Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
Bridge deformation monitoring usually adopts contact sensors,and the implementation process is often limited by the environment and observation conditions,resulting in unsatisfactory monitoring accuracy and effect.Gro...Bridge deformation monitoring usually adopts contact sensors,and the implementation process is often limited by the environment and observation conditions,resulting in unsatisfactory monitoring accuracy and effect.Ground-Based Synthetic Aperture Radar(GBSAR)combined with corner reflectors was used to perform static load-loaded deformation destruction experiments on solid model bridges in a non-contact manner.The semi parametric spline filtering and its optimization method were used to obtain the monitoring results of the GBSAR radar’s line of sight deformation,and the relative position of the corner reflector and the millimeter level deformation signals under different loading conditions were successfully extracted.The deformation transformation model from the radar line of sight direction to the vertical vibration direction was deduced.The transformation results of deformation monitoring and the measurement data such as the dial indicator were compared and analyzed.The occurrence and development process of bridge deformation and failure were successfully monitored,and the deformation characteristics of the bridge from continuous loading to eccentric loading until bridge failure were obtained.The experimental results show that GBSAR combined with corner reflector can be used for deformation feature acquisition,damage identification and health monitoring of bridges and other structures,and can provide a useful reference for design,construction and safety evaluation.展开更多
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
基金Science and Technology Innovation Program of Hunan Province(No.2021RC4037)National Natural Science Foundation of China:Deformation Monitoring Key Technology and Damage Mechanism Research on Data Fusion among GB-SAR and Multi-sensors(No.41877283)Scientific Research Project of Hunan Provincial Department of Natural Resources(No.2021-18)
文摘Bridge deformation monitoring usually adopts contact sensors,and the implementation process is often limited by the environment and observation conditions,resulting in unsatisfactory monitoring accuracy and effect.Ground-Based Synthetic Aperture Radar(GBSAR)combined with corner reflectors was used to perform static load-loaded deformation destruction experiments on solid model bridges in a non-contact manner.The semi parametric spline filtering and its optimization method were used to obtain the monitoring results of the GBSAR radar’s line of sight deformation,and the relative position of the corner reflector and the millimeter level deformation signals under different loading conditions were successfully extracted.The deformation transformation model from the radar line of sight direction to the vertical vibration direction was deduced.The transformation results of deformation monitoring and the measurement data such as the dial indicator were compared and analyzed.The occurrence and development process of bridge deformation and failure were successfully monitored,and the deformation characteristics of the bridge from continuous loading to eccentric loading until bridge failure were obtained.The experimental results show that GBSAR combined with corner reflector can be used for deformation feature acquisition,damage identification and health monitoring of bridges and other structures,and can provide a useful reference for design,construction and safety evaluation.
