非线性系统的模糊辨识方法与应用研究
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摘要
由于传统方法不能有效地对复杂和不确定系统进行建模，因此需要寻找一种能够描述非线性系统的全局函数或解析结构。查德(L.A.Zadeh)提出一种有效的方法来描述不能用精确数学模型表达的复杂或病态系统。但由于非线性系统的复杂性和模糊系统是一个年轻的领域，有很多尚待解决的问题。本文紧紧围绕着非线性系统模糊建模和辨识方法展开讨论和研究。
考虑到一般的聚类算法对于设置聚类中心的初值存在很多困难，Hough变换通过自动获得数据的线性划分解决了此问题。首先利用Hough变换的方法得到聚类中心的初始值，然后通过模糊C-均值聚类法辨识前提参数，采用递推最小二乘辨识模糊模型的结论参数。其次，提出了一种新的基于T-S模糊模型的建模方法。该方法是基于输入空间的模糊划分计算给定样本在各模糊子空间的隶属度，利用正交最小二乘算法辨识模糊模型的结论参数。最后通过仿真结果验证了该方法的有效性与实用性。
针对以往模糊C-聚类法(FCM)在搜索聚类中心时计算量大，不适于在线建模与控制这一问题，提出一种改进的方法：将多步随机采样模糊C-划分聚类方法(mrFCM)应用到模糊模型辨识中。与以往的模糊聚类辨识方法相比，所需CPU时间大大缩短，具有较高的辨识精度。
怎样从给定规则库中选取重要规则，即规则化简，是个很重要的研究课题。John Yen和Liang Wang介绍了几种应用于模糊模型的信息优化准则，本论文在此基础上对统计信息准则进行一些改进，并与快速模糊聚类和正交最小二乘方法结合，提高了模型的辨识精度和泛化能力。
最后，为了验证模糊辨识方法的实用性，本文将模糊系统逼近时变参数的实时辨识算法与具有较强鲁棒性的广义预测控制算法相结合，提出了基于模糊辨识的非线性系统多变量自适应广义预测控制策略，通过仿真实例进行了验证，并且取得了较好的控制效果。
Complex and uncertain systems are often poorly modeled with
conventional approaches that attempt to find a global function or analytical
structure for a nonlinear system. A new approach is outlined by L.A.Zadeh that
"provides an approximate and yet affective means of describing the behavior
of systems which are too complex or too ill-defined to admit use of precise
mathematical analysis." But due to nonlinear systems are too complex and the
fuzzy system is immature research domain. There exist many issues should be
improved to be solved. This dissertation closely surrounds fuzzy modeling and
identification methods for nonlinear systems to discuss and to research.
First of all, according to the difficulty in setting the initial number of
cluster, Hough transform solves this problem by automatically specifying the
number of linear segments. Firstly, the initial values of cluster are obtained by
Hough transform, which consider the linearity and continuity, then the premise
and consequent parameters are identified based on Fuzzy C-means and
recursive least square. This method not only has higher approximate precision,
but also has simple computation and the procedure is realized easily. Secondly,
This paper presents a new fuzzy modeling based on T-S fuzzy model, which
calculates the membership grade of each fuzzy subspace using fuzzy partition
of input space, the consequence parameter identification is obtained by
orthogonal least square. Finally, the effectiveness and practicability of this
method is demonstrated by the simulation results of the famous Box-Jenkins
gas furnace data and Mackey-Glass Chaotic Time Series.
In accordance with the problem that the FCM algorithm is quite
time-consuming for search out cluster cancroids and may not be suitable for
on-line modeling and control. This dissertation proposed an improved fuzzy
identification method based Multistage Random Sampling Fuzzy c-means
Clustering Algorithm (mrFCM). It has higher approximate precision and the
CPU time has slowed down sharply compared with the common fuzzy
clustering method.
An important issue is how to select a set of important fuzzy rules from a
given rule base, namely simplifying fuzzy rule. Because the removal of
redundant or less important fuzzy rules from the rule base can result in a
compact fuzzy model with better generalizing ability. John Yen, Liang Wang
has introduced several statistical information optimal criteria applied in fuzzy
modeling. In this paper, the simplifying fuzzy rule-based models are obtained
using improved criteria. fast fuzzy clustering and orthogonal least square.
Finally, to demonstrate the applicability of fuzzy identifying methods, we
combined real-time identification algorithm that can approximate time-varying
parameter with fuzzy' systems with GPC with strong robust, and proposed
on-line adaptive GPC strategy based on fuzzy identification for nonlinear
systems. In the end, the simulation results demonstrate the effectiveness of the
method, and better performance of control and predication are achieved.
考虑到一般的聚类算法对于设置聚类中心的初值存在很多困难，Hough变换通过自动获得数据的线性划分解决了此问题。首先利用Hough变换的方法得到聚类中心的初始值，然后通过模糊C-均值聚类法辨识前提参数，采用递推最小二乘辨识模糊模型的结论参数。其次，提出了一种新的基于T-S模糊模型的建模方法。该方法是基于输入空间的模糊划分计算给定样本在各模糊子空间的隶属度，利用正交最小二乘算法辨识模糊模型的结论参数。最后通过仿真结果验证了该方法的有效性与实用性。
针对以往模糊C-聚类法(FCM)在搜索聚类中心时计算量大，不适于在线建模与控制这一问题，提出一种改进的方法：将多步随机采样模糊C-划分聚类方法(mrFCM)应用到模糊模型辨识中。与以往的模糊聚类辨识方法相比，所需CPU时间大大缩短，具有较高的辨识精度。
怎样从给定规则库中选取重要规则，即规则化简，是个很重要的研究课题。John Yen和Liang Wang介绍了几种应用于模糊模型的信息优化准则，本论文在此基础上对统计信息准则进行一些改进，并与快速模糊聚类和正交最小二乘方法结合，提高了模型的辨识精度和泛化能力。
最后，为了验证模糊辨识方法的实用性，本文将模糊系统逼近时变参数的实时辨识算法与具有较强鲁棒性的广义预测控制算法相结合，提出了基于模糊辨识的非线性系统多变量自适应广义预测控制策略，通过仿真实例进行了验证，并且取得了较好的控制效果。
Complex and uncertain systems are often poorly modeled with
conventional approaches that attempt to find a global function or analytical
structure for a nonlinear system. A new approach is outlined by L.A.Zadeh that
"provides an approximate and yet affective means of describing the behavior
of systems which are too complex or too ill-defined to admit use of precise
mathematical analysis." But due to nonlinear systems are too complex and the
fuzzy system is immature research domain. There exist many issues should be
improved to be solved. This dissertation closely surrounds fuzzy modeling and
identification methods for nonlinear systems to discuss and to research.
First of all, according to the difficulty in setting the initial number of
cluster, Hough transform solves this problem by automatically specifying the
number of linear segments. Firstly, the initial values of cluster are obtained by
Hough transform, which consider the linearity and continuity, then the premise
and consequent parameters are identified based on Fuzzy C-means and
recursive least square. This method not only has higher approximate precision,
but also has simple computation and the procedure is realized easily. Secondly,
This paper presents a new fuzzy modeling based on T-S fuzzy model, which
calculates the membership grade of each fuzzy subspace using fuzzy partition
of input space, the consequence parameter identification is obtained by
orthogonal least square. Finally, the effectiveness and practicability of this
method is demonstrated by the simulation results of the famous Box-Jenkins
gas furnace data and Mackey-Glass Chaotic Time Series.
In accordance with the problem that the FCM algorithm is quite
time-consuming for search out cluster cancroids and may not be suitable for
on-line modeling and control. This dissertation proposed an improved fuzzy
identification method based Multistage Random Sampling Fuzzy c-means
Clustering Algorithm (mrFCM). It has higher approximate precision and the
CPU time has slowed down sharply compared with the common fuzzy
clustering method.
An important issue is how to select a set of important fuzzy rules from a
given rule base, namely simplifying fuzzy rule. Because the removal of
redundant or less important fuzzy rules from the rule base can result in a
compact fuzzy model with better generalizing ability. John Yen, Liang Wang
has introduced several statistical information optimal criteria applied in fuzzy
modeling. In this paper, the simplifying fuzzy rule-based models are obtained
using improved criteria. fast fuzzy clustering and orthogonal least square.
Finally, to demonstrate the applicability of fuzzy identifying methods, we
combined real-time identification algorithm that can approximate time-varying
parameter with fuzzy' systems with GPC with strong robust, and proposed
on-line adaptive GPC strategy based on fuzzy identification for nonlinear
systems. In the end, the simulation results demonstrate the effectiveness of the
method, and better performance of control and predication are achieved.
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