We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterizatio...This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterization. This problem was stated by Semushin in [2]. The solution to the problem can be considered as the development of API approach to parameter identification in stochastic dynamic systems.展开更多
This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in ...This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm.To demonstrate the validity of the algorithm,an identification test is carried out on the ship‘SWAN’with only 26 sets of test data.Furthermore,the identification effects of the least squares algorithm,original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared.Generally,the stochastic gradient algorithm is not suitable for the condition of small test data.The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2%up compared with the least squares algorithm.Then the effectiveness of the algorithm is verified by another identification test on the ship‘Galaxy’,the accuracy of parameter identification can reach more than 95%which can be used in ship motion simulation and controller design.The proposed algorithm has advantages of the small test data,fast speed and high accuracy of identification,which can be extended to other parameter identification systems with less sample data.展开更多
This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in...This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in state space (instead of response space) is given.展开更多
This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightl...This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightly coupled functions: model identification and change point detection. After a brief introduction, the pa-per discusses the generalized principles of adaptation based both on the engineering and statistical literature. The stochastic multiinput multioutput (MIMO) system under consideration is mathematically described and the problem statement is given, followed by a definition of the active adaptation principle. The distinctive property of the principle as compared with the Minimum Prediction Error approach is outlined, and a plan for a more detailed exposition to be provided in forthcoming papers is given.展开更多
By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the S...By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.展开更多
考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯...考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯度算法的收敛速度慢,为了解决这些不足,在增广随机梯度算法中引入遗忘因子,来改善参数估计精度,进一步通过仿真来比较算法的估计误差以及收敛速度。展开更多
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
文摘This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterization. This problem was stated by Semushin in [2]. The solution to the problem can be considered as the development of API approach to parameter identification in stochastic dynamic systems.
基金funded by the National Natural Science Foundation of China,grant number 51679024,51909018the Science and Technology Innovation Fundation of Dalian City,grant number 2019J12GX026+1 种基金the Fundamental Research Funds for the Central University,grant number 3132019343,3132021132the University 111 Project of China,grant number B08046.
文摘This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data,a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm.To demonstrate the validity of the algorithm,an identification test is carried out on the ship‘SWAN’with only 26 sets of test data.Furthermore,the identification effects of the least squares algorithm,original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared.Generally,the stochastic gradient algorithm is not suitable for the condition of small test data.The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2%up compared with the least squares algorithm.Then the effectiveness of the algorithm is verified by another identification test on the ship‘Galaxy’,the accuracy of parameter identification can reach more than 95%which can be used in ship motion simulation and controller design.The proposed algorithm has advantages of the small test data,fast speed and high accuracy of identification,which can be extended to other parameter identification systems with less sample data.
文摘This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author’s research in this field is summarized and a novel solution for fitting an adaptive model in state space (instead of response space) is given.
文摘This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightly coupled functions: model identification and change point detection. After a brief introduction, the pa-per discusses the generalized principles of adaptation based both on the engineering and statistical literature. The stochastic multiinput multioutput (MIMO) system under consideration is mathematically described and the problem statement is given, followed by a definition of the active adaptation principle. The distinctive property of the principle as compared with the Minimum Prediction Error approach is outlined, and a plan for a more detailed exposition to be provided in forthcoming papers is given.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60574051 and 60674092) the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2007017) and by Program for Innovative Research Team of Jiangnan University
文摘By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.
文摘考虑有色噪声干扰的Hamm erste in非线性系统的辨识,通过梯度搜索原理推导了增广投影算法,简化增广投影算法和增广随机梯度辨识算法。基本思想是将增广信息向量中的未知噪声项用其估计残差代替。增广投影算法对噪声非常敏感,增广随机梯度算法的收敛速度慢,为了解决这些不足,在增广随机梯度算法中引入遗忘因子,来改善参数估计精度,进一步通过仿真来比较算法的估计误差以及收敛速度。
