• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2100-2107
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• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

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

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Computers and Concrete
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• v.20 no.5
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• pp.555-562
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• 2017

The accuracy and integrity of stress data acquired by bridge heath monitoring system is of significant importance for bridge safety assessment. However, the missing and abnormal data are inevitably existed in a realistic monitoring system. This paper presents a data reconstruction approach for bridge heath monitoring based on the wavelet multi-resolution analysis and support vector machine (SVM). The proposed method has been applied for data imputation based on the recorded data by the structural health monitoring (SHM) system instrumented on a prestressed concrete cable-stayed bridge. The effectiveness and accuracy of the proposed wavelet-based SVM prediction method is examined by comparing with the traditional autoregression moving average (ARMA) method and SVM prediction method without wavelet multi-resolution analysis in accordance with the prediction errors. The data reconstruction analysis based on 5-day and 1-day continuous stress history data with obvious preternatural signals is performed to examine the effect of sample size on the accuracy of data reconstruction. The results indicate that the proposed data reconstruction approach based on wavelet multi-resolution analysis and SVM is an effective tool for missing data imputation or preternatural signal replacement, which can serve as a solid foundation for the purpose of accurately evaluating the safety of bridge structures.

• Ocean and Polar Research
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• v.29 no.4
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• pp.303-310
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• 2007

2-D wavelet analysis is applied to bathymetric data from the KR1 area of Korea Deepsea Mining Area. The wavelet analysis is one of the quantitative methods to analyze the topography. The wavelet allows us to create filters to select for topography in a continuous variety of shapes, sizes, and orientation. The 2-D Linear B-spline filter, 100 BS and 100 NF, is convolved with bathymetric data to identify the location of abyssal hills and abyssal troughs in bathymetry. In addition, the 2-D derivative of Cubic B-spline filter, 60 BS and 60 NF, is applied to bathymetric data to find the slope of abyssal hill in bathymetry. These filters were rotated $5^{\circ}$ counterclockwise from NS to match the dominant orientation of seafloor lineament. Both filters result in good match with abyssal hills, troughs, and slopes. This method can apply to fault, fold, and other lineament structures description with variable size. The result of application shows that wavelet analysis of bathymetric data could be used with fundamental data of geophysical analysis.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1580-1586
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• 2009

Wavelet transform is utilized to the field of the signal processing and the digital communication. In this paper, the performance for wavelets is analyzed for Haar and Daubechies series in the wavelet shift keying. It is mainly utilized to Haar, Daubechies 4tap, 8tap and 12tap in this paper. The analysis scheme is utilized by the eye pattern and the error probability. As a results of simulation, we confirmed that the proposed scheme was superior to performance when the number of the filler coefficient is small.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.8
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• pp.369-373
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• 2000

High impedance fault(HIF) is defined as a fault that the general overcurrent relay can not detect or interrupt. Especially when HIF occurs in residential areas, energized high voltage conductor results in fire hazard, equipment damage or personal threat. This paper proposes a fault location estimation algorithm for high impedance fault using wavelet transform. The algorithm is based on the wavelet analysis of the fault voltage and current signals. The performance of the proposed algorithm is tested on a typical 154kV korean transmission line system under various fault conditions. From the tests presented in this paper it can be concluded that a fault location estimation algorithm using wavelet transform can precisely calculate the fault point for HIF.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1232-1237
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• 2008

This paper introduces an application of wavelet analysis to the sensor fusion of GPS/INS/baroaltimeter. Using wavelet analysis the baro-inertial altitude is decomposed into the low frequency content and the high frequency content. The high frequency components, 'details', represent the perturbed altitude change from the long time trend. GPS altitude is also broken down by a wavelet decomposition. The low frequency components, 'approximations', of the decomposed signal address the long-term trend of altitude. It is proposed that the final altitude be determined as the sum of both the details of the baro-inertial altitude and the approximations of GPS altitude. Then the final altitude exclude long-term baro-inertial errors and short-term GPS errors. Finally, it is shown from the test results that the proposed method produces continuous and sensitive altitude successfully.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.11
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• pp.905-910
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• 2008

Vibration analysis is widely used in machinery diagnosis and the wavelet transform has also been implemented in many applications in the condition monitoring of machinery. In contrast to previous applications, this paper examines whether acoustic signal can be used effectively along vibration signal to detect the various local fault, in local fault of gearboxes using the wavelet transform. Moreover, envelop analysis is well known as useful tool for the detection of rolling element bearing fault. In this paper, a acoustic emission (AE) sensor is employed to detect gearbox damage by installing them around bearing housing at driven-end side. Signal processing is conducted by wavelet transform and enveloping to detect her fault all at once gearbox using AE signal.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.39 no.4
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• pp.363-369
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• 2002

In this paper, it could improved on the arbitrary nonlinear function learning approximation which have the wavelet neural network based on Adaptive Neuro-Fuzzy Inference System(ANFIS) and the multi-resolution Analysis(MRA) of the wavelet transform. ANFIS structure is composed of a bell type fuzzy membership function, and the wavelet neural network structure become composed of the forward algorithm and the backpropagation neural network algorithm. This wavelet composition has a single size, and it is used the backpropagation algorithm for learning of the wavelet neural network based on ANFIS. It is confirmed to be improved the wavelet base number decrease and the convergence speed performances of the wavelet neural network based on ANFIS Model which is using the wavelet translation parameter learning and bell type membership function of ANFIS than the conventional algorithm from 1 dimension and 2 dimension functions.