Citation: Zhang, T.; Wang, Z.
Self-Organized Fuzzy Neural
Network Nonlinear System
Modeling Method Based on
Clustering Algorithm. Appl. Sci. 2022,
12, 11435. https://doi.org/10.3390/
app122211435
Academic Editors: Rodolfo Haber,
Krzysztof Ejsmont, Aamer
Bilal Asghar and Yong Wang
Received: 9 October 2022
Accepted: 8 November 2022
Published: 11 November 2022
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Article
Self-Organized Fuzzy Neural Network Nonlinear System
Modeling Method Based on Clustering Algorithm
Tong Zhang * and Zhendong Wang
College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China
* Correspondence: zhang_tong66@126.com
Abstract:
In this paper, an improved self-organizing fuzzy neural network (SOFNN-CA) based
on a clustering algorithm is proposed for nonlinear systems modeling in industrial processes. In
order to reduce training time and increase training speed, we combine offline learning and online
identification. The unsupervised clustering algorithm is used to generate the initial centers of the
network in the offline learning phase, and, in the self-organizing phase of the system, the Mahalanobis
distance (MD) index and error criterion are adopted to add neurons to learn new features. A new
density potential index (DPI) combined with neuron local field potential (LFP) is designed to adjust
the neuron width, which further improves the network generalization. The similarity index calculated
by the Gaussian error function is used to merge neurons to reduce redundancy. Meanwhile, the
convergence of SOFNN-CA in the case of structural self-organization is demonstrated. Simulations
and experiments results show that the proposed SOFNN-CA has a more desirable modeling accuracy
and convergence speed compared with SOFNN-ALA and SOFNN-AGA.
Keywords:
self-organizing fuzzy neural networks (SOFNN); nonlinear system modeling;
Mahalanobis distance; density potential index
1. Introduction
Nonlinear system modeling is a frequently encountered problem in industrial pro-
cesses. Since most systems are nonlinear in nature, control models based on linear systems
can no longer meet the needs of industrial control, so numerous scholars have conducted
extensive and in-depth research on nonlinear systems modeling [
1
–
3
]. The methods used
for nonlinear system modeling mainly include first-principles modeling, data-driven mod-
eling, and gray-box modeling [
4
]. Among them, data-driven modeling mainly establishes a
mathematical regression model based on the measured data, and it is the most commonly
used at present. Furthermore, many modeling methods based on data-driven principles are
proposed, such as a fuzzy neural network, support vector regression, an extreme learning
machine, an error correction algorithm [
5
], etc. Akhtar et al. [
6
] used fuzzy inference to
predict the average monthly power generation, and their results can be used in microgrid
and smart grid applications. Czarnowski et al. [
7
] proposed similarity and fuzzy c-mean
clustering based on neural network structure and verified its effectiveness. Wilamowski
et al. [
5
] trained neural networks with an extreme learning machine and an error correction
algorithm and conducted a comparative study. At the same time, how to improve the
real-time ability and generalization of system modeling is still the focus of current research.
Fuzzy neural networks have been widely used in industrial processes due to their char-
acteristics such as interpretability and fast convergence. Zhou et al. [
8
] developed a hierar-
chical pruning scheme to implement a compact wastewater treatment model (
SOFNN-HPS
),
with a longer hyperparameter table, so only the same center neurons can be merged. Gho-
lami et al. [
9
] developed the co-active neuro-fuzzy inference system (CANFIS) to predict soil
splash erosion in the Tarar Basin in northern Iran and achieved good performance. A fuzzy
neural network is a hybrid approach that combines the semantic transparency of fuzzy
Appl. Sci. 2022, 12, 11435. https://doi.org/10.3390/app122211435 https://www.mdpi.com/journal/applsci
