A t-covering array of size N, degree k, order v and strength t is an N x k array with entries from a set of v symbols such that any N x t subarray contains a t-tuple of v symbols at least once as a row. This paper pre...A t-covering array of size N, degree k, order v and strength t is an N x k array with entries from a set of v symbols such that any N x t subarray contains a t-tuple of v symbols at least once as a row. This paper presents a new algebraic recursive method for constructing covering arrays based on difference matrices. The method can extend parameter factors on the existing covering arrays and cover all the combinations of any t parameter factors （t≥2）. The method, which recursively generates high strength covering arrays, is practical. Meanwhile, the theoretical derivation and realization of the proposed algebraic recursive algorithm are given.展开更多
In order to improve the frequency response and anti-interference characteristics of the smart electromechanical actuator(EMA)system,and aiming at the force fighting problem when multiple actuators work synchronously,a...In order to improve the frequency response and anti-interference characteristics of the smart electromechanical actuator(EMA)system,and aiming at the force fighting problem when multiple actuators work synchronously,a multi input multi output(MIMO)position difference cross coupling control coordinated strategy based on double‑closed-loop load feedforward control is proposed and designed.In this strategy,the singular value method of return difference matrix is used to design the parameter range that meets the requirements of system stability margin,and the sensitivity function and the H_(∞)norm theory are used to design and determine the optimal solution in the obtained parameter stability region,so that the multi actuator system has excellent synchronization,stability and anti-interference.At the same time,the mathematical model of the integrated smart EMA system is established.According to the requirements of point-to-point control,the controller of double-loop control and load feedforward compensation is determined and designed to improve the frequency response and anti-interference ability of single actuator.Finally,the 270 V high-voltage smart EMA system experimental platform is built,and the frequency response,load feedforward compensation and coordinated control experiments are carried out to verify the correctness of the position difference cross coupling control strategy and the rationality of the parameter design,so that the system can reach the servo control indexes of bandwidth 6 Hz,the maximum output force 20000 N and the synchronization error≤0.1 mm,which effectively solves the problem of force fighting.展开更多
The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
The better compression rate can be achieved by the traditional vector quantization （VQ） method, and the quality of the recovered image can also be accepted. But the decompressed image quality can not be promoted eff...The better compression rate can be achieved by the traditional vector quantization （VQ） method, and the quality of the recovered image can also be accepted. But the decompressed image quality can not be promoted efficiently, so how to balance the image compression rate and image recovering quality is an important issue, in this paper, an image is transformed by discrete wavelet transform （DWT） to generate its DWT transformed image which can be compressed by the VQ method further. Besides, we compute the values between the DWT transformed image and decompressed DWT transformed image as the difference matrix which is the adjustable basis of the decompressed image quality. By controlling the deviation of the difference matrix, there can be nearly Iossless compression for the VQ method. Experimental results show that when the number of compressed bits by our method is equal to the number of those bits compressed by the VQ method, the quality of our recovered image is better. Moreover, the proposed method has more compression capability comparing with the VQ scheme.展开更多
Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional ...Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean restriction.Methodologically,our test allows heteroscedastic regression models without imposing any condition on the distribution of the error,utilizes effectively important information contained in the distance of the vector of covariates,has a simple form,is easy to implement,and is free of the subjective choice of parameters.Theoretically,our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model diagnostics.The asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also presented.In particular,we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence matrix.Since the asymptotic null distribution of the test statistic depends on data generating process,we propose a wild bootstrap scheme to approximate its null distribution.The consistency of the bootstrap scheme is justified.Numerical studies are undertaken to show the good performance of the new test.展开更多
Error model is the basis for accuracy-related computations and analyses for parallel kinematic machines（PKMs）.Traditional error modeling methods are usually based on differentiation of kinematic solutions,but the so...Error model is the basis for accuracy-related computations and analyses for parallel kinematic machines（PKMs）.Traditional error modeling methods are usually based on differentiation of kinematic solutions,but the solving process is often complex and has limitations for certain specialized PKMs.A concise numerical error modeling method with the inverse kinematic solution as its only requirement is presented in this paper.To avoid complex Jacobian matrix computations,the difference matrix that can be quickly calculated by kinematic solutions was used to replace the differential matrix.The quasi-Newton method,which has high speed and high precision,was introduced to solve the numerical forward kinematic problem.To verify the efficiency of this numerical error modeling method,three applications in error transformation matrix（ETM） modeling,error analysis,and kinematic calibration were simulated on a 4RRR PKM.A comparison with the results obtained by the traditional method shows that the numerical method is accurate,convenient,and has lower requirements and wider applicability,especially for certain specialized and manufactured PKMs.展开更多
By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal array...By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal arrays are constructed.展开更多
In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrice...In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrices,we present some general recursive methods for constructing OAs of such type.Several families of OAs with high percent saturation are constructed.In particular,for any integerλ≥3,such a two-level OA of run 4λcan always be obtained if the corresponding Hadamard matrix exists.展开更多
In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented....In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.展开更多
In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary ...In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.展开更多
We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can b...We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.展开更多
基金The National Natural Science Foundation of China (No.90818027, 61003020, 91018005, 60873050)the National High Technology Research and Development Program of China (863 Program ) (No.2009AA01Z147)the National Basic Research Program of China (973 Program) ( No. 2009CB320703)
文摘A t-covering array of size N, degree k, order v and strength t is an N x k array with entries from a set of v symbols such that any N x t subarray contains a t-tuple of v symbols at least once as a row. This paper presents a new algebraic recursive method for constructing covering arrays based on difference matrices. The method can extend parameter factors on the existing covering arrays and cover all the combinations of any t parameter factors （t≥2）. The method, which recursively generates high strength covering arrays, is practical. Meanwhile, the theoretical derivation and realization of the proposed algebraic recursive algorithm are given.
基金supported by the National Natural Science Foundation of China(No.52077100)the Aviation Science Foundation(No.201958052001)
文摘In order to improve the frequency response and anti-interference characteristics of the smart electromechanical actuator(EMA)system,and aiming at the force fighting problem when multiple actuators work synchronously,a multi input multi output(MIMO)position difference cross coupling control coordinated strategy based on double‑closed-loop load feedforward control is proposed and designed.In this strategy,the singular value method of return difference matrix is used to design the parameter range that meets the requirements of system stability margin,and the sensitivity function and the H_(∞)norm theory are used to design and determine the optimal solution in the obtained parameter stability region,so that the multi actuator system has excellent synchronization,stability and anti-interference.At the same time,the mathematical model of the integrated smart EMA system is established.According to the requirements of point-to-point control,the controller of double-loop control and load feedforward compensation is determined and designed to improve the frequency response and anti-interference ability of single actuator.Finally,the 270 V high-voltage smart EMA system experimental platform is built,and the frequency response,load feedforward compensation and coordinated control experiments are carried out to verify the correctness of the position difference cross coupling control strategy and the rationality of the parameter design,so that the system can reach the servo control indexes of bandwidth 6 Hz,the maximum output force 20000 N and the synchronization error≤0.1 mm,which effectively solves the problem of force fighting.
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
文摘The better compression rate can be achieved by the traditional vector quantization （VQ） method, and the quality of the recovered image can also be accepted. But the decompressed image quality can not be promoted efficiently, so how to balance the image compression rate and image recovering quality is an important issue, in this paper, an image is transformed by discrete wavelet transform （DWT） to generate its DWT transformed image which can be compressed by the VQ method further. Besides, we compute the values between the DWT transformed image and decompressed DWT transformed image as the difference matrix which is the adjustable basis of the decompressed image quality. By controlling the deviation of the difference matrix, there can be nearly Iossless compression for the VQ method. Experimental results show that when the number of compressed bits by our method is equal to the number of those bits compressed by the VQ method, the quality of our recovered image is better. Moreover, the proposed method has more compression capability comparing with the VQ scheme.
基金supported by the National Natural Science Foundation of China(No.12271005 and No.11901006)Natural Science Foundation of Anhui Province(2308085Y06,1908085QA06)+2 种基金Young Scholars Program of Anhui Province(2023)Anhui Provincial Natural Science Foundation(Grant No.2008085MA08)Foundation of Anhui Provincial Education Department(Grant No.KJ2021A1523)。
文摘Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean restriction.Methodologically,our test allows heteroscedastic regression models without imposing any condition on the distribution of the error,utilizes effectively important information contained in the distance of the vector of covariates,has a simple form,is easy to implement,and is free of the subjective choice of parameters.Theoretically,our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model diagnostics.The asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also presented.In particular,we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence matrix.Since the asymptotic null distribution of the test statistic depends on data generating process,we propose a wild bootstrap scheme to approximate its null distribution.The consistency of the bootstrap scheme is justified.Numerical studies are undertaken to show the good performance of the new test.
基金Supported by the National Natural Science Foundation of China(Nos 50775117 and 50775125)the National High-Tech Researchand Development (863) Program of China (No 2007AA041901)+1 种基金the National Key Technology Research and Development Program(No 2006BAF01B09)the Technology Innovation Fund ofAVIC (No 2009E13224)
文摘Error model is the basis for accuracy-related computations and analyses for parallel kinematic machines（PKMs）.Traditional error modeling methods are usually based on differentiation of kinematic solutions,but the solving process is often complex and has limitations for certain specialized PKMs.A concise numerical error modeling method with the inverse kinematic solution as its only requirement is presented in this paper.To avoid complex Jacobian matrix computations,the difference matrix that can be quickly calculated by kinematic solutions was used to replace the differential matrix.The quasi-Newton method,which has high speed and high precision,was introduced to solve the numerical forward kinematic problem.To verify the efficiency of this numerical error modeling method,three applications in error transformation matrix（ETM） modeling,error analysis,and kinematic calibration were simulated on a 4RRR PKM.A comparison with the results obtained by the traditional method shows that the numerical method is accurate,convenient,and has lower requirements and wider applicability,especially for certain specialized and manufactured PKMs.
基金The research is supported by the National Natural Science Foundation of China under Grant No. 10571045University Backbone Teachers Foundation of the Education Department of Henan ProvinceNatural Science Foundation of Henan Province under Grant No. 0411011100.
文摘By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal arrays are constructed.
基金supported by NSFC grants 11971004 and 11571094supported by NSFC grants 11901199 and 71931004+2 种基金supported by NSFC grants 12071014 and 12131001Shanghai Sailing Program 19YF1412800SSFC grant 19ZDA121 and LMEQF。
文摘In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrices,we present some general recursive methods for constructing OAs of such type.Several families of OAs with high percent saturation are constructed.In particular,for any integerλ≥3,such a two-level OA of run 4λcan always be obtained if the corresponding Hadamard matrix exists.
基金Supported by the National Natural Science Foundation of China(Nos.11571094 and 11171093)
文摘In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.
基金Supported by National Natural Science Foundation of China (Grant No.10771013)
文摘In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.
文摘We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.
