Adaptive Wavelet Research Articles

Incipient Gear Fault Detection Using Adaptive Impulsive Wavelet Filter Based on Spectral Negentropy

Adaptive wavelet filtering is a very important fault feature extraction method in the domain of condition monitoring; however, owing to the time-consuming computation and difficulty of choosing criteria used to represent incipient faults, the engineering applications are limited to some extent. To detect incipient gear faults at a fast speed, a new criterion is proposed to optimize the parameters of the modified impulsive wavelet for constructing an optimal wavelet filter to detect impulsive gear faults. First, a new criterion based on spectral negentropy is proposed. Then, a novel search strategy is applied to optimize the parameters of the impulsive wavelet based on the new criterion. Finally, envelope spectral analysis is applied to determine the incipient fault characteristic frequency. Both the simulation and experimental validation demonstrated the superiority of the proposed approach.

SQNN: A Spike-wave index Quantification Neural Network with a pre-labeling algorithm for epileptiform activity identification and quantification in children.

Electrical status epilepticus during slow sleep (ESES) is a phenomenon identified by strong activation of epileptiform activity in the electroencephalogram (EEG) during sleep. For children disturbed by ESES, spike-wave index (SWI) is defined to quantify the epileptiform activity in the EEG during sleep. Accurate SWI quantification is important for clinical diagnosis and prognosis. To quantify SWI automatically, a deep learning method is proposed in this paper. Firstly, a pre-labeling algorithm (PreLA) composed of the adaptive wavelet enhanced decomposition and a slow-wave discrimination rule is designed to efficiently label the EEG signal. It enables the collection of large-scale EEG dataset with fine-grained labels. Then, an SWI Quantification Neural Network (SQNN) is constructed to accurately classify each sample point as normal or abnormal and to identify the abnormal events. SWI can be calculated automatically based on the total duration of abnormalities and the length of the signal. Experiments on two datasets demonstrate that the PreLA is effective and robust for labeling the EEG data and the SQNN accurately and reliably quantifies SWI without using any thresholds. The average estimation error of SWI is 3.12%, indicating that our method is more accurate and robust than experts and previous related works. The processing speed of SQNN is 100 times faster than that of experts. Deep learning provides a novel approach to automatic SWI quantification and PreLA provides an easy way to label the EEG data with ESES syndromes. The results of the experiments indicate that the proposed method has a high potential for clinical diagnosis and prognosis of epilepsy in children.

Improving the sensitivity of early rub detection in rotating machines with an adaptive orthogonal filter

The early detection of rotor-casing rub helps to prevent permanent damage or catastrophic failure, saves maintenance costs and decreases the downtime of rotating machines. In aeroderivative gas turbines, rub detection is possible only with the use of casing sensors such as accelerometers. In previous works, the Wavelet Synchrosqueezed Transform (WSST) was proposed for very early detection of rub in aeroderivative gas turbines with accelerometer signals. In a quest for even better detection performances, this manuscript aims to design adaptive orthogonal wavelet filter banks for optimal rub feature separation from accelerometer signals. The outputs of the adaptive filter bank show improved feature separation between the no-rub and the rub regimes within a validation set from an experimental machine. Ultimately, it is demonstrated that the combination of the WSST and the adaptive orthogonal filter outperforms other methodologies for the early detection of rotor-casing rub with accelerometer signals, also when white noise is present in the data.

SQNN: a spike-wave index quantification neural network with a pre-labeling algorithm for epileptiform activity identification and quantification in children

Objective. Electrical status epilepticus during slow sleep (ESES) is a phenomenon identified by strong activation of epileptiform activity in the electroencephalogram (EEG) during sleep. For children disturbed by ESES, spike-wave index (SWI) is defined to quantify the epileptiform activity in the EEG during sleep. Accurate SWI quantification is important for clinical diagnosis and prognosis. To quantify SWI automatically, a deep learning method is proposed in this paper. Approach. Firstly, a pre-labeling algorithm (PreLA) composed of the adaptive wavelet enhanced decomposition and a slow-wave discrimination rule is designed to efficiently label the EEG signal. It enables the collection of large-scale EEG dataset with fine-grained labels. Then, an SWI quantification neural network (SQNN) is constructed to accurately classify each sample point as normal or abnormal and to identify the abnormal events. SWI can be calculated automatically based on the total duration of abnormalities and the length of the signal. Main results. Experiments on two datasets demonstrate that the PreLA is effective and robust for labeling the EEG data and the SQNN accurately and reliably quantifies SWI without using any thresholds. The average estimation error of SWI is 3.12%, indicating that our method is more accurate and robust than experts and previous related works. The processing speed of SQNN is 100 times faster than that of experts. Significance. Deep learning provides a novel approach to automatic SWI quantification and PreLA provides an easy way to label the EEG data with ESES syndromes. The results of the experiments indicate that the proposed method has a high potential for clinical diagnosis and prognosis of epilepsy in children.

Design and Analysis of a novel 2D Edge Preservation Adaptive Wavelet Anisotropic Bilateral Filter for Image Restoration of Palm Leaf Manuscripts

Design and Analysis of a novel 2D Edge Preservation Adaptive Wavelet Anisotropic Bilateral Filter for Image Restoration of Palm Leaf Manuscripts

Period-assisted adaptive parameterized wavelet dictionary and its sparse representation for periodic transient features of rolling bearing faults

Accurate extraction of fault-induced periodic transient features from noise interference containing harmonics and large-amplitude random impulses is a key to fault detection of rolling bearings. Therefore, this paper proposes a sparse representation method based on a period-assisted adaptive parameterized wavelet dictionary to extract periodic transient features of rolling bearing faults. First, considering the influence of noise and vibration transmission paths on impulse response generated by bearing faults, an asymmetric bilateral exponential attenuation wavelet is constructed according to a vibration model of impulse response, which can be more flexible to match impulse features in vibration signals. Meanwhile, an adaptive correlation filtering method and a benchmark atom obtained by a standard K-SVD are utilized to determine optimal parameters of the constructed wavelet, which is less disturbed by noise and harmonics. On this basis, by introducing a priori knowledge of an impulse period, a method of constructing a period-assisted parameterized wavelet dictionary is proposed to get a dictionary that is suitable to characterize periodic transient features. Finally, a periodic transient signal is recovered using the constructed dictionary and the orthogonal matching pursuit (OMP) algorithm. Comparisons with the K-SVD, a sparse representation method based on a db8 wavelet dictionary, spectral correlation and spectral kurtosis demonstrate that the proposed method can more accurately extract periodic transient features in simulated and experimental vibration signals, which provides an effective analysis tool for rolling bearing fault detection.

Simulation of time-series groundwater parameters using a hybrid metaheuristic neuro-fuzzy model.

The estimation of qualitative and quantitative groundwater parameters is an essential task. In this regard, artificial intelligence (AI) techniques are extensively utilized as accurate, trustworthy, and cost-effective tools. In the present paper, two hybrid neuro-fuzzy models are implemented for the prediction of groundwater level (GWL) fluctuations, as well as variations of Cl - and HCO3 - in the Karnachi well, Kermanshah, Iran in monthly intervals within a 13-year period from 2005 to 2018. In order to develop AI models, the adaptive neuro-fuzzy inference system (ANFIS), firefly algorithm (FA), and wavelet transform (WT) are used. In other words, two hybrid models including ANFIS-FA (adaptive neuro-fuzzy inference system-firefly algorithm) and WANFIS-FA (wavelet-adaptive neuro-fuzzy inference system-firefly algorithm) are utilized for the estimation of the quantitative and qualitative parameters. Firstly, influencing lags of the time-series of the qualitative and quantitative parameters are identified using the autocorrelation function. Then, four and eight separate models are developed for the approximation of GWLs and qualitative parameters (i.e. Cl - and HCO3 -), respectively. It is worth to mention that about 75% of observed values are assigned to train the hybrid AI models, while the rest (i.e. 25%) to test them. Sensitivity analysis results reveal that the WANFIS-FA models display more acceptable performance than the ANFIS-FA ones. Also, the estimations of MAE, NSC, and SI for the simulation of HCO3 - by the superior model of the WANFIS-FA are obtained to be 0.040, 0.988, and 0.022, respectively. In addition, the lags (t-1), (t-2), (t-3), and (t-4) are ascertained as the most effective time-series lags for the estimation of Cl - .

Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms and cannot adapt to signals residing on graphs and tasks at hand. In this paper, we propose a novel class of graph neural networks that realizes graph filters with adaptive graph wavelets. Specifically, the adaptive graph wavelets are learned with neural network-parameterized lifting structures, where structure-aware attention-based lifting operations are developed to jointly consider graph structures and node features. We propose to lift based on diffusion wavelets to alleviate the structural information loss induced by partitioning non-bipartite graphs. By design, the locality and sparsity of the resulting wavelet transform as well as the scalability of the lifting structure are guaranteed. We further derive a soft-thresholding filtering operation by learning sparse graph representations in terms of the learned wavelets, yielding a localized, efficient, and scalable wavelet-based graph filters. To ensure that the learned graph representations are invariant to node permutations, a layer is employed at the input of the networks to reorder the nodes according to their local topology information. We evaluate the proposed networks in both node-level and graph-level representation learning tasks on benchmark citation and bioinformatics graph datasets. Extensive experiments demonstrate the superiority of the proposed networks over existing SGNNs in terms of accuracy, efficiency, and scalability.

Adaptive wavelet transform based on artificial fish swarm optimization and fuzzy C-means method for noisy image segmentation

Aiming at the problem that traditional fuzzy C-means (FCM) clustering algorithm is susceptible to noise in processing noisy images, a noisy image segmentation method based on FCM wavelet domain feature enhancement is proposed. Firstly, the noise image is decomposed by two-dimensional wavelet. Secondly, the edge enhancement of the approximate coefficient is carried out, and the artificial fish swarm (AFS) optimization algorithm is used to process the threshold value of the detail coefficient, and the processed coefficient is reconstructed by wavelet transform. Finally, the reconstructed image is segmented by FCM algorithm. Five typical gray-scale images are selected by adding Gaussian noise and Salt& pepper noise, respectively, and segmented by various methods. The peak signal-to-noise ratio (PSNR) and error rate (MR) of segmented images are used as performance indexes. Experimental results show that compared with traditional FCM clustering algorithm segmentation method, particle swarm optimization (PSO) segmentation method and other methods, the indexes of image segmentation by the proposed method is greatly improved. It can be seen that the proposed segmentation method retains the texture information of image edge well, and its anti-noise performance and segmentation performance are improved.

A novel method for UWB weak signal detection based on stochastic resonance and wavelet transform

Pulse ultra-wideband (UWB) signal is a transient pulse in time domain with very low power spectral density; In the long-distance communication, it is difficult to detect the low signal to noise ratio (SNR) pulse UWB signal submerged in strong noise. To solve the above problems, a novel adaptive stochastic resonance fusion wavelet transform method for UWB weak signal detection is proposed. Firstly, the adaptive optimization method which is based on the improved stochastic resonance potential well model is used to match the optimal parameters of the stochastic resonance (SR) system for the noisy signal, so that the noise energy can be transferred to the UWB signal and the signal amplification can be realized; Secondly, in view of the problem that SR method is insensitive to phase transient information and amplitude shift, wavelet transform is used to extract mutation information, so as to realize the accurate detection of UWB weak signal. The simulation results show that the proposed method can solve the problem that it is difficult to distinguish the change of signal state by using stochastic resonance method alone. Finally, two groups of actual signals with bandwidth of 10 MHz and 20 MHz are collected by the experimental system to test the effectiveness of the method.

Enhancement method of weak Lidar signal based on adaptive variational modal decomposition and wavelet threshold denoising

Aiming to identify and detect the weak signal of lidar, a cascade method of adaptive variational modal decomposition (VMD) and wavelet threshold (WT) denoising is proposed in this paper. Firstly, VMD is used to decompose the echo signal, and the criterion of adaptive mode selection is improved. Furthermore, the “db4” wavelet and soft threshold denoising method are used to process the denoised signal by AVMD. The optimal threshold value is obtained by minimizing Stein's unbiased risk estimator. In order to verify the superity of the proposed method, Bumps signal is employed in simulation. When the input signal-to-noise ratio (SNR) is −3dB, the SNR of proposed method can reach 7.8587 dB. Compared with three methods, the SNR of proposed method is the highest under different input SNRs. The real Lidar signal is recorded to be denoised. The root mean square errors of WT-db4, EMD-DT, SVD-WT and the proposed method are 0.0046, 0.0044, 0.0044 and 0.0043. Compared with three state-of-art denoising methods, the proposed denoising method can effectively eliminate the spike noise and fully retain the echo signal.

Adaptive multiple second-order synchrosqueezing wavelet transform and its application in wind turbine gearbox fault diagnosis

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing time-frequency (TF) analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated time-frequency representation (TFR), this paper proposes a new TFA method, namely adaptive multiple second-order synchrosqueezing wavelet transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical continuous wavelet transform, and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus adaptive wavelet transform is generated. Then, on the basis of the theoretical framework of synchrosqueezing transform and accurate instantaneous frequency estimation by the utilization of second-order local demodulation operator, adaptive second-order synchrosqueezing wavelet transform (AWSST2) is formed. Considering that the quality of actual TFA is greatly disturbed by noise components, through performing multiple synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

A BiLSTM hybrid model for ship roll multi-step forecasting based on decomposition and hyperparameter optimization

The forecasting of ship's roll motion is the key to ensuring the safety of ship surface operations and improving operations efficiency. A new hybrid multi-step forecasting model is proposed in this paper. The proposed model combines three methodologies, including adaptive empirical wavelet transform (EWT), multi-step forecasting under the multi-input multi-output (MIMO) strategy of bidirectional long short-term memory (BiLSTM) model, and hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) hyperparameter optimization. The three sets of ship roll datasets in the South China Sea are selected to verify the performance of the hybrid multi-step prediction model. In the end, the results of the research indicate that: (a) The proposed model has a superior prediction accuracy in multi-step prediction, taking dataset #1 as an example, the root mean square error (RMSE) of the prediction result is 0.0934°, the mean average error (MAE) is 0.0742°, and the mean absolute percentage error (MAPE) is 2.9878%; (b) The proposed hybrid multi-step forecasting model is suitable for different datasets and has strong robustness. Taking the 3-step prediction of dataset #1 to #3 as examples, the RMSEs of the proposed model are 0.0879°, 0.0742°, and 0.0991°, respectively.

Power quality disturbance classification under noisy conditions using adaptive wavelet threshold and DBN-ELM hybrid model

To solve the problems of noise interference and artificial feature extraction in power quality disturbance (PQD) classification, a new method combining adaptive wavelet threshold denoising and deep belief network fusion extreme learning machine (DBN-ELM) is proposed. Firstly, the noise content of the layer is determined by calculating the energy ratio of the wavelet coefficients of each layer, and an adaptive wavelet threshold is constructed based on the energy ratio to denoise the PQD signals. Secondly, the feature extraction capability of DBN is used to extract the feature from the PQD signals after denoising. Finally, a novel PQD classifier called DBN-ELM is constructed by integrating an ELM into a DBN, which avoids global fine-tuning of DBN and improves PQD classification efficiency. The simulation result and experimental verification show that the proposed method can effectively suppress PQD noise and performs well on DBN-ELM classification.

An adaptive wavelet collocation method for the optimal heat source problem

PurposeThis paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).Design/methodology/approachThe main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction.FindingsThis paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution.Originality/valueThe proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

Automated Image Super Resolution with the Aid of Activation Function Optimized Deep CNN and Adaptive Wavelet Lifting Approach

Diverse image super-resolution (SR) techniques have been implemented to reconstruct the high-resolution (HR) images from input images through lower spatial resolutions. However, the evaluation of the perceptual quality of SR images remains an important and complex research problem. This paper proposes a new image SR model with the intention of attaining maximum Peak Signal-to-Noise Ratio (PSNR). The conversion of low-resolution (LR) images from the HR images is performed by bicubic interpolation-based downsampling and upsampling. Then, the four sub-bands of LR and HR images are generated by the novel Adaptive Wavelet Lifting approach, in which the filter modes are optimized using the proposed SA-CBO. From this technique, LR wavelet sub-bands (LRSB) for LR images and HR wavelet sub-bands (HRSB) for HR images are formed. With the help of the LRSB and HRSB images, the residual images are formed by the adoption of the optimized Activation function and optimized hidden neurons in a deep convolutional neural network (CNN). The improvement in both the adaptive wavelet lifting approach and deep CNN is made by the self-adaptive-colliding bodies optimization (SA-CBO). Finally, the inverse adaptive wavelet lifting approach is used to produce the final SR image. Experimental results on publicly available SR image quality databases confirm the effectiveness and generalization ability of the proposed method compared with the traditional image quality assessment algorithms.

A Novel Approach for Image Denoising and Performance Analysis using SGO and APSO

Image denoising is essential to extract the information contained in an image without errors. A technique of using both wavelets and evolutionary computing tools is proposed to denoise and to improve the image quality. An adaptive thresholding-based wavelet denoising technique in the threshold function is coordinated by novel social group optimization (SGO) and accelerated particle swarm optimization (APSO) is proposed. The simulation oriented experimentation is taken out employing MATLAB and the analysis is carried out using the image property metrics similar to peak signal to noise ratio (PSNR), mean square error (MSE) and other structural similarity index metrics (SSIM).

Crack Growth Signal Processing Approach Combining Wavelet Threshold Denoising and Variable Amplitude DCPD Technique

The direct current potential drop (DCPD) method is widely used in laboratory environments to monitor the crack initiation and propagation of specimens. In this study, an anti-interference signal processing approach, combining wavelet threshold denoising and a variable current amplitude DCPD signal synthesis technique, was proposed. Adaptive wavelet threshold denoising using Stein’s unbiased risk estimate was applied to the main potential drop signal and the reference potential signal under two different current amplitudes to reduce the interference caused by noise. Thereafter, noise-reduced signals were synthesized to eliminate the time-varying thermal electromotive force. The multiplicative interference signal was eliminated by normalizing the main potential drop signal and the reference potential drop signal. This signal processing approach was applied to the crack growth monitoring data of 316 L stainless steel compact tension specimens in a laboratory environment, and the signal processing results of static cracks and propagation cracks under different load conditions were analyzed. The results showed that the proposed approach can significantly improve the signal-to-noise ratio as well as the accuracy and resolution of the crack growth measurement.

An adaptive wavelet optimized finite difference B-spline polynomial chaos method for random partial differential equations

In this paper, wavelet optimized finite difference B-spline polynomial chaos method is proposed for solving stochastic partial differential equations. The generalized polynomial chaos is applied by considering linear B-spline wavelet basis. Then, stochastic Galerkin projection is executed for evaluating the deterministic coefficients of the generalized polynomial chaos. In the next step, the system of equations is discretized by using Crank-–Nicolson scheme for time integration and for approximating the differential operators, central finite difference matrices are considered. An adaptive grid is generated using the linear B-spline generalized polynomial chaos for optimizing the numerical solution. The method is then tested on three problems namely heat equation with uncertain initial conditions, Burger’s equation with random initial conditions and Burger’s equation with random viscosity as well as uncertain initial conditions. For the three test problems, grid modifications are displayed by taking periodic boundary conditions into consideration. Mean and standard deviation are plotted for each test problem. Moreover, for the third test problem, computational time comparison is performed by computing CPU time taken by the proposed method and the CPU time taken by the finite difference method on a uniform grid.

A Novel Noise Reduction Method of UAV Magnetic Survey Data Based on CEEMDAN, Permutation Entropy, Correlation Coefficient and Wavelet Threshold Denoising

Despite the increased attention that has been given to the unmanned aerial vehicle (UAV)-based magnetic survey systems in the past decade, the processing of UAV magnetic data is still a tough task. In this paper, we propose a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), permutation entropy (PE), correlation coefficient and wavelet threshold denoising. The original signal is first decomposed into several intrinsic mode functions (IMFs) by CEEMDAN, and the PE of each IMF is calculated. Second, IMFs are divided into four categories according to the quartiles of PE, namely, noise IMFs, noise-dominant IMFs, signal-dominant IMFs, and signal IMFs. Then the noise IMFs are removed, and correlation coefficients are used to identify the real signal-dominant IMFs. Finally, the wavelet threshold denoising is applied to the real signal-dominant IMFs, the denoised signal can be obtained by combining the signal IMFs and the denoised IMFs. Both synthetic and field experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can eliminate the interference to a great extent, which lays a foundation for the further interpretation of UAV magnetic data.