To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey sy...To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.展开更多
Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource stru...Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource structure before andafter the regulation. This method can be applied as one of the mathematical tools in forest harvest regulation.展开更多
The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the p...The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.展开更多
In this paper,some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made.First,the effects of the distance between pseudo and main boundaries o...In this paper,some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made.First,the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested.In some cases,the resulting system of equations becomes ill-conditioned for which,the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used.Moreover,a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations.By solving two example problems with stress concentration,the effectiveness of the proposed methods is demonstrated.展开更多
In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to...In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.展开更多
基金the Doctorate Foundation of Northwestern Polytechnical University (Grant No.CX200304)
文摘To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.
文摘Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource structure before andafter the regulation. This method can be applied as one of the mathematical tools in forest harvest regulation.
基金co-supported by the National Nature Science Foundation of China(No.12303071)the Shanghai Science and Technology Plan Project,China(No.23YF1455500)+1 种基金the China Postdoctoral Science Foundation(No.2023M743653)Ministry of Industry and Information Technology of China through the High Precision Timing Service Project(No.TC220A04A-80)。
文摘The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.
文摘In this paper,some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made.First,the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested.In some cases,the resulting system of equations becomes ill-conditioned for which,the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used.Moreover,a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations.By solving two example problems with stress concentration,the effectiveness of the proposed methods is demonstrated.
基金supported by the NSFC(Grant Nos.12171148,11771138)the NSFC(Grant Nos.12101252,11971007)+2 种基金the NSFC(Grant No.11901185)the National Key R&D Program of China(Grant No.2021YFA1001300)by the Fundamental Research Funds for the Central Universities(Grant No.531118010207).
文摘In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.
