• Journal of Korea Water Resources Association
• /
• v.52 no.11
• /
• pp.905-916
• /
• 2019

This study explores the effect of mother wavelet in the bivariate wavelet analysis. A total of four mother wavelets (Bump, Mexican hat, Morlet, and Paul) which are frequently used in the related studies is selected. These mother wavelets are applied to several bivariate time series like white noise and sine curves with different periods, whose results are then compared and evaluated. Additionally, two real time series such as the arctic oscillation index (AOI) and the southern oscillation index (SOI) are analyzed to check if the results in the analysis of generated time series are consistent with those in the analysis of real time series. The results are summarized as follows. First, the Bump and Morlet mother wavelets are found to provide well-matched results with the theoretical predictions. On the other hand, the Mexican hat and Paul mother wavelets show rather short-periodic and long-periodic fluctuations, respectively. Second, the Mexican hat and Paul mother wavelets show rather high scale intervention, but rather small in the application of the Bump and Morlet mother wavelets. The so-called co-movement can be well detected in the application of Morlet and Paul mother wavelets. Especially, the Morlet mother wavelet clearly shows this characteristic. Based on these findings, it can be concluded that the Morlet mother wavelet can be a soft option in the bivariate wavelet analysis. Finally, the bivariate wavelet analysis of AOI and SOI data shows that their periodic components of about 2-4 years co-move regularly every about 20 years.

• Journal of Korea Water Resources Association
• /
• v.38 no.6 s.155
• /
• pp.439-448
• /
• 2005

This paper introduces the wavelet transform that was improved by the fourier transform to assess periodicities and trends, we assessed propriety with examples of two monthly precipitation data, annual precipitation, SOI index and SST index. The wavelet transform can effectively assess the power spectrum corresponding to frequency as maintaining chronological characteristics. The results of the analysis using the wavelet transform showed that the monthly precipitation have the strongest power spectrum near that of 1 year, and the annual precipitation represent the dominated spectrum in the band of 2-8 years. Also, the SOI index and SST index indicate the strongest power spectrum in the band of 2-8 years.

• The Transactions of the Korean Institute of Power Electronics
• /
• v.26 no.1
• /
• pp.32-37
• /
• 2021

This study proposes a DC series arc fault detector using a frequency analysis method called the discrete wavelet transform (DWT), in which the processing speed of the DWT algorithm is improved effectively. The processing time can be shortened because of the time characteristic of the DWT result. The performance of the developed DC series arc fault detector for a large photovoltaic system is verified with various DC series arc generation conditions. Successful DC series arc detection and improved calculation time were both demonstrated through the measured actual arc experimental result.

• Wind and Structures
• /
• v.3 no.3
• /
• pp.159-175
• /
• 2000

Many practical time series, including pressure signals measured on roof-corners of low-rise buildings in quartering winds, consist of relatively quiescent periods interrupted by intermittent transients. The dyadic wavelet transform is used to detect these transients in pressure time series and a relatively simple pattern classification scheme is used to detect underlying structure in these transients. Statistical analysis of the resulting pattern classes yields a library of signal "building blocks", which are useful for detailed characterization of transients inherent to the signals being analyzed.

• Journal of Korea Water Resources Association
• /
• v.52 no.8
• /
• pp.575-587
• /
• 2019

This study evaluated the effect of a mother wavelet in the wavelet analysis of various times series made by combining white noise and/or sine function. The result derived is also applied to short-memory arctic oscillation index (AOI) and long-memory southern oscillation index (SOI). This study, different from previous studies evaluating one or two mother wavelets, considers a total of four generally-used mother wavelets, Bump, Morlet, Paul, and Mexican Hat. Summarizing the results is as follows. First, the Bump mother wavelet is found to have some limitations to represent the unstationary behavior of the periodic components. Its application results are more or less the same as the spectrum analysis. On the other hand, the Morlet and Paul mother wavelets are found to represent the non-stationary behavior of the periodic components. Finally, the Mexican Hat mother wavelet is found to be too complicated to interpret. Additionally, it is also found that the application result of Paul mother wavelet can be inconsistent for some specific time series. As a result, the Morlet mother wavelet seems to be the most stable one for general applications, which is also assured by the recent trend that the Morlet mother wavelet is most frequently used in the wavelet analysis research.

• Journal of Korea Multimedia Society
• /
• v.3 no.5
• /
• pp.461-469
• /
• 2000

A wavelet analysis in a field of analytics is to create a reconstruction theorem of Plancherel form. And a series of wavelet is to create a discrete is to create a discrete reconstruction theorem for a frame theory and a multiresolution analysis theory. As a generation of reconstruction theorem, a wavelet correspond to it is generated. That is to be like a basic wavelet which is satisfied an admissibility condition in CWT and a Daubechies wavelet using MRA in wavelet series and a Meyer wavelet using a frame theory. In this paper, we discover a discrete reconstruction theorem which is superior to a conventional discrete reconstruction theorem by extending admissibility condition used in CWT and develop a New $L^1$-wavelet group. A new $L^1$-wavelet is applied to a signal reconstruction and a signal analysis in time-frequency region.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.57 no.8
• /
• pp.1470-1477
• /
• 2008

In this paper, a new detection method of series arc-fault signals occurring at the wiring of home appliances is proposed. The discrete wavelet transform was used for the numerical analysis of the variation rate in peak, RMS, noise energy, shoulder of the arc-fault current wave. As a results, the arc distinction threshold value of these variation rates was about 0.1 in most cases. The arc-fault current of the loads with the active PFC circuit showed a high rate of variation in noise energy and shoulder, but arc-fault current of the loads without the active PFC circuit showed a high rate of variation in peak and RMS. The arc fault current in resistive loads showed a high rate of variation in shoulder.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2003.05a
• /
• pp.324-329
• /
• 2003

Spectral analysis is an important signal processing tool for time series data. The transformation of a time series into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. Recently developed transforms based on the new mathematical field of wavelet analysis bypass the resolution limitation and offer superior spectral decomposition. The discrete wavelet transform of Sonar data provides spectral localization of noises, hence noises can be filtered out successfully.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.4
• /
• pp.355-364
• /
• 2011

In this study, the details of WSA(wavelet series analysis) have been demonstrated to solve the 4th-order elliptic differential equation. It is clear to solve the 2nd-order elliptic differential equation with the basis function of Hat wavelet series that is used in the previous study existed in $H^1$-space. However, it is difficult to solve the 4th order differential equation with same basis function of Hat wavelet series because of insufficient differentiability and integrability. To overcome this problem, the linear equations in terms of moment and deflection have been formulated and solved sequentially that are similar to extension of Elastic Load Method and Moment Area Method in some senses. Also, the differences and common points between the proposed method and the meshless method are discussed in the procedure of WSA formulation. As we expect, it is easy to ascertain that the more terms of Hat wavelet series are used, the better numerical solutions are improved. Also the solutions obtained by WSA have been compared with the conventional FEM solutions in case of Euler beam problems with stress singularity.

• International Journal of Control, Automation, and Systems
• /
• v.6 no.5
• /
• pp.639-650
• /
• 2008

Electricity price forecasting has become an integral part of power system operation and control. In this paper, a wavelet transform (WT) based neural network (NN) model to forecast price profile in a deregulated electricity market has been presented. The historical price data has been decomposed into wavelet domain constitutive sub series using WT and then combined with the other time domain variables to form the set of input variables for the proposed forecasting model. The behavior of the wavelet domain constitutive series has been studied based on statistical analysis. It has been observed that forecasting accuracy can be improved by the use of WT in a forecasting model. Multi-scale analysis from one to seven levels of decomposition has been performed and the empirical evidence suggests that accuracy improvement is highest at third level of decomposition. Forecasting performance of the proposed model has been compared with (i) a heuristic technique, (ii) a simulation model used by Ontario's Independent Electricity System Operator (IESO), (iii) a Multiple Linear Regression (MLR) model, (iv) NN model, (v) Auto Regressive Integrated Moving Average (ARIMA) model, (vi) Dynamic Regression (DR) model, and (vii) Transfer Function (TF) model. Forecasting results show that the performance of the proposed WT based NN model is satisfactory and it can be used by the participants to respond properly as it predicts price before closing of window for submission of initial bids.