Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our appro...Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our approach is that it uses a new Clifford-multiwavelet transform to insert copyright data in a multiresolution domain,allowing us to greatly expand the size of the watermark.After that,our method does two rounds of insertion,each applying a different type of Clifford-wavelet transform.Before being placed into the Clifford-multiwavelet coefficients,the watermark,which is a mixture of the mesh description,source mesh signature(produced using SHA512),and a logo encrypted using the RSA(Ronald Shamir Adleman)technique,is encoded using Turbo-code.Using the Least Significant Bit method steps,data embedding involves modulation and insertion processes.Finally,the watermarked mesh is reconstructed using the inverse Cliffordmultiwavelet transform.Due to the utilization of a hybrid insertion domain,our technique has demonstrated a very high insertion rate while retaining mesh quality.The mesh is watermarked,and the extracted data is acquired in real-time.Our approach is also resistant to the most common types of attacks.Our findings reveal that the current approach improves on previous efforts.展开更多
The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperfor...The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.展开更多
In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-leve...In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-level decomposition of the function and uses the method of the valve's value to construct adaptive grid to improve AUSMPW scheme.The obtained press and density have beed compared with those of results calculated by original AUSMPW scheme and WENO scheme.The numerical results demonstrate that this method has higher resolution.展开更多
In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition ...In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.展开更多
Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length bior...Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.展开更多
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting Rs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, ...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting Rs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, two theorems are given for constructing biorthogonal(orthogonal) two-direction refinable functions in L2(Rs) and their biorthogonal(orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal(orthogonal)two-direction wavelets, symmetric biorthogonal(orthogonal) multiwaveles in L2(Rs) can be obtained easily. Applying the projection method to biorthogonal(orthogonal) two-direction wavelets in L2(Rs), we can get dual(tight) two-direction wavelet frames in L2(Rm), where m ≤ s. From the projected dual(tight) two-direction wavelet frames in L2(Rm), symmetric dual(tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be...A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be simply presented. A brief overview of multiwavelets is presented at first. Iris identification system and iris texture feature presentation and recognition based on multiwavelets are introduced subsequently. And the experiment indicates the validity of this method finally.展开更多
A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to...A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to classify the textures in the presence of additive white Gaussian noise (AWGN). The proposed approach extracts features such as energy, entropy, local homogeneity and max-min ratio from the selected singular values of multiwavelets transformation coefficients of image textures. The classification was carried out using probabilistic neural network (PNN). Performance of the proposed approach was compared with conventional wavelet domain gray level co-occurrence matrix (GLCM) based features, discrete multiwavelets transformation energy based approach, and HMM based approach. Experimental results showed the superiority of the proposed algorithms when compared with existing algorithms.展开更多
This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these ...This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis multifilter. Using these new results, we present the parametrization of orthogonal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.展开更多
Synthetic aperture radar (SAR) images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelet...Synthetic aperture radar (SAR) images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees (SPIHT) algorithm, our method achieves favorable peak signal to noise ratio (PSNR) and superior speckle noise reduction performances.展开更多
The element of pesedospectral-multiwavelet-Galerkin method, and how to combine it with penalty method for treating boundary conditions are given.Multiwavelet bases don't overlap on the given scale, and possess the...The element of pesedospectral-multiwavelet-Galerkin method, and how to combine it with penalty method for treating boundary conditions are given.Multiwavelet bases don't overlap on the given scale, and possess the same compact set in a group of several functions, so they can be directly used to the numerical discretion on the finite interval.Numerical tests show that general boundary conditions can be enforced with the penalty method, and that pesedospectral-multiwavelet-Galerkin method can well track the solutions' development.This also proves that pesedospectral-multiwavelet-Galerkin method is effective.展开更多
Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize....Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize. Compared with Wornell's single wavelet method, the new method has r filtering factors at each scale and has higher filtering speed, where r is the multiplicity of multiwavelet. Also due to the advantages of multiwavelet, the multiwavelet method performs better than that of Wornell's. Simulation results verify the analysis, and Wornell's method is the special case of our method when r = 1.展开更多
Deviation is essential to classic soft threshold denoising in wavelet domain. Texture features ofnoised image denoised by wavelet transform were weakened. Gibbs effect is distinct at edges of image.Image blurs compari...Deviation is essential to classic soft threshold denoising in wavelet domain. Texture features ofnoised image denoised by wavelet transform were weakened. Gibbs effect is distinct at edges of image.Image blurs comparing with original noised image. To solve the questions, a blind denoising method basedon single-wavelet transform and multiwavelets transform was proposed. The method doesn’t depend onsize of image and deviation to determine threshold of wavelet coefficients, which is different from classicalsoft-threshold denoising in wavelet domain. Moreover, the method is good for many types of noise. Gibbseffect disappeared with this method, edges of image are preserved well, and noise is smoothed andrestrained effectively.展开更多
In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness,a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed.Multiwavelets ...In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness,a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed.Multiwavelets have several scaling functions and wavelet functions,and possess excellent properties that a scalar wavelet cannot satisfy simultaneously,and match the different characteristics of signals.Moreover,the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising.Therefore,the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process.The algorithm of balanced orthogonal multiwavelet and the implementation steps of this denoising are described.The experimental comparison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done.The experiments indicate that this method is effective and feasible to extract the fault feature submerged in heavy noise.展开更多
Fault diagnosis of rolling mills, especially the main drive gearbox, is of great importance to the high quality products and long-term safe operation. However, the useful fault information is usually submerged in heav...Fault diagnosis of rolling mills, especially the main drive gearbox, is of great importance to the high quality products and long-term safe operation. However, the useful fault information is usually submerged in heavy background noise under the severe condition. Thereby, a novel method based on multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution is proposed for gearbox fault diagnosis in rolling mills. The emerging multiwavelets can seize the important signal processing properties simultaneously. Owing to the multiple scaling and wavelet basis functions, they have the supreme possibility of matching various features. Due to the periodicity of gearbox signals, sliding window is recommended to conduct local threshold denoising, so as to avoid the "overkill" of conventional universal thresholding techniques. Meanwhile, neighboring coefficient denoising, considering the correlation of the coefficients, is introduced to effectively process the noisy signals in every sliding window. Thus, multiwavelet sliding window neighboring coefficient denoising not only can perform excellent fault extraction, but also accords with the essence of gearbox fault features. On the other hand, optimal blind deconvolution is carried out to highlight the denoised features for operators' easy identification. The filter length is vital for the effective and meaningful results. Hence, the foremost filter length selection based on the kurtosis is discussed in order to full benefits of this technique. The new method is applied to two gearbox fault diagnostic cases of hot strip finishing mills, compared with multiwavelet and scalar wavelet methods with/without optimal blind deconvolution. The results show that it could enhance the ability of fault detection for the main drive gearboxes.展开更多
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vector...In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vectors of functions in the Sobolev space (Hμ(Rs))r for some μ > 0. We provide a characterization for the sequences {ψjk : = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jk : = 1, . . . , r, j ∈ Z, k ∈ Zs} to form two Riesz sequences for L2(Rs), where ψjk = mj/2ψ (M j ·k) and ψjk = mj/2 ψ (M j ·k), M is an s × s integer matrix such that limn→∞ Mn = 0 and m = |detM|. Furthermore, let = (1, . . . , r)T and = ( 1, . . . , r)T be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, a and M, where a and a are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1, . . . , ψνr)T and ψν = ( ψν1, . . . , ψ?νr)T , ν = 1, . . . , m 1 such that two sequences {ψjνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} form two Riesz multiwavelet bases for L2(Rs). The bracket product [f, g] of two vectors of functions f, g in (L2(Rs))r is an indispensable tool for our characterization.展开更多
基金This research work was funded by the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia through the project number(IF-PSAU-2021/01/17567)。
文摘Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our approach is that it uses a new Clifford-multiwavelet transform to insert copyright data in a multiresolution domain,allowing us to greatly expand the size of the watermark.After that,our method does two rounds of insertion,each applying a different type of Clifford-wavelet transform.Before being placed into the Clifford-multiwavelet coefficients,the watermark,which is a mixture of the mesh description,source mesh signature(produced using SHA512),and a logo encrypted using the RSA(Ronald Shamir Adleman)technique,is encoded using Turbo-code.Using the Least Significant Bit method steps,data embedding involves modulation and insertion processes.Finally,the watermarked mesh is reconstructed using the inverse Cliffordmultiwavelet transform.Due to the utilization of a hybrid insertion domain,our technique has demonstrated a very high insertion rate while retaining mesh quality.The mesh is watermarked,and the extracted data is acquired in real-time.Our approach is also resistant to the most common types of attacks.Our findings reveal that the current approach improves on previous efforts.
文摘The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50476028)
文摘In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-level decomposition of the function and uses the method of the valve's value to construct adaptive grid to improve AUSMPW scheme.The obtained press and density have beed compared with those of results calculated by original AUSMPW scheme and WENO scheme.The numerical results demonstrate that this method has higher resolution.
文摘In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.
文摘Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.
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 Rs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, two theorems are given for constructing biorthogonal(orthogonal) two-direction refinable functions in L2(Rs) and their biorthogonal(orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal(orthogonal)two-direction wavelets, symmetric biorthogonal(orthogonal) multiwaveles in L2(Rs) can be obtained easily. Applying the projection method to biorthogonal(orthogonal) two-direction wavelets in L2(Rs), we can get dual(tight) two-direction wavelet frames in L2(Rm), where m ≤ s. From the projected dual(tight) two-direction wavelet frames in L2(Rm), symmetric dual(tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.
文摘A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be simply presented. A brief overview of multiwavelets is presented at first. Iris identification system and iris texture feature presentation and recognition based on multiwavelets are introduced subsequently. And the experiment indicates the validity of this method finally.
文摘A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to classify the textures in the presence of additive white Gaussian noise (AWGN). The proposed approach extracts features such as energy, entropy, local homogeneity and max-min ratio from the selected singular values of multiwavelets transformation coefficients of image textures. The classification was carried out using probabilistic neural network (PNN). Performance of the proposed approach was compared with conventional wavelet domain gray level co-occurrence matrix (GLCM) based features, discrete multiwavelets transformation energy based approach, and HMM based approach. Experimental results showed the superiority of the proposed algorithms when compared with existing algorithms.
文摘This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis multifilter. Using these new results, we present the parametrization of orthogonal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.
基金This work was supported by the National Natural Science Foundation of China under Grant No. 60472048.
文摘Synthetic aperture radar (SAR) images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees (SPIHT) algorithm, our method achieves favorable peak signal to noise ratio (PSNR) and superior speckle noise reduction performances.
基金This project is supported by National Natural Science Foundation of China(No. 19971020) Multidiseipline Scientific Research Foundation of Harbin Institute of Technology, China(No.HIT.MD2001.26).
文摘The element of pesedospectral-multiwavelet-Galerkin method, and how to combine it with penalty method for treating boundary conditions are given.Multiwavelet bases don't overlap on the given scale, and possess the same compact set in a group of several functions, so they can be directly used to the numerical discretion on the finite interval.Numerical tests show that general boundary conditions can be enforced with the penalty method, and that pesedospectral-multiwavelet-Galerkin method can well track the solutions' development.This also proves that pesedospectral-multiwavelet-Galerkin method is effective.
基金Supported by the National Laboratory of Space Microwave Technology Foundation(No.51473030105JB3201).
文摘Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize. Compared with Wornell's single wavelet method, the new method has r filtering factors at each scale and has higher filtering speed, where r is the multiplicity of multiwavelet. Also due to the advantages of multiwavelet, the multiwavelet method performs better than that of Wornell's. Simulation results verify the analysis, and Wornell's method is the special case of our method when r = 1.
文摘Deviation is essential to classic soft threshold denoising in wavelet domain. Texture features ofnoised image denoised by wavelet transform were weakened. Gibbs effect is distinct at edges of image.Image blurs comparing with original noised image. To solve the questions, a blind denoising method basedon single-wavelet transform and multiwavelets transform was proposed. The method doesn’t depend onsize of image and deviation to determine threshold of wavelet coefficients, which is different from classicalsoft-threshold denoising in wavelet domain. Moreover, the method is good for many types of noise. Gibbseffect disappeared with this method, edges of image are preserved well, and noise is smoothed andrestrained effectively.
基金supported by Scientific and Technological Foundation of Henan Province under Grant No.112102210128Science Research Project of Educational Department of Henan Province under Grant No.2011C510005
文摘In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness,a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed.Multiwavelets have several scaling functions and wavelet functions,and possess excellent properties that a scalar wavelet cannot satisfy simultaneously,and match the different characteristics of signals.Moreover,the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising.Therefore,the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process.The algorithm of balanced orthogonal multiwavelet and the implementation steps of this denoising are described.The experimental comparison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done.The experiments indicate that this method is effective and feasible to extract the fault feature submerged in heavy noise.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200806980011)National Natural Science Foundation of China (Grant No. 50875197)
文摘Fault diagnosis of rolling mills, especially the main drive gearbox, is of great importance to the high quality products and long-term safe operation. However, the useful fault information is usually submerged in heavy background noise under the severe condition. Thereby, a novel method based on multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution is proposed for gearbox fault diagnosis in rolling mills. The emerging multiwavelets can seize the important signal processing properties simultaneously. Owing to the multiple scaling and wavelet basis functions, they have the supreme possibility of matching various features. Due to the periodicity of gearbox signals, sliding window is recommended to conduct local threshold denoising, so as to avoid the "overkill" of conventional universal thresholding techniques. Meanwhile, neighboring coefficient denoising, considering the correlation of the coefficients, is introduced to effectively process the noisy signals in every sliding window. Thus, multiwavelet sliding window neighboring coefficient denoising not only can perform excellent fault extraction, but also accords with the essence of gearbox fault features. On the other hand, optimal blind deconvolution is carried out to highlight the denoised features for operators' easy identification. The filter length is vital for the effective and meaningful results. Hence, the foremost filter length selection based on the kurtosis is discussed in order to full benefits of this technique. The new method is applied to two gearbox fault diagnostic cases of hot strip finishing mills, compared with multiwavelet and scalar wavelet methods with/without optimal blind deconvolution. The results show that it could enhance the ability of fault detection for the main drive gearboxes.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123)
文摘In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vectors of functions in the Sobolev space (Hμ(Rs))r for some μ > 0. We provide a characterization for the sequences {ψjk : = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jk : = 1, . . . , r, j ∈ Z, k ∈ Zs} to form two Riesz sequences for L2(Rs), where ψjk = mj/2ψ (M j ·k) and ψjk = mj/2 ψ (M j ·k), M is an s × s integer matrix such that limn→∞ Mn = 0 and m = |detM|. Furthermore, let = (1, . . . , r)T and = ( 1, . . . , r)T be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, a and M, where a and a are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1, . . . , ψνr)T and ψν = ( ψν1, . . . , ψ?νr)T , ν = 1, . . . , m 1 such that two sequences {ψjνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} form two Riesz multiwavelet bases for L2(Rs). The bracket product [f, g] of two vectors of functions f, g in (L2(Rs))r is an indispensable tool for our characterization.