# Self-Organized Fuzzy Neural Network Nonlinear System Modeling Method Based on Clustering Algorithm
###### Abstract
Considering the characteristics of offline identification and online identification and in order to improve the training efficiency and rate, this paper adopts the clustering algorithm to initialize the training data. Self-organizing fuzzy neural networks are a type of evolutionary fuzzy system, and the types of evolutionary fuzzy systems and current research results have been described in detail in [16; 17]. According to different structural divisions, evolutionary fuzzy systems include Mamdani fuzzy systems, Takagi-Sugeno (TS) fuzzy systems, Type-2 fuzzy systems, etc., which are widely used in clustering, regression, identification, and classification. SOFNN-CA mainly considers that the pre-training of the network by offline learning can effectively improve the performance of SOFNN, and, at the same time, for the evolution method of SOFNN, we propose the neuron width adjustment criterion based on the index of neuron activation intensity and density, which can improve the generalization performance of the network. The main methods for parameter estimation of fuzzy neural networks are the evolutionary method, gradient descent method, and second order algorithm. Among them, the evolutionary method has the advantages of good effect and moderate structure. [PERSON] et al. [18] trained a FNN with the genetic algorithm and particle swarm optimization (GA-PSO) to design an air-quality-prediction system. [PERSON] et al. [19] used the genetic algorithm to optimize the parameters of SOFNN (GA-SOFNN), but computational cost is an issue to consider due to its evolutionary learning approach. Although the gradient descent algorithm has the advantage of simple organization, it may fall into local minima. [PERSON] et al. [10] improved the gradient descent method and designed a gradient descent algorithm with an adaptive learning rate to update the parameters (SOFNN-AGA). The second-order algorithm is a trust domain method to fine-tune the parameters within a certain range,which has the advantages of second-order convergence and fast convergence speed, so it is widely used. [PERSON] et al. [20] proposed an adaptive learning algorithm to update the SOFNN parameters (SOFNN-ALA), which can effectively improve the generalization ability. In addition, [PERSON] [21] proposed to update the evolving fuzzy system based on a more robust recursive weighted total least squares (RWTLS) algorithm and compare it with the recursive fuzzily weighted least squares (RFWLS) algorithm, which can effectively suppress noise and improve accuracy; however, because the algorithm is an analytical solution parameter algorithm, it is not suitable for adjusting the center and width of neurons and takes a long time for a single operation. [PERSON] et al. [22] designed an improved LM algorithm that can reduce the computational effort and, thus, improve the computational speed, which was applied in [8; 20; 23]. Since the LM algorithm combines the advantages of gradient descent and the Gaussian Newton method with quick convergence, in this paper we use the adaptive LM algorithm to optimize the antecedent and consequent parameters of FNN. Based on the above analysis, in the design of SOFNN-CA, a simple structured initial model is firstly generated by the k-means clustering algorithm. The model is pre-trained using clustering algorithms, which saves time and speeds up training in the subsequent online training. A Mahalanobis distance index is used in the self-organization phase to increase the neurons and reduce the computational effort. A density potential indicator is proposed to realize the adaptive adjustment of neuron width according to the neuron-firing characteristics. Finally, we decide whether to merge neurons according to the similarity index between neurons and then obtain a network with compact structure and excellent generalization performance. The organization of the remaining papers is as follows: Section 2 briefly introduces the foundations of offline clustering and FNN.