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IntroductionPredicting river flow is one of the most crucial aspects in water resources management. Improving forecasting methods can lead to a reduction in damages caused by hydrological phenomena. Studies indicate that artificial neural network models provide better predictions for river flow compared to physical and conceptual models. However, since these models may not offer reliable performance in estimating unstable data, using preprocessing techniques is necessary to enhance the accuracy and performance of artificial neural networks in estimating hydrological time series with nonlinear relationships. One of these methods is wavelet transformation, which utilizes signal processing techniques. Materials and MethodsIn this study, to evaluate the efficiency of discrete and continuous wavelet types in the Wavelet-Artificial Neural Network (WANN) hybrid model for monthly flow prediction, a case study was conducted on the Kardeh Dam watershed in the northeast of Iran, serving as a water source for part of Mashhad city and irrigation downstream agricultural lands. Monthly streamflow estimates for the upstream sub-basin of the Kardeh Dam were obtained from the meteorological and hydrometric stations' monthly statistics over a 30-year period (1991-2020). The WANN model is a hybrid time series model where the output of the wavelet transform serves as a data preprocessing method entering an artificial neural network as the predictive model. The combination of wavelet analysis and artificial neural network implies using wavelet capabilities for feature extraction, followed by the neural network to learn patterns and predict data, potentially enhancing the models' performance by leveraging both methods. The 4-fold cross-validation method was employed for the artificial neural network model validation, where the model underwent validation and accuracy assessment four times, each time using 75% of the data for training and the remaining 25% for model validation. The final results were presented by averaging the validation and accuracy results obtained from each of the four model runs. To evaluate and compare the performance of the models used in this study, three evaluation indices, Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), and Pearson correlation coefficient (R), were employed. Results and DiscussionThe analysis of meteorological and hydrometric data in this study revealed that monthly streamflow in two time steps, T-1 and T-2, were the most effective predictive variables. Each of the two runoff variables of the previous month (Qt-1) and the previous two months (Qt-2) were analyzed by each of the Haar and Fejer-Korovkin2 discrete wavelet transforms and the two continuous Symlet3 and Daubechies2 wavelets at three levels. The results of each level of decomposition was given as input to the ANN model. The presented results at each decomposition level indicated that hybrid models could accurately predict lower flows compared to the single ANN model, and the estimation of maximum values also significantly improved in the hybrid models. Among the wavelets used, Haar wavelets exhibited the weakest performance, and the less commonly employed Kf2 wavelet showed a moderate performance. Since the Haar and Fk2 wavelets, with their discrete structure, did not perform well in decomposing continuous monthly streamflow data, continuous wavelet models outperformed discrete wavelet models. The hybrid models, combining wavelet analysis and artificial neural networks, demonstrated up to an 11% improvement over the performance of the single neural network model. ConclusionStreamflow is a crucial element in the hydrological cycle, and predicting it is vital for purposes such as flood prediction and providing water for consumption. The objective of this research was to evaluate the performance of different types of discrete and continuous wavelet models at various decomposition levels in enhancing the efficiency of artificial neural network (ANN) models for streamflow prediction. Since climate and watershed characteristics can influence the nature of data fluctuations and, consequently, the results of the wavelet model decomposition, choosing an appropriate wavelet model is essential for obtaining the best results. Considering the existing variations in the results of different studies regarding the selection of the best wavelet type, it is suggested to use both continuous and discrete wavelet types in modeling to achieve the best predictions and select the optimal results. Given that a lower number of input variables in neural network models lead to higher accuracy in modeling results, it is recommended to perform decomposition at a two-level depth to reduce input components to the neural network model, thereby reducing the model execution time.

IntroductionPredicting river flow is one of the most crucial aspects in water resources management. Improving forecasting methods can lead to a reduction in damages caused by hydrological phenomena. Studies indicate that artificial neural network models provide better predictions for river flow compared to physical and conceptual models. However, since these models may not offer reliable faformance in estimating unstable data, using preprocessing techniques is necessary to enhance the accuracy and faformance of artificial neural networks in estimating hydrological time series with nonlinear relationships. One of these methods is wavelet transformation, which utilizes signal processing techniques. Materials and MethodsIn this study, to evaluate the efficiency of discrete and continuous wavelet types in the Wavelet-Artificial Neural Network (WANN) hybrid model for monthly flow prediction, a case study was conducted on the Kardeh Dam watershed in the northeast of Iran, serving as a water source for part of Mashhad city and irrigation downstream agricultural lands. Monthly streamflow estimates for the upstream sub-basin of the Kardeh Dam were obtained from the meteorological and hydrometric stations' monthly statistics over a 30-year faiod (1991-2020). The WANN model is a hybrid time series model where the output of the wavelet transform serves as a data preprocessing method entering an artificial neural network as the predictive model. The combination of wavelet analysis and artificial neural network implies using wavelet capabilities for feature extraction, followed by the neural network to learn patterns and predict data, potentially enhancing the models' faformance by leveraging both methods. The 4-fold cross-validation method was employed for the artificial neural network model validation, where the model underwent validation and accuracy assessment four times, each time using 75% of the data for training and the remaining 25% for model validation. The final results were presented by averaging the validation and accuracy results obtained from each of the four model runs. To evaluate and compare the faformance of the models used in this study, three evaluation indices, Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), and Pearson correlation coefficient (R), were employed. Results and DiscussionThe analysis of meteorological and hydrometric data in this study revealed that monthly streamflow in two time steps, T-1 and T-2, were the most effective predictive variables. Each of the two runoff variables of the previous month (Qt-1) and the previous two months (Qt-2) were analyzed by each of the Haar and Fejer-Korovkin2 discrete wavelet transforms and the two continuous Symlet3 and Daubechies2 wavelets at three levels. The results of each level of decomposition was given as input to the ANN model. The presented results at each decomposition level indicated that hybrid models could accurately predict lower flows compared to the single ANN model, and the estimation of maximum values also significantly improved in the hybrid models. Among the wavelets used, Haar wavelets exhibited the weakest faformance, and the less commonly employed Kf2 wavelet showed a moderate faformance. Since the Haar and Fk2 wavelets, with their discrete structure, did not faform well in decomposing continuous monthly streamflow data, continuous wavelet models outfaformed discrete wavelet models. The hybrid models, combining wavelet analysis and artificial neural networks, demonstrated up to an 11% improvement over the faformance of the single neural network model. ConclusionStreamflow is a crucial element in the hydrological cycle, and predicting it is vital for purposes such as flood prediction and providing water for consumption. The objective of this research was to evaluate the faformance of different types of discrete and continuous wavelet models at various decomposition levels in enhancing the efficiency of artificial neural network (ANN) models for streamflow prediction. Since climate and watershed characteristics can influence the nature of data fluctuations and, consequently, the results of the wavelet model decomposition, choosing an appropriate wavelet model is essential for obtaining the best results. Considering the existing variations in the results of different studies regarding the selection of the best wavelet type, it is suggested to use both continuous and discrete wavelet types in modeling to achieve the best predictions and select the optimal results. Given that a lower number of input variables in neural network models lead to higher accuracy in modeling results, it is recommended to faform decomposition at a two-level depth to reduce input components to the neural network model, thereby reducing the model execution time. [ABSTRACT FROM AUTHOR]

Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time‐scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals. [ABSTRACT FROM AUTHOR]

This study examines time-frequency connectedness between COVID-19 pandemic and economic indicators through a continuous wavelet transformation approach in the US and China. The study also assesses the dynamic conditional correlations (DCCs) between macroeconomic indicators and domestic sectoral returns during the pandemic. The findings display higher coherencies between COVID-19 and long-term predictive economic indicators in China compared to the US. Moreover, the results indicate that the stock market spillovers are more pronounced on domestic sectoral returns than other economic indicators during the COVID-19 outburst. Besides, the findings exhibit that exchange market instability has significant negative repercussions on the domestic sectors in China, however, weaker correlations are discerned between exchange market and domestic sectors in the US. The findings offer several policy implications and endorsements for portfolio managers, policymakers, practitioners, and other market participants. [ABSTRACT FROM AUTHOR]

We introduce an extension of continuous wavelet theory that enables an efficient implementation of multiplicative operators in the coefficient space. In the new theory, the signal space is embedded in a larger abstract signal space – the so called window–signal space. There is a canonical extension of the wavelet transform to an isometric isomorphism between the window–signal space and the coefficient space. Hence, the new framework is called a wavelet-Plancherel theory, and the extended wavelet transform is called the wavelet-Plancherel transform. Since the wavelet-Plancherel transform is an isometric isomorphism, any operation in the coefficient space can be pulled-back to an operation in the window–signal space. It is then possible to improve the computational complexity of methods that involve a multiplicative operator in the coefficient space, by performing all computations directly in the window–signal space. As one example application, we show how continuous wavelet multipliers (also called Calderón–Toeplitz operators), with polynomial symbols, can be implemented with linear complexity in the resolution of the 1D signal. As another example, we develop a framework for efficiently computing greedy sparse approximations to signals based on elements of continuous wavelet systems. [ABSTRACT FROM AUTHOR]

In the recent coronavirus pandemic, several researchers have focused on the drivers of cryptocurrency behavior. In particular, this study provides insights into what can drive Islamic cryptocurrency markets and how do they react during the COVID-19 pandemic. We explore the cryptocurrency volatility and the connectedness between the Islamic, conventional, and COVID-19 confirmed cases and deaths using the wavelet approaches. The preliminary results show that faith-based cryptocurrencies have reduced risk exposure than their conventional counterparts, in the long run, making them more appealing for investment, particularly for investors seeking low-risk and Shariah-compliant assets. Furthermore, the empirical results indicate that both Islamic and conventional cryptocurrencies are more sensitive to the death toll than the newly confirmed cases. We also observe significant positive co-movements between Bitcoin and Islamic cryptocurrencies. Besides, Bitcoin exhibits a substantial response during various time scales while compared with Islamic cryptocurrencies. This study contributes to the literature by investigating the sensitivity and the vulnerability of a new category of cryptocurrencies backed by tangible assets to pandemic shocks. To the extent of the author's knowledge, this study is the first attempt that examines the co-movement between Islamic and conventional cryptocurrencies using the wavelet approach. A viable, ethical, and alternative investment route for faith-based investors can be provided by the Shariah-Compliant cryptocurrencies as they are risk-reduced and less sensitive to the pandemic than conventional benchmarks. Besides, this study creates opportunities in portfolio diversification for investors. [ABSTRACT FROM AUTHOR]

The study of the relationship between economic growth and the gap between real GDP and unemployment has a special place in the economic literature. In this study to investigate the causal relationship between economic growth (with and without oil sector) and unemployment and growth of production gap (with and without oil sector) and unemployment in the Iranian economy in the period 1396: 1346-4: 1 from the wavelet approach Used continuously. The continuous wavelet approach by examining and analyzing the dynamics of causal relationships between variables at different times and scales is a powerful method for examining causal relationships between variables over time. The results of the first model showed that economic growth (with the oil sector) and unemployment were not in the same time phase and were only in the short term in the period 1375: 139: 3-1369: 3. The results of the second model showed that the growth of the production gap (with the oil sector) and unemployment were not in the same time phase and were only in the short period of 2012: 1-189-2011: 1. The results of the third model showed that economic growth (excluding the oil sector) and unemployment were not parallel in all time horizons. The results of the fourth model showed that the growth of the production gap (excluding the oil sector) and unemployment in the short run in different time periods have both phase and non-phase fluctuations and in the medium term the relationship between these two variables Were not observed and were not in the long run. [ABSTRACT FROM AUTHOR]

In a machining system, tool condition monitoring systems are required to get a high-quality product and to prevent the downtime of machine tools due to tool failures. For this purpose, tool condition monitoring systems have become very important during the years since the mechanical faults can cause high cost. This study introduces a multistage cutting tool fault diagnosis method to detect the presence and level of the involute form cutter faults on the by the cutting force and vibration signal analysis. Therefore, different fault levels (low, medium and high) were generated on the involute form cutter as a tool breakage. During the experiments, the cutting force, vibration and acoustic signals were gathered with three different feed rates for each fault level. The gathered signals were processed by a multistage signal processing algorithm developed in the MATLAB environment. As an initial step, the continuous wavelet transform of the obtained signals was taken and saved as an image by the developed algorithm. After that, a convolutional neural network model is trained and tested by using the obtained images. The developed algorithm firstly checks the presence of the cutting tool fault. Once the algorithm labels the cutting tool is damaged, it then checks the damage level of the cutting tool fault. It is observed from the results, cutting force analysis is sufficient for the detection of cutting tool fault. On the other hand, the cutting force signal analysis is insufficient to detect the damage level of the cutting tool. Therefore, the vibration signal analysis is required to detect the damage level of the cutting tool. Results prove that, by the vibration analysis, the developed algorithm could detect not only the presence of the damage on the cutting tool but also the damage level. The results of the algorithm for each stage and signal are given in the results section. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups H < GL (3 , R) that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups. [ABSTRACT FROM AUTHOR]

In this paper, a method of multiple cracks detection in a cantilever reinforced concrete beam based on wavelet transform is presented. For this purpose, different damage scenarios in concrete beam were considered. Then, the four first mode shapes of undamaged and damaged beam using ABAQUS software were extracted. The estimated mode shapes of the beam are analyzed by the continuous and discrete wavelet transform (CWT & DWT) to detect the damage scenarios. It was found that DWT is more sensitive to damage location than CWT in the concrete beam which introduced in this paper. Also, the influence of the mode order and the effect of damage distance from support on the effectiveness of damage detection was evaluated. It was observed that the distance of cracks to each other have no effect on identifying their location.

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The current study investigates the relationship between stock prices and exchange rate by using wavelets approach and more focused the continuous, power spectrum, cross and coherence wavelet. The result of Bayer and Hanck (2013) and Gregory and Hansen (1996) confirm the presence of long-run association between stock price and exchange rate in Pakistan. The results of wavelet coherence reveal the dominance of SP during 2005–2006 and 2011–2012 in the period of 8–16 and 16–32 weeks cycle in approximately all the exchange rates against Pakistani rupees. For almost the entire studied period in long scale, the study evidences the strong coherence between both the series. The most interesting part of this coherence is the existence of bidirectional causality in the long timescale. The arrows in this long region are pointing both left up and left down. This suggests that during the time period, our variables are exhibiting out phase relationship with mutually leading and lagging the market. These results are in contrast with many earlier studies of Pakistan. [ABSTRACT FROM AUTHOR]