It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based ...It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.展开更多
Lower and upper bounds for eigenvalues help estimate the location interval of eigenvalues,which is of practical meanings especially for those problems of which the eigenvalues cannot be exactly obtained.In this paper,...Lower and upper bounds for eigenvalues help estimate the location interval of eigenvalues,which is of practical meanings especially for those problems of which the eigenvalues cannot be exactly obtained.In this paper,we study the lower and upper bounds for linear elasticity eigenvalues by displacement-pressure mixed finite element schemes.By applying expansion identities for the error of eigenvalues,lower and upper numerically computable bounds for the eigenvalues are derived based on certain mathematical hypotheses.For the schemes studied here,roughly speaking,the accuracy loss of the local approximation of the discrete displacement may lead to lower bound and that of pressure to upper bound.By utilizing the min-max principle and perturbation theory for the solution operator,theoretical lower and upper bounds can be controlled by setting proper Laméparameters.展开更多
A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. ...A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.展开更多
A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displac...A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.展开更多
The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenva...The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.展开更多
We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the l...We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis.展开更多
Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2...Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2xnis also called the cone Laplacian. In this paper,by using Mellin-Fourier transform,we prove thatλk Cnk2 n for any k 1,where Cn=(nn+2)(2π)2(|B0|Bn)-2n,which gives the lower bounds of the Dirchlet eigenvalues of-ΔB. On the other hand,by using the Rayleigh-Ritz inequality,we deduce the upper bounds ofλk,i.e.,λk+1 1 +4n k2/nλ1. Combining the lower and upper bounds of λk,we can easily obtain the lower bound for the first Dirichlet eigenvalue λ1 Cn(1 +4n)-12n2.展开更多
We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tenso...We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, Btensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP;and hence, they are very easy to calculate.展开更多
By analyzing the bus operation environment and accounting for prediction uncertainties,a bus arrival interval prediction model was developed utilizing a gated recur-rent unit(GRU)neural network.To reduce the impact of...By analyzing the bus operation environment and accounting for prediction uncertainties,a bus arrival interval prediction model was developed utilizing a gated recur-rent unit(GRU)neural network.To reduce the impact of irrelevant data and boost prediction accuracy,an attention mechanism was integrated into the point model to concen-trate on important input sequence information.Based on the point predictions,the lower upper bound estimation(LUBE)method was used,providing a range for the bus interval times predicted by the model.The model was vali-dated using data from 169 bus routes in Nanchang,Jiangxi Province.The results indicated that the attention-GRU model outperformed neural network,long short-term memory and GRU models.Compared with the Bootstrap method,the LUBE method has a narrower average interval width.The coverage width-based criterion(CWC)was reduced by 8.1%,2.2%,and 5.7%at confidence levels of 85%,90%,and 95%,respectively,during the off-peak period,and by 23.2%,26.9%,and 27.3%at confidence levels of 85%,90%,and 95%,respectively,during the peak period.Therefore,it can accurately describe the fluctuation range in bus arrival times with higher accuracy and stability.展开更多
基金National Natural Science Foundation of China(No.40927001)
文摘It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.
基金Supported by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XD-B41020204)National Key R&D Program of China(Grant Nos.2022YFA1004500,2024YFA1012503)+1 种基金National Natural Science Foundation of China(Grant Nos.12371372,12271512)Natural Science Foundation of Fujian Province of China(Grant No.2025J01026)。
文摘Lower and upper bounds for eigenvalues help estimate the location interval of eigenvalues,which is of practical meanings especially for those problems of which the eigenvalues cannot be exactly obtained.In this paper,we study the lower and upper bounds for linear elasticity eigenvalues by displacement-pressure mixed finite element schemes.By applying expansion identities for the error of eigenvalues,lower and upper numerically computable bounds for the eigenvalues are derived based on certain mathematical hypotheses.For the schemes studied here,roughly speaking,the accuracy loss of the local approximation of the discrete displacement may lead to lower bound and that of pressure to upper bound.By utilizing the min-max principle and perturbation theory for the solution operator,theoretical lower and upper bounds can be controlled by setting proper Laméparameters.
文摘A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.
基金supported by the National Natural Science Foundation of China (11072068 and 11002041)
文摘A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the upper and lower bounds on the effective elastic moduli of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal in- clusions on the bounds of the effective elastic moduli are an- alyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.
文摘The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.
基金supported by National Science Foundations of China (Grant Nos. 11001259,11031006)Croucher Foundation of Hong Kong Baptist University
文摘We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis.
基金supported by National Natural Science Foundation of China(Grant No.11131005)
文摘Let λkbe the k-th Dirichlet eigenvalue of totally characteristic degenerate elliptic operator-ΔB defined on a stretched cone B0 ■ [0,1) × X with boundary on {x1 = 0}. More precisely,ΔB=(x1αx1)2+ α2x2+ + α2xnis also called the cone Laplacian. In this paper,by using Mellin-Fourier transform,we prove thatλk Cnk2 n for any k 1,where Cn=(nn+2)(2π)2(|B0|Bn)-2n,which gives the lower bounds of the Dirchlet eigenvalues of-ΔB. On the other hand,by using the Rayleigh-Ritz inequality,we deduce the upper bounds ofλk,i.e.,λk+1 1 +4n k2/nλ1. Combining the lower and upper bounds of λk,we can easily obtain the lower bound for the first Dirichlet eigenvalue λ1 Cn(1 +4n)-12n2.
文摘We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, Btensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP;and hence, they are very easy to calculate.
基金The National Natural Science Foundation of China(No.52162042)General Science and Technology Project of Jiangxi Provincial Department of Transportation(No.2024YB039).
文摘By analyzing the bus operation environment and accounting for prediction uncertainties,a bus arrival interval prediction model was developed utilizing a gated recur-rent unit(GRU)neural network.To reduce the impact of irrelevant data and boost prediction accuracy,an attention mechanism was integrated into the point model to concen-trate on important input sequence information.Based on the point predictions,the lower upper bound estimation(LUBE)method was used,providing a range for the bus interval times predicted by the model.The model was vali-dated using data from 169 bus routes in Nanchang,Jiangxi Province.The results indicated that the attention-GRU model outperformed neural network,long short-term memory and GRU models.Compared with the Bootstrap method,the LUBE method has a narrower average interval width.The coverage width-based criterion(CWC)was reduced by 8.1%,2.2%,and 5.7%at confidence levels of 85%,90%,and 95%,respectively,during the off-peak period,and by 23.2%,26.9%,and 27.3%at confidence levels of 85%,90%,and 95%,respectively,during the peak period.Therefore,it can accurately describe the fluctuation range in bus arrival times with higher accuracy and stability.
