基于核方法的模糊模型辨识研究
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摘要
模糊模型辨识是智能控制理论重要的研究分支之一。传统数学建模方法对当前信息科技所带来的各种复杂研究对象往往无能为力,而模糊模型具有易于表达结构性知识,可把数学函数逼近器与过程信息相结合等优点。基于模糊模型发展的系统辨识、智能控制理论和模式识别新方法等已在众多领域得到了成功应用。因此,模糊模型辨识是智能控制基础理论研究的关键问题之一。
在过去的二十多年里,国内外学者在模糊模型辨识理论方面已经作了大量的研究工作,但现有辨识算法仍面临着如何避免“维数灾难”和提高模型泛化能力等难题。模糊模型辨识主要分为结构辨识和参数辨识两个部分,其中结构辨识是关键,也是难点,目前尚未形成完善的理论。此外,如何在模糊模型的多个性能指标(如复杂度和精度)间作出折衷,从而为参数辨识提供合理的依据,目前还缺乏有效的理论指导。而且,将模糊模型辨识方法应用于实际工业生产过程也还存在不少的困难,其中一个主要的原因就是一些传统的辨识方法所产生的庞大规则库以及巨大的辨识计算消耗。因此,如何设计简洁有效的辨识算法,提高模型的泛化性能,并降低辨识算法的计算复杂度等就成为本文研究的主要出发点。
本文致力于将核方法引入模糊模型辨识领域以期获得新颖而有效的辨识算法,从而克服传统辨识方法存在的一些不足。核方法是对使用核技巧的一类学习算法的总称,它是目前机器学习领域中最具活力的研究方向之一。在本文中,首先设计了基于支持向量机的模糊模型辨识算法,使用支持向量机来完成结构辨识以提高模型的泛化性能,再利用卡尔曼滤波实现参数估计;然后通过改进遗传算法来解决核函数和核参数选择问题,并同时考虑辨识精度和模型复杂度以实现多性能指标折衷;再针对辨识的计算消耗问题,提出基于增量核学习的辨识算法以加快辨识速度减小计算消耗;最后针对支持向量模糊系统可能存在的规则冗余问题提出了一种基于双重核学习(核模糊聚类和支持向量回归)的支持向量组合策略来实现规则库的简化,以保证模型的简洁性。该方法同时避免了传统基于模糊聚类的辨识算法存在对初始聚类个数敏感的缺点。
具体地说,本文主要有以下几个创新点:
1、适当核函数的选择和核参数的优化一直是核方法应用的关键和难点。本文采用凸组合方式将两类代表性的核函数加以组合,并将加权系数和其他核参数一起交由遗传算法(Genetic Algorithm)加以优化,从而实现将核函数的选择问题转化为一个参数优化问题。再引入参数不敏感变化步长概念以改进遗传算子,加快进化速度。优化目标函数中我们综合考虑了辨识的精度和模型的复杂度,从而实现了模糊模型的多性能指标设计要求。
2、对于基于支持向量机的模糊辨识方法,辨识的计算复杂度与训练样本个数呈指数关系。为此文中提出了一种新的支持向量机训练算法。首先使用核马氏距离(Kernel Mahalanobis Distance)来定义一个椭圆区域,以挑选出可能成为支持向量的样本,以此来减小训练样本的规模,再以增量学习(Incremental Learning)方式来完成支持向量机的训练,最后的模糊规则可从支持向量学习结果中直接提取。该方法为开发模糊模型的在线辨识技术提供了方案。
3、支持向量模糊系统的规则个数由支持向量个数决定,一旦支持向量很多,就可能导致规则冗余。为此,本文提出一种基于双重核学习机的规则库简化策略来避免这一缺点。首先提出一种新的核模糊聚类(Kernel fuzzy clustering)算法将样本集做出初始划分,再针对每个聚类使用支持向量回归机定位支持向量,再对这些获得的支持向量加以组合压缩以达到减少支持向量个数的目的,而最终模糊模型的结构则由这些组合后的支持向量来确定。该支持向量组合策略(Combination strategy for support vectors)能够有效地确保模型的简洁性。此外,该算法不再像传统基于聚类的辨识算法那样对初始的聚类个数敏感,而且由于条件正定核的使用,使得辨识算法免去了核参数优化的过程。
Fuzzy model identification is one of the most important research branches in intelligent control theory. Traditional mathematical modeling approaches are always not amenable to various complex research objects which come up with the developing information technology. However, fuzzy model possesses some advantages such as expressing structural knowledge easily and being able to combine mathematical function approximators with process information, etc. Many new approaches based on fuzzy model have been successfully applied in fields such as system identification, intelligent control and pattern recognition, etc. Thus, fuzzy model identification has become one of the key issues in basic theory research of intelligent control.
In the past two decades, scholars at home and abroad have done a lot of work about the theory research of fuzzy model identification. But identification algorithms in existence are still faced with some tough questions, such as how to avoid“the curse of dimensionality”, and how to improve the generalization ability of fuzzy model. Generally, fuzzy model identification is composed of two main parts: structure identification and parameter estimation. The former is not only a difficulty, but also is a key to the whole identification process. However, it remains a pity that structure identification has not developed into a perfect theory. Moreover, how to make a tradeoff between multiple performance indexes (such as complexity and accuracy) to provide reasonable criterions for parameter estimation is still short of effective theory guidance. In addition, there also exist many difficulties in applying fuzzy model identification approaches to real industrial processes, such as the excessive fuzzy rules and the huge computational cost. So, how to design simple and effective identification algorithms, improve generalization ability and cut down computational complexity become the main goals of our research.
This dissertation focuses on developing a novel and effective identification algorithm which can overcome some shortages existing in conventional methods by introducing kernel methods to the field of fuzzy model identification. Kernel method is a general appellation for the class of learning algorithms using kernel mapping techniques. It is one of the most active research issues in the machine learning field at present. In this dissertation, we firstly develop a new support vector machine (SVM)-based fuzzy identification algorithm, which uses SVM to achieve structure identification to improve generalization capability, and utilizes Kalman filtering to implement the parameter estimation. Then for the problem of selecting a proper kernel function and optimizing kernel parameters, we develop an improved genetic algorithm (GA) to tackle with it. The tradeoff between multiple performance indexes is achieved by designing an objective function in GA which simultaneously concerns accuracy and complexity. For the purpose of cutting down computational cost of identification, this dissertation proposes a new identification algorithm based on incremental kernel-based learning. Finally, to overcome the rule redundancy which probably exists in the support vector fuzzy system, we develop a novel identification algorithm based on dual kernel-based learning machines (kernel fuzzy clustering and support vector regression), and propose a combination strategy for support vectors to guarantee the conciseness. This approach simultaneously avoids the shortcoming that the performance of traditional clustering-based identification algorithm is sensitive to the initial clustering number,
Specifically, the main contributions of this dissertation are as follows:
1. The selection of proper kernel function and the optimization of kernel parameters are always difficult and critical to the use of kernel method. We combine two typical kernel functions by means of convex combination. The weighting coefficient and other kernel parameters are optimized by an improved GA. So, the selection of kernel functions is converted into a parameter optimization problem. By introducing the concept of the insensitive variance step of parameters, we improve the genetic operators to speed up evolution speed. In the optimization objective function, we simultaneously consider the identification accuracy and the model complexiy to meet the requirement of multiple performance indexes of fuzzy model.
2. For the fuzzy identification approaches based on SVM, the computational cost of identification assumes the exponential growth along with the number of training samples. We use the kernel Mahalanobis distance to define an ellipse area to pick up some samples which are candidates for support vectors. By this means, the scale of training samples can be effectively decreased. Then the training of SVM is achieved by using incremental learning, finally the fuzzy rules can be directly extracted from the results of support vector learning. This approach provides a good solution to developments of online identification techniques.
3. The rule number of support vector fuzzy system is determined by the number of support vectors. Once too many support vectors are produced, the fuzzy rules will probably appear redundant. For this, this dissertation proposes a new simplification strategy for the fuzzy rule base by using dual kernel-based learning machines. Firstly, a new kernel fuzzy clustering is proposed to partition the sample set. Then support vector regression is further used to locate support vector points in each cluster. A combination strategy for these obtained support vectors is developed to cut down the number of support vectors. Finally, these compressed support vectors are used to determine the structure of fuzzy model. The simplification strategy can effectively assure the conciseness of fuzzy model. In addition, this algorithm is not only insensitive to initial clustering number just like traditional methods, but also free of the optimization process for kernel parameters due to the use of conditionally positive definite kernel.
在过去的二十多年里,国内外学者在模糊模型辨识理论方面已经作了大量的研究工作,但现有辨识算法仍面临着如何避免“维数灾难”和提高模型泛化能力等难题。模糊模型辨识主要分为结构辨识和参数辨识两个部分,其中结构辨识是关键,也是难点,目前尚未形成完善的理论。此外,如何在模糊模型的多个性能指标(如复杂度和精度)间作出折衷,从而为参数辨识提供合理的依据,目前还缺乏有效的理论指导。而且,将模糊模型辨识方法应用于实际工业生产过程也还存在不少的困难,其中一个主要的原因就是一些传统的辨识方法所产生的庞大规则库以及巨大的辨识计算消耗。因此,如何设计简洁有效的辨识算法,提高模型的泛化性能,并降低辨识算法的计算复杂度等就成为本文研究的主要出发点。
本文致力于将核方法引入模糊模型辨识领域以期获得新颖而有效的辨识算法,从而克服传统辨识方法存在的一些不足。核方法是对使用核技巧的一类学习算法的总称,它是目前机器学习领域中最具活力的研究方向之一。在本文中,首先设计了基于支持向量机的模糊模型辨识算法,使用支持向量机来完成结构辨识以提高模型的泛化性能,再利用卡尔曼滤波实现参数估计;然后通过改进遗传算法来解决核函数和核参数选择问题,并同时考虑辨识精度和模型复杂度以实现多性能指标折衷;再针对辨识的计算消耗问题,提出基于增量核学习的辨识算法以加快辨识速度减小计算消耗;最后针对支持向量模糊系统可能存在的规则冗余问题提出了一种基于双重核学习(核模糊聚类和支持向量回归)的支持向量组合策略来实现规则库的简化,以保证模型的简洁性。该方法同时避免了传统基于模糊聚类的辨识算法存在对初始聚类个数敏感的缺点。
具体地说,本文主要有以下几个创新点:
1、适当核函数的选择和核参数的优化一直是核方法应用的关键和难点。本文采用凸组合方式将两类代表性的核函数加以组合,并将加权系数和其他核参数一起交由遗传算法(Genetic Algorithm)加以优化,从而实现将核函数的选择问题转化为一个参数优化问题。再引入参数不敏感变化步长概念以改进遗传算子,加快进化速度。优化目标函数中我们综合考虑了辨识的精度和模型的复杂度,从而实现了模糊模型的多性能指标设计要求。
2、对于基于支持向量机的模糊辨识方法,辨识的计算复杂度与训练样本个数呈指数关系。为此文中提出了一种新的支持向量机训练算法。首先使用核马氏距离(Kernel Mahalanobis Distance)来定义一个椭圆区域,以挑选出可能成为支持向量的样本,以此来减小训练样本的规模,再以增量学习(Incremental Learning)方式来完成支持向量机的训练,最后的模糊规则可从支持向量学习结果中直接提取。该方法为开发模糊模型的在线辨识技术提供了方案。
3、支持向量模糊系统的规则个数由支持向量个数决定,一旦支持向量很多,就可能导致规则冗余。为此,本文提出一种基于双重核学习机的规则库简化策略来避免这一缺点。首先提出一种新的核模糊聚类(Kernel fuzzy clustering)算法将样本集做出初始划分,再针对每个聚类使用支持向量回归机定位支持向量,再对这些获得的支持向量加以组合压缩以达到减少支持向量个数的目的,而最终模糊模型的结构则由这些组合后的支持向量来确定。该支持向量组合策略(Combination strategy for support vectors)能够有效地确保模型的简洁性。此外,该算法不再像传统基于聚类的辨识算法那样对初始的聚类个数敏感,而且由于条件正定核的使用,使得辨识算法免去了核参数优化的过程。
Fuzzy model identification is one of the most important research branches in intelligent control theory. Traditional mathematical modeling approaches are always not amenable to various complex research objects which come up with the developing information technology. However, fuzzy model possesses some advantages such as expressing structural knowledge easily and being able to combine mathematical function approximators with process information, etc. Many new approaches based on fuzzy model have been successfully applied in fields such as system identification, intelligent control and pattern recognition, etc. Thus, fuzzy model identification has become one of the key issues in basic theory research of intelligent control.
In the past two decades, scholars at home and abroad have done a lot of work about the theory research of fuzzy model identification. But identification algorithms in existence are still faced with some tough questions, such as how to avoid“the curse of dimensionality”, and how to improve the generalization ability of fuzzy model. Generally, fuzzy model identification is composed of two main parts: structure identification and parameter estimation. The former is not only a difficulty, but also is a key to the whole identification process. However, it remains a pity that structure identification has not developed into a perfect theory. Moreover, how to make a tradeoff between multiple performance indexes (such as complexity and accuracy) to provide reasonable criterions for parameter estimation is still short of effective theory guidance. In addition, there also exist many difficulties in applying fuzzy model identification approaches to real industrial processes, such as the excessive fuzzy rules and the huge computational cost. So, how to design simple and effective identification algorithms, improve generalization ability and cut down computational complexity become the main goals of our research.
This dissertation focuses on developing a novel and effective identification algorithm which can overcome some shortages existing in conventional methods by introducing kernel methods to the field of fuzzy model identification. Kernel method is a general appellation for the class of learning algorithms using kernel mapping techniques. It is one of the most active research issues in the machine learning field at present. In this dissertation, we firstly develop a new support vector machine (SVM)-based fuzzy identification algorithm, which uses SVM to achieve structure identification to improve generalization capability, and utilizes Kalman filtering to implement the parameter estimation. Then for the problem of selecting a proper kernel function and optimizing kernel parameters, we develop an improved genetic algorithm (GA) to tackle with it. The tradeoff between multiple performance indexes is achieved by designing an objective function in GA which simultaneously concerns accuracy and complexity. For the purpose of cutting down computational cost of identification, this dissertation proposes a new identification algorithm based on incremental kernel-based learning. Finally, to overcome the rule redundancy which probably exists in the support vector fuzzy system, we develop a novel identification algorithm based on dual kernel-based learning machines (kernel fuzzy clustering and support vector regression), and propose a combination strategy for support vectors to guarantee the conciseness. This approach simultaneously avoids the shortcoming that the performance of traditional clustering-based identification algorithm is sensitive to the initial clustering number,
Specifically, the main contributions of this dissertation are as follows:
1. The selection of proper kernel function and the optimization of kernel parameters are always difficult and critical to the use of kernel method. We combine two typical kernel functions by means of convex combination. The weighting coefficient and other kernel parameters are optimized by an improved GA. So, the selection of kernel functions is converted into a parameter optimization problem. By introducing the concept of the insensitive variance step of parameters, we improve the genetic operators to speed up evolution speed. In the optimization objective function, we simultaneously consider the identification accuracy and the model complexiy to meet the requirement of multiple performance indexes of fuzzy model.
2. For the fuzzy identification approaches based on SVM, the computational cost of identification assumes the exponential growth along with the number of training samples. We use the kernel Mahalanobis distance to define an ellipse area to pick up some samples which are candidates for support vectors. By this means, the scale of training samples can be effectively decreased. Then the training of SVM is achieved by using incremental learning, finally the fuzzy rules can be directly extracted from the results of support vector learning. This approach provides a good solution to developments of online identification techniques.
3. The rule number of support vector fuzzy system is determined by the number of support vectors. Once too many support vectors are produced, the fuzzy rules will probably appear redundant. For this, this dissertation proposes a new simplification strategy for the fuzzy rule base by using dual kernel-based learning machines. Firstly, a new kernel fuzzy clustering is proposed to partition the sample set. Then support vector regression is further used to locate support vector points in each cluster. A combination strategy for these obtained support vectors is developed to cut down the number of support vectors. Finally, these compressed support vectors are used to determine the structure of fuzzy model. The simplification strategy can effectively assure the conciseness of fuzzy model. In addition, this algorithm is not only insensitive to initial clustering number just like traditional methods, but also free of the optimization process for kernel parameters due to the use of conditionally positive definite kernel.
引文
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