Research On Fuzzy Modeling Method Based On Objective Cluster Analysis

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.