This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
The damped least squares inversion principle is applied to the transient electromagnetic one-dimensional inversion of electrical sources,and a new model is obtained by continuously iterating the initial model,thereby ...The damped least squares inversion principle is applied to the transient electromagnetic one-dimensional inversion of electrical sources,and a new model is obtained by continuously iterating the initial model,thereby fitting the observed transient electromagnetic response,and performing one-dimensional inversion through induced electromotive force play.In this paper,in the damped least squares inversion,constraints are added to the Jacobian matrix,and simultaneous constraint equations and conventional inversion equations are solved.By weighting the constraint parameters,the difference between adjacent resistivities and layer thicknesses is minimized.Finally,K-type and H-type theoretical models were used to verify the reliability of the algorithm,and compared with the conventional transient electromagnetic damping least squares inversion.展开更多
Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points o...Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure.However,CV methods produce significantly more measurement errors.Thus,computer vision-based structural health monitoring(CVSHM)requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data.In this paper a complete CVSHM framework is proposed,and three damage assessment methods are tested.The first is the augmented inverse estimate(AIE),proposed by Peng et al.in 2021.This method is designed to work with highly contaminated measurement data,but it fails with a large noise provided by CV measurement.The second method,as proposed in this paper,is based on the AIE,but it introduces a weighting matrix that enhances the conditioning of the problem.The third method,also proposed in this paper,introduces additional constraints in the optimization process;these constraints ensure that the stiffness of structural elements can only decrease.Both proposed methods perform better than the original AIE.The latter of the two proposed methods gives the best results,and it is robust with respect to the selected coefficients,as required by the algorithm.展开更多
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
基金sponsored by geological Survey Project of China Geological Survey(DD20189210).
文摘The damped least squares inversion principle is applied to the transient electromagnetic one-dimensional inversion of electrical sources,and a new model is obtained by continuously iterating the initial model,thereby fitting the observed transient electromagnetic response,and performing one-dimensional inversion through induced electromotive force play.In this paper,in the damped least squares inversion,constraints are added to the Jacobian matrix,and simultaneous constraint equations and conventional inversion equations are solved.By weighting the constraint parameters,the difference between adjacent resistivities and layer thicknesses is minimized.Finally,K-type and H-type theoretical models were used to verify the reliability of the algorithm,and compared with the conventional transient electromagnetic damping least squares inversion.
基金National Science Centre,Poland Granted Through the Project 2020/39/B/ST8/02615。
文摘Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure.However,CV methods produce significantly more measurement errors.Thus,computer vision-based structural health monitoring(CVSHM)requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data.In this paper a complete CVSHM framework is proposed,and three damage assessment methods are tested.The first is the augmented inverse estimate(AIE),proposed by Peng et al.in 2021.This method is designed to work with highly contaminated measurement data,but it fails with a large noise provided by CV measurement.The second method,as proposed in this paper,is based on the AIE,but it introduces a weighting matrix that enhances the conditioning of the problem.The third method,also proposed in this paper,introduces additional constraints in the optimization process;these constraints ensure that the stiffness of structural elements can only decrease.Both proposed methods perform better than the original AIE.The latter of the two proposed methods gives the best results,and it is robust with respect to the selected coefficients,as required by the algorithm.
