposes a novel manifold embedded discriminative joint distribution adaptation method to perform cross-domain feature discriminative joint distribution alignment in a Grassmann manifold subspace. Finally, it utilizes a random forest classifier to train the cross-domain fault diagnosis model. To verify the performances of the proposed methods, extensive experiments have been conducted on two real rolling bearing datasets. The results demonstrate that the proposed methods can achieve the desirable diagnosis results and significantly outperform comparative classical transfer learning-based models when there is the class imbalance between source and target domains.

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-based bipolar neutrosophic cross entropy measure for identification of rotor defects

This study propounds a novel methodology for automatic identification of rotor defects severity, when the machine is operated at constant speed, through maximal overlap discrete wavelet packet transforms (MODWPT) and proposed cross entropy measures of bipolar neutrosophic sets, single valued neutrosophic sets and fuzzy sets respectively. After the 3rd level of decomposition of raw vibration signals into eight frequency bands (called as WPT3 bands) through MODWPT, the energy reading in each WPT3 band is monitored. Thereafter, the lower (here called as truth membership degrees) and upper energy bounds from the training and testing samples of various rotor defect conditions at each WPT3 band are extracted and then normalized to lie in [0,1]. Finally, the energy intervals are constructed and thereafter converted into the desired forms of fuzzy sets, bipolar neutrosophic sets and single valued neutrosophic sets consecutively. The minimum cross entropy measure values between the fuzzy sets (Method 1), single valued neutrosophic sets (Method 2) and bipolar neutrosophic sets (Method 3) of training and testing samples of rotor defect conditions are computed and utilized to identify defect conditions such as angular/parallel misalignment of 10 Mils, unbalance, rub and defect free respectively. The novelty of the proposed rotor defect identification methodology lies in the fact that all the proposed variants of bipolar neutrosophic cross entropy measure have been found skilled enough to identify the desired rotor defects under study. On another hand, the existing cosine similarity measure [1] does not possess the necessary capability of identifying all rotor defects, especially, the rub defect condition. Furthermore, like the existing cosine similarity measure, our proposed variants of bipolar neutrosophic cross entropy measures have been found equally compatible for fairly furnishing the consistent and feasible results under intuitive analysis.

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.

Maximal Overlap Discrete Wavelet Packet Transforms-Based Bipolar Neutrosophic Cross Entropy Measure for Identification of Rotor Defects

Maximal Overlap Discrete Wavelet Packet Transforms-Based Bipolar Neutrosophic Cross Entropy Measure for Identification of Rotor Defects

A New Transferable Fault Diagnosis Approach of Rotating Machinery Based on Deep Autoencoder and Dominant Features Selection under Different Operating Conditions

In the actual industrial scenarios, most existing fault diagnosis approaches are faced with two challenges, insufficient labeled training data and distribution divergences between training and testing datasets. For the above issues, a new transferable fault diagnosis approach of rotating machinery based on deep autoencoder and dominant features selection is proposed in this article. First, maximal overlap discrete wavelet packet transform is applied for signals processing and mix-domains statistical feature extraction. Second, dominant features selection by importance score and differences between domains is proposed to select dominant features with high fault-discriminative ability and domain invariance. Then, selected dominant features are used for pretraining deep autoencoder (source model), which helps in enhancing the fault representative ability of deep features. The parameters of the source model are transferred to the target model, and normal state features from target domain are adopted for fine-tuning the target model. Finally, the target model is applied for fault patterns classification. Motor and bearing fault datasets are used for a series of experiments, and the results verify that the proposed methods have better cross-domain diagnosis performance than comparative models.

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.

Bearing incipient fault feature extraction using adaptive period matching enhanced sparse representation

Bearing incipient fault feature extraction is crucial and challenging throughout its life cycle. In this paper, an adaptive period matching enhanced sparse representation (APMESR) algorithm is developed to address this issue. First, a novel methodology for estimating the period of faulty impulses is proposed from the perspective of mining the periodicity-related numerical patterns. Second, the period estimation methodology is embedded in a sparse representation model to implement adaptive period matching to form APMESR, which is capable of achieving periodic sparsity. Third, maximal overlap discrete wavelet packet transform is selected as the linear transformation of APMESR for improving its ability to reduce noise and highlight periodic impulse signatures. Furthermore, evaluations and comparisons are conducted using simulations to demonstrate the validity and performance of the proposed period estimation methodology, linear transformation, and APMESR. Experimental results indicate that APMESR can effectively extract incipient bearing fault features and outperforms other well-advanced methods.

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.