不确定性环境下维纳模型的随机变分贝叶斯学习  被引量:1

Stochastic Variational Bayesian Learning of Wiener Model in the Presence of Uncertainty

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作  者:刘切 李俊豪 王浩 曾建学 柴毅[1] LIU Qie;LI Jun-Hao;WANG Hao;ZENG Jian-Xue;CHAI Yi(School of Automation,Chongqing University,Chongqing 400044)

机构地区:[1]重庆大学自动化学院,重庆400044

出  处:《自动化学报》2024年第6期1185-1198,共14页Acta Automatica Sinica

基  金:国家重点研发计划(2021YFB1715000);国家自然科学基金(61903051,U2034209)资助。

摘  要:多重不确定性环境下的非线性系统辨识是一个开放问题.贝叶斯学习在描述、处理不确定性方面具有显著优势,已在线性系统辨识方面得到广泛应用,但在非线性系统辨识的应用较少,且面临概率估计复杂、计算量大等难题.针对上述问题,以典型维纳(Wiener)非线性过程为对象,提出基于随机变分贝叶斯的非线性系统辨识方法.首先对过程噪声、测量噪声以及参数不确定性进行概率描述;然后利用随机变分贝叶斯方法对模型参数进行后验估计.在估计过程中,利用随机优化思想,仅利用部分中间变量概率信息估计模型参数分布的自然梯度期望,与利用所有中间变量概率信息估计模型参数比较,显著降低了计算复杂性.该方法是首次在系统辨识领域中的应用.最后,利用一个仿真实例和一个维纳模型的Benchmark问题,证明了该方法在对大规模数据下非线性系统辨识的有效性.Nonlinear system identification in multiple uncertain environment is an open problem.Bayesian learning has significant advantages in describing and dealing with uncertainties and has been widely used in linear system identification.However,the use of Bayesian learning for nonlinear system identification has not been well studied,confronted with the complexity of the estimation of the probability and the high computational cost.Motivated by these problems,this paper proposes a nonlinear system identification method based on stochastic variational Bayesian for Wiener model,a typical nonlinear model.First,the process noise,measurement noise and parameter uncertainty are described in terms of probability distribution.Then,the posterior estimation of model parameters is carried out by using the stochastic variational Bayesian approach.In this framework,only a few intermediate variables are used to estimate the natural gradient of the lower bound function of the likelihood function based on the stochastic optimization idea.Compared with classical variational Bayesian approach,where the estimation of model parameters depends on the information of all the intermediate variables,the computational complexity is significantly reduced for the proposed method since it only depends on the information of a few intermediate variables.To the best of our knowledge,it is the first time to use the stochastic variational Bayesian to system identification.A numerical example and a Benchmark problem of Wiener model are used to show the effectiveness of this method in the nonlinear system identification in the presence of large-scale data.

关 键 词:非线性系统辨识 随机优化 变分贝叶斯 维纳模型 

分 类 号:O212.8[理学—概率论与数理统计] N945.14[理学—数学]

 

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