中文摘要：

针对污水处理过程出水总磷预测问题存在的强非线性、大时变等特征，提出了一种基于偏最小二乘回归自适应深度信念网络（partial least square regression adaptive deep belief network，PLSR-ADBN）的出水总磷预测方法。PLSR-ADBN是基于深度学习模型DBN的一种改进型建模方法。首先，将自适应学习率引入到DBN的无监督预训练（pre-training）阶段，来提高网络收敛速度。其次，利用PLSR方法取代传统DBN中基于梯度的逐层权值精调ffine-tuning）方法，来提高网络预测精度。同时，通过构造李雅普诺夫函数证明了PLSR-ADBN学习过程的收敛性。最后，将PLSR-ADBN用于实际污水处理过程出水总磷预测中。实验结果表明所提出的PLSR-ADBN收敛速度快且预测精度高，能够满足实际污水处理过程对出水总磷监测精度和运行效率的要求。

英文摘要：

Considered high nonlinearity and large transient variation, a PLSR-adaptive deep belief network （PLSR-ADBN） was proposed for prediction of total phosphorus （TP） in effluent of wastewater treatment process （WWTP）. The PLSR-ADBN was an improved DBN, a deep learning model. First, an adaptive learning rate was introduced into the unsupervised pre-training stage of DBN so as to accelerate convergence rate. Secondly, PLSR was used to replace gradient fine-tuning method in conventional DBN for improving prediction accuracy. Meanwhile, a Lyapunov function was constructed to prove convergence of the PLSR-ADBN learning process. Finally, the proposed PLSR-ADBN was applied to an actual TP prediction in WWTE The experimental results show that the method has a fast convergence rate and a high prediction accuracy, which can meet the demands for TP detection accuracy and WWTP operating efficiency.