Data coming from different sources have different types and temporal states. Relations between one type of data and another ones, or between data and unknown parameters are almost nonlinear. It is not accurate and rel...Data coming from different sources have different types and temporal states. Relations between one type of data and another ones, or between data and unknown parameters are almost nonlinear. It is not accurate and reliable to process the data in building the digital earth with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method was put forward to process data in building the digital earth. A separating solution model and the iterative calculation method were used to solve the generalized nonlinear dynamic least squares problem. In fact, a complex problem can be separated and then solved by converting to two sub problems, each of which has a single variable. Therefore the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations.展开更多
Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters a...Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.展开更多
Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad appl...Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.展开更多
Data, including the spatial data and the non-spatial data, are the basis of all digital scientific engineering projects, such as the digital earth and the digital nation, the digital mine. The spatial data have the ch...Data, including the spatial data and the non-spatial data, are the basis of all digital scientific engineering projects, such as the digital earth and the digital nation, the digital mine. The spatial data have the characteristics of many sources, multi-dimension, multi-type, many time states and different accuracy. The spatial data firstly must be processed before using these data. The parameter estimation model to process the data is commonly the more complex nonlinear model including random parameters and non-random parameters. So a generalized nonlinear dynamic least squares method to process these data is put forward. According to the special structure of the generalized nonlinear dynamic least squares problem and the solution to the first order, a new solving model and a corresponding method to process the problem are put forward. The complex problem can be divided into two sub-problems so that the number of the unknown parameters is reduced largely. Therefore it reduces the computing difficulty and load.展开更多
A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in tr...A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.展开更多
文摘Data coming from different sources have different types and temporal states. Relations between one type of data and another ones, or between data and unknown parameters are almost nonlinear. It is not accurate and reliable to process the data in building the digital earth with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method was put forward to process data in building the digital earth. A separating solution model and the iterative calculation method were used to solve the generalized nonlinear dynamic least squares problem. In fact, a complex problem can be separated and then solved by converting to two sub problems, each of which has a single variable. Therefore the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations.
文摘Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
基金Chinese NSF grant 10231060the CAS Knowledge Innovation Program
文摘Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.
基金Project (40174003) supported by the National Natural Science Foundation of China
文摘Data, including the spatial data and the non-spatial data, are the basis of all digital scientific engineering projects, such as the digital earth and the digital nation, the digital mine. The spatial data have the characteristics of many sources, multi-dimension, multi-type, many time states and different accuracy. The spatial data firstly must be processed before using these data. The parameter estimation model to process the data is commonly the more complex nonlinear model including random parameters and non-random parameters. So a generalized nonlinear dynamic least squares method to process these data is put forward. According to the special structure of the generalized nonlinear dynamic least squares problem and the solution to the first order, a new solving model and a corresponding method to process the problem are put forward. The complex problem can be divided into two sub-problems so that the number of the unknown parameters is reduced largely. Therefore it reduces the computing difficulty and load.
基金National Natural Science Foundation of China(No.61374044)Shanghai Municipal Science and Technology Commission,China(No.15510722100)+2 种基金Shanghai Municipal Education Commission,China(No.14ZZ088)Shanghai Talent Development Plan,ChinaShanghai Baoshan Science and Technology Commission,China(No.bkw2013120)
文摘A new identification method of neuro-uzzy Hammerstein model based on probability density function(PDF) is presented,which is different from the idea that mean squared error(MSE) is employed as the index function in traditional identification methods.Firstly,a neuro-fuzzy based Hammerstein model is constructed to describe the nonlinearity of Hammerstein process without any prior process knowledge.Secondly,a kind of special test signal is used to separate the link parts of the Hammerstein model.More specifically,the conception of PDF is introduced to solve the identification problem of the neuro-fuzzy Hammerstein model.The antecedent parameters are estimated by a clustering algorithm,while the consequent parameters of the model are identified by designing a virtual PDF control system in which the PDF of the modeling error is estimated and controlled to converge to the target.The proposed method not only guarantees the accuracy of the model but also dominates the spatial distribution of PDF of the model error to improve the generalization ability of the model.Simulated results show the effectiveness of the proposed method.
