Wavelet Filter Banks Research Articles

A new approach to identify obstructive sleep apnea using an optimal orthogonal wavelet filter bank with ECG signals

Abstract Obstructive sleep apnea (OSA) is a severe sleep ailment. It manifests when a person's breathing is interrupted while sleeping due to an inadequate supply of oxygen to the brain and physical body. The detection of OSA at an early stage can provide better mitigation from severe health impairments. An accurate method to detect OSA can improve the quality of life significantly. The computer-aided diagnosis (CAD) system of OSA developed using single-channel, single-signal physiological signals can efficiently cut costs, and can be used even at home. Therefore, a simple and portable OSA-CAD system using single-channel electrocardiogram (ECG) is introduced in this paper. This study proposes the automated identification of ECG signal affected from OSA employing an optimal two-band filter bank (FB) technique. While designing the filter bank, our central objective is to minimize the spectral localization, subjected to exact regeneration and regularity criteria. The identification of OSA using ECG signals is duly based on the newly designed FB. Using the proposed FB, ECG signals were split into wavelet frequency-bands (WFBs). The fuzzy-entropy (FUEN) and the log of signal-energy (LOEN) of WFBs have been employed as the distinguishing features. The 35-fold cross-validation technique was exercised using various classifiers, namely K nearest neighbor (KNN), decision tree (DT), linear discriminant, logistic regression, and support vector machine (SVM) to separate into normal and OSA affected subjects. The proposed model has attained respective highest average accuracy (AVAC), average sensitivity (AVSE), average specificity (AVSP) and F1-score of 90.87%, 92.43% 88.33% and 92.61%. Our proposed model outperformed the existing systems developed using the same database and was found to be more efficient, robust, and easy to use.

Design and FPGA implementation of 11th order Efficient IIR Wavelet Filter Banks with Approximate Linear-phase

In this paper. Bireciprocal Lattice Wave Digital Filters (BLWDFs) are utilized in an approximate linear-phase in pass-band design of order IIR wavelet filter banks (FBs). These filter banks are efficiently designed by replacement one of branches for (BLWDFs) by only a unit delay. The coefficients of the designed filter are achieved by simulating the IIR response suggested in [1]. The design is first simulated using Matlab programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength for the BLWDFs coefficients. FPGA implemtation of the proposed IIR wavelet filter bank is also achived for three levels with less complexity and high operating frequency.

Design and FPGA implementation of 11th order Efficient IIR Wavelet Filter Banks with Approximate Linear-phase

In this paper. Bireciprocal Lattice Wave Digital Filters (BLWDFs) are utilized in an approximate linear-phase in pass-band design of order IIR wavelet filter banks (FBs). These filter banks are efficiently designed by replacement one of branches for (BLWDFs) by only a unit delay. The coefficients of the designed filter are achieved by simulating the IIR response suggested in [1]. The design is first simulated using Matlab programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength for the BLWDFs coefficients. FPGA implemtation of the proposed IIR wavelet filter bank is also achived for three levels with less complexity and high operating frequency.

Automatic discrimination of earthquakes and quarry blasts using wavelet filter bank and support vector machine

False discrimination between earthquakes and quarry blasts may lead to an unrealistic characterization of the natural seismicity of a region. The similarity in seismograms between earthquakes and quarry blasts is the primary reason for incorrect discrimination. Therefore, in this paper, we propose a discriminative algorithm utilizing wavelet filter bank to extract unique features between earthquakes and quarry blasts. The discriminative features are found to be in the first five seconds after the onset time. The proposed algorithm is divided into two stages: first, wavelet filter bank extracts the features of the seismic signals; then, support vector machine classifies the event based on these extracted features. The proposed algorithm achieves a discrimination accuracy of 98.5% when applied to 900 earthquakes and quarry blast waveforms.

An empirical wavelet transform based approach for multivariate data processing application to cardiovascular physiological signals

Abstract Background This article proposes an extension of empirical wavelet transform (EWT) algorithm for multivariate signals specifically applied to cardiovascular physiological signals. Materials and methods EWT is a newly proposed algorithm for extracting the modes in a signal and is based on the design of an adaptive wavelet filter bank. The proposed algorithm finds an optimum signal in the multivariate data set based on mode estimation strategy and then its corresponding spectra is segmented and utilized for extracting the modes across all the channels of the data set. Results The proposed algorithm is able to find the common oscillatory modes within the multivariate data and can be applied for multichannel heterogeneous data analysis having unequal number of samples in different channels. The proposed algorithm was tested on different synthetic multivariate data and a real physiological trivariate data series of electrocardiogram, respiration, and blood pressure to justify its validation. Conclusions In this article, the EWT is extended for multivariate signals and it was demonstrated that the component-wise processing of multivariate data leads to the alignment of common oscillating modes across the components.

CORE-PI: Non-iterative convolution-based reconstruction for parallel MRI in the wavelet domain.

To develop and test a novel parameter-free non-iterative wavelet domain method for reconstruction of undersampled multicoil MR data. A linear parallel MRI method that operates in the Stationary Wavelet Transform (SWT) domain is proposed. The method is coined COnvolution-based REconstruction for Parallel MRI (CORE-PI). This method computes the SWT of the unknown MR image directly from subsampled k-space measurements, without modifying the RF excitation pulse. It then reconstructs the image using the wavelet filter bank approach, with simple linear computations. The CORE-PI implementation is demonstrated by experiments with a numeric brain phantom and invivo brain scans data, with various wavelet types and high reduction factors. It is compared to the well-known parallel MRI methods GRAPPA and l1-SPIRiT. The experimental results show that CORE-PI is suitable for different 1D Cartesian k-space undersampling schemes, including regular and irregular ones, and for wavelets of different families. CORE-PI accurately reconstructs the SWT coefficients of the unknown MR image; this wavelet-domain decomposition is fully computed despite the k-space undersampling. Furthermore, CORE-PI provides high-quality final reconstructions, with an average NRMSE of 0.013, which is significantly lower than that obtained by GRAPPA and l1-SPIRiT. Moreover, CORE-PI offers significantly faster computation times: the typical CORE-PI runtime is about 60seconds, which is about 20% shorter than that of l1-SPIRiT and 55%-75% shorter than that of GRAPPA. COnvolution-based REconstruction for Parallel MRI advantageously offers: (a) flexible 1D undersampling of a Cartesian k-space, (b) a parameter-free non-iterative implementation, (c) reconstruction performance comparable or better than that of GRAPPA and l1-SPIRiT, and (d) robust fast computations.

An Efficient Saliency Detection Model Based on Wavelet Generalized Lifting

Saliency detection refers to the segmentation of all visually conspicuous objects from various backgrounds. The purpose is to produce an object-mask that overlaps the salient regions annotated by human vision. In this paper, we propose an efficient bottom-up saliency detection model based on wavelet generalized lifting. It requires no kernels with implicit assumptions and prior knowledge. Multiscale wavelet analysis is performed on broadly tuned color feature channels to include a wide range of spatial-frequency information. A nonlinear wavelet filter bank is designed to emphasize the wavelet coefficients, and then a saliency map is obtained through linear combination of the enhanced wavelet coefficients. This full-resolution saliency map uniformly highlights multiple salient objects of different sizes and shapes. An object-mask is constructed by the adaptive thresholding scheme on the saliency maps. Experimental results show that the proposed model outperforms the existing state-of-the-art competitors on two benchmark datasets.

Optimization of segmentation fragments in empirical wavelet transform and its applications to extracting industrial bearing fault features

Empirical wavelet transform is a wavelet filter bank to decompose a bearing fault signal into several sub-signals for extracting bearing fault features and it attracts lots of attention recently because it looks like a hybrid of wavelet transform and empirical mode decomposition. However, an assumption for use of empirical wavelet transform is that segmentation fragments in empirical wavelet transform must be established in advance. To satisfy this assumption, an artificial rule based on local maxima of the frequency spectrum of a signal was previously proposed to establish segmentation fragments in empirical wavelet transform. Obviously, because the artificial rule completely relies on local maxima, it is not always reliable and not optimal to establish segmentation fragments in empirical wavelet transform for bearing fault feature extraction. In this paper, empirical wavelet transform for extracting bearing fault features is formulated as a constrained optimization problem. Segmentation fragments in empirical wavelet transform are optimized to jointly maximize bearing fault signatures in squared envelope spectra obtained by empirical wavelet transform. Industrial bearing fault signals are used to illustrate how the constrained optimization problem can find the optimal segmentation fragments in empirical wavelet transform. Comparisons with empirical wavelet transform guided by the artificial rule as well as two advanced fault diagnosis algorithms including spectral kurtosis and spectral correlation are made to experimentally demonstrate that the optimal segmentation fragments in empirical wavelet transform can result in higher detection performance.

Analysis of knee-joint vibroarthographic signals using bandwidth-duration localized three-channel filter bank

A vibrarthographic (VAG) signal is the recorded vibration signal produced by human knee-joints during movements of the leg. These signals are useful in quantifying lubrication and roughness of articular cartilage layers of the knee-joint. The early detection and treatment of an abnormal knee-joint will help in providing a better quality of life for the suffering patients. The VAG signals are nonlinear and non-stationary. Hence, in the proposed study, we have employed an optimal bandwidth-duration localized three-band (OBDLTB) orthogonal wavelet filter banks (OWFB) to automatically identify the health of knee-joints using VAG signals. We have used the database created at the University of Calgary containing a total of 89 VAG signals (51 normal and 38 pathological). The log-energy (LOEN) features are obtained from various sub-bands using OBDLTB-OWFB. The extracted LOEN features are separated using supervised machine learning algorithms into normal and abnormal VAG signals. Our automated system obtained an average classification accuracy of 89.89% and F1-score of 87.67% with 10-fold cross-validation. The performance of the model indicates that the proposed technique is able to identify the abnormal knee-joint reliably and thus this technique can aid the orthopedic surgeons in the early diagnosis of knee-joint abnormalities.

Design of high performance QRS complex detector for wearable healthcare devices using biorthogonal spline wavelet transform

A high performance QRS complex detector applicable for wearable healthcare devices is proposed in the present work. Since, higher SNR results in better detection accuracy and lesser number of coefficients reduces the hardware resources as well as power dissipation during on chip implementation. Biorthogonal spline wavelet transform is chosen for the proposed detector as it has high signal to noise ratio (SNR) and uses only four coefficients for decomposition. In the proposed approach, a Biorthogonal wavelet filter bank with fourth level decomposition is first used to separate the different frequency components and then a fourth level wavelet filter bank is used to get the denoised electrocardiogram (ECG) signals. Wavelet filter bank outputs are multiplied and soft threshold method is applied to get the QRS complex peaks by the QRS complex peak detector block. Add and shift multiplier used in the earlier designs has been replaced by a Booth multiplier in our approach to achieve the higher performance. Booth multiplier and QRS complex peak detector blocks have been designed for low hardware complexity, high performance and accurate detection of the QRS complex peaks. Time interval between the consecutive QRS peaks is calculated using the R-R peak time calculator block and the heart rate (HR) by the HR calculator block. Heart Rate Variability (HRV) and arrhythmia are detected based on these heart rate calculations. Proposed design has been tested for its robustness on multiple datasets (namely, MIT-BIH arrhythmia, MIT-BIH noise stress test, and MIT-BIH atrial fibrillation databases). Sensitivity of 99.31%, positive predictivity of 99.19% and the Detection Error Rate (DER) of 1.49% shown by the proposed design makes it preferable for QRS complex detectors used in wearable healthcare devices.

Mel scaled M-band wavelet filter bank for speech recognition

A Mel scaled M-band wavelet filter bank structure is used to extract the robust acoustic feature for speech recognition application. The proposed filter bank can provide flexibility of frequency partition that decomposes the speech signal into the M-frequency band. To estimate the difference between Mel scaled M-band wavelet and dyadic wavelet filter bank, relative bandwidth deviation (RBD) and root mean square bandwidth deviation (RMSBD) with respect to baseline (Mel filter bank bandwidth) is calculated. Proposed filter bank gives 40.90 and 49.84% reduction for RBD and RMSBD respectively, over 24-dyadic wavelet filter bank. Feature extraction from the proposed filter bank using AMUAV corpus shows an improvement in terms of word recognition accuracy (WRA) at all SNR range (20 dB to 0 dB) over baseline (MFCC) features. For AMUAV corpus, the proposed feature shows the maximum improvement in WRA of 3.93% over baseline features and 3.90% over dyadic wavelet filter bank features. When applied to the VidTIMIT corpus, proposed features show the maximum improvement in WRA of 1.64% over baseline features and 4.43% over dyadic features.

An automated diagnosis of depression using three-channel bandwidth-duration localized wavelet filter bank with EEG signals

Depression is a mental illness. If not diagnosed and treated quickly, it can affect one’s mood and quality of life. Modern life is stressful and fast paced, owing to which depression has emerged as a major source of mental health disorder. The electroencephalogram (EEG) signals, which are used to diagnose depression, are non-stationary, non-linear and complex. Their visual interpretation is difficult and takes time. This makes computer-aided depression diagnosis systems highly desirable for the early detection of the depression. This study aims towards the development of depression detection system using EEG based measures. We propose a computer aided depression diagnosis system using newly designed bandwidth-duration localized (BDL) three-channel orthogonal wavelet filter bank (TCOWFB) and EEG signal for the detection of depression. The EEG signal is decomposed into seven wavelet sub-bands (WSBs) using a optimal six-length TCOWFB. The logarithm of L2 norm (LL2N) of six detailed WSBs and one approximate WSB are used as discriminating features.These features are used in the classification of normal or depression EEG signals by applying them to the least square support vector machine (LS-SVM). The proposed system attained the perfect value of 1 for area under the curve (AUC) of receiver’s operating characteristics (ROC) using seven features. The proposed system with ten-fold cross validation (CV) strategy attained an average classification accuracy (ACA) of 99.58%. The proposed model obtained better ACA than the existing automated depression diagnosis systems (ADDS) and perfect AUC-ROC. Hence, it can be used in a clinical setup to diagnose the depression disorder accurately in lesser time, without any subjectivity due to human intervention.

A novel automated diagnostic system for classification of myocardial infarction ECG signals using an optimal biorthogonal filter bank

Myocardial infarction (MI), also referred to as heart attack, occurs when there is an interruption of blood flow to parts of the heart, due to the acute rupture of atherosclerotic plaque, which leads to damage of heart muscle. The heart muscle damage produces changes in the recorded surface electrocardiogram (ECG). The identification of MI by visual inspection of the ECG requires expert interpretation, and is difficult as the ECG signal changes associated with MI can be short in duration and low in magnitude. Hence, errors in diagnosis can lead to delay the initiation of appropriate medical treatment. To lessen the burden on doctors, an automated ECG based system can be installed in hospitals to help identify MI changes on ECG. In the proposed study, we develop a single-channel single lead ECG based MI diagnostic system validated using noisy and clean datasets. The raw ECG signals are taken from the Physikalisch-Technische Bundesanstalt database. We design a novel two-band optimal biorthogonal filter bank (FB) for analysis of the ECG signals. We present a method to design a novel class of two-band optimal biorthogonal FB in which not only the product filter but the analysis lowpass filter is also a halfband filter. The filter design problem has been composed as a constrained convex optimization problem in which the objective function is a convex combination of multiple quadratic functions and the regularity and perfect reconstruction conditions are imposed in the form linear equalities. ECG signals are decomposed into six subbands (SBs) using the newly designed wavelet FB. Following to this, discriminating features namely, fuzzy entropy (FE), signal-fractal-dimensions (SFD), and renyi entropy (RE) are computed from all the six SBs. The features are fed to the k-nearest neighbor (KNN). The proposed system yields an accuracy of 99.62% for the noisy dataset and an accuracy of 99.74% for the clean dataset, using 10-fold cross validation (CV) technique. Our MI identification system is robust and highly accurate. It can thus be installed in clinics for detecting MI.

MMSFL-OWFB: A novel class of orthogonal wavelet filters for epileptic seizure detection

The optimal filters with minimal bandwidth are highly desirable in many applications such as communication and biomedical signal processing. In this study, we design optimally frequency localized orthogonal wavelet filters and evaluate their performance using electroencephalogram (EEG) signals for automated detection of the epileptic seizure. The paper presents a novel method for designing optimal orthogonal wavelet filter banks (OWFB) with the objective of minimizing their frequency spreads. The designed wavelet filter also possesses the desired degree of regularity. The regularity condition has been imposed analytically so as to satisfy the constraint accurately. We propose a novel semi-definite programming (SDP) formulation which does not involve any parametrization. The solution of the SDP yields optimal orthogonal wavelet filter for the given length of the filter. We have developed an automated diagnosis system that identifies epileptic seizure EEG signals using the features obtained from the designed minimally mean squared frequency localized (MMSFL) OWFB. We have tested the performance of the proposed model using two independent EEG databases in order to ensure the consistency and robustness of the model. Interestingly, the proposed MMSFL-OWFB feature-based model exhibits ceiling level of performance, with classification accuracy ≥ 99% in classifying seizure (ictal) and seizure-free (non-ictal) EEG signals for both databases. Our developed system can be employed in hospitals and community cares to aid the epileptologists in the accurate diagnosis of seizures.

An integrated acoustic echo and noise cancellation system using cross-band adaptive filters and wavelet thresholding of multitaper spectrum

An efficient integrated system for acoustic echo and noise cancellation in hands free devices is proposed in this paper. Adaptive filters are usually employed in such systems for the acoustic echo cancellation. In order to reduce the computational complexity, sub band adaptive filters are commonly used since the order of filter required will be less but at the cost of distortion due to aliasing effect. In this work, cross-band adaptive filters are developed in wavelet domain/wavelet packet domain in tune with psychoacoustic model, to reduce the above distortion and thereby effectively estimate the echo and cancel it. The system uses wavelet thresholding technique for smoothening the log multitaper spectrum which eliminates the annoying musical noise in the processed output. To achieve efficient echo and noise cancellation, a novel switching mechanism to switch between wavelet filter bank and perceptual wavelet packet filter bank with most matching wavelet basis, from a dictionary of wavelet bases, depending on the type of noise present in each frame of the noisy speech is designed and developed in this work. The performance of the proposed integrated system is evaluated in terms of Acoustic Interference Cancellation (AIC) and Noise Attenuation (NA) under different Signal to Noise Ratio (SNR) conditions. The system exhibits very good performance even at very low SNRs close to −10 dB when compared with other such competitive systems.

Application of an optimal class of antisymmetric wavelet filter banks for obstructive sleep apnea diagnosis using ECG signals

Obstructive sleep apnea (OSA) is a sleep disorder caused due to interruption of breathing resulting in insufficient oxygen to the human body and brain. If the OSA is detected and treated at an early stage the possibility of severe health impairment can be mitigated. Therefore, an accurate automated OSA detection system is indispensable. Generally, OSA based computer-aided diagnosis (CAD) system employs multi-channel, multi-signal physiological signals. However, there is a great need for single-channel bio-signal based low-power, a portable OSA-CAD system which can be used at home. In this study, we propose single-channel electrocardiogram (ECG) based OSA-CAD system using a new class of optimal biorthogonal antisymmetric wavelet filter bank (BAWFB). In this class of filter bank, all filters are of even length. The filter bank design problem is transformed into a constrained optimization problem wherein the objective is to minimize either frequency-spread for the given time-spread or time-spread for the given frequency-spread. The optimization problem is formulated as a semi-definite programming (SDP) problem. In the SDP problem, the objective function (time-spread or frequency-spread), constraints of perfect reconstruction (PR) and zero moment (ZM) are incorporated in their time domain matrix formulations. The global solution for SDP is obtained using interior point algorithm. The newly designed BAWFB is used for the classification of OSA using ECG signals taken from the physionet's Apnea-ECG database. The ECG segments of 1 min duration are decomposed into six wavelet subbands (WSBs) by employing the proposed BAWFB. Then, the fuzzy entropy (FE) and log-energy (LE) features are computed from all six WSBs. The FE and LE features are classified into normal and OSA groups using least squares support vector machine (LS-SVM) with 35-fold cross-validation strategy. The proposed OSA detection model achieved the average classification accuracy, sensitivity, specificity and F-score of 90.11%, 90.87% 88.88% and 0.92, respectively. The performance of the model is found to be better than the existing works in detecting OSA using the same database. Thus, the proposed automated OSA detection system is accurate, cost-effective and ready to be tested with a huge database.

An accurate sleep stages classification system using a new class of optimally time-frequency localized three-band wavelet filter bank

Sleep related disorder causes diminished quality of lives in human beings. Sleep scoring or sleep staging is the process of classifying various sleep stages which helps to detect the quality of sleep. The identification of sleep-stages using electroencephalogram (EEG) signals is an arduous task. Just by looking at an EEG signal, one cannot determine the sleep stages precisely. Sleep specialists may make errors in identifying sleep stages by visual inspection. To mitigate the erroneous identification and to reduce the burden on doctors, a computer-aided EEG based system can be deployed in the hospitals, which can help identify the sleep stages, correctly. Several automated systems based on the analysis of polysomnographic (PSG) signals have been proposed. A few sleep stage scoring systems using EEG signals have also been proposed. But, still there is a need for a robust and accurate portable system developed using huge dataset. In this study, we have developed a new single-channel EEG based sleep-stages identification system using a novel set of wavelet-based features extracted from a large EEG dataset. We employed a novel three-band time-frequency localized (TBTFL) wavelet filter bank (FB). The EEG signals are decomposed using three-level wavelet decomposition, yielding seven sub-bands (SBs). This is followed by the computation of discriminating features namely, log-energy (LE), signal-fractal-dimensions (SFD), and signal-sample-entropy (SSE) from all seven SBs. The extracted features are ranked and fed to the support vector machine (SVM) and other supervised learning classifiers. In this study, we have considered five different classification problems (CPs), (two-class (CP-1), three-class (CP-2), four-class (CP-3), five-class (CP-4) and six-class (CP-5)). The proposed system yielded accuracies of 98.3%, 93.9%, 92.1%, 91.7%, and 91.5% for CP-1 to CP-5, respectively, using 10-fold cross validation (CV) technique.

The lifting factorization of 2D 4-channel nonseparable wavelet transforms

One-dimensional (1D) wavelet transform was lifted successfully using the division with remainder of univariate Laurent polynomials. However, division with remainder does not exist in the case of a bivariate polynomial. Thus, it makes sense that the polyphase matrix of a two-dimensional (2D) nonseparable wavelet transform cannot be decomposed into the lifting format using the same solution as that of the 1D wavelet transform. In this research, we present a new lifting factorization method of two-dimensional four-channel (2D 4-channel) nonseparable wavelet filter banks. According to the uniform constructing format of high-dimensional multivariate wavelet filter banks, the general form of 2D 4-channel nonseparable wavelet filter bank is given. With these filter banks, the polyphase matrix of 2D 4-channel nonseparable wavelet transform is found and proven. Then, we present the lifting factorization of the polyphase matrix and some examples are demonstrated in the factorization procedures. Finally, the lifting performances of the proposed method are analyzed. This lifting method factorizes the polyphase matrix into the product of a series of unit lower left triangular numerical matrices, unit upper right triangular numerical matrices, diagonal numerical matrices, and diagonal polynomial matrices whose elements on the diagonal line are 1, x, y, and xy. The original filter banks that all leading principal minors of the numerical matrices are not equal to zero can be factorized into lifting format. The proposed method transforms the lifting factorization of the polyphase matrix into the decompositions of the numerical matrices without Euclidian division. Thereby, only multiplication and addition operations are performed with no Fourier transformation involved. When compared with the lifting method of the tensor product lifting wavelet transform and the contourlet transform, the proposed lifting method can extract more edge information of images. The computational complexity of the original 2D 4-channel nonseparable wavelet transform for image decomposition is N+1 times as much as that of the proposed lifting factorization method and the original wavelet transform is accelerated. Furthermore, the proposed lifting factorization method is faster than the conventional 2D 4-channel nonseparable wavelet transform based on Fourier transformation theory and convolution operation when the size of each filter in the latter is greater than 4(N+1). The proposed lifting factorization has better sparsity than that of its original 2D 4-channel nonseparable wavelet transform and other typical 2D 4-channel nonseparable wavelet transforms.

Gait Recognition by Cross Wavelet Transform and Graph Model

In this paper, a multi-view gait based human recognition system using the fusion of two kinds of features is proposed. We use cross wavelet transform to extract dynamic feature and bipartite graph model to extract static feature which are coefficients of quadrature mirror filter U+0028 QMF U+0029-graph wavelet filter bank. Feature fusion is done after normalization. For normalization of features, min-max rule is used and mean-variance method is used to find weights for normalized features. Euclidean distance between each feature vector and center of the cluster which is obtained by k-means clustering is used as similarity measure in Bayesian framework. Experiments performed on widely used CASIA B gait database show that, the fusion of these two feature sets preserve discriminant information. We report 99.90 U+0025 average recognition rate.

Consumption prediction of bearing spare parts based on a hybrid model

Aiming at improving the accuracy of consumption prediction, a hybrid model was constructed, which designs an empirical wavelet filter bank to remove noise factors in original data. Besides the value prediction, the EWT-PGPR model can also give a certain credible interval, which effectively improves the practicability of the model.