This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a c...This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.展开更多
Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in r...Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.展开更多
In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) m...In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.展开更多
Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under sat...Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.展开更多
For the inverse designs of centrifugal and mixed-flow pump impellers,clarifying the generation process of secondary flows and putting forward corresponding suppression measures is an important approach to improve the ...For the inverse designs of centrifugal and mixed-flow pump impellers,clarifying the generation process of secondary flows and putting forward corresponding suppression measures is an important approach to improve the impeller performance.In this paper,to provide a better qualitative insight into the generation mechanism of secondary flows in the impeller,a simple kinematic equation is derived based on the ideal assumptions,which indicates that the potential rothalpy gradient(PRG)is the most important dynamic source that actively induces secondary vortical flows.Induced by the natural adverse PRG on the S1 and S2 stream surfaces,two typical secondary flows,H-S and P-S secondary flows,are clearly presented.To specially suppress these typical secondary flows,a general alternate loading technique(GALT)is proposed,aiming to adjust the real blade loadingδp to control the PRG features.At the blade fore part,theδp on the hub streamline should be slowly increased to avoid breakneck growth of the potential rothalpy to reduce adverse streamwise PRG on the S2 streamsurface.At the blade middle part,theδp should be moderately decreased to reduce adverse streamwise PRG on the S1 streamsurface.At the blade aft part,the difference in theδp between the shroud and hub streamlines should be decreased faster to control the exit uniformity.By applying the GALT to the impeller designs of three typical pump types in hydraulic engineering,the organizational effect of the PRG on fundamental flow structures is proven.The GALT can effectively control the PRG distributions and suppress the secondary flows,thereby widening the pump’s high-efficiency zone,improving flow uniformity and suppressing pressure fluctuations.Compared with the current Z-G method and the ALT,the GALT can meet the requirements of"de-experience"better,thereby enabling the designers to obtain good products explicitly and quickly.展开更多
文摘This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.
基金Projected supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natura Science Foundation of China(Grant No.61372172)
文摘Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.
文摘In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.
基金the support from the University Transportation Center for Underground Transportation Infrastructure at the Colorado School of Mines for partially funding this research under Grant No. 69A3551747118 of the Fixing America's Surface Transportation Act (FAST Act) of U.S. DoT FY2016
文摘Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.
基金supported by the National Natural Science Foundation of China(Grant Nos.51836010,51779258,51839001)the National Key Research and Development Program of China(Grant No.2018YFB0606103)the Beijing Natural Science Foundation of China(Grant No.3182018)。
文摘For the inverse designs of centrifugal and mixed-flow pump impellers,clarifying the generation process of secondary flows and putting forward corresponding suppression measures is an important approach to improve the impeller performance.In this paper,to provide a better qualitative insight into the generation mechanism of secondary flows in the impeller,a simple kinematic equation is derived based on the ideal assumptions,which indicates that the potential rothalpy gradient(PRG)is the most important dynamic source that actively induces secondary vortical flows.Induced by the natural adverse PRG on the S1 and S2 stream surfaces,two typical secondary flows,H-S and P-S secondary flows,are clearly presented.To specially suppress these typical secondary flows,a general alternate loading technique(GALT)is proposed,aiming to adjust the real blade loadingδp to control the PRG features.At the blade fore part,theδp on the hub streamline should be slowly increased to avoid breakneck growth of the potential rothalpy to reduce adverse streamwise PRG on the S2 streamsurface.At the blade middle part,theδp should be moderately decreased to reduce adverse streamwise PRG on the S1 streamsurface.At the blade aft part,the difference in theδp between the shroud and hub streamlines should be decreased faster to control the exit uniformity.By applying the GALT to the impeller designs of three typical pump types in hydraulic engineering,the organizational effect of the PRG on fundamental flow structures is proven.The GALT can effectively control the PRG distributions and suppress the secondary flows,thereby widening the pump’s high-efficiency zone,improving flow uniformity and suppressing pressure fluctuations.Compared with the current Z-G method and the ALT,the GALT can meet the requirements of"de-experience"better,thereby enabling the designers to obtain good products explicitly and quickly.
