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The purpose of this paper is to provide a fault diagnosis method for rolling bearings. Rolling bearings are widely used in industrial appliances, and their fault diagnosis is of great importance and has drawn more and more attention. Based on the common failure mechanism of failure modes of rolling bearings, this paper proposes a novel compound data classification method based on the discrete wavelet transform and the support vector machine (SVM) and applies it in the fault diagnosis of rolling bearings.

Vibration signal contains large quantity of information of bearing status and this paper uses various types of wavelet base functions to perform discrete wavelet transform of vibration and denoise. Feature vectors are constructed based on several time-domain indices of the denoised signal. SVM is then used to perform classification and fault diagnosis. Then the optimal wavelet base function is determined based on the diagnosis accuracy.

Experiments of fault diagnosis of rolling bearings are carried out and wavelet functions in several wavelet families were tested. The results show that the SVM classifier with the db4 wavelet base function in the db wavelet family has the best fault diagnosis accuracy.

This method provides a practical candidate for the fault diagnosis of rolling bearings in the industrial applications.

This research paper aims to discuss the effects of exchange rates on interest rates by using wavelet network methodology, which is a combination of wavelets and neural networks.

The paper employs wavelet networks to analyse the relationships between the financial time series. Empirically, the research examines the effects of foreign exchanges on the interest rates in Turkish financial markets by using daily USD/TRY rates and interest rates in Turkish Lira (TRY).

The results indicate that the wavelet network model is the most successful methodology among the alternatives such as Hodrick‐Prescott filter, feed‐forward neural network, wavelet causality, and wavelet correlation analysis in capturing the non‐linear dynamics between the selected time series.

The research results have both methodological and practical originality. On the theoretical side, the wavelet network is superior in modelling the causal linkages of the financial time series. For practical aims, on the other hand, the results show that the level of the effects of the exchange rates on the interest rates varies on the time‐scale used. Wavelet networks shows that the causality relationship is strong in the short run, while the effect decreases in the mid‐run.

This paper aims to explore a new wavelet adaptive threshold de-noising method to resolve the shortcomings of wavelet hard-threshold method and wavelet soft-threshold method, which are usually used in gear fault diagnosis.

A new threshold function and a new determined method of threshold for each layer are proposed. The principle and the implementation of the algorithm are given. The simulated signal and the measured gear fault signal are analyzed, and the obtained results are compared with those from wavelet soft-threshold method, wavelet hard-threshold method and wavelet modulus maximum method.

The presented wavelet adaptive threshold method overcomes the defects of the traditional wavelet threshold method, and it can effectively eliminate the noise hidden in the gear fault signal at different decomposition scales. It provides more accurate information for the further fault diagnosis.

A new threshold function is adopted and the multi-resolution unbiased risk estimation is used to determine the adaptive threshold, which overcomes the defect of the traditional wavelet method.

We describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements and multigrid. The wavelet method, however, offers several advantages over traditional methods. Wavelets have the ability to represent functions at different levels of resolution, thereby providing a logical means of developing a hierarchy of solutions. Furthermore, compactly supported wavelets (such as those due to Daubechies) are localized in space, which means that the solution can be refined in regions of high gradient, e.g. stress concentrations, without having to regenerate the mesh for the entire problem. To demonstrate the wavelet technique, we consider Poisson's equation in two dimensions. By comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed. Dirichlet boundary conditions are then imposed, using the capacitance matrix method described by Proskurowski and Widlund and others. The convergence of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions. Preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method.

Fabric defects detection is vital in the automation of textile industry. The purpose of this paper is to develop and implement a new fabric defects detection method based on adaptive wavelet.

Fabric defects can be regarded as the abrupt features of textile images with uniform background textures. Wavelets have compact support and can represent these textures. When there is an abrupt feature existed, the response is totally different with the response of the background textures, so wavelets can detect these abrupt features. This method designs the appropriate wavelet bases for different fabric images adaptively. The defects can be detected accurately.

The proposed method achieves accurate detection of fabric defects. The experimental results suggest that the approach is effective.

This paper develops an appropriate method to design wavelet filter coefficients for detecting fabric defects, which is called adaptive wavelet. And it is helpful to realize the automation of textile industry.

Provides an introduction into wavelets and illustrates their application with two examples. The wavelet transform provides the analyst with a scaleable time‐frequency representation of the signal, which may uncover details not evidenced by conventional signal processing techniques. The signals used in this paper are Doppler ultrasound recordings of blood flow velocity taken from the internal carotid artery and the femoral artery. Shows how wavelets can be used as an alternative signal processing tool to the short time Fourier transform for the extraction of the time‐frequency distribution of Doppler ultrasound signals. Implements wavelet‐based adaptive filtering for the extraction of maximum blood velocity envelopes in the post processing of Doppler signals.

This research unfolds a holistic association between economic policy uncertainty (EPU) and three important markets (oil, stock and gold) in the Indian context. To do same, the current study uses the monthly dataset of each variable spanning from November 2005 to March 2022.

The authors have portrayed the wavelet-based coherence, correlation and covariance plots to explore the interaction between EPU and markets' behavior. Then, a wavelet-based quantile on quantile regression model and wavelet-based Granger causality has been applied to examine the cause-and-effect relation and causality between the EPU and markets.

The authors’ findings report that the Indian crude oil buyers do not need to consider Indian EPU while negotiating the oil deals in the short term and medium term. However, in case of the long-term persistence of uncertainty, it becomes difficult for a buyer to negotiate oil deals at cheap rates. EPU causes unfavorable fluctuation in the stock market because macroeconomic decisions have a substantial impact on it. The authors have also found that gold is a gauge for economic imbalances and an accurate observer of inflation resulting from uncertainty, showing a safe haven attribute.

The authors’ work is original in two aspects. First, their study solely focused on the Indian economy to investigate the impact and causal power of Indian EPU on three major components of the Indian economy: oil, stock and gold. Second, they will provide their findings after analyzing data at a very microlevel using a wavelet-based quantile on quantile and wavelet-based Granger causality.

In this article, the authors aims to introduce a novel Vieta–Lucas wavelets method by generalizing the Vieta–Lucas polynomials for the numerical solutions of fractional linear and non-linear delay differential equations on semi-infinite interval.

The authors have worked on the development of the operational matrices for the Vieta–Lucas wavelets and their Riemann–Liouville fractional integral, and these matrices are successfully utilized for the solution of fractional linear and non-linear delay differential equations on semi-infinite interval. The method which authors have introduced in the current paper utilizes the operational matrices of Vieta–Lucas wavelets to converts the fractional delay differential equations (FDDEs) into a system of algebraic equations. For non-linear FDDE, the authors utilize the quasilinearization technique in conjunction with the Vieta–Lucas wavelets method.

The purpose of utilizing the new operational matrices is to make the method more efficient, because the operational matrices contains many zero entries. Authors have worked out on both error and convergence analysis of the present method. Procedure of implementation for FDDE is also provided. Furthermore, numerical simulations are provided to illustrate the reliability and accuracy of the method.

Many engineers or scientist can utilize the present method for solving their ordinary or Caputo–fractional differential models. To the best of authors’ knowledge, the present work has not been used or introduced for the considered type of differential equations.

The presence of random noise as well as narrow band coherent noise makes the structural health monitoring a really challenging issue and to achieve efficient structural health assessment methodology, very good extraction of noise and analysis of the signals are essential. The purpose of this paper is to provide optimal noise filtering technique for Lamb waves in the diagnosis of structural singularities.

Filtration of time-frequency information of multimode Lamb waves through the noisy signal is investigated in the present analysis using matched filtering technique and wavelet denoising methods. Using Shannon’s entropy criterion, the optimal wavelet function is selected and verification is made via the analysis of root mean square error of filtered signal.

The authors propose wavelet matched filter method, a combination of the wavelet transform and matched filtering method, which can significantly improve the accuracy of the filtered signal and identify relatively small damage, especially in enormously noisy data. Correlation coefficient and root mean square error are additionally computed for performance evaluation of the filters.

The present study provides detailed information about various noise filtering methods and a first attempt to apply the combination of the different techniques in signal processing for the structural health monitoring application. A comparative study is performed using the statistical tool to know whether filtered signals obtained through three different methods are acceptable and practicable for guided wave application or not.

The traditional total variation (TV) models in wavelet domain use thresholding directly in coefficients selection and show that Gibbs' phenomenon exists. However, the nonzero coefficient index set selected by hard thresholding techniques may not be the best choice to obtain the least oscillatory reconstructions near edges. This paper aims to propose an image denoising method based on TV and grey theory in the wavelet domain to solve the defect of traditional methods.

In this paper, the authors divide wavelet into two parts: low frequency area and high frequency area; in different areas different methods are used. They apply grey theory in wavelet coefficient selection. The new algorithm gives a new method of wavelet coefficient selection, solves the nonzero coefficients sort, and achieves a good image denoising result while reducing the phenomenon of “Gibbs.”

The results show that the method proposed in this paper can distinguish between the information of image and noise accurately and also reduce the Gibbs artifacts. From the comparisons, the model proposed preserves the important information of the image very well and shows very good performance.

The proposed image denoising model introducing grey relation analysis in the wavelet coefficients selecting and modifying is original. The proposed model provides a viable tool to engineers for processing the image.