A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES

Cascade algorithms play an important role in wavelet analysis and computer graphics. The paper considers the convergence of cascade algorithms in Sobolev spaces. With the help of the factorization of matrix masks, we give a sufficient condition for the convergence. The condition is expressed in the time domain. More importantly, an algorithm for the construction of convergent cascade algorithms in Sobolev space starting from any matrix mask satisfying a mild condition is presented. Examples are given to illustrate our theorems.

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Fault Detection of Induction Motors Using Fourier and Wavelet Analysis

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2004.p0431 ◽

2004 ◽

Vol 8 (4) ◽

pp. 431-436 ◽

Cited By ~ 3

Author(s):

Hyeon Bae ◽

◽

Youn-Tae Kim ◽

Sungshin Kim ◽

Sang-Hyuk Lee ◽

...

Keyword(s):

Neural Network ◽

Fault Detection ◽

Wavelet Analysis ◽

Time Domain ◽

Induction Motors ◽

Fuzzy Inference ◽

Classification Model ◽

Diagnosis And Prognosis ◽

Signal Features ◽

The Time Domain

The motor is the workhorse of industries. The issues of preventive and condition-based maintenance, online monitoring, system fault detection, diagnosis, and prognosis are of increasing importance. This paper introduces fault detection for induction motors. Stator currents are measured by current meters and stored by time domain. The time domain is not suitable for representing current signals, so the frequency domain is applied to display signals. The Fourier Transform is employed to convert signals. After signal conversion, signal features must be extracted by signal processing such as wavelet and spectrum analysis. Features are entered in a pattern classification model such as a neural network model, a polynomial neural network, or a fuzzy inference model. This paper describes fault detection results that use Fourier and wavelet analysis. This combined approach is very useful and powerful for detecting signal features.

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Financial Index Prediction Based on Wavelet Analysis and SVM

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.303-306.1114 ◽

2013 ◽

Vol 303-306 ◽

pp. 1114-1118

Author(s):

Xian Tan

Keyword(s):

Wavelet Analysis ◽

Frequency Domain ◽

Time Domain ◽

Financial Time Series ◽

Support Vector ◽

Frequency Domain Method ◽

Signal Characteristics ◽

Vector Machines ◽

Financial Index ◽

The Time Domain

The analysis of the time sequence can be two ways in the time domain and frequency domain. But many financial time series exhibit strong non-stationary and long memory, which makes many traditional individually focused on the research and analysis of the time domain or frequency domain method is no longer applicable. In this paper, wavelet analysis and support vector machines for use in the time domain and frequency domain have the ability to characterize the local signal characteristics, location and mutation of the singular points and irregular mutation analysis, these mutations detected the degree of significance.

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Multipliers Between Sobolev Spaces

Canadian Mathematical Bulletin ◽

10.4153/cmb-1991-075-7 ◽

1991 ◽

Vol 34 (4) ◽

pp. 465-473

Author(s):

R. C. Fabec

Keyword(s):

Sobolev Space ◽

Sobolev Spaces ◽

Higher Dimensions ◽

Sufficient Condition

AbstractA sufficient condition for the boundedness of a multiplier from a Sobolev space of index t > 1 / 4 to one of opposite index — t is obtained. The condition relates the indices of the Sobolev spaces to which the multiplier belongs to the pairs of Sobolev spaces between which the multiplier is bounded. The result is applied to homogeneous multipliers and a description of these multipliers in this setting is presesented. Extensions to higher dimensions are indicated.

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A generic gust definition and detection method based on wavelet-analysis

Advances in Science and Research ◽

10.5194/asr-16-143-2019 ◽

2019 ◽

Vol 16 ◽

pp. 143-148

Author(s):

Helge Knoop ◽

Felix Ament ◽

Björn Maronga

Keyword(s):

High Resolution ◽

Wavelet Analysis ◽

Wind Velocity ◽

Time Domain ◽

Velocity Measurement ◽

Measurement Data ◽

Direct Link ◽

Velocity Signal ◽

Characteristic Period ◽

The Time Domain

Abstract. Wind gusts can have destructive effects on many structures and objects deemed valuable to humans. The aviation industry, for example, views gusts as a major hazard. Their destructive effect is proportional to the momentum that a specific gust imposes onto an object. The actual definition of a gust has a strong influence on how its impact can be quantified. Existing gust definitions, however, are largely based on fixed parameters describing shape requirements and thresholds and are often developed only for specific use cases. These gust definitions do not provide a direct link to the physical impact a particular gust has on a structure or object. The overall goal of this study is to provide such a direct link. The application of a wavelet-analysis to a turbulence-resolving wind velocity signal allows for the localization of signal amplitudes in the period as well as in the time domain. In this paper, we use wavelet-analysis in order to develop a straight-forward method of deriving information about gusts from a wind velocity signal. In order to define what a particular gust might be, we suggest the specification of a characteristic period and amplitude in the time-domain. We define a generic gust as a section of a wind velocity signal, where the wavelet-analysis detects that characteristic amplitude to be matched or exceeded within that characteristic period. The characteristic amplitudes and periods are generic and span a two-dimensional space of generic gust definitions. The method can be applied to turbulence resolving simulation data as well as high-resolution wind velocity measurement data. It can detect gusts of any shape, it is unbiased regarding any specific use case and invariant to changes of the mean wind. We provide a detailed description of the method, its capabilities and demonstrate its application to high resolution wind velocity measurement data.

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Research on signals extrapolation in the time domain based on wavelet analysis

The Journal of Engineering ◽

10.1049/joe.2019.0405 ◽

2019 ◽

Vol 2019 (20) ◽

pp. 6533-6536 ◽

Cited By ~ 2

Author(s):

Huan Liu ◽

Hongmei Ren ◽

Zhihe Xiao ◽

Tao Zhao

Keyword(s):

Wavelet Analysis ◽

Time Domain ◽

The Time Domain

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An Introduction to Harmonic Wavelet Analysis of Machine Vibrations

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/97-gt-058 ◽

1997 ◽

Cited By ~ 3

Author(s):

Jose I. Bonel-Cerdan ◽

Jorgen L. Nikolajsen

Keyword(s):

Wavelet Analysis ◽

Condition Monitoring ◽

Time Domain ◽

Time Window ◽

Three Dimensional ◽

Harmonic Wavelet ◽

To Come ◽

Commercial Applications ◽

The Time Domain ◽

Fft Analysis

The Fast Wavelet Transform (FWT) is a powerful new tool which can be used for vibration analysis and condition monitoring of advanced rotating machinery. The main advantage of wavelet analysis for condition monitoring is that so-called wavelet maps can be produced showing three dimensional plots of amplitude versus frequency and time. This is in contrast to Fast Fourier Transform (FFT) analysis, in which the time domain of the signal is lost. The wavelet maps provide striking visual indications of tiny changes in machine behaviour which cannot be detected in a normal frequency spectrum. This improves the chances of averting catastrophic failures and expands the time window available to take corrective action. Additional advantages of wavelet analysis over FFT analysis include: (1) no requirements for periodicity of the signal, (2) extremely fast computation, (3) the location of patterns in the time domain and (4) an effective detection of high frequency details. Wavelet analyses of all types are available but user-friendly information is hard to come by and this has a detrimental effect on progress towards practical commercial applications. Thus, the main purpose of this paper is to provide a simple and clear introduction to wavelet analysis and its use in machine condition monitoring. The paper has been written for an audience having some familiarity with spectrum analysis but no prior knowledge of wavelets.

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Application of Wavelet Analysis in the Virtual Measurement of Roundness/Cylindricalness for Shaft-Like Components

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.392-394.69 ◽

2008 ◽

Vol 392-394 ◽

pp. 69-73

Author(s):

Li Zhi Gu ◽

Chun Jiang Xiang

Keyword(s):

Wavelet Transform ◽

Wavelet Analysis ◽

Time Domain ◽

Least Square Method ◽

Virtual Manufacturing ◽

Least Square ◽

Time Saving ◽

Individual Step ◽

The Time Domain

Wavelet analysis was applied to detect the greatest deviation from the perfect circle for the roundness and cylindricalness of shaft-like components in the virtual manufacturing engineering. Based on the concepts of the roundness and cylindricalness, the least square method was adopted into the determination of the reference—the least square circle from which the deviation was calculated. In order to obtain the extremum of the errors, wavelet transform was carried out with binary wavelet from the time domain to frequency domain. A virtual probe was used to have the signals for the measured point by using WTnode_gettranslation() function. The accuracy of the measurement depends, to a large extent, on the length of individual step along the axis and the density of the measured points on the sections. Experiments have shown that the measuring processing was time-saving and the results from the wavelet analysis were much reliable.

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A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems

Volume 9: 13th ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications ◽

10.1115/detc2017-68270 ◽

2017 ◽

Cited By ~ 15

Author(s):

Sara Dadras ◽

Soodeh Dadras ◽

Hadi Malek ◽

YangQuan Chen

Keyword(s):

Exponential Stability ◽

Fractional Order ◽

Lyapunov Stability ◽

Time Domain ◽

Sufficient Conditions ◽

Lyapunov Stability Theory ◽

Sufficient Condition ◽

Fractional Order Systems ◽

The Stability ◽

The Time Domain

In this paper, stability of fractional order (FO) systems is investigated in the sense of the Lyapunov stability theory. A new definition for exponential stability of the fractional order systems is given and sufficient conditions are obtained for the exponential stability of the FO systems using the notion of Lyapunov stability. Besides, a less conservative sufficient condition is derived for asymptotical stability of FO systems. The stability analysis is done in the time domain. Numerical examples are given to show that the obtained conditions are effective and applicable in practice.

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