模糊系统辨识及其在机车粘着中的应用
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摘要
模糊系统在实际系统的建模和控制中具有很多的应用。这种成功的应用主要原因在于模糊系统可以融入人类的知识,以至于使许多来源于客观实际系统的信息可以用模糊命题来描述。这样,人们就可以利用语言规则来理解和描述客观世界的信息。构建模糊系统的过程就是模糊系统辨识,模糊系统辨识需要建立基于模糊规则形式的模糊模型结构,然后利用不同的参数辨识技术来学习模型,最后得到最终的模糊系统模型。
本文主要着眼于数据驱动的模糊系统辨识,目标是利用现有的或改进的数据分析技术试图建立可理解的模糊模型,建立的模糊模型应该具有高透明度模糊规则库;同时,还应该具有良好的逼近能力和推广能力。一般来说,作为辨识使用的数据都通常含有不同形式的不确定性,例如随机性,非特异性及模糊性。因此,针对不同的实际情况,我们应该选择不同形式的模糊模型进行处理。在这里,主要考虑两种类型的模糊系统模型:类型1模糊模型和类型2模糊模型。针对这两种模糊模型,本文作了如下的分析和讨论。
在传统的模糊聚类的框架下,为了利用单峰的、凸的模糊集合来重构模糊划分矩阵中的模糊关系,提出了一种改进的模糊学习向量量化算法。该算法抛弃了传统的模糊指数下降机制,采用了冷却表控制,在迭代的过程中,模糊指数根据某种优化性能指标自动地调节,以至于使得到的隶属度函数更加容易理解。同时,该算法还被用于进行类型1模糊基函数模型的建模。
当采用支持向量学习机制进行类型1模糊模型建模的时候,过多的支持向量数将导致一个复杂的类型1模糊模型。因此,一种基于简约集向量的TS(RV-TS)模型被提出来解决这一问题。RV-TS模型通过抽取简约集向量来产生模糊规则,规则的前件隶属度函数为Mercer核构建的多维隶属度函数,后件为结构一致的非线性函数。为了辨识提出的模型的结构和参数,提升RV-TS模型的性能,分别采用了两种学习规则:自下而上简化算法和ε不敏感学习相结合的规则以及面向经验的混合学习规则。
针对类型2模糊理论,本论文还提出一种新的交替迭代结构的聚类算法,鲁棒区间类型2可能性C均值(IT2PCM)聚类算法。它实质上是采用了交替迭代结构进行聚类的交替类估计,但是隶属度函数则通过区间类型2模糊集合来选择。在提出的方法中,类的原型的更新方程通过降型与解模糊相结合的形式来计算。在鲁棒统计的框架下,通过φ函数的分析指出这种更新方程对类内不确定的模式以及野点具有鲁棒性。
以鲁棒IT2PCM算法为主要工具,建立了一种快速原型方法进行区间类型2模糊建模。该方法首先利用IT2PCM算法在输入输出空间聚类,然后抽取类的原型生成区间类型2模糊规则对区间类型2模糊逻辑系统(IT2FLS)进行一次逼近。这个一次逼近模型是一个初始的模糊模型,可被引入作为优化调节IT2FLS参数的一个好的初始结构。
最后,分析了机车牵引动态模型,并且建立了干扰观测器的粘着系数估计系统。通过仿真实验,采集蠕滑速度和粘着系数的数据,利用RV-TS模型对粘着特性曲线进行模糊建模。
Fuzzy systems have demonstrated their ability for modeling or control in a huge number of applications. The keys for their success and interest are the ability to incorporate human knowledge, so the information mostly provided for many real-world systems could be discovered or described by fuzzy statements. In this way, the existing information in objective world could be comprehended as linguistic rules. To develop and establish fuzzy systems is fuzzy system identification, which considers model structures in the form of fuzzy rule-based systems and constructs them by means of different parametric system identification techniques.
This paper mainly focuses on data-driven approaches to fuzzy system identification. The aim is to utilize existing or modified data analysis techniques and try to establish an interpretable fuzzy model which usually has a transparency rule base; simultaneously the model possesses excellent approximation and generalization performance. In general, the data measured is usually endowed with various types of uncertainties, such as randomness, non-specificity and fuzziness. Hence, it is vital for selecting the form of fuzzy model in order to deal with different circumstances in real world. Here, two kinds of fuzzy models are under consideration: type-1 fuzzy model and type-2 fuzzy model. With regard to them, some important issues have been discussed in this paper as follows.
In the framework of traditional fuzzy clustering, in order to reconstruct fuzzy relation in fuzzy partition matrix using unimodal and convex fuzzy set, a modified fuzzy learning vector quantization (M-FLVQ) algorithm is proposed. It abandons the descending mechanism, and employs the cooling schedule. In the iteration process, the weighting exponent is automatically adjusted so that the resulting memberships are more interpretable than those derived by traditional fuzzy clustering. At the same time, this algorithm is also used as a tool to identify the type-1 fuzzy basis function model.
When one uses support vector learning mechanism to type-1 fuzzy modeling, too many support vectors will lead to a complicated fuzzy model. Therefore, a reduced-set vector-based Takagi-Sugeno fuzzy model (RV-TSFM) which alternatively extracts reduced-set vectors for generating fuzzy rules is presented. The product type multidimensional fuzzy membership functions in antecedents of rules can be directly created by Mercer kernels, and the nonlinear functions represent the consequents. The model structure and parameters can be effectively identified by utilizing bottom-up simplification algorithm combinedε-insensitive learning or experience-oriented hybrid learning.
Utilizing type-2 fuzzy theory, this paper also presents alternating iteration architecture for clustering called robust interval type-2 possibilistic c-means (IT2PCM) clustering algorithm. It is actually alternating cluster estimation, but membership functions are selected directly with interval type-2 fuzzy sets by the users. In proposed algorithm, the cluster prototype update equation is calculated by type reduction combined with defuzzification, and it is robust to uncertain inliers and outliers on the basis of itsφfunction analysis in the framework of robust statistics.
Consequently, with robust IT2PCM clustering algorithm as main tool, a rapid-prototyping approach to interval type-2 fuzzy modeling is proposed. Firstly, the IT2PCM clustering is carried out in input and output space, and then cluster prototypes are extracted to generate interval type-2 fuzzy rules that can be used to obtain a first approximation to the interval type-2 fuzzy logic system (IT2FLS). This first approximation model is an initial fuzzy model, so it can be introduced as a good initial structure of IT2FLS for further tuning in a subsequent process.
Finally, the dynamics of locomotive traction are analyzed, and a disturbance observer is used to estimate adhesion coefficient. According to the simulation data of slip velocity and adhesion coefficient, a fuzzy model, RV-TS model, is built to describe the adhesion characteristic curve.
本文主要着眼于数据驱动的模糊系统辨识,目标是利用现有的或改进的数据分析技术试图建立可理解的模糊模型,建立的模糊模型应该具有高透明度模糊规则库;同时,还应该具有良好的逼近能力和推广能力。一般来说,作为辨识使用的数据都通常含有不同形式的不确定性,例如随机性,非特异性及模糊性。因此,针对不同的实际情况,我们应该选择不同形式的模糊模型进行处理。在这里,主要考虑两种类型的模糊系统模型:类型1模糊模型和类型2模糊模型。针对这两种模糊模型,本文作了如下的分析和讨论。
在传统的模糊聚类的框架下,为了利用单峰的、凸的模糊集合来重构模糊划分矩阵中的模糊关系,提出了一种改进的模糊学习向量量化算法。该算法抛弃了传统的模糊指数下降机制,采用了冷却表控制,在迭代的过程中,模糊指数根据某种优化性能指标自动地调节,以至于使得到的隶属度函数更加容易理解。同时,该算法还被用于进行类型1模糊基函数模型的建模。
当采用支持向量学习机制进行类型1模糊模型建模的时候,过多的支持向量数将导致一个复杂的类型1模糊模型。因此,一种基于简约集向量的TS(RV-TS)模型被提出来解决这一问题。RV-TS模型通过抽取简约集向量来产生模糊规则,规则的前件隶属度函数为Mercer核构建的多维隶属度函数,后件为结构一致的非线性函数。为了辨识提出的模型的结构和参数,提升RV-TS模型的性能,分别采用了两种学习规则:自下而上简化算法和ε不敏感学习相结合的规则以及面向经验的混合学习规则。
针对类型2模糊理论,本论文还提出一种新的交替迭代结构的聚类算法,鲁棒区间类型2可能性C均值(IT2PCM)聚类算法。它实质上是采用了交替迭代结构进行聚类的交替类估计,但是隶属度函数则通过区间类型2模糊集合来选择。在提出的方法中,类的原型的更新方程通过降型与解模糊相结合的形式来计算。在鲁棒统计的框架下,通过φ函数的分析指出这种更新方程对类内不确定的模式以及野点具有鲁棒性。
以鲁棒IT2PCM算法为主要工具,建立了一种快速原型方法进行区间类型2模糊建模。该方法首先利用IT2PCM算法在输入输出空间聚类,然后抽取类的原型生成区间类型2模糊规则对区间类型2模糊逻辑系统(IT2FLS)进行一次逼近。这个一次逼近模型是一个初始的模糊模型,可被引入作为优化调节IT2FLS参数的一个好的初始结构。
最后,分析了机车牵引动态模型,并且建立了干扰观测器的粘着系数估计系统。通过仿真实验,采集蠕滑速度和粘着系数的数据,利用RV-TS模型对粘着特性曲线进行模糊建模。
Fuzzy systems have demonstrated their ability for modeling or control in a huge number of applications. The keys for their success and interest are the ability to incorporate human knowledge, so the information mostly provided for many real-world systems could be discovered or described by fuzzy statements. In this way, the existing information in objective world could be comprehended as linguistic rules. To develop and establish fuzzy systems is fuzzy system identification, which considers model structures in the form of fuzzy rule-based systems and constructs them by means of different parametric system identification techniques.
This paper mainly focuses on data-driven approaches to fuzzy system identification. The aim is to utilize existing or modified data analysis techniques and try to establish an interpretable fuzzy model which usually has a transparency rule base; simultaneously the model possesses excellent approximation and generalization performance. In general, the data measured is usually endowed with various types of uncertainties, such as randomness, non-specificity and fuzziness. Hence, it is vital for selecting the form of fuzzy model in order to deal with different circumstances in real world. Here, two kinds of fuzzy models are under consideration: type-1 fuzzy model and type-2 fuzzy model. With regard to them, some important issues have been discussed in this paper as follows.
In the framework of traditional fuzzy clustering, in order to reconstruct fuzzy relation in fuzzy partition matrix using unimodal and convex fuzzy set, a modified fuzzy learning vector quantization (M-FLVQ) algorithm is proposed. It abandons the descending mechanism, and employs the cooling schedule. In the iteration process, the weighting exponent is automatically adjusted so that the resulting memberships are more interpretable than those derived by traditional fuzzy clustering. At the same time, this algorithm is also used as a tool to identify the type-1 fuzzy basis function model.
When one uses support vector learning mechanism to type-1 fuzzy modeling, too many support vectors will lead to a complicated fuzzy model. Therefore, a reduced-set vector-based Takagi-Sugeno fuzzy model (RV-TSFM) which alternatively extracts reduced-set vectors for generating fuzzy rules is presented. The product type multidimensional fuzzy membership functions in antecedents of rules can be directly created by Mercer kernels, and the nonlinear functions represent the consequents. The model structure and parameters can be effectively identified by utilizing bottom-up simplification algorithm combinedε-insensitive learning or experience-oriented hybrid learning.
Utilizing type-2 fuzzy theory, this paper also presents alternating iteration architecture for clustering called robust interval type-2 possibilistic c-means (IT2PCM) clustering algorithm. It is actually alternating cluster estimation, but membership functions are selected directly with interval type-2 fuzzy sets by the users. In proposed algorithm, the cluster prototype update equation is calculated by type reduction combined with defuzzification, and it is robust to uncertain inliers and outliers on the basis of itsφfunction analysis in the framework of robust statistics.
Consequently, with robust IT2PCM clustering algorithm as main tool, a rapid-prototyping approach to interval type-2 fuzzy modeling is proposed. Firstly, the IT2PCM clustering is carried out in input and output space, and then cluster prototypes are extracted to generate interval type-2 fuzzy rules that can be used to obtain a first approximation to the interval type-2 fuzzy logic system (IT2FLS). This first approximation model is an initial fuzzy model, so it can be introduced as a good initial structure of IT2FLS for further tuning in a subsequent process.
Finally, the dynamics of locomotive traction are analyzed, and a disturbance observer is used to estimate adhesion coefficient. According to the simulation data of slip velocity and adhesion coefficient, a fuzzy model, RV-TS model, is built to describe the adhesion characteristic curve.
引文
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