The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years. As a result, many linear methods and nonlinear methods have been developed. But the methods for processing general...The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years. As a result, many linear methods and nonlinear methods have been developed. But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed. A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.展开更多
In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonline...In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.展开更多
Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient m...Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.展开更多
Outlier in one variable will smear the estimation of other measurements in data reconciliation （DR）. In this article, a novel robust method is proposed for nonlinear dynamic data reconciliation, to reduce the influe...Outlier in one variable will smear the estimation of other measurements in data reconciliation （DR）. In this article, a novel robust method is proposed for nonlinear dynamic data reconciliation, to reduce the influence of outliers on the result of DR. This method introduces a penalty function matrix in a conventional least-square objective function, to assign small weights for outliers and large weights for normal measurements. To avoid the loss of data information, element-wise Mahalanobis distance is proposed, as an improvement on vector-wise distance, to construct a penalty function matrix. The correlation of measurement error is also considered in this article. The method introduces the robust statistical theory into conventional least square estimator by constructing the penalty weight matrix and gets not only good robustness but also simple calculation. Simulation of a continuous stirred tank reactor, verifies the effectiveness of the proposed algorithm.展开更多
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When thi...The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.展开更多
This paper studies the nonlinear mixed problem for a class of symmetric hyperbolic systems with the boundary condition satisfying the dissipative condition about discontinuous data in higher dimension spaces, establis...This paper studies the nonlinear mixed problem for a class of symmetric hyperbolic systems with the boundary condition satisfying the dissipative condition about discontinuous data in higher dimension spaces, establishes the local existence theorem by using the method of a prior estimates, and obtains the structure of singularities of the solutions of such problems.展开更多
In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher prec...In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.展开更多
In this paper, we present a sampled-data nonlinear extended state observer （NLESO） design method for a class of nonlinear systems with uncertainties and discrete time output measurement. To accommodate the inter-sam...In this paper, we present a sampled-data nonlinear extended state observer （NLESO） design method for a class of nonlinear systems with uncertainties and discrete time output measurement. To accommodate the inter-sample dynamics, an inter-sample output predictor is employed in the structure of the NLESO to estimate the system output in the sampling intervals, where the prediction is used in the proposed observer instead of the system output. The exponential convergence of the sampled-data NLESO is also discussed and a sufficient condition is given by the Lyapunov method. A numerical example is provided to illustrate the performance of the proposed observer.展开更多
In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. O...In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).展开更多
This paper addresses the stabilization problem for a class of nonlinear systems. It is assumed that the controller can only receive the transmitted sequence of finite coded signals via a limited digital communication ...This paper addresses the stabilization problem for a class of nonlinear systems. It is assumed that the controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both state and output feedback coder-decoder-controller procedures are proposed. Stabilization conditions involving the size of coding alphabet, the sampling period, system state growth rate and data packet dropout rate are obtained. Finally, an example is given to illustrate the design procedures and effectiveness of the proposed results.展开更多
This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data ...This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.展开更多
It is now recognized that many geomaterials have nonlinear failure envelopes. This non-linearity is most marked at lower stress levels, the failure envelope being of quasi-parabolic shape. It is not easy to calibrate ...It is now recognized that many geomaterials have nonlinear failure envelopes. This non-linearity is most marked at lower stress levels, the failure envelope being of quasi-parabolic shape. It is not easy to calibrate these nonlinear failure envelopes from triaxial test data. Currently only the power-type failure envelope has been studied with an established formal procedure for its determination from triaxial test data. In this paper, a simplified procedure is evolved for the development of four different types of nonlinear envelopes. These are of invaluable assistance in the evaluation of true factors of safety in problems of slope stability and correct computation of lateral earth pressure and bearing capacity. The use of the Mohr-Coulomb failure envelopes leads to an overestimation of the factors of safety and other geotechnical quantities.展开更多
文摘The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years. As a result, many linear methods and nonlinear methods have been developed. But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed. A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
基金This project is supported by Special Foundation for Major State Basic Research of China (Project 973, No.G1998030415)
文摘In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.
文摘Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.
基金Supported by the National Natural Science Foundation of China （No.60504033）
文摘Outlier in one variable will smear the estimation of other measurements in data reconciliation （DR）. In this article, a novel robust method is proposed for nonlinear dynamic data reconciliation, to reduce the influence of outliers on the result of DR. This method introduces a penalty function matrix in a conventional least-square objective function, to assign small weights for outliers and large weights for normal measurements. To avoid the loss of data information, element-wise Mahalanobis distance is proposed, as an improvement on vector-wise distance, to construct a penalty function matrix. The correlation of measurement error is also considered in this article. The method introduces the robust statistical theory into conventional least square estimator by constructing the penalty weight matrix and gets not only good robustness but also simple calculation. Simulation of a continuous stirred tank reactor, verifies the effectiveness of the proposed algorithm.
文摘The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
文摘This paper studies the nonlinear mixed problem for a class of symmetric hyperbolic systems with the boundary condition satisfying the dissipative condition about discontinuous data in higher dimension spaces, establishes the local existence theorem by using the method of a prior estimates, and obtains the structure of singularities of the solutions of such problems.
基金supported by the National High Technology Research and Development Program of China(863 Program)(2014AA06A503)the National Natural Science Foundation of China(61422307,61673361)+3 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of Chinasupports from the Youth Top-notch Talent Support Programthe 1000-talent Youth Programthe Youth Yangtze River Scholarship
文摘In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.
基金This work was supported by the National Natural Science Foundation of China （Nos. 61327003, 61004004）, the China Fundamental Research Funds for the Central Universities （Nos. 10062013YWF13-ZY-68, 10062014YWF-14-ZDHXY-018） and the Tsinghua University Initiative Scientific Research Program （No. 2010Z02270）
文摘In this paper, we present a sampled-data nonlinear extended state observer （NLESO） design method for a class of nonlinear systems with uncertainties and discrete time output measurement. To accommodate the inter-sample dynamics, an inter-sample output predictor is employed in the structure of the NLESO to estimate the system output in the sampling intervals, where the prediction is used in the proposed observer instead of the system output. The exponential convergence of the sampled-data NLESO is also discussed and a sufficient condition is given by the Lyapunov method. A numerical example is provided to illustrate the performance of the proposed observer.
基金Supported by National High Technology Research and Development Program of China （863 Program） （2006AA040308）, National Natural Science Foundation of China （60736021）, and the National Creative Research Groups Science Foundation of China （60721062）
基金The project supported by NNSFC (19631040), NSSFC (04BTJ002) and the grant for post-doctor fellows in SELF.
文摘In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).
基金supported by the National Natural Science Foundation of China(No.60874021,60974016)the National Natural Science Foundation of Jiangsu Province(No.BK2007061)Qing Lan Project from the Jiangsu Provincial Department for Education and the National Natural Science Foundation of Nantong University(No.08Z001)
文摘This paper addresses the stabilization problem for a class of nonlinear systems. It is assumed that the controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both state and output feedback coder-decoder-controller procedures are proposed. Stabilization conditions involving the size of coding alphabet, the sampling period, system state growth rate and data packet dropout rate are obtained. Finally, an example is given to illustrate the design procedures and effectiveness of the proposed results.
基金This work was supported by the National Natural Science Foundation of China （Nos. 61104068, 61273119） Natural Science Foundation of Jiangsu Province （No. BK2010200）+1 种基金 China Postdoctoral Science Foundation Founded Project （No. 2012M511176） the Fundamental Research Funds for the Central Universities （No. 2242013R30006）.
文摘This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
文摘It is now recognized that many geomaterials have nonlinear failure envelopes. This non-linearity is most marked at lower stress levels, the failure envelope being of quasi-parabolic shape. It is not easy to calibrate these nonlinear failure envelopes from triaxial test data. Currently only the power-type failure envelope has been studied with an established formal procedure for its determination from triaxial test data. In this paper, a simplified procedure is evolved for the development of four different types of nonlinear envelopes. These are of invaluable assistance in the evaluation of true factors of safety in problems of slope stability and correct computation of lateral earth pressure and bearing capacity. The use of the Mohr-Coulomb failure envelopes leads to an overestimation of the factors of safety and other geotechnical quantities.
