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The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices. Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems. The wavelet transformation part of the method can be added as a black box to existing BEM codes.

Numerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented. The results show that the proposed method is efficient for large problems.

Application of the proposed method is restricted to problems with number of DOF equal to an integer power of 2.

The novel algorithm to solve transformed algebraic linear equations uses NS‐form of the modified matrix, taking the advantage of the hierarchical nature of Multi‐Resolution Analysis (MRA) to decompose a parent system into descendant systems with reduced size. These smaller systems are then solved iteratively using generalized minimal residual method.

The purpose of this paper is to investigate the condition of insulation in high-voltage equipments using partial discharge (PD) measurements. It proposes the methods to eliminate several noises like white noise, random noise and discrete spectral interferences which severely pollutes the PD signals. The study aims to remove these noises from the PD signal effectively by preserving the signal features.

This paper employs fast Fourier transform, discrete wavelet transform and translational invariant wavelet transform (TIWT) for denoising the PD signals. The simulated damped exponential pulse and damped oscillatory pulse with low- and high-level noises and a measured PD signal are considered for this analysis. The conventional wavelet denoising approach is also improved by estimating the automated global optimum threshold value using genetic algorithm (GA). The statistical parameters are evaluated and compared. Among these methods, GA-based TIWT approach provides robustness and reduces computational complexity.

This paper provides effective condition monitoring of power apparatus using GA-based TIWT approach. This method provides the low value of mean square error, pulse amplitude distortion and also high reduction in noise level due to its robustness and reduced computational complexity. It suggests that this approach works well for both signals immersed in noise as well as for noise immersed in signals.

Because of the chosen PD signals, the research results may lack for multiple discharges. Therefore, researchers are encouraged to test the proposed propositions further.

The paper includes implication for the development of online testing for equipment analysis and diagnostics during normal operating condition. Corrective actions can be planned and implemented, resulting in reduced unscheduled downtime.

This PD-based analysis often present well in advance of insulation failure, asset managers can monitor it over time and make informed strategic decisions regarding the repair or replacement of the equipment. These predictive diagnostics help society to prioritize investments before an unexpected outage occurs.

This paper provides an enhanced study of condition monitoring of HV power apparatus by which life time of insulation can be increased by taking preventive measures.

The purpose of this paper is to examine the causal relationship between Chinese housing and stock markets. The authors discuss the three transmission mechanisms between the two markets: wealth effect, modern portfolio theory and credit-price effect. Moreover, the authors focus on the effects of inflation on the relationship between the two markets.

This paper uses wavelet analysis to test the housing and stock markets relationship both in the frequency domain and time domain.

The empirical results indicate that housing prices have a positive effect on stock prices, and these have the same effect on housing prices. Moreover, this positive effect means that stock prices have a wealth effect on housing prices and these have a credit-price effect on stock prices.

These results provide information to financial institutions and individual investors in China to assist them in constructing investment portfolios within these two asset markets.

The authors first use wavelet analysis to analyze Chinese housing and stock markets and to provide information both on the frequency domain and time domain. Moreover, the authors take the inflation factor as a control variable in the causal relationship between the housing and stock markets.

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.

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.

In real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).

In each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.

Resonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.

Proposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.

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.

Denoising of the vibration signal is crucial to identify a structure's damage. Based on noise frequency character, the “real” vibration signal can be gotten. The purpose of this paper is to propose a novel method for denoising a signal based on the wavelet transform.

The vibration signal with noise which can be collected by wireless network is decomposed by wavelet transform. In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal de‐noising with Gaussian noise.

A novel method has been described in his paper. Based on the relationship between vibration signal's character and noise frequency, the way to get rid of noise is combined wavelet transform with power spectral density.

In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal denoising with Gaussian noise.

This paper aims to examine the comovement among green bonds, energy commodities and stock market to determine the advantages of adding green bonds to a diversified portfolio.

Generic 1 Natural Gas and Energy Select SPDR Fund are used as proxies to measure energy commodities, bonds index of S&P Dow Jones and Bloomberg Barclays MSCI are used to represent green bonds and the New York Stock Exchange is considered to measure the stock market. Granger causality test, wavelet analysis and network analysis are applied to daily price for the select markets from August 26, 2014, to March 30, 2021.

Results from the Granger causality test indicate no causality between any pair of variables, while cross wavelet transform and wavelet coherence analysis confirm strong coherence at a high scale during the pandemic, validating comovement among the three asset classes. In addition, network analysis further corroborates this connectedness, implying a strong association of the stock market with the energy commodity market.

This study offers new evidence of the temporal association among the US stock market, energy commodities and green bonds during the COVID-19 crisis. It presents a novel approach that measures and evaluates comovement among the constituent series, simultaneously using both wavelet and network analysis.

A major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).

Here, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.

Implicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.

A future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.

This paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.

In most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.