Wavelet methods for pointwise regularity and local oscillations of functions

In this paper we estimate the parameters of a multidimensional system from a record of noisy output measurements by using a multiwavelet denoising technique. In this output-only identification scheme, we extend wavelet denoising methods to the multiwavelet case. After the noise has been removed from the output records by wavelet methods, either full model identification or deterministic subspace identification can be performed. In the former case, full information on the system such as modal values and shapes becomes available by postprocessing. In the latter case, the observable modal values of the system as well as modal shapes at the sensor locations can be extracted from the identified parameters. Additionally, we discuss the requirements on the measuring devices to be compatible with wavelet transforms of a particular type. The validity and merit of the developed scheme are illustrated by examples of numerically simulated and experimentally measured signals, including comparisons with stochastic identification methods.

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Comparison of Two Wavelet Methods for Accurate Solution of Two-Dimensional Nonlinear Volterra Integral Equation

Iranian Journal of Science and Technology Transactions A Science ◽

10.1007/s40995-021-01198-x ◽

2021 ◽

Author(s):

S. Saha Ray ◽

S. Behera

Keyword(s):

Integral Equation ◽

Volterra Integral Equation ◽

Accurate Solution ◽

Two Dimensional ◽

Nonlinear Volterra Integral Equation ◽

Wavelet Methods

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Monitoring Offshore Pipelines Using Forced Transverse Vibration: Data Analysis

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0384 ◽

1995 ◽

Author(s):

Hugh E. M. Hunt

Keyword(s):

Fluid Flow ◽

Data Analysis ◽

Transverse Vibration ◽

Vibration Amplitude ◽

Support Condition ◽

Offshore Pipelines ◽

Vibration Data ◽

Wavelet Methods

Abstract Vibration methods are used to identify faults, such as spanning and loss of cover, in long off-shore pipelines. A pipeline ‘pig’, propelled by fluid flow, generates transverse vibration in the pipeline and the measured vibration amplitude reflects the nature of the support condition. Large quantities of vibration data are collected and analysed by Fourier and wavelet methods.

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Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Discrete Dynamics in Nature and Society ◽

10.1155/2017/3148257 ◽

2017 ◽

Vol 2017 ◽

pp. 1-18 ◽

Cited By ~ 3

Author(s):

Tongzhou Zhao ◽

Liang Wu ◽

Dehua Li ◽

Yiming Ding

Keyword(s):

Time Series ◽

Water Level ◽

Multifractal Analysis ◽

Simulation Models ◽

Northern China ◽

Fluctuation Analysis ◽

Multifractal Detrended Fluctuation Analysis ◽

Wavelet Leaders ◽

Detailed Characteristic ◽

Wavelet Methods

We study the multifractal properties of water level with a high-frequency and massive time series using wavelet methods (estimation of Hurst exponents, multiscale diagram, and wavelet leaders for multifractal analysis (WLMF)) and multifractal detrended fluctuation analysis (MF-DFA). The dataset contains more than two million records from 10 observation sites at a northern China river. The multiscale behaviour is observed in this time series, which indicates the multifractality. This multifractality is detected via multiscale diagram. Then we focus on the multifractal analysis using MF-DFA and WLMF. The two methods give the same conclusion that at most sites the records satisfy the generalized binomial multifractal model, which is robust for different times (morning, afternoon, and evening). The variation in the detailed characteristic parameters of the multifractal model indicates that both human activities and tributaries influence the multifractality. Our work is useful for building simulation models of the water level of local rivers with many observation sites.

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Gamma-Ray Spectrum Analysis of Chang’E-1 for Lunar Detection

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4002846 ◽

2010 ◽

Vol 133 (5) ◽

Cited By ~ 2

Author(s):

Xu HongKun ◽

Fang Fang ◽

Ni Shijun ◽

He Jianfeng ◽

You Lei

Keyword(s):

Spectral Characteristic ◽

Spectrum Analysis ◽

Gamma Ray ◽

Low Energy ◽

Elemental Abundance ◽

Nuclear Engineering ◽

Gamma Ray Spectrometer ◽

Lunar Prospector ◽

Spectrometer Data ◽

Wavelet Methods

Gamma-ray spectrum analysis was essential for radioactive environmental monitoring, and it had been widely used in many areas of nuclear engineering. However, for the low-energy region of gamma-ray spectrum, weak peaks were contained in the fast-decreasing background, so it was difficult to extract characteristic information from original spectra. In order to get a better analytic result based on wavelet methods in frequency domain, we had processed the gamma-ray spectrometer data of Chang’E-1 and well extracted some useful information of spectral characteristic peaks. Then, we preliminarily mapped the distribution of net peak counts for potassium on lunar surface, which indirectly reflected the distribution of elemental abundance. At last, we compared our analytic result with that of Apollo and Lunar Prospector and found some consistencies and differences.

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