For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtaine...For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.展开更多
Current research in broken rotor bar （BRB） fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the...Current research in broken rotor bar （BRB） fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estima- tion cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection, a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the fre- quencies of the fundamental and fault characteristic com- ponents with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally, the proposed method is applied to a simulated current and an actual motor, the results of which indicate that, not only parametric spectrum estimation technique.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can n...In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can not solve an identification problem with infinitely many solutions well.Then we propose PRCs identification based on the minimal norm method,which satisfies observability conditions and has advantages of high computing efficiency and short time consumption.The two identification methods are applied in a water network,and their identification results are compared under the same conditions.From the results,we know that PRCs identification based on the minimal norm method has advantages of higher computing efficiency,shorter time consumption and higher precision.展开更多
This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zer...This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.展开更多
The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Syl...The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Sylvester matrix. This paper demonstrates a method based on structured total least norm (STLN) algorithm for matrices with Sylvester structure. We demonstrate the algorithm to compute an approximate GCD. Both the theoretical analysis and the computational results show that the method is feasible.展开更多
We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessar...We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well.展开更多
In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coeffic...In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.展开更多
In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm ...Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.展开更多
基金supported by Aeronautical Science Foundation of China (No. 20100251006)Technological Foundation Project of China (No. J132012C001)
文摘For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.
基金Supported by National Natural Science Foundation of China(Grant No.51607180)
文摘Current research in broken rotor bar （BRB） fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estima- tion cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection, a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the fre- quencies of the fundamental and fault characteristic com- ponents with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally, the proposed method is applied to a simulated current and an actual motor, the results of which indicate that, not only parametric spectrum estimation technique.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金The Major State Basic Research Program (19871051) of China and the NNSP (19972039) of China.
文摘In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
基金Sponsored by the National"Eleventh-five"Tackle Key Problem Program-China Science and Technology Support Project(Grant No.2006BAJ01A04)
文摘In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can not solve an identification problem with infinitely many solutions well.Then we propose PRCs identification based on the minimal norm method,which satisfies observability conditions and has advantages of high computing efficiency and short time consumption.The two identification methods are applied in a water network,and their identification results are compared under the same conditions.From the results,we know that PRCs identification based on the minimal norm method has advantages of higher computing efficiency,shorter time consumption and higher precision.
基金supported by the Development of airborne gravity gradiometer(No.2017YFC0601601)open subject of Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences(No.KLOR2018-8)
文摘This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.
文摘The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Sylvester matrix. This paper demonstrates a method based on structured total least norm (STLN) algorithm for matrices with Sylvester structure. We demonstrate the algorithm to compute an approximate GCD. Both the theoretical analysis and the computational results show that the method is feasible.
基金Supported by the National Natural Science Foundation of China
文摘We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well.
基金Supported by the national natural science foundation.
文摘In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.
基金the Doctoral Program of Higher Education of China(No.20120032110034)
文摘Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.
