In this paper, a novel self-organizing fuzzy neural network with an adaptive learning algorithm (SOFNN-ALA) for nonlinear system modeling and identification in industrial processes is proposed. To efficiently enhance the generalization capability, the proposed SOFNN-ALA is designed by using both structure identification and parameter estimation simultaneously in the learning process. In the structure identification phase, the rule neuron with the highest neuronal activity will be split into two new rule neurons. Meanwhile, the redundant rule neurons with small singular values will be removed to simplify the network structure. In the parameter estimation phase, an adaptive learning algorithm (ALA), which is designed based on the widely used Levenberg-Marquardt (LM) optimization algorithm, is adopted to optimize the network parameters. The ALA-based learning algorithm can not only speed up the convergence speed but also enhance the modeling performance. Moreover, we carefully analyze the convergence of the proposed SOFNN-ALA to guarantee its successful practical application. Finally, the effectiveness and efficiency of the proposed SOFNN-ALA is validated by several examples. The experimental results demonstrate that the proposed SOFNN-ALA exhibits a better comprehensive performance than some other state-of-the-art SOFNNs for nonlinear system modeling in industrial applications. The source code can be downloaded from https://github.com/hyitzhb/SOFNN-ALA.git.

本文提出了一种新颖的具有自适应学习算法的自组织模糊神经网络（SOFNN-ALA），用于工业过程的非线性系统建模和辨识。为了有效地提高泛化能力，在学习过程中同时使用结构识别和参数估计来设计提出的SOFNN-ALA。在结构识别阶段，具有最高神经元活性的规则神经元将被分为两个新的规则神经元。同时，将去除具有奇异值小的冗余规则神经元，以简化网络结构。在参数估计阶段，采用了基于广泛使用的Levenberg-Marquardt（LM）优化算法设计的自适应学习算法（ALA），以优化网络参数。基于ALA的学习算法不仅可以加快收敛速度​​，而且可以提高建模性能。此外，我们仔细分析了提出的SOFNN-ALA的收敛性，以确保其成功的实际应用。最后，通过几个例子验证了所提出的SOFNN-ALA的有效性和效率。实验结果表明，对于工业应用中的非线性系统建模，所提出的SOFNN-ALA具有比其他一些最新的SOFNN更好的综合性能。可以从https://github.com/hyitzhb/SOFNN-ALA.git下载源代码。我们仔细分析了拟议的SOFNN-ALA的收敛性，以确保其成功的实际应用。最后，通过几个例子验证了所提出的SOFNN-ALA的有效性和效率。实验结果表明，对于工业应用中的非线性系统建模，所提出的SOFNN-ALA具有比其他一些最新的SOFNN更好的综合性能。可以从https://github.com/hyitzhb/SOFNN-ALA.git下载源代码。我们仔细分析了拟议的SOFNN-ALA的收敛性，以确保其成功的实际应用。最后，通过几个例子验证了所提出的SOFNN-ALA的有效性和效率。实验结果表明，对于工业应用中的非线性系统建模，所提出的SOFNN-ALA具有比其他一些最新的SOFNN更好的综合性能。可以从https://github.com/hyitzhb/SOFNN-ALA.git下载源代码。