Improved error analysis for adaptive wavelet algorithms

Jiang, Ying-chun

doi:10.1016/j.amc.2012.08.058

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…14 Wavelet-based algorithms were attempted to numerically solve elliptic equations. [15][16][17][18][19] More significantly, CWT is coupled with filtering techniques in many applications. For example, the window width and scaling factor of signals were optimized for gearbox fault diagnosis according to the kurtosis maximization principle.…”

Section: Introductionmentioning

confidence: 99%

Adaptive wavelet transform: Definition, parameter optimization algorithms, and application for concrete delamination detection from impact echo responses

Chen

2018

Structural Health Monitoring

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In this study, an amplitude-adaptive wavelet transform is proposed and defined as an average of overlapped short-time wavelet transforms with optimized time-varying resolution in a time-frequency domain of interest. A flowchart of two optimization algorithms for time and frequency resolution updating is proposed and developed to determine the wavelet parameters for a desirable time-frequency representation of dynamic responses. Numerical example with two closely spaced, frequency-modulated sinusoids and two closely spaced delta functions indicates that the time and frequency resolution of the proposed method are approximately 7.7 times as uniform as those of the continuous wavelet transform. The end effect of short-time response segments is significantly less than 10% in amplitude except at the beginning and ending of the overall response. When the proposed method is applied to the impact echo responses experimentally recorded from a 60$ 3 36$ 3 7.25$ concrete slab, this improvement in time and frequency resolution leads to seven more successful detections of deep or shallow delamination of 40 sets of analyzed test data, with the error in estimation of deep delamination depth less than 3%. The selection process of time-varying central frequencies, scaling factors, and window lengths proves robust.

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Section: Introductionmentioning

confidence: 99%

Adaptive wavelet transform: Definition, parameter optimization algorithms, and application for concrete delamination detection from impact echo responses

Chen

2018

Structural Health Monitoring

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“…Furthermore, wavelet bases have been used to solve optimal control problems , and eigenvalue problems . The role of wavelets in devising an adaptive algorithm has been analyzed in .…”

Section: Introductionmentioning

confidence: 99%

An adaptive wavelet space-time SUPG method for hyperbolic conservation laws

Minbashian

Adibi

Dehghan

2017

Numer. Methods Partial Differential Eq.

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This article concerns with incorporating wavelet bases into existing streamline upwind Petrov‐Galerkin (SUPG) methods for the numerical solution of nonlinear hyperbolic conservation laws which are known to develop shock solutions. Here, we utilize an SUPG formulation using continuous Galerkin in space and discontinuous Galerkin in time. The main motivation for such a combination is that these methods have good stability properties thanks to adding diffusion in the direction of streamlines. But they are more expensive than explicit semidiscrete methods as they have to use space‐time formulations. Using wavelet bases we maintain the stability properties of SUPG methods while we reduce the cost of these methods significantly through natural adaptivity of wavelet expansions. In addition, wavelet bases have a hierarchical structure. We use this property to numerically investigate the hierarchical addition of an artificial diffusion for further stabilization in spirit of spectral diffusion. Furthermore, we add the hierarchical diffusion only in the vicinity of discontinuities using the feature of wavelet bases in detection of location of discontinuities. Also, we again use the last feature of the wavelet bases to perform a postprocessing using a denosing technique based on a minimization formulation to reduce Gibbs oscillations near discontinuities while keeping other regions intact. Finally, we show the performance of the proposed combination through some numerical examples including Burgers’, transport, and wave equations as well as systems of shallow water equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2062–2089, 2017

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Improved error analysis for adaptive wavelet algorithms

Cited by 2 publications

References 9 publications

Adaptive wavelet transform: Definition, parameter optimization algorithms, and application for concrete delamination detection from impact echo responses

Adaptive wavelet transform: Definition, parameter optimization algorithms, and application for concrete delamination detection from impact echo responses

An adaptive wavelet space-time SUPG method for hyperbolic conservation laws

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