【作者】 姚兰；

【导师】 肖建；

【作者基本信息】 西南交通大学 ， 电气系统控制与信息技术， 2014， 博士

【摘要】 为了弥补一型模糊集合在处理不确定性时具有局限性的缺陷,Zadeh于1975年将一型模糊集合的隶属度值再次进行模糊化,提出二型模糊集合的概念。由于采用了三维隶属度函数,比一型模糊集合多了一维处理不确定性的自由度,二型模糊集合更适合解决现实环境中具有高度不确定性的问题。特别是区间二型模糊集合具有结构简单、计算效率高的优点,成为了目前模糊理论研究与应用的热点。本论文以区间二型模糊系统理论为基础，着重研究其在系统辨识与图像处理领域的理论和应用。针对区间二型模糊模型建模中因规则冗余而引起的复杂性问题,进行了区间二型模糊模型规则精简方法的研究。基于列主元SVD-QR的规则精简方法是一种有效的模糊模型规则精简方法,但该方法没有解决有效秩选取的问题,为此,提出了奇异值归一化差值的概念,通过放大相邻奇异值的差异来更加清楚地描述奇异值的突变特性,实现有效秩的优选。与现有方法的比较结果表明：该方法获得的规则集保证了模型的精度,实现了模糊模型的结构简化。此外,与统计信息准则相结合,提出了基于列主元QR分解的区间二型模糊模型规则精简方法。仿真结果验证了该方法的有效性,且与基于列主元SVD-QR方法的比较实验结果表明,该方法提高了模型的泛化能力。模糊神经网络融合了模糊推理能力和神经网络的自学习能力而被广泛应用于系统辨识,其研究重点在于结构辨识和参数辨识两方面。为此,提出一种基于聚类的自组织区间二型模糊神经网络学习算法。采用具有两个不同加权参数的FCM算法对输入数据进行划分,利用聚类有效性标准确定规则数目,自动完成了结构辨识和规则前件参数辨识。在此基础上,基于梯度下降法和Lyapunov函数提出了规则后件权向量学习速率的自适应学习算法。通过非线性系统辨识实例,验证了该算法具有较快的收敛速度和良好的泛化性能；并且采用该算法建立了某市电力短期负荷预测模型,仿真结果表明该模型的误差较小、预测精度较高。基于模糊熵的图像阈值分割方法是图像处理领域中的一种重要方法,但其面临着如何设计有效的模糊熵测度和隶属度函数及减少运行时间的问题。为了解决这些问题,利用严格等价函数提出了一种区间二型模糊集距离测度和模糊熵的构建方法,由此获得了一系列新的模糊熵计算表达式。同时,利用严格等价函数构造图像的区间二型模糊隶属函数,并通过理论分析,给出了利用最小熵准则选取最优阈值的方法。仿真结果表明,该方法获得了准确的分割结果,且与现有的其它模糊阈值分割法和改进的2维Otsu法等相比,该方法的分割结果更加准确,运行时间更少,具有广泛的适应性。受电弓滑板故障检测对于保障电力机车安全与稳定运行非常重要。为此,提出一种基于区间二型模糊熵和Hough变换的受电弓滑板裂纹检测方法。该方法依据像素邻域内的灰度分布,提出一种基于区间二型模糊熵的边缘检测方法,获得主体特征增强的滑板边缘图像；然后,采用连通域方法去除孤立噪声点,获得了主要包含边界线、接缝、螺钉和裂纹四类图形元素的滑板边缘图像；在此基础上,采用Hough变换分析各类图形元素在参数空间的特征分布,由此提出一种基于极角约束Hough变换的裂纹提取方法,通过有效地排除非裂纹图形元素的特征点,最终实现滑板裂纹的提取。仿真实验表明,本文的边缘检测方法能够获得线性特征增强的滑板边缘图像,为后续的Hough变换提供有利基础；本文的裂纹提取方法能够准确实现滑板裂纹的识别与定位。更多还原

【Abstract】 In order to make up for the limitations of type-1 fuzzy sets in dealing with uncertainties, in 1975 Professor Zaheh originally presented the type-2 fuzzy sets, which is essentially "fuzzy fuzzy" sets where the fuzzy degree of membership is a type-1 fuzzy set. Since the type-2 fuzzy set is to use three-dimensional membership functions, with more than one dimensional degree of freedom for dealing with uncertainties compared with type-1 fuzzy set, it is more effective in solving the problems with high uncertainties in realistic environment, especially the interval type-2 fuzzy set with advantages of simple structure and high computation efficiency becomes a hot issue in the research and application of fuzzy theory. Based on the theory of the interval type-2 fuzzy system, this thesis focuses research on its theory and application in the field of system identification and image processing.Firstly, for the complicated problems of interval type-2 fuzzy system modeling caused by rules redundancy, rules reduction method of interval type-2 fuzzy system is studied. In order to solve the problem of rule reduction method based on Singular Value Decomposition-QR (SVD-QR) in determining the number of effective singular value, the concept of normalized difference of singular value is proposed.Through magnifying the difference of adjacent singular values to more clearly describe the mutation characteristics of singular values, the optimal choise of the number of effective singular values is realized. Comparing results with other methods show that the fuzzy model obtained by the instruction of the normalized difference of singular value maintains high approximation accuracy. Then, combined with statistical information criteria, the rules reduction method based on the pivoted QR (P-QR) decomposition is proposed. Experiments demonstrate that the simplifized model obtains less error and has better generalizing capabilities than the one with method based on SVD-QR.Secondly, combined with fuzzy reasoning and self-learning ability of neural network fuzzy neural network is widely used in system identification, the research is focused on structure identification and parameter identification. Therefore, a type-2 fuzzy neural network with self organizing structure and learning algorithm is proposed. The fuzzy C-means algorithm with two different weighting parameters is used for partition of input data and the number of fuzzy rules is determined with cluster validity criterion, so that the structure and parameters of rule antecedent identification are completed automatically. Then based on the gradient descent method and Lyapunov function, the adaptive learning algorithm for weight vectors of rules consequent is proposed. The experiment results of two nonlinear systems identification indicate that the proposed algorithm has faster convergence rate and more accurate approximate precision than other algorithms. Additional, based on the power load data of a city, a short-term load-forecasting model developed by the algorithm has high prediction precision and better generalization perfomance.Thirdly, image threshold segmentation method based on fuzzy entropy is an important method in the field of image processing, but it is facing problems of how to design effective membership functions, fuzzy entropy measure and reducing the running time. To overcome these problems, a novel image thresholding method based on entropy of interval type-2 fuzzy sets is proposed. On the basis of the axiom definition, a construction method of distance measure of interval type-2 fuzzy sets is given, then, according to axiomatic definition of entropy for interval type-2 fuzzy sets based on distance, a construction method of entropy measure of interval type-2 fuzzy sets is given so that some different formulas are derived to calculate this kind of entropy. Then, through theory justification the best formulae and threshold can be determined by minimum fuzzy entropy criterion. The experiments demonstrate that, compared with other fuzzy thresholding methods, improved 2-D Otsu’s methods and so forth, the new method can achieve accurate segmentation results and has excellent adaptive capability.Finally, due to the fault detection of pantograph slide is very important for the secure and stable operation of the electric locomotive, a novel method of pantograph slide crack detection based on fuzzy entropy and Hough transform is proposed. Based on the gray distribution of pixels in the neighborhood, an edge detection method based on entropy of interval type-2 fuzzy sets is proposed so that slide edge image with enhanced feature was obtained; then, the connected domain method is used to remove isolated noises. As a result, the slide edge image mainly includes four kinds of graphic elements such as the boundary line, joint, rivet and cracks. On this basis, the characteristics distribution of the various types of graphic elements in the parameter space are analyzed by Hough transform, and thus a method to extract the slide crack based on Hough transform with angle constraint is proposed. Through effectively excluding feature points of others graphic elements, the slide crack can be determined finally. The experiment results indicate that this edge detection method can obtain slide edge image with enhanced linear feature which is benefit for subsequent Hough transform; the crack extraction method can accurately identify and locate the slide crack.更多还原