首页|非对称偏斜噪声条件下一种鲁棒概率系统辨识算法研究

非对称偏斜噪声条件下一种鲁棒概率系统辨识算法研究

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在现有的系统辨识算法中，常用的高斯、学生氏t(Student's t，St)、拉普拉斯等噪声分布均呈现出对称的统计特性，难以描述非对称性、有偏的输出噪声，使得在非对称偏斜噪声条件下算法的性能下降。基于此，研究一类广义双曲倾斜学生氏t(Generalized hyperbolic skew student's t，GHSkewt)分布，并在非对称偏斜噪声条件下，提出一种线性系统鲁棒辨识算法。首先，对GHSkewt分布的重尾特性和偏斜特性进行详细阐述，数学上证明了标准学生氏t分布可看作是GHSkewt分布的一个特例;其次，引入隐含变量将GHSkewt分布进行数学分解，以方便算法的推导和实现;最后，在期望最大化(Expectation-maximization，EM)算法下，重构具有隐含变量系统的代价函数，通过迭代优化的方式，不断从被污染数据集中学习过程的动态特性和噪声分布，实现噪声参数和模型参数的联合估计。
Research on Robust Probabilistic System Identification Method With Asymmetric and Skewed Noise
In the existing system identification algorithms,the commonly used Gaussian,student's t(St)and Laplace distributions all show symmetric statistical characteristics which makes them difficult to describe the asym-metric and skewed noise,therefore the performance of the corresponding algorithms may largely degrade with the skewed noise.To this end,this paper introduces the generalized hyperbolic skew student's t(GHSkewt)distribu-tion and proposes a robust identification algorithm for linear systems with the asymmetric and skewed noise.Firstly,the thick-tailed and skewed characteristics of the GHSkewt distribution are introduced detailedly and it is also proved that the standard student's t-distribution can be regarded as a special case of the GHSkewt distribu-tion;Secondly,the latent variables are introduced to mathematically decompose the GHSkewt distribution in order to facilitate the derivation and implementation of the algorithm;Finally,the system cost function with the latent variables is reconstructed under the expectation-maximization(EM)algorithm.The dynamic characteristics and noise distribution of the system are continuously learned from the contaminated data with iterative optimization,then the estimation of noise parameters and model parameters are realized.

Robust system identificationasymmetric and skewed noisegeneralized hyperbolic skew student's t(GHSkewt)distributionexpectation-maximization(EM)algorithm

刘鑫、陈强、王兰豪、代伟

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中国矿业大学人工智能研究院 徐州 221116

中国矿业大学信息与控制工程学院 徐州 221116

中国矿业大学炼焦煤资源绿色开发全国重点实验室 徐州 221116

鲁棒系统辨识 非对称偏斜噪声 广义双曲倾斜学生氏t分布 期望最大化算法

国家自然科学基金国家自然科学基金国家自然科学基金国家重点研发计划中国博士后科学基金

6210313462373361523043092022YFB33047002023M743776

2024

10.16383/j.aas.c230624

自动化学报
中国自动化学会 中国科学院自动化研究所

自动化学报

CSTPCD北大核心
影响因子：1.762
ISSN：0254-4156
年,卷(期)：2024.50(10)