In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinea...In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.展开更多
The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. Th...The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.展开更多
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
In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the...In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method.展开更多
An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace def...An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.展开更多
Study on solving nonlinear least squares adjustment by parameters is one of the most important and new subjects in modern surveying and mapping field . Many researchers have done a lot of work and gained some solving ...Study on solving nonlinear least squares adjustment by parameters is one of the most important and new subjects in modern surveying and mapping field . Many researchers have done a lot of work and gained some solving methods. These methods mainly include iterative algorithms and direct algorithms mainly. The former searches some methods of rapid convergence based on which surveying adjustment is a kind of problem of nonlinear programming. Among them the iterative algorithms of the most in common use are the Gauss-Newton method, damped least quares, quasi-Newton method and some mutations etc. Although these methods improved the quantity of the observation results to a certain degree, and increased the accuracy of the adjustment results, what we want is whether the initial values of unknown parameters are close to their real values. Of course, the model of the latter has better degree in linearity, that is to say, they nearly have the meaning of deeper theories researches. This paper puts forward a kind of method of solving the problems of nonlinear least squares adjustment by parameters based on neural network theory, and studies its stability and convergency. The results of calculating of living example indicate the method acts well for solving parameters problems by nonlinear least squares adjustment without giving exact approximation of parameters.展开更多
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method, a new switch is proposed to form a hybrid method. Nu...A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method, a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual, small-residual and large-residual problems.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
Aiming at the interferometric inverse synthetic aperture radar （InlSAR） imaging in the presence of squint, we investigate the influence of squint on the InlSAR imaging. First, coupling of the squint additive phase a...Aiming at the interferometric inverse synthetic aperture radar （InlSAR） imaging in the presence of squint, we investigate the influence of squint on the InlSAR imaging. First, coupling of the squint additive phase and the target azimuth/altitude coordinates to be solved may make the solution more difficult. Second, the squint angle may lead to estimation error of the vertical coordinates and distortion of the ultimate image. Traditional InlSAR imaging algorithms can not solve the above two problems effectively, so we propose a new method which combines the nonlinear least square （NLS） and coordinates transform （CT） to estimate the target coordinates, and a three-dimensional （3-D） image consistent with the real target is obtained accordingly. Simulations show that the proposed method is effective for the squint-mode InlSAR imaging.展开更多
This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second ...This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.展开更多
This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration（Log-ACD） model. We establish the strong consistency and asymptotic normality for our estimator u...This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration（Log-ACD） model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.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
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm m...The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.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
Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straig...Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.展开更多
Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimat...Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is un- known or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.展开更多
The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter gamma and multi-step prediction capabilities of the LS-SVM network are discussed. Then we e...The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter gamma and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values.. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.展开更多
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
A model of correcting the nonlinear error of photoelectric displacement sensor was established based on the least square support vector machine.The parameters of the correcting nonlinear model,such as penalty factor a...A model of correcting the nonlinear error of photoelectric displacement sensor was established based on the least square support vector machine.The parameters of the correcting nonlinear model,such as penalty factor and kernel parameter,were optimized by chaos genetic algorithm.And the nonlinear correction of photoelectric displacement sensor based on least square support vector machine was applied.The application results reveal that error of photoelectric displacement sensor is less than 1.5%,which is rather satisfactory for nonlinear correction of photoelectric displacement sensor.展开更多
基金National Natural Science Foundation of China Under Grant No.10572058the Science Foundation of Aeronautics of China Under Grant No.2008ZA52012
文摘In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.
基金Supported by the National Natural Science Foundation of China (40174003)
文摘The unknown parameter’s variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now, which didn’t appear in the internal and external referencing documents. The unknown parameter’s vari- ance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source, multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
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 （10231060）, the Special Research Found of Doctoral Program of Higher Education of China（200d0319003 ）, the Research Project of Xuzhou Institute of Technology（ XKY200622）.
基金State Major Key Project for Basic ResearchesDecision Making and Information System Laboratory+1 种基金 Academy of Science of China Natural Science Foundation of Tsinghua University.
文摘In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method.
基金Supported by The Natural Science Fundations of China and Jiangsu
文摘An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.
基金Project (40174003) supported by the National Natural Science Foundation of China
文摘Study on solving nonlinear least squares adjustment by parameters is one of the most important and new subjects in modern surveying and mapping field . Many researchers have done a lot of work and gained some solving methods. These methods mainly include iterative algorithms and direct algorithms mainly. The former searches some methods of rapid convergence based on which surveying adjustment is a kind of problem of nonlinear programming. Among them the iterative algorithms of the most in common use are the Gauss-Newton method, damped least quares, quasi-Newton method and some mutations etc. Although these methods improved the quantity of the observation results to a certain degree, and increased the accuracy of the adjustment results, what we want is whether the initial values of unknown parameters are close to their real values. Of course, the model of the latter has better degree in linearity, that is to say, they nearly have the meaning of deeper theories researches. This paper puts forward a kind of method of solving the problems of nonlinear least squares adjustment by parameters based on neural network theory, and studies its stability and convergency. The results of calculating of living example indicate the method acts well for solving parameters problems by nonlinear least squares adjustment without giving exact approximation of parameters.
文摘A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method, a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual, small-residual and large-residual problems.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金supported by the China National Funds for Distinguished Young Scientists (Grant No.61025006)
文摘Aiming at the interferometric inverse synthetic aperture radar （InlSAR） imaging in the presence of squint, we investigate the influence of squint on the InlSAR imaging. First, coupling of the squint additive phase and the target azimuth/altitude coordinates to be solved may make the solution more difficult. Second, the squint angle may lead to estimation error of the vertical coordinates and distortion of the ultimate image. Traditional InlSAR imaging algorithms can not solve the above two problems effectively, so we propose a new method which combines the nonlinear least square （NLS） and coordinates transform （CT） to estimate the target coordinates, and a three-dimensional （3-D） image consistent with the real target is obtained accordingly. Simulations show that the proposed method is effective for the squint-mode InlSAR imaging.
文摘This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.
基金The research was supported by the National Natural Science Foundation of China(11690014,11690015,10871188)the Research Funds of Renmin University of China(No.16XNB025)the Social Science Foundation of Beijing(No.17GLB022)
文摘This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration（Log-ACD） model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.
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.
文摘The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
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Financial support from the German Research Foundation(SFB917)is acknowledgedOpen Access funding enabled and organized by Projekt DEAL.
文摘Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.
基金Project supported by the National Basic Research Program (973) of China (No. 2002CB312200), and the Hi-Tech Research and Devel-opment Program (863) of China (No. 2002AA412010)
文摘Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is un- known or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.
文摘The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter gamma and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values.. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.
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.
基金Project(50925727) supported by the National Fund for Distinguish Young Scholars of ChinaProject(60876022) supported by the National Natural Science Foundation of China+1 种基金Project(2010FJ4141) supported by Hunan Provincial Science and Technology Foundation,ChinaProject supported by the Fund of the Key Construction Academic Subject (Optics) of Hunan Province,China
文摘A model of correcting the nonlinear error of photoelectric displacement sensor was established based on the least square support vector machine.The parameters of the correcting nonlinear model,such as penalty factor and kernel parameter,were optimized by chaos genetic algorithm.And the nonlinear correction of photoelectric displacement sensor based on least square support vector machine was applied.The application results reveal that error of photoelectric displacement sensor is less than 1.5%,which is rather satisfactory for nonlinear correction of photoelectric displacement sensor.
