To predict the effluent ammonia nitrogen (NH₄-N) of wastewater treatment process (WWTP), the soft computing methods are widely used, in which the mean square error (MSE) is usually adopted as the performance criterion. However, the MSE based methods cannot fully utilize the statistic information of data and are vulnerable to the nonzero-mean noise. To address these issues, the modeling-error probability density function based fuzzy neural network (PDF-FNN) is proposed in this paper. Firstly, the modeling error PDF criterion is generated to minimize the spatial deviation between the modeling error distribution and the predefined target. Then, a gradient descent method with adaptive learning rate is presented to update the parameters of PDF-FNN. Furthermore, the convergence of PDF-FNN is analyzed from a mathematical point of view. Finally, a nonlinear system modeling and the effluent NH₄-N prediction in WWTP are applied to prove the effectiveness of the proposed PDF-FNN. The results indicate that the PDF-FNN has better prediction accuracy and model stability than other methods, especially in the noisy environment.

预测废水中的氨氮（NH ₄-N）废水处理过程（WWTP），软计算方法被广泛使用，其中通常采用均方差（MSE）作为性能标准。但是，基于MSE的方法不能充分利用数据的统计信息，并且容易受到非零均值噪声的影响。为了解决这些问题，本文提出了基于建模误差概率密度函数的模糊神经网络（PDF-FNN）。首先，生成建模误差PDF准则以最小化建模误差分布与预定义目标之间的空间偏差。然后，提出了一种具有自适应学习率的梯度下降方法来更新PDF-FNN的参数。此外，从数学角度分析了PDF-FNN的收敛性。最后，进行非线性系统建模和污水NH在污水处理厂中采用₄ -N预测来证明所提出的PDF-FNN的有效性。结果表明，PDF-FNN具有比其他方法更好的预测准确性和模型稳定性，尤其是在嘈杂的环境中。