In this paper, a self-organizing fuzzy neural network with hierarchical pruning scheme (SOFNN-HPS) is proposed for nonlinear systems modelling in industrial processes. In SOFNN-HPS, to strike the optimal balance between system accuracy and network complexity, an online self-organizing scheme for identifying the structure and parameters of the network simultaneously is developed. First, to enhance the characterization ability of the fuzzy rules for nonlinear systems, the asymmetric Gaussian functions that can partition the input space more flexibly are introduced as membership functions. Second, a hierarchical pruning scheme, which is designed by rule density and rule significance, is used to delete the redundant fuzzy rules while using the geometric growing criteria to generate fuzzy rules automatically, which can avoid the requirement of pre-setting the pruning threshold and prevent the mistaken deletion of significant rules. Third, an adaptive allocation strategy is adopted to set the antecedent parameters of the fuzzy rules in the learning process, which can not only adjust the region of generalized ellipsoidal basis functions for better local approximation, but also balance the accuracy of the system and the interpretability of the rule base obtained. Finally, to speed up the convergence of the estimation error, a modified recursive least square algorithm is used to update the consequent parameters of the resulting fuzzy rules online. In addition, the convergence proofs of the estimation error and the network linear parameters of SOFNN-HPS are given, and they are helpful in successfully applying the SOFNN-HPS in practical engineering. To verify the effectiveness of SOFNN-HPS, two benchmark test problems and a key water quality parameter prediction experiment in the wastewater treatment process are examined. The simulation results demonstrate that the proposed SOFNN-HPS algorithm can obtain a self-organizing fuzzy neural network with compact structure and powerful generalization performance. The source codes of SOFNN-HPS and other competitors can be downloaded from https://github.com/hyitzhb/SOFNN-HPS.

针对工业过程中的非线性系统建模问题，提出了一种具有层次修剪方案的自组织模糊神经网络（SOFNN-HPS）。在SOFNN-HPS中，为了在系统精度和网络复杂性之间取得最佳平衡，开发了一种同时识别网络结构和参数的在线自组织方案。首先，为了增强非线性系统模糊规则的表征能力，引入了可以更灵活地划分输入空间的非对称高斯函数作为隶属函数。其次，采用规则密度和规则重要性设计的分层修剪方案，删除多余的模糊规则，同时使用几何增长准则自动生成模糊规则，这样可以避免预先设置修剪阈值的要求，并防止错误删除重要规则。第三，采用自适应分配策略设置学习过程中模糊规则的先验参数，不仅可以调整广义椭球基函数的区域以获得更好的局部逼近，而且可以在系统精度和可解释性之间取得平衡。获得的规则库。最后，为了加快估计误差的收敛速度，使用了一种改进的递归最小二乘算法来在线更新生成的模糊规则的结果参数。此外，给出了SOFNN-HPS估计误差和网络线性参数的收敛性证明，有助于将SOFNN-HPS成功应用于实际工程中。为了验证SOFNN-HPS的有效性，研究了两个基准测试问题和废水处理过程中的关键水质参数预测实验。仿真结果表明，提出的SOFNN-HPS算法可以得到结构紧凑，泛化性能强的自组织模糊神经网络。SOFNN-HPS和其他竞争者的源代码可以从https://github.com/hyitzhb/SOFNN-HPS下载。