The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secur...The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.展开更多
Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets...Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.展开更多
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ...In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.展开更多
Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in...Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.展开更多
Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays were introduced. In the current paper, we propose the wavelets to an...Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays were introduced. In the current paper, we propose the wavelets to analyze such images. The wavelets are built on these reference functions as on the scaling functions of the wavelet analysis. The continuous wavelet transform was successfully applied to the testing wireframe binary objects. The restored locations correspond to the structure of the testing wireframe binary objects.展开更多
Recently, we found that side lobes of wavelets have a large impact on the identification of thin sand reservoirs when studying some gas fields in a basin in Northwest China. Reflections from the top of the H Formation...Recently, we found that side lobes of wavelets have a large impact on the identification of thin sand reservoirs when studying some gas fields in a basin in Northwest China. Reflections from the top of the H Formation, in which there are gas-bearing thin sand bodies, have the main wavelet lobe between two weak peak side lobes. The lower one always mixes with another peak reflected from the top of a thin sand reservoir. That makes it difficult to identify the sand reservoir. In order to solve this, many forward models were set up using typical well logs. 2D synthetic profiles were produced using Ricker wavelets to study the relationships between the effects of wavelet side lobes and thin sand position and frequency and between amplitude and the thin sand body. We developed the following conclusions： First, it is easier to identify thin sands in a shallower position. Second, a good way to tell sand body reflections from side lobes is by comparing profiles with different frequency windows. Third, it is helpful and effective to describe sand extent using amplitude attributes.展开更多
This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characterist...This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characteristics of a signal both in the time and frequency domains, the occurring instants of abnormal status of a sensor in the output signal can be identified by the multi-scale representation of the signal. Once the instants are detected, the distribution differences of the signal energy on all decomposed wavelet scales of the signal before and after the instants are used to claim and classify the sensor faults.展开更多
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displac...The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.展开更多
After some permutation of conjugate quadrature filter, new conjugate quadrature filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal ...After some permutation of conjugate quadrature filter, new conjugate quadrature filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal wavelets from univariate orthogonal wavelets. Non-separable orthogonal wavelets can be achieved. To demonstrate this method, an example is given.展开更多
A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent pea...A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum （EPS）. Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average （ARMA） filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals＇ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.展开更多
Structural health monitoring (SHM) is a relevant topic for civil systems and involves the monitoring, data processing and interpretation to evaluate the condition of a structure, in order to detect damage. In real str...Structural health monitoring (SHM) is a relevant topic for civil systems and involves the monitoring, data processing and interpretation to evaluate the condition of a structure, in order to detect damage. In real structures, two or more sites or types of damage can be present at the same time. It has been shown that one kind of damaged condition can interfere with the detection of another kind of damage, leading to an incorrect assessment about the structure condition. Identifying combined damage on structures still represents a challenge for condition monitoring, because the reliable identification of a combined damaged condition is a difficult task. Thus, this work presents a fusion of methodologies, where a single wavelet-packet and the empirical mode decomposition (EMD) method are combined with artificial neural networks (ANNs) for the automated and online identification-location of single or multiple-combined damage in a scaled model of a five-bay truss-type structure. Results showed that the proposed methodology is very efficient and reliable for identifying and locating the three kinds of damage, as well as their combinations. Therefore, this methodology could be applied to detection-location of damage in real truss-type structures, which would help to improve the characteristics and life span of real structures.展开更多
In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by ...In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the fam...The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).展开更多
An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of...An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented.Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations.And the convergence of the Euler wavelets basis is given.The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.展开更多
Continuous Morlet and Mexican hat wavelets are used to analyze a highly irregular rough surface replicated from real turbine blades which are roughened by deposi-tion of foreign materials. The globally dominant aspect...Continuous Morlet and Mexican hat wavelets are used to analyze a highly irregular rough surface replicated from real turbine blades which are roughened by deposi-tion of foreign materials. The globally dominant aspect ratio, length scale, and orientation of the roughness elements are determined. These parameters extracted from this highly irregular rough surface are important for the future studies of their effects on turbulent flows over this kind of rough surfaces encountered in Washington aerospace and power generating industries.展开更多
This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing ima...This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding.It transfers images into subband details and approximations using a modified Haar wavelet(MHW),and then applies a threshold.PSO is applied for selecting a particle assigned to the threshold values for the subbands.Nine positions assigned to particles values are used to represent population.Every particle updates its position depending on the global best position(gbest)(for all details subband)and local best position(pbest)(for a subband).The fitness value is developed to terminate PSO when the difference between two local best(pbest)successors is smaller than a prescribe value.The experiments are applied on five different medical image types,i.e.,MRI,CT,and X-ray.Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio(PSNR)and compression ratio(CR)points of views.展开更多
基金"La derivada fraccional generalizada,nuevos resultados y aplicaciones a desigualdades integrales"Cod UIO-077-2024supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446).
文摘The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.
基金supported by the Geosciences and Technology Academy of China University of Petroleum(East China)
文摘Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.
文摘In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.
基金Supported by the State Key Laboratory of Acoustics and Marine Information Chinese Academy of Sciences(SKL A202507).
文摘Accurate time delay estimation of target echo signals is a critical component of underwater target localization.In active sonar systems,echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment.This paper proposes a novel method for estimating target time delay using multi-bright spot echoes,assuming the target’s size and depth are known.Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise,the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes.Using the highlighting model theory and the target size information,an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles.Aiming to accurately estimate the target’s time delay,waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays.Simulation results show that,compared to the conventional matched filter,the proposed algorithm reduces the relative error by 65.9%-91.5%at a signal-to noise ratio of-25 dB,and by 66.7%-88.9%at a signal-to-reverberation ratio of−10 dB.This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.
文摘Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays were introduced. In the current paper, we propose the wavelets to analyze such images. The wavelets are built on these reference functions as on the scaling functions of the wavelet analysis. The continuous wavelet transform was successfully applied to the testing wireframe binary objects. The restored locations correspond to the structure of the testing wireframe binary objects.
文摘Recently, we found that side lobes of wavelets have a large impact on the identification of thin sand reservoirs when studying some gas fields in a basin in Northwest China. Reflections from the top of the H Formation, in which there are gas-bearing thin sand bodies, have the main wavelet lobe between two weak peak side lobes. The lower one always mixes with another peak reflected from the top of a thin sand reservoir. That makes it difficult to identify the sand reservoir. In order to solve this, many forward models were set up using typical well logs. 2D synthetic profiles were produced using Ricker wavelets to study the relationships between the effects of wavelet side lobes and thin sand position and frequency and between amplitude and the thin sand body. We developed the following conclusions： First, it is easier to identify thin sands in a shallower position. Second, a good way to tell sand body reflections from side lobes is by comparing profiles with different frequency windows. Third, it is helpful and effective to describe sand extent using amplitude attributes.
文摘This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characteristics of a signal both in the time and frequency domains, the occurring instants of abnormal status of a sensor in the output signal can be identified by the multi-scale representation of the signal. Once the instants are detected, the distribution differences of the signal energy on all decomposed wavelet scales of the signal before and after the instants are used to claim and classify the sensor faults.
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
基金The project supported by the National Natural Science Foundation of China
文摘The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.
基金This research was partially supported by National Natural Science Foundation of China (10371033 60403011).
文摘After some permutation of conjugate quadrature filter, new conjugate quadrature filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal wavelets from univariate orthogonal wavelets. Non-separable orthogonal wavelets can be achieved. To demonstrate this method, an example is given.
文摘A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum （EPS）. Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average （ARMA） filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals＇ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.
基金Project (No. PIFI-2012 U. de Gto.) supported by the Secretariat of Public Education (SEP), Mexico
文摘Structural health monitoring (SHM) is a relevant topic for civil systems and involves the monitoring, data processing and interpretation to evaluate the condition of a structure, in order to detect damage. In real structures, two or more sites or types of damage can be present at the same time. It has been shown that one kind of damaged condition can interfere with the detection of another kind of damage, leading to an incorrect assessment about the structure condition. Identifying combined damage on structures still represents a challenge for condition monitoring, because the reliable identification of a combined damaged condition is a difficult task. Thus, this work presents a fusion of methodologies, where a single wavelet-packet and the empirical mode decomposition (EMD) method are combined with artificial neural networks (ANNs) for the automated and online identification-location of single or multiple-combined damage in a scaled model of a five-bay truss-type structure. Results showed that the proposed methodology is very efficient and reliable for identifying and locating the three kinds of damage, as well as their combinations. Therefore, this methodology could be applied to detection-location of damage in real truss-type structures, which would help to improve the characteristics and life span of real structures.
基金Sponsored by the NSFC (10871003, 10701008, 10726064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
文摘In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
基金This work is pastially supported by NNSFCthe Foundation of Zhongshan University Advanced Reseasch Centre
文摘The explicit form for the orthonormal periodic trigonometric spline wavelet is given. We also give the decomposition and reconstruction equations.Each of the two equations involves onlytwo terms. We prove that the family of periodic trigonometric spline wavelets is dense in L2([0,2π]).
基金The authors are grateful to the editor,the associate editor and the anonymous reviewers for their constructive and helpful comments.This work was supported by the Zhejiang Provincial Natural Science Foundation of China(No.LY18A010026),the National Natural Science Foundation of China(No.11701304,11526117)Zhejiang Provincial Natural Science Foundation of China(No.LQ16A010006)+1 种基金the Natural Science Foundation of Ningbo City,China(No.2017A610143)the Natural Science Foundation of Ningbo City,China(2018A610195).
文摘An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented.Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations.And the convergence of the Euler wavelets basis is given.The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.
基金supported by Wright State UniversityDayton+2 种基金OHU.S.A.The authors thank Professor K.T.CHRISTENSEN at University of Illinois at Urbana-Champaign for providing the roughness topography data
文摘Continuous Morlet and Mexican hat wavelets are used to analyze a highly irregular rough surface replicated from real turbine blades which are roughened by deposi-tion of foreign materials. The globally dominant aspect ratio, length scale, and orientation of the roughness elements are determined. These parameters extracted from this highly irregular rough surface are important for the future studies of their effects on turbulent flows over this kind of rough surfaces encountered in Washington aerospace and power generating industries.
基金funded by the University of Jeddah,Saudi Arabia,under Grant No.UJ-20-043-DR。
文摘This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding.It transfers images into subband details and approximations using a modified Haar wavelet(MHW),and then applies a threshold.PSO is applied for selecting a particle assigned to the threshold values for the subbands.Nine positions assigned to particles values are used to represent population.Every particle updates its position depending on the global best position(gbest)(for all details subband)and local best position(pbest)(for a subband).The fitness value is developed to terminate PSO when the difference between two local best(pbest)successors is smaller than a prescribe value.The experiments are applied on five different medical image types,i.e.,MRI,CT,and X-ray.Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio(PSNR)and compression ratio(CR)points of views.
