【作者】 王娜；

【导师】 杨煜普；

【作者基本信息】 上海交通大学 ， 控制理论与控制工程， 2009， 博士

【摘要】 模糊模型易于表达结构性的知识,可将专家的先验知识与过程的数据信息相结合,利用模糊规则库来精确逼近和描述建模对象中不同系统变量间的函数关系,能有效地克服机理模型难以解析复杂的非线性关系、且构建成本较高的缺点,从而使被控过程及其相关特性更加易于描述、理解和分析。在模糊建模中,模型的精确性、解释性及其相互折衷问题一直是非常活跃的研究领域。模糊辨识作为模糊建模中有效的数据驱动手段,主要分为结构辨识和参数辨识两部分。其中结构辨识是关键环节,但就整体而言,由于通常采用启发式方法和数值方法,致使目前仍缺乏系统化的指导方法,所以尚未形成完善的理论体系。因此在各种噪声和人为决策等不确定因素的影响下,应用现有模糊辨识技术处理不同折衷程度的模糊建模问题时,仍面临着严峻的挑战。为此,本文基于客观聚类的思想,并结合各种优化方法,对上述的模糊建模问题开展了相应的研究工作。主要研究内容包括以下几个方面:在传统鲁棒聚类算法中,聚类有效性的计算及其综合评判直接影响着聚类结果的分类精度。但受噪声和评判准则间缺乏公度性的影响,准确的聚类结果,即聚类个数和聚类中心难以直接确定。为此,提出了一种新型的鲁棒聚类算法——改进客观聚类分析算法。利用偶极子分级策略进行初始划分,从而降低了噪声可能导致的冗余;并在原始客观聚类分析算法的基础上,引入了相对不相似性测度,以提高算法对于形状不规则和边界模糊聚类的准确判别;此外,为了提高一致性计算的收敛性,还提出了改进的一致性准则;并且还借助于GMDH理论中最优复杂度聚类的原则,避免了外部准则约束的施加,可以直接获得准确的聚类结果。除理论分析外,还在加入白噪声情况下,借助于数值例子对改进客观聚类分析算法的鲁棒性进行了分析;并利用IRIS标准测试分类问题,在加入Markov有色噪声情况下验证了本方法的鲁棒性和良好的分类精度。在T-S模糊辨识中,前件结构及其参数的辨识精度既决定了模型对于已有训练数据的拟合精度,又直接影响了模型对于未建模数据的泛化能力,因而对模型的精确性具有至关重要的作用。然而传统聚类方法对于训练数据学习的弱鲁棒性,难以保证模型的辨识精度,并且计算量较大。为此,本文提出了一种基于客观模糊聚类的鲁棒T-S模糊辨识算法。首先将改进客观聚类分析算法引入到模糊c均值聚类算法中,形成了客观模糊聚类分析算法,以确定最优的前件模糊划分。因此既有效提高了模糊辨识算法的鲁棒性,实现了对前件结构及其参数的精确估计,又通过一次学习直接确定了前件辨识的结果,从而提高了算法的计算效率。此外,采用了稳态卡尔曼滤波方法确定后件参数,避免了最小二乘估计中存在的非数值解问题,提高了计算结果的有效性。在性能分析中,与模糊c均值聚类算法相比较,验证了客观模糊聚类分析算法的计算复杂性,并利用加白噪声的人工测试函数验证了本辨识方法的鲁棒性。最后在有无外加噪声两种情况下,采用仿真实例Box-Jenkins煤气炉系统验证了本方法的鲁棒性以及良好的逼近和泛化能力。在T-S解释性模糊建模研究中,模型的解释性与精确性之间的矛盾始终存在。而传统方法一般采用过估计手段或者基于全局划分策略来初始化模型,难以精确逼近系统的局部非线性特性,因此可能导致规则库的冗余,或者模型拟合精度和泛化能力的下降,很难实现解释性与精确性之间的良好折衷。针对这类问题,本文将客观聚类思想与遗传学习策略相结合,提出了一种基于遗传——客观聚类的解释性T-S模糊建模算法。一方面,基于客观聚类的初始模糊划分优先考虑了规则库的约简,从而降低了过估计和全局划分的强一致性对异常数据的敏感,大大减少了冗余。另一方面,在迭代学习过程中,采用了基于局部误差准则的模糊划分扩展策略,改善了局部拟合的精确性;并在此基础上,利用遗传算法从候选集中选择最优子集,从而降低了过分强调局部精度而可能引起的全局精度的损失,确定了最佳规则数。电力应用问题的仿真研究验证了本方法模型的紧凑性与精确性。针对Mamdani模糊建模研究中,Mamdani模型的解释性因素,即规则库的紧凑性、规则库的相容性和模糊划分的清晰性等特性易受传统策略过学习的影响而导致下降的问题,在客观聚类策略的基础上,引入了进化学习的机制,提出了一种基于进化——客观聚类的Mamdani模糊建模算法。首先基于改进的客观聚类分析算法,并结合模糊聚类和最小二乘优化技术,实现了对初始Mamdani模型的简明模糊辨识,不仅将客观聚类辨识的思想由T-S模型自然推广到Mamdani模型中,而且通过一次学习可以有效确保规则库的紧凑性。其次基于经典的(1+1)进化策略简单实现了对规则前、后件参数语义值的优化。在进化学习过程中,采用规则覆盖率和遗传小生境作为约束条件来联合设计适应度函数,可以有效实现对另外两种解释性因素——规则间的相容性和模糊划分中相邻子集间适度交叠性的同时兼顾。电力应用问题的仿真研究表明了本方法模型的紧凑性、清晰性和适度的精确性。更多还原

【Abstract】 Fuzzy model possesses the following advantages, such as expressing structural knowledge easily, being able to combine the prior knowledge of experts with the data information in process, and accurately approximating and describing the function relationship among the different system variables in the modeling objective by means of constructing the fuzzy rule base. Therefore the disadvantages of being difficult to analyze the complex nonlinear relationships and expending high cost in mechanism model can be overcome effectively. Consequently, the control process and its dynamic characteristics are easily described, understood and analyzed. In fuzzy modeling, the study on accuracy, interpretability and the trade-off between them are very attractive research fields. As an effective data-driven tool in fuzzy modeling, fuzzy identification is mainly divided into two parts: structure identification and parameter identification. Comparatively, structure identification is the key part. Usually, structure identification adopts the heuristic and numerical methods in terms of the entirety. Thus it results in that the current structure identification methods lack systematic guideline. Then there is no the perfect theory. For this reason, affected by different uncertain factors, such as noise or human decision-making, the common fuzzy identification techniques are facing challenges when handling various trade-off problems in fuzzy modeling. In this thesis, based on the idea of Objective Cluster Analysis (OCA), and combined with different optimization methods, the corresponding research work about fuzzy modeling is developed. The main contents are as follows:In the traditional robust clustering algorithms, the classification precision of the clustering result is directly influnced by the computation of the cluster validity and the overall judgment among them. However, it is difficult to determine the correct clustering result including the number of clusters and the cluster centers directly for being affected by the noise and lack of commensurability among the evaluation criteria. In this paper, a new type robust clustering algorithm——the Enhanced Objective Cluster Analysis (EOCA) algorithm is proposed. In this algorithm, the initial partition is formed using the dipole classification strategy, which reduces the possible redundancy clusters produced by noise; additionally, on basis of the OCA, the Relative Dissimilarity Measure is introduced in order to enhance the accuracy of discrimination for the clusters with abnormal shape or fuzzy boundary. Simultaneously, for strengthening the convergence of consistency computation, an enhanced consistency criterion is presented. Furthermore, by the optimal complexity-based clustering principle, the constraint resulted from the external criterion is avoided, and the correct clustering result is directly obtained. Besides the theory analysis, the numerical example containing the white noise is used to analyze the robustness of the EOCA algorithm. Moreover, the robustness and the well classification performance of the proposed method are validated using the Iris benchmark test classification problem with the addition of the Markov color noise.In T-S fuzzy identification, the identification precision of the premise structures and the premise parameters not only decides the fitting accuracy of the model for the existing training data, but also directly influence the generalization ability of the model for the unmodeling samples. Therefore it is of vital importance for the accuracy of the model. Nevertheless, the weak robustness of the traditional methods for learning the training data could not guarantee the moderate identification precision, and the computation amount is enormous. In this paper, a robust T-S fuzzy identification algorithm via Objective Fuzzy Cluster Analysis is proposed. Firstly, the EOCA algorithm is introduced into the Fuzzy c -Means algorithm to formulate the Objective Fuzzy Cluster Analysis (OFCA) method which is used to determine the optimal fuzzy partition of the premises. By OFCA, not only the robustness in the fuzzy identification is effectively enhanced by which the accurate estimation for the premise structures and the premise parameters is realized, but also the result of premise identification is decided directly by one-pass learning such that the computational efficiency of the algorithm is increased. Additionally, the Stable Kalman Filter algorithm is adopted to determine the consequent parameters, which avoids the non-numerical solution problem exsiting in the traditional Least Square Estimation. This strengthens the effectiveness of the computational result. Compared with the Fuzzy c-Means algorithm, the computational complexity of the OFCA algorithm is low. Simultaneously, the robustness of the presented identification method is validated using the artificial test function with the superimposition of white noise. Under the conditions being with or without external noise, the robustness, the well approximation and the generalization ability of the presented method is verified by the Box-Jenkins gas furnace system.On the research of the interpretable T-S fuzzy modeling, the conflicts between the interpretability and the accuracy of the model always exist. The conventional methods adopt over-estimation measures or global partitioning-based strategy to initialize the model. As a result, it is difficult to approximate the local non-linear characteristics of the system, which possibly either produces the redundant rules or decreases the fitting presicion and the generalization ability. Therefore the good trade-off between the interpretability and the accuracy is difficult to be realized. Then, in this paper, the idea of OCA is incorporated with the genetic learning strategy to formulate a Genetic-Objective Cluster Analysis-based interpretable T-S fuzzy modeling algorithm. On the one hand, the reduction of rule base is preferentially considered by means of the initial fuzzy partition via OCA. Therefore the sensitivity of the overfitting and the strong consistency to the outliers in global partitioning is weakened such that the redundancy is reduced greatly. On the other hand, during the iterative learning process, the fuzzy partition expansion strategy via local error criterion is adopted, which improves the precision of the local fitting. On basis of this expansion, the Genetic Algorithm is used to choose the optimal subset from the candidate set. Then the possible loss of the global presicion due to over-emphasizing the local precision is decreased, and the optimal number of rules is determined. The simulation study of the electric application problem verifies the conciseness and the accuracy of the model by the proposed method.On the study of Mamdani fuzzy modeling, the interpretable factors of the Mamdani model, such as the conciseness and the compatibility of the rule base and the distinguishability of the fuzzy partition, et al., may be decreased due to the influence of over-learning in the traditional strategy. Considering this, based on the OCA strategy, the evolutionary learning mechanism is introduced. The Mamdani fuzzy modeling algorithm via the Evolution-Objective Cluster Analysis is presented. Firstly, through combining EOCA algorithm, the fuzzy clustering and the Least Square optimization technique, the concise fuzzy identification for the initial Mamdani model is realized. By this means, not only the idea of the OCA is expanded from the T-S model to the Mamdani model, but also the conciseness of the rule base is effectively garanteed just by one pass-learning. Secondly, the optimization for the semantic values of parameters in the premises and the consequences is simply realized by the classic (1+1) Evolutionary Strategy. During the evolutionary learning process, the adaptive fitness function is designed by the combination of two constraints, i.e., the criteria of rule covering degree and Genetic Niching. As a result, another two interpretable factors, namely, the compatibility among the rules and the appropriate over-lapping between the adjacent fuzzy subsets in the fuzzy partition could be considered in the same time. The simulation study on the electric application problem demonstrates the conciseness, distinguishability and the moderate accuracy of the model by the presented method.更多还原