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The real challenges in online crack detection testing based on guided waves are random noise as well as narrow-band coherent noise; and to achieve efficient structural health assessment methodology, magnificent 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 guided elastic waves through the noisy signal is investigated in the present analysis using matched filtering technique which “sniffs” the signal buried in noise and most favorable mother wavelet based denoising methods. The optimal wavelet function is selected using Shannon’s entropy criterion and verified by the analysis of root mean square error of the filtered signal.

Wavelet matched filter method, a newly developed filtering technique in this work and which is a combination of the wavelet transform and matched filtering method, significantly improves the accuracy of the filtered signal and identifies relatively small damage, especially in enormously noisy data. A comparative study is also performed using the statistical tool to know acceptability and practicability of filtered signals for guided wave application.

The proposed filtering techniques can be utilized in online monitoring of civil and mechanical structures. The algorithm of the method is easy to implement and found to be successful in accurately detecting damage.

Although many techniques have been developed over the past several years to suppress random noise in Lamb wave signal but filtration of interferences of wave modes and boundary reflection is not in a much matured stage and thus needs further investigation. The present study contains detailed information about various noise filtering methods, newly developed filtration technique and their efficacy in handling the above mentioned issues.

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 purpose of this paper is to apply the wavelet thresholding technique in order to analyze economic socio-political situations in Tunisia using textual data sets. This technique is used to remove noise from contingency table. A comparative study is done on correspondence analysis and classification results (using k-means algorithm) before and after denoising.

Textual data set is collected from an electronic newspaper that offers actual economic news about Tunisia. Both the hard and the soft-thresholding techniques are applied based on various Daubechies wavelets with different vanishing moments.

The results obtained have proved the effectiveness of wavelet denoising method in textual data analysis. On one hand, this technique allowed reducing the loss of information generated by correspondence analysis, ensured a better quality of representation of the factorial plan, neglected the interest of lemmatization in textual analysis and improved the results of classification by k-means algorithm. On the other hand, the proximities provided by the factorial visualization validate the economic situation of Tunisia during the studied period showing mainly a stable situation before the revolution and a deteriorated one after the revolution.

The results are the first to analyze economic socio-political relations using textual data. The originality of this paper comes also from the joint use of correspondence analysis and wavelet thresholding in textual data analysis.

The purpose of this paper is to identify significant factors of environmental variables and pollutants that have an effect on PM_2.5 through wavelet and regression analysis.

In order to provide stable data set for regression analysis, multiresolution analysis using wavelets is conducted. For the sampled data, multicollinearity among the independent variables is removed by using principal component analysis and multiple linear regression analysis is conducted using PM_2.5 as a dependent variable.

It is found that few pollutants such as NO₂, NO_x, SO₂, benzene and environmental factors such as ambient temperature, solar radiation and wind direction affect PM_2.5. The regression model developed has high R² value of 91.9 percent, and the residues are stationary and not correlated indicating a sound model.

The research provides a framework for extracting stationary data and other important features such as change points in mean and variance, using the sample data for regression analysis. The work needs to be extended across all areas in India and for various other stationary data sets there can be different factors affecting PM_2.5.

Control measures such as control charts can be implemented for significant factors.

Rules and regulations can be made more stringent on the factors.

The originality of this paper lies in the integration of wavelets with regression analysis for air pollution data.

The purpose of this paper is to study the fault diagnosis of internal combustion (IC) engine gearbox using vibration signals with signal processing and machine learning (ML) techniques.

Vibration signals from the gearbox are acquired for healthy and induced faulty conditions of the gear. In this study, 50% tooth fault and 100% tooth fault are chosen as gear faults in the driver gear. The acquired signals are processed and analyzed using signal processing and ML techniques.

The obtained results show that variation in the amplitude of the crankshaft rotational frequency (CRF) and gear mesh frequency (GMF) for different conditions of the gearbox with various load conditions. ML techniques were also employed in developing the fault diagnosis system using statistical features. J48 decision tree provides better classification accuracy about 85.1852% in identifying gearbox conditions.

The proposed approach can be used effectively for fault diagnosis of IC engine gearbox. Spectrum and continuous wavelet transform (CWT) provide better information about gear fault conditions using time–frequency characteristics.

In this paper, experiments are conducted on real-time running condition of IC engine gearbox while considering combustion. Eddy current dynamometer is attached to output shaft of the engine for applying load. Spectrum, cepstrum, short-time Fourier transform (STFT) and wavelet analysis are performed. Spectrum, cepstrum and CWT provide better information about gear fault conditions using time–frequency characteristics. ML techniques were used in analyzing classification accuracy of the experimental data to detect the gearbox conditions using various classifiers. Hence, these techniques can be used for detection of faults in the IC engine gearbox and other reciprocating/rotating machineries.

The purpose of this paper is the comparative analysis of Haar Wavelet Method and Optimal Homotopy Asymptotic Method for fractional Fisher type equation. In this paper, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), have been presented. The Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like the Fisher type. The approximate solutions of the fractional Fisher-type equation are compared with those of OHAM and with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than the Haar wavelet method.

Comparisons between the solutions obtained by the Haar wavelet method and OHAM with the exact solutions exhibit that both featured methods are effective and efficient in solving nonlinear problems.

The comparative results indicate that OHAM provides a more accurate value than the Haar wavelet method.

In this paper, two reliable techniques, the Haar wavelet method and OHAM, have been proposed for solving nonlinear fractional partial differential equation, i.e. fractional Fisher-type equation. The proposed novel methods are well suited for only nonlinear fractional partial differential equations. It also exhibits that the proposed method is a very efficient and powerful technique in finding the solutions for the nonlinear time fractional differential equations. The main significance of the proposed method is that it requires less amount of computational overhead in comparison to other numerical and analytical approximate methods. The application of the proposed methods for the solutions of time fractional Fisher-type equations satisfactorily justifies its simplicity and efficiency.

In this paper, it is set out a hybrid data analysis method based on the combination of wavelet techniques and principal‐components regression (PCR). The purpose of this paper is to study the dynamics of the stock returns within the French stock market.

Wavelet‐based thresholding techniques are applied to the stock price series in order to obtain a set of explanatory variables that are practically noise‐free. The PCR is then carried out on the new set of regressors.

The empirical results show that the suggested method allows extraction and interpretation of the factors that influence the stock price changes. Moreover, the wavelet‐PCR improves the explanatory power of the regression model as well as its forecasting quality.

The proposed technique offers investors a better understanding of the mechanisms that explain the stock return dynamics as it removes the noise that affects financial time series.

The paper uses a new denoising framework for financial assets. The paper thinks that this framework might be of great value for academics as well as for financial investors.

The world is nowadays facing major environmental damage and climate change everywhere. Carbon dioxide emissions are major causes of such change. It is in this respect that the current study provides a fresh insight into the dynamic nexus between energy consumption (EC), economic growth (EG) and CO₂ emissions in Algeria, as it is considered as one of the top CO₂ emitters in Africa.

The authors use the wavelet approaches and Breitung and Candelon (2006) causality test to gauge the association between EC, EG and CO₂ emissions over the period 1971–2018. Specifically, this study implements the wavelet power spectrum (WPS) to identify the power and variability of each variable at different time scales. The wavelet coherence, phase differences and partial wavelet coherence are also used to assess the co-movement and lead lag relationship between economic growth, energy consumption and CO₂ emissions over different time scale. Finally, Breitung and Candelon (2006) causality test is used to find the causality among variables.

The wavelet power spectrum results indicate that economic growth, energy consumption and CO₂ emissions share common strong variance in the medium and long run. Furthermore, the wavelet coherence results suggest that there is a significant co-movement between EG and CO₂ emissions, and EG is the leading variable for CO₂ emissions and EC. The results also unveil that both EG and EC cause CO₂ emissions both in short and long run. The results suggest that Algeria should take suitable measures towards the promotion of renewable energy sources.

The present empirical study filled the literature gap of applying the wavelet approach and frequency domain spectral causality test to examine this relevant issue for Algeria.

In GIS applications for a realistic representation of a terrain a great number of triangles are needed that ultimately increases the data size. For online GIS interactive programs it has become highly essential to reduce the number of triangles in order to save more storing space. Therefore, there is need to visualize terrains at different levels of detail, for example, a region of high interest should be in higher resolution than a region of low or no interest. Wavelet technology provides an efficient approach to achieve this. Using this technology, one can decompose a terrain data into hierarchy. On the other hand, the reduction of the number of triangles in subsequent levels should not be too small; otherwise leading to poor representation of terrain.

This paper proposes a new computational code (please see Appendix for the flow chart and pseudo code) for triangulated irregular network (TIN) using Delaunay triangulation methods. The algorithms have proved to be efficient tools in numerical methods such as finite element method and image processing. Further, second generation wavelet techniques popularly known as “lifting schemes” have been applied to compress the TIN data.

A new interpolation wavelet filter for TIN has been applied in two steps, namely splitting and elevation. In the splitting step, a triangle has been divided into several sub‐triangles and the elevation step has been used to “modify” the point values (point coordinates for geometry) after the splitting. Then, this data set is compressed at the desired locations by using second generation wavelets.

A new algorithm for second generation wavelet compression has been proposed for TIN data compression. The quality of geographical surface representation after using proposed technique is compared with the original terrain. The results show that this method can be used for significant reduction of data set.

This study aims to answer the following questions which have not been investigated in the literature to the best knowledge: Is there any bubble in the German housing sector between 2005–2009 and 2012–2017? and Is there any linkage between economic policy uncertainty and the housing sector price index?

This study aims to shed some light on the German’s housing sector by investigating the housing sector bubble and the causal link between the housing sector index and economic policy uncertainty in Germany, using GSADF, Granger causality, Toda Yamamoto causality and wavelet coherence tests.

The findings reveal that there are some bubbles in the housing sector in Germany for the periods investigated, there is a positive correlation between economic policy uncertainty and housing sector price index at different frequencies and different periods and between 2008 and 2009 and between 2011 and 2013, economic policy uncertainty leads housing sector price index. The consistency of the findings from wavelet coherence is confirmed by the outcomes of Granger causality and Toda Yamamoto causality tests.

To the best knowledge, this is the first study that empirically investigates the relationship between the housing sector and EPU using a novel wavelet econometric method. In addition, this paper extends the research focused on the associations between the housing sector and EPU, by checking the bubbles in the market in different time horizons by using the longest available data span. Furthermore, the consistency of the findings from wavelet causality is confirmed by the outcomes of Granger causality and Toda Yamamoto causality tests. Finally, compared to the previous literature on the relationship between housing and EPU, the study uses a hedonic index for housing for the first time in the case of Germany.