This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the pea...This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.展开更多
Let T:Td→Td,defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ1|≤|λ2|≤…≤|λd|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈Td:Tn...Let T:Td→Td,defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ1|≤|λ2|≤…≤|λd|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈Td:Tnx∈B(x,ψ(n))for infinitely many n}forα≥log|λd/λ1|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim infn→∞-logψ(n).In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.展开更多
Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage...Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage transformer errors, particularly minor variations in multi-channel setups, remains challenging. This paper proposes a method for online error tracking of multi-channel capacitive voltage transformers using a Co-Prediction Matrix. The approach leverages the strong correlation between in-phase channels, particularly the invariance of the signal proportions among them. By establishing a co-prediction matrix based on these proportional relationships, The influence of voltage changes on the primary measurements is mitigated. Analyzing the relationships between the co-prediction matrices over time allows for inferring true measurement errors. Experimental validation with real-world data confirms the effectiveness of the method, demonstrating its capability to continuously track capacitive voltage transformer measurement errors online with precision over extended durations.展开更多
By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg (...By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg (D-H) transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.展开更多
UE-Brzier (unified and extended Brzier) basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brz...UE-Brzier (unified and extended Brzier) basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.展开更多
This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with...This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.展开更多
The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relatio...The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relation between the input and output wavelengths of the AWG multiplexer, the wavelength transmission routings of the space switching and wavelength switching OXC nodes are determined.展开更多
The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twenty-six ...The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twenty-six rats were randomly divided into control group (C, n=8), diabetic group (D, n=9), and diabetes+heparin group (DH, n=9). After 8-week therapy of heparin (200 U once daily by abdominal injection), TGF-β 1, LN and FN expression in glomeruli was detected by immunohistochemical method. The results showed that the expression levels of TGF-β 1, LN and FN were higher in group D than in group C. It was found that heparin could reduce 24-h urinary albumin excretion and inhibit overexpression of TGF-β 1, LN and FN in glomeruli of diabetic rats. It suggested that the inhibitory effect of heparin on diabetic glomerular sclerosis was at least partly related with the inhibition of TGF-β 1 expression.展开更多
In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the import...In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.展开更多
The commonly used global sensitivity analysis(GSA)can quantify the influence of random input variables on the variance of target outputs.To avoid the extremely large computational burden of the Monte Carlo simulation ...The commonly used global sensitivity analysis(GSA)can quantify the influence of random input variables on the variance of target outputs.To avoid the extremely large computational burden of the Monte Carlo simulation method(MCSM),a discrete Fourier transformation matrix(DFTM)method is developed for the first time to efficiently tackle the variancebased GSA of transmission systems in the probabilistic optimal power flow(POPF)with correlated random inputs.The proposed DFTM method has a flexible sampling strategy and includes two sub-methods named the discrete sine/cosine transformation matrix(DSTM/DCTM).The superiority of the DFTM in both accuracy and efficiency for the variance-based GSA in POPF is demonstrated by its comparisons with Hong's point estimate method(HPEM),the unscented transformation method(UTM)and the first-order second-moment method(FOSMM).Based on Nataf transformation,it is found through a theoretical derivation in the paper that both HPEM and UTM may lead to a negative variance of output in some cases,which will cause erroneous results of the GSA.In contrast,the proposed DFTM has an immunity to such variance abnormality.The tests and comparisons are implemented on a modified IEEE 118-bus power system,where MCSM is used as a reference for accuracy.展开更多
应用超声检测装配式钢结构防护涂层厚度时,由于涂覆涂层非常薄,会造成回波信号发生混叠,影响厚度检测的准确度。针对此问题,探索了一种基于自适应特征字典和经典字典学习(K singular value decomposition,简称K-SVD)算法的信号时域特征...应用超声检测装配式钢结构防护涂层厚度时,由于涂覆涂层非常薄,会造成回波信号发生混叠,影响厚度检测的准确度。针对此问题,探索了一种基于自适应特征字典和经典字典学习(K singular value decomposition,简称K-SVD)算法的信号时域特征提取方法。首先,利用小波变换对信号奇异值敏感的特性,识别信号的极值并将其作为新的待处理信号;其次,将经过小波变换提取出的特征信号变换为Hankel矩阵形式,并通过周期分割与随机提取的方式构造初始化特征字典;然后,通过改进K-SVD算法获得优化后的特征字典;最后,通过优化后的特征字典重构时域信号。仿真和实验结果表明,与传统的小波变换和基于Gabor字典的匹配追踪(matching pursuit,简称MP)算法相比,该方法分离混叠信号、提取信号时域特征信息的能力更准确,更有利于检测防护涂层的厚度。展开更多
基金supported by the Key Natural Science Research of Guangdong Province,China P.R(Grant No.05Z003)the Project of Tackling Key Problem of Guangdong Province,China P.R(Grant No.2006B12401008)the National Natural Science Foundation of China(Grant No.10672067).
摘要This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
摘要Let T:Td→Td,defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ1|≤|λ2|≤…≤|λd|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈Td:Tnx∈B(x,ψ(n))for infinitely many n}forα≥log|λd/λ1|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim infn→∞-logψ(n).In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
摘要Capacitive voltage transformers (CVTs) are essential in high-voltage systems. An accurate error assessment is crucial for precise energy metering. However, tracking real-time quantitative changes in capacitive voltage transformer errors, particularly minor variations in multi-channel setups, remains challenging. This paper proposes a method for online error tracking of multi-channel capacitive voltage transformers using a Co-Prediction Matrix. The approach leverages the strong correlation between in-phase channels, particularly the invariance of the signal proportions among them. By establishing a co-prediction matrix based on these proportional relationships, The influence of voltage changes on the primary measurements is mitigated. Analyzing the relationships between the co-prediction matrices over time allows for inferring true measurement errors. Experimental validation with real-world data confirms the effectiveness of the method, demonstrating its capability to continuously track capacitive voltage transformer measurement errors online with precision over extended durations.
基金National Natural Science Foundation of China(No.51275486)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20111420110005)
摘要By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg (D-H) transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.
基金Supported by National Science Foundation of China(No.60904070,61272032)the Natural Science Foundation of Zhejiang Province(No.LY12F02002,Y1111101)
摘要UE-Brzier (unified and extended Brzier) basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.
基金Supported by Natural Science Foundations of China (11101108, 11171301, 10771191 and 10471124)Natural Science Foundation of Zhejiang Province of China (Y6090105)
摘要Let X and Y be Banach spaces, 0 〈 q 〈 +∞, i ≤ p 〈 +∞. In this paper, we characterize matrix transformations of lq ( X ) to lp ( Y ).
摘要This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.
基金NationalKeyLabofBroadBandFiberTransmissionandCommunicatonSystemTechnology ElectronicUniversityofScienceandTechnology China
摘要The structures of the space switching and the wavelength switching optical cross connect (OXC) nodes which are based on the arrayed waveguide grating (AWG) multiplexer are analyzed.By the matrix transformation relation between the input and output wavelengths of the AWG multiplexer, the wavelength transmission routings of the space switching and wavelength switching OXC nodes are determined.
摘要The effects of heparin on the expression of transforming growth factor-β 1 (TGF-β 1) and two extracellular matrix components laminin (LN) and fibronectin (FN) in diabetic rat glomeruli were investigated. Twenty-six rats were randomly divided into control group (C, n=8), diabetic group (D, n=9), and diabetes+heparin group (DH, n=9). After 8-week therapy of heparin (200 U once daily by abdominal injection), TGF-β 1, LN and FN expression in glomeruli was detected by immunohistochemical method. The results showed that the expression levels of TGF-β 1, LN and FN were higher in group D than in group C. It was found that heparin could reduce 24-h urinary albumin excretion and inhibit overexpression of TGF-β 1, LN and FN in glomeruli of diabetic rats. It suggested that the inhibitory effect of heparin on diabetic glomerular sclerosis was at least partly related with the inhibition of TGF-β 1 expression.
摘要In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.
基金supported by the National Natural Science Foundation of China(Project No.:52177071)。
摘要The commonly used global sensitivity analysis(GSA)can quantify the influence of random input variables on the variance of target outputs.To avoid the extremely large computational burden of the Monte Carlo simulation method(MCSM),a discrete Fourier transformation matrix(DFTM)method is developed for the first time to efficiently tackle the variancebased GSA of transmission systems in the probabilistic optimal power flow(POPF)with correlated random inputs.The proposed DFTM method has a flexible sampling strategy and includes two sub-methods named the discrete sine/cosine transformation matrix(DSTM/DCTM).The superiority of the DFTM in both accuracy and efficiency for the variance-based GSA in POPF is demonstrated by its comparisons with Hong's point estimate method(HPEM),the unscented transformation method(UTM)and the first-order second-moment method(FOSMM).Based on Nataf transformation,it is found through a theoretical derivation in the paper that both HPEM and UTM may lead to a negative variance of output in some cases,which will cause erroneous results of the GSA.In contrast,the proposed DFTM has an immunity to such variance abnormality.The tests and comparisons are implemented on a modified IEEE 118-bus power system,where MCSM is used as a reference for accuracy.
摘要应用超声检测装配式钢结构防护涂层厚度时,由于涂覆涂层非常薄,会造成回波信号发生混叠,影响厚度检测的准确度。针对此问题,探索了一种基于自适应特征字典和经典字典学习(K singular value decomposition,简称K-SVD)算法的信号时域特征提取方法。首先,利用小波变换对信号奇异值敏感的特性,识别信号的极值并将其作为新的待处理信号;其次,将经过小波变换提取出的特征信号变换为Hankel矩阵形式,并通过周期分割与随机提取的方式构造初始化特征字典;然后,通过改进K-SVD算法获得优化后的特征字典;最后,通过优化后的特征字典重构时域信号。仿真和实验结果表明,与传统的小波变换和基于Gabor字典的匹配追踪(matching pursuit,简称MP)算法相比,该方法分离混叠信号、提取信号时域特征信息的能力更准确,更有利于检测防护涂层的厚度。