A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single mode...A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（H...This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.展开更多
Historically,Lop Nur was a large and famous salt lake that acted as an important geographic position along the ancient‘Silk Road’,and was associated with the surrounding old civilizations,such as Loulan and Haitou.H...Historically,Lop Nur was a large and famous salt lake that acted as an important geographic position along the ancient‘Silk Road’,and was associated with the surrounding old civilizations,such as Loulan and Haitou.However,it dried up before 1972.It shows a clear‘Ear’feature on synthetic aperture radar(SAR)images.The objective of this paper is to interpret Lop Nur’s environmental evolution during its drying-up process based on an analysis of its sodium sedimentary feature.The genetic algorithm-partial least squares approach is introduced as a modeling method to retrieve the subsurface sodium content from polarimetric parameters obtained by Cloude decomposition.As a result,the R2 and root-mean-square error can reach 0.7 and 9.1 g/kg.It is suggested that the subsurface salt content was the primary reason for the bright-grey strips textures on SAR images.Furthermore,our results show that the sodium content along the same strip changed,with its distribution exhibiting consistency with the lake body’s movement driven by the strong wind.In future,high-precision topographical data will be considered,and should be helpful in the analysis of lake body movement.The method of this paper can also be applied in other similar dried salt lakes.展开更多
基金supported by Innovation Project of Chinese Academy of Sciences
文摘A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
基金supported by the National Natural Science Foundation of China(6120300761304239+1 种基金61503392)the Natural Science Foundation of Shaanxi Province(2015JQ6213)
文摘This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.
基金This work was funded by the National Natural Science Foundation of China[grant number 41571363][grant number 41431174]+4 种基金[grant number U1303285][grant number 41201346][grant number 61471358]the fund of the State Key Laboratory of Remote Sensing Science[grant number Y1Y00201KZ]and major special industry application projects[grant number 05-Y30B02–9001–13/15–03].
文摘Historically,Lop Nur was a large and famous salt lake that acted as an important geographic position along the ancient‘Silk Road’,and was associated with the surrounding old civilizations,such as Loulan and Haitou.However,it dried up before 1972.It shows a clear‘Ear’feature on synthetic aperture radar(SAR)images.The objective of this paper is to interpret Lop Nur’s environmental evolution during its drying-up process based on an analysis of its sodium sedimentary feature.The genetic algorithm-partial least squares approach is introduced as a modeling method to retrieve the subsurface sodium content from polarimetric parameters obtained by Cloude decomposition.As a result,the R2 and root-mean-square error can reach 0.7 and 9.1 g/kg.It is suggested that the subsurface salt content was the primary reason for the bright-grey strips textures on SAR images.Furthermore,our results show that the sodium content along the same strip changed,with its distribution exhibiting consistency with the lake body’s movement driven by the strong wind.In future,high-precision topographical data will be considered,and should be helpful in the analysis of lake body movement.The method of this paper can also be applied in other similar dried salt lakes.
