Wavelet Basis Research Articles

Intelligent aerodynamic identification method based on wavelet transform and deep learning

Abstract Wind tunnel force testing is particularly crucial for the aerodynamic characteristics of hypersonic vehicles, and the intelligent and high-precision aerodynamic identification technology serves as the key supporting technology. Due to the short effective test time of the pulse combustion wind tunnel, the inertial force vibration generated by the force measurement system is difficult to be attenuated completely at the start of the wind tunnel. At the same time, there are many interference signals in the output signal during the test, which makes it difficult to achieve high-precision aerodynamic load identification. Therefore, in order to eliminate the influence of interference signals on aerodynamic identification accuracy and obtain accurate aerodynamic loads, this paper introduces an intelligent aerodynamic identification method based on wavelet transform and deep learning. Firstly, meyer wavelet is selected as the wavelet basis, and signal processing is performed on the output signal through wavelet transform to eliminate interference signals and improve signal quality. Then, through RNN-GRU network model to identify the load. The reliability of the method is verified by the rod balance test platform. The results show that the method can effectively reduce the influence of interference signal, and the relative error between the identified load and the real load is about 2%. At the same time, the identification results of the method are compared with those of the mean value method, which further verifies the accuracy of the proposed method.

Application of Fractional Modified Taylor Wavelets in the Dynamical Analysis of Fractional Electrical Circuits under Generalized Caputo Fractional Derivative

Abstract This study examines the application of fractional calculus in the analysis and modeling of electrical circuits of fractional order, highlighting its potential to explain the behaviour of complex electrical circuits accurately. In the domain of electrical circuits, fractional differential equations are employed in the analysis and simulation of systems that consist of resistors, capacitors and inductors. In the present paper, a novel approach utilizing fractional order modified Taylor wavelets is implemented to solve the fractional model of RL, LC, RC and RLC electrical circuits under generalized Caputo fractional derivative which offers precise and flexible modeling of non-locality and hereditary characteristics in complex systems. Furthermore, an additional parameter $\sigma$ (time scale parameter) is incorporated in fractional circuit dynamics to maintain the physical dimensionality. The considered wavelets with the collocation technique offer an efficient solution by converting the fractional model of electrical circuits into a set of algebraic equations which are further solved by using the Newton iteration method. Moreover, this study discusses the significance of Ulam-Hyers stability, emphasizing its role in ensuring stable and reliable circuit performance. The impact of fractional order on the dynamics of the electric circuit model is presented by tables and graphs. The approximate solutions obtained by the proposed method are well comparable with exact solutions and some other existing wavelet-based techniques. The residual errors are also evaluated under various model parameters for fractional orders. Furthermore, the graphs illustrate that the error progressively decreases as the number of wavelets basis increases.

Underwater acoustic target recognition based on multi-resolution wavelet feature deep learning

The application of underwater acoustic target recognition is extensive, exploration of marine resources, submarine vehicle detection and so on. However, traditional feature extraction methods are susceptible to the influence of complex marine environments and target operating conditions, leading to a significant reduction in the correct recognition rate. This paper introduces an underwater acoustic target recognition method that integrates multi-resolution wavelet features with deep learning algorithms, aiming to overcome the limitations of traditional time-frequency analysis techniques, which are unable to extract multiple signal characteristics simultaneously due to the trade-off between time and frequency resolution. Specifically, the essence of this technique is twofold: (1) Selecting suitable wavelet bases and decomposition levels to capture signal characteristics at different resolutions, effectively seizing the signal's local features within the time-frequency domain; (2) Fusing signal features across different resolutions to optimize the feature extraction process and enhance the distinguishability of target features. Finally, by applying deep learning algorithms to experimentally measured underwater acoustic data, the results demonstrate that this method can effectively enhance the accuracy of underwater acoustic target recognition.

Intelligent computing framework to analyze the transmission risk of COVID-19: Meyer wavelet artificial neural networks

The optimum control methods for the epidemiology of the COVID-19 model are acknowledged using a novel advanced intelligent computing infrastructure that joins artificial neural networks with unsupervised learning-based optimizers i.e., Genetic Algorithms (GA) and sequential quadratic programming (SQP). Unsupervised learning strategy is provided which depends on the wavelet basis's sequential deconstruction of stochastic data. The weights or selection values of neural networks are utilizing cumulative algorithms of Meyer wavelet artificial neural networks (MWANNs) optimized with global search Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP), referred to as MWANNs-GA-SQP and the design technique is utilized to determine the COVID-19 model for five different scenarios employing different step sizes and input intervals. The findings of this research article examined that in order to minimize the total disease transmission at the lowest cost and complexity, safety, focused medical care, and exterior sterilization methods applicability. The provided data is validated through various graphical simulations, which surely authenticate the effectiveness and robustness of the proposed solver. The suggested solver, MWANNs-GA-SQP, is tested in a variety of circumstances to examine that how reliable, safe, and tolerant. Using the proposed MWANNs hubristic intelligent approach, an objective optimization function is created in feed forward neural networking to minimize the mean square error. An investigation of the hybrid GA-SQP is used to confirm the accuracy and dependability of the MWANNs model results. Mean absolute graphs have been constructed to assess the integrity and efficiency of the proposed methodology. The accuracy and reliability of the suggested method are demonstrated by constantly achieving maximum variables of analytical assessment criteria computed for a large appropriate variety of distinct trials.

A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection-diffusion problems

In this paper, the authors used wavelet-based Galerkin finite element technique constructed with Iweobodo-Mamadu-Njoseh wavelet as the basis function, for the numerical solution of time-fractional advection-diffusion equations. To achieve this, the authors used the Iweobodo-Mamadu-Njoseh wavelet as well as fractional calculus, wavelet and wavelet transform, and the Galerkin finite element technique. Also, time and space discretization in relation to the finite element technique were considered, followed by the steps in implementing numerical solutions to TFADE with the new technique. The new technique was considered in seeking numerical solutions of some Caputo type TFADE test problems, and the resulting numerical evidence displayed the effectiveness and accuracy of the method as the results obtained with the new method converged at a good pace to the exact solutions. The results obtained at different fractional order were also compared and the resulting evidence showed that at certain fractional value the convergence behavior displayed slight differences. Every numerical computation was done with the use of MAPLE 18 software.

WPConvNet: An Interpretable Wavelet Packet Kernel-Constrained Convolutional Network for Noise-Robust Fault Diagnosis.

Deep learning (DL) has present great diagnostic results in fault diagnosis field. However, the poor interpretability and noise robustness of DL-based methods are still the main factors limiting their wide application in industry. To address these issues, an interpretable wavelet packet kernel-constrained convolutional network (WPConvNet) is proposed for noise-robust fault diagnosis, which combines the feature extraction ability of wavelet bases and the learning ability of convolutional kernels together. First, the wavelet packet convolutional (WPConv) layer is proposed, and constraints are imposed to convolutional kernels, so that each convolution layer is a learnable discrete wavelet transform. Second, a soft threshold activation is proposed to reduce the noise component in feature maps, whose threshold is adaptively learned by estimating the standard deviation of noise. Third, we link the cascaded convolutional structure of convolutional neutral network (CNN) with wavelet packet decomposition and reconstruction using Mallat algorithm, which is interpretable in model architecture. Extensive experiments are carried out on two bearing fault datasets, and the results show that the proposed architecture outperforms other diagnosis models in terms of interpretability and noise robustness.

Fusion of Wavelet Features and Gabor Features for SVM-based Iris Verification

Iris verification now become increasingly prominent in biometric-based person verification systems. It has gained a significant role in biometric systems due to its stability, high uniqueness, contactless and non-invasive properties. Iris has more inherent distinctive features than other biometrics. Feature extraction of iris plays a crucial role in this system for accurate person verification. Using the feature extraction process, unique iris features like textural patterns, crypts, and furrows of iris are extracted. In our study, we did a fusion of Discrete Wavelet Transform (DWT) features with multiple wavelet bases (db4, haar, coif3, and sym4) and Gabor features, which contain a good amount of textural and localized information. Fusion here indicates the concatenation of the extracted features using the above techniques. In this work, we studied this method on the full iris only so that a maximum number of features can be extracted. This combined approach yielded a significant 112 number of features. The extracted features are then verified using a support vector machine (SVM) classifier based on radial basis function (RBF) kernel with training vs testing split ratios of 8:2, 6:4, 4:6 and 2:8. In this study, we achieved the highest overall verification accuracy of 95.9% with training vs testing split ratio of 8:2. For other training vs testing split ratios of 6:4, 4:6 and 2:8 we achieved overall verification accuracies of 91.4%, 93.2% and 91.2% respectively. We got an overall verification accuracy of 92.9%, considering training vs testing ratios of 8:2, 6:4, 4:6 and 2:8.

Deep Learning-Based Nonparametric Identification and Path Planning for Autonomous Underwater Vehicles

As the nonlinear and coupling characteristics of autonomous underwater vehicles (AUVs) are the challenges for motion modeling, the nonparametric identification method is proposed based on dung beetle optimization (DBO) and deep temporal convolutional networks (DTCNs). First, the improved wavelet threshold is utilized to select the optimal threshold and wavelet basis functions, and the raw model test data are denoising. Second, the bidirectional temporal convolutional networks, the bidirectional gated recurrent unit, and the attention mechanism are used to achieve the nonlinear nonparametric model of the AUV motion. And the hyperparameters are optimized by the DBO. Finally, the lazy-search-based path planning and the line-of-sight-based path following control are used for the proposed AUV model. The simulation shows that the prediction accuracy of the DBO-DTCN is better than other artificial intelligence methods and mechanical models, and the path following of AUV is feasible. The methods proposed in this paper can provide an effective strategy for AUV modeling, searching, and rescue cruising.

Study on the detection of power line operation anomalies in the Hexi Corridor based on multi-scale filtering of BeiDou satellite signals

In the artificial intelligence detection of power line anomalies, the identification effect is determined by the positioning process of two-dimensional map, which is also a difficult point in this field Therefore, this paper proposes a method to detect the abnormal operation of power lines in Hexi Corridor based on multi-scale filtering of Beidou satellite signals. Multi-scale processing is carried out by wavelet transform to obtain multiple wavelet basis functions of different scales. On this basis, a two-dimensional time–frequency diagram is drawn according to the results of continuous wavelet transform. The adaptive multi-time frequency entropy method is selected to divide the two-dimensional time–frequency map into multiple layers and scales, and the adaptive multi-scale time–frequency entropy of the time–frequency plane is calculated. After smoothing the obtained power line position signal by S-G filtering method, the power line position signal of Hexi Corridor is obtained by GPS/ Beidou dual-mode satellite positioning system, and the positioning signal is optimized by using the positioning mechanism of multiple receiving stations. Realize the abnormal operation detection of power lines in Hexi Corridor. The experimental results show that this method can obtain more accurate positioning signals, and the geometric accuracy factor GDOP fluctuates in the range of 0 ∼ 2. The unsmooth signal can be effectively removed; The maximum error result of abnormal position detection is 1.22kn；; At the same time, the abnormal displacement section of the line can be determined.

Compressing and Recovering Short-Range MEMS-Based LiDAR Point Clouds Based on Adaptive Clustered Compressive Sensing and Application to 3D Rock Fragment Surface Point Clouds.

Short-range MEMS-based (Micro Electronical Mechanical System) LiDAR provides precise point cloud datasets for rock fragment surfaces. However, there is more vibrational noise in MEMS-based LiDAR signals, which cannot guarantee that the reconstructed point cloud data are not distorted with a high compression ratio. Many studies have illustrated that wavelet-based clustered compressive sensing can improve reconstruction precision. The k-means clustering algorithm can be conveniently employed to obtain clusters; however, estimating a meaningful k value (i.e., the number of clusters) is challenging. An excessive quantity of clusters is not necessary for dense point clouds, as this leads to elevated consumption of memory and CPU resources. For sparser point clouds, fewer clusters lead to more distortions, while excessive clusters lead to more voids in reconstructed point clouds. This study proposes a local clustering method to determine a number of clusters closer to the actual number based on GMM (Gaussian Mixture Model) observation distances and density peaks. Experimental results illustrate that the estimated number of clusters is closer to the actual number in four datasets from the KEEL public repository. In point cloud compression and recovery experiments, our proposed approach compresses and recovers the Bunny and Armadillo datasets in the Stanford 3D repository; the experimental results illustrate that our proposed approach improves reconstructed point clouds' geometry and curvature similarity. Furthermore, the geometric similarity increases to 0.9 above in our complete rock fragment surface datasets after selecting a better wavelet basis for each dimension of MEMS-based LiDAR signals. In both experiments, the sparsity of signals was 0.8 and the sampling ratio was 0.4. Finally, a rock outcrop point cloud data experiment is utilized to verify that the proposed approach is applicable for large-scale research objects. All of our experiments illustrate that the proposed adaptive clustered compressive sensing approach can better reconstruct MEMS-based LiDAR point clouds with a lower sampling ratio.

A fault diagnosis method for analog circuits based on EEMD-PSO-SVM

Analog circuit is an crucial component of electronic equipment, and the ability to diagnose its fault state quickly and accurately is essential for ensuring the safety and reliability of these electronic equipment. This paper addresses the problems of low diagnostic accuracy and the difficulties associated with model parameter selection in traditional fault diagnosis methods, particularly when dealing with nonlinear and non-stationary fault signals. A fault diagnosis method for analog circuits is proposed, which utilizes Ensemble Empirical Mode Decomposition (EEMD) for features extraction, the Maximum Information Coefficient algorithm (MIC) for features selection, and Particle Swarm Optimization (PSO) for optimizing Support Vector Machine (SVM) classification. Firstly, EEMD is used to adaptively decompose the fault signals in the circuit to extract multi-scale fault features. Secondly, the extracted features are quantitatively evaluated using the Pearson correlation coefficient and energy value analysis, leading to the construction of a fault feature vector is constructed. On this basis, the MIC feature selection algorithm is applied to further optimize the feature vector. Finally, an efficient fault classification model is developed by optimizing the hyperparameters of the SVM model using PSO. The simulation results show that the proposed method effectively overcome the problems of model complexity and low classification accuracy caused by improper selection of wavelet basis function. The accuracy of fault diagnosis and the efficiency of model training are significantly superior to those of traditional methods.

Finite Adelic Wavelet Bases and a Pseudodifferential Equation

Finite Adelic Wavelet Bases and a Pseudodifferential Equation

A novel simulation-assisted transfer method for bearing unknown fault diagnosis

Abstract Supervised data-driven bearing fault diagnosis methods rely on completed datasets of faults, which can be challenging for signals collected in real engineering. Recognizing unknown faults using a data-driven approach is particularly difficult, as purposefully modeling these faults is complex. To address this challenge, this study proposes a new simulation-assisted transfer bearing unknown fault diagnosis method for realizing unknown compound fault diagnosis of rotating machinery. Firstly, finite element method is used to obtain the compound fault data that does not exist in the historical data, and wavelet packet transform is performed on the simulated and measured signals to enhance the detailed features of the signals. Then, a deep convolutional feature fusion network based on hybrid multi-wavelet spatial attention is constructed to fuse the time-frequency information processed by different wavelet bases. Finally, by integrating the concepts of intra-class splitting and transfer learning, the model is fine-tuned using simulation data to recognize unknown compound faults of rolling bearings. The method validates the simulated signals’ feasibility and the unknown faults’ diagnostic validity under the publicly available rolling bearings dataset. Compared to the comparison methods, the method’s accuracy increased by 2.86%, 2.61%, 5.41%, 4.77%, and 7.07%, respectively.

Airborne transient electromagnetic imaging method based on wavelet neural network

The airborne transient electromagnetic method is a crucial technique for near-surface exploration in rugged terrains. In this study, we introduce a multi-input, single-output double-hidden wavelet neural network design for airborne transient electromagnetic pseudo-resistivity imaging. We construct uniform half-space, stratified stratum, and three-dimensional geoelectric models. By evaluating various performance indicators of neural networks that employ different wavelet basis functions as activation functions, we identify the most suitable wavelet basis functions. The quasi-resistivity is computed using both the wavelet neural network and the backpropagation neural network and then juxtaposed with traditional apparent resistivity. Our findings indicate that the wavelet neural network's quasi-resistivity aligns more closely with the resistivity of the real model. It is also more responsive to low resistivity anomalies than the conventional apparent resistivity translation algorithm. The wavelet approach moderates the undershoot or overshoot occurrences during abrupt stratum changes, offering a more accurate representation of subterranean electrical properties. When compared to the backpropagation neural network, the wavelet neural network provides a superior fit for the model, rendering a smoother quasi-resistivity depth curve. Therefore, it stands out as an improved method for pseudo-resistivity imaging. By processing survey data via the trained wavelet neural network, we find that the all-time apparent resistivity and quasi-resistivity align well with real-world situations. The wavelet neural network prominently showcases the low-resistance calculation results, offering a broader resistivity range. This clarity enhances anomaly detection, confirming the wavelet neural network's applicability and practicality for airborne transient electromagnetic imaging.

Research on the identification method based on energy distribution of adaptive WPD for railway tunnel lining void

ABSTRACT As the main disease of railway tunnels, void disease affects the safe operation of railways. The traditional detection technology recognition void relies on the intuitive characteristics of the signal, there are still problems such as poor void edge recognition capability and low intelligence level. To solve this problem, this study used Comsol software to establish a sound-solid coupling finite element model of the tunnel, extracted the acoustic signals of voids under various conditions, analysed the acoustic signal characteristics under different conditions and proposed the acoustic sensitive frequency band of tunnel lining void. The test model of Partial tunnel lining is established by the method of layering pouring. The wavelet packet algorithm is improved by the maximum cross correlation coefficient, the optimal wavelet basis decomposition algorithm is proposed. The layer number of the wavelet packet decomposition (WPD) algorithm was calculated based on the sensitive frequency band and the energy distribution of the sub-signal is obtained. Then, the energy distribution of the sensitive frequency band is used to estimate the void boundary. The experimental results show that the acoustic frequency band of the tunnel void mainly distributes in the range of 0–10,000 Hz and the sensitive frequency band of the void concentrated around 0–3000 Hz. According to the sampling frequency and the sensitive frequency band of the void, the sub-signal energy distribution of each layer is obtained. The energy distribution of sub-signal 1 has strong void boundary recognition ability. The research results will be beneficial to the damage detection and state assessment of tunnel lining.

Analysis of finite Haar wavelet transform and its implementation

In this paper, we give frame‐based finite Haar wavelet transform of ‐scale and ‐level (FHWT( ). The formulation of FHWT is based on the finite nonuniform wavelet transform (FNUWT), and the reconstruction is done using ‐frame reconstruction property. We formulate the FNUWT based on the technique of nonuniform sampling and study the reconstruction property of FNUWT in terms of the ‐frame reconstruction property. FHWT is a particular model of FNUWT based on critical sampling. Using the principles of ‐frame, we prove that FHWT( is a unitary operator. Also, our formulation enables us to define the finite Haar wavelet basis (FHWB) explicitly. In our study, we establish another variant of the fast Haar wavelet transform with varying rate of sampling, and with fast computations. Finally, we formulate the algorithms of finite Haar wavelet transform and its inverse through block implementations of ‐frame. It is observed that the number of computations involved in FHWT( ) is far less than the number of computations required in the fast Fourier transform.

Impact force identification for composite structures using adaptive wavelet-regularised deconvolution

Impact force identification (IFI) through deconvolution methods from measured structural responses poses a challenge due to the ill-posed nature of the inversion problem. Regularisation techniques, such as Tikhonov, sparse, and wavelet regularisation, offer potential solutions to mitigate the ill-posedness. However, determining suitable regularisation parameters is time-consuming. This study presents an adaptive wavelet-regularised time-domain deconvolution method for efficient IFI, based on wavelet transform and multi-resolution analysis. By analysing impact sensor signals using wavelets, adaptive impact windows covering the entire impact duration are generated, reducing signal length for deconvolution. Multi-resolution analysis of sensor signals enables identification of wavelet bases for the multi-resolution representation of impact force history. Regularisation is achieved by filtering out insignificant wavelet bases based on their energy contributions. Validation is performed through experiments involving small-mass hammer and large-mass drop tower impacts, comparing against various deconvolution methods. Results demonstrate the superior computational efficiency and comparable accuracy of the proposed adaptive method in IFI across different time windows. Notably, accurate force deconvolution for large-mass impacts confirms the effectiveness of the deconvolution methods for IFI, particularly when the structure undergoes significant local deformation.

Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative

In the present paper, we consider an effective computational method to analyze a coupled dynamical system with Caputo–Fabrizio fractional derivative. The method is based on expanding the approximate solution into a symmetry Haar wavelet basis. The Haar wavelet coefficients are obtained by using the collocation points to solve an algebraic system of equations in mathematical physics. The error analysis of this method is characterized by a good convergence rate. Finally, some numerical examples are presented to prove the accuracy and effectiveness of this method.

Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method.

WBUN: an interpretable convolutional neural network with wavelet basis unit embedded for fault diagnosis

Convolutional Neural Network (CNN) is extensively applied in mechanical system fault diagnosis. However, the absence of transparent decision mechanisms in CNNs hinders credibility. To address these challenges, this paper proposes an interpretable wavelet basis unit convolutional network (WBUN). This network incorporates meticulously designed wavelet basis unit (WBU) functions into convolutional layer, creating the interpretable wavelet basis unit convolutional (WBUConv) layer. Convolutional kernels with clear physical significance enable the WBUConv layer to extract fault-related features in both time and frequency domains, enhancing diagnostic performance, and interpreting the CNN’s attention frequency along with the convolutional kernel’s training outcomes. In this paper, three WBU functions are designed to construct the corresponding WBUNs, and their effectiveness and interpretability are verified through three sets of mechanical fault diagnosis experiments. Meanwhile, experimental results demonstrate the WBUConv layer’s remarkable advantages in noise robustness, convergence speed, and strong generalization ability.