Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper s...Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.展开更多
When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the...When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.展开更多
Conical membrane structures are a typical form of tensile membrane structures. In the past, most studies focused on the static performance, but few on dynamic performance. In this paper, systematic parameter analysis ...Conical membrane structures are a typical form of tensile membrane structures. In the past, most studies focused on the static performance, but few on dynamic performance. In this paper, systematic parameter analysis of wind-induced response of conical membrane structures has been performed with nonlinear random simulation method in a time domain, by considering some parameters, such as span, rise-span ratio, prestress of membrane, and characteristic of the approaching wind flow. Moreover, formulas of the dynamic coefficient and nonlinear adjustment factor are advised, which can be conveniently used in wind-resistant design of conical membrane structures.展开更多
The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigate...The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.展开更多
To improve the precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes,researchers and regulatory agencies recommend using g com...To improve the precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes,researchers and regulatory agencies recommend using g computation as a reliable method of covariate adjustment.How-ever,the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest.To fill this gap,we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that the variance estimators can be reliably applied in practice.展开更多
文摘Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50338010).
文摘Conical membrane structures are a typical form of tensile membrane structures. In the past, most studies focused on the static performance, but few on dynamic performance. In this paper, systematic parameter analysis of wind-induced response of conical membrane structures has been performed with nonlinear random simulation method in a time domain, by considering some parameters, such as span, rise-span ratio, prestress of membrane, and characteristic of the approaching wind flow. Moreover, formulas of the dynamic coefficient and nonlinear adjustment factor are advised, which can be conveniently used in wind-resistant design of conical membrane structures.
基金supported by the National Natural Science Foundation of China, Project No. 42174045under National Key Research and Development Program of China, Project No.2020YFB0505805the National Natural Science Foundation of China, Project No. 41874012。
文摘The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.
基金This work was supported by National Institute of Allergy and Infectious Diseases[NIAID 5 UM1 AI068617].
文摘To improve the precision of estimation and power of testing hypothesis for an unconditional treatment effect in randomized clinical trials with binary outcomes,researchers and regulatory agencies recommend using g computation as a reliable method of covariate adjustment.How-ever,the practical application of g-computation is hindered by the lack of an explicit robust variance formula that can be used for different unconditional treatment effects of interest.To fill this gap,we provide explicit and robust variance estimators for g-computation estimators and demonstrate through simulations that the variance estimators can be reliably applied in practice.
