随着我国环保标准的不断提升，污水处理过程中关键指标参数的实时监测已成为环境工程领域中的研究热点。然而，传统的检测方法存在操作繁琐、响应滞后等问题，很难满足实际工业中的应用需求。为此，本研究提出了一种基于概率密度的模块化神经网络软测量模型，旨在提高污水处理过程的监测与控制效率，其主要研究内容如下：

（1）传统网络模型在处理具有非线性和多维特征的污水数据时，难以有效捕捉其复杂的分布结构，导致预测性能不足，泛化能力较差，针对此问题，本文提出了一种自适应概率模块化神经网络模型（Adaptive probabilistic modular neural network model, APMNN）。该模型基于概率密度实时划分样本空间，在提高聚类质量的同时，还增强了对时变数据的适应能力；在此基础上，利用概率隶属集将划分好的工况数据分配至相应的子网中进行学习；最后通过集成权重整合各子网的学习结果，得到最终的预测输出。实验表明，APMNN在多维数据上的处理性能显著优于传统方法，不仅具备更高的预测精度，还拥有更为简洁的网络结构。

（2）针对在线模块化神经网络子网结构难以确定的问题，在（1）的基础上提出了贝叶斯自组织模块化神经网络（Bayesian self-organizing modular neural networks, ABMNN）。该方法以网络误差为驱动，结合误差补偿和贝叶斯推理，实现子网结构的动态优化：当模型学习能力不足时，自适应添加隐含层神经元，并通过权重迁移策略确保其有效初始化；当结构冗余时，计算剪枝前后的后验概率分布差异，依据最小化KL散度准则选择最优结构。实验表明，在Mackey-Glass数据集上，该方法将网络结构减少了约32.56%的同时，预测精度提升了约35.89%；在太阳黑子预测和污水处理等实际应用场景中，该模型同样展现出了优秀的预测性能和泛化能力，验证了该方法的有效性。

（3）针对污水关键参数NH3难以实时监测的问题，设计并开发了一套软测量系统。首先，通过需求分析明确系统的功能，并将系统划分为多个不同的子模块进行开发；其次，编写代码实现各个功能模块；最终实现对NH3浓度的在线预测，并对其风险等级进行实时评估，为城市污水处理工作提供了更高效的方法和工具。

With the continuous enhancement of environmental standards in China, real-time monitoring of key parameters in the wastewater treatment process has become a focal point in environmental engineering research. However, traditional detection methods are often cumbersome to operate and suffer from delayed response times, making them inadequate for practical industrial applications. To address these challenges, this study proposes a modular neural network-based soft measurement model driven by probability density functions. The aim is to enhance the efficiency of monitoring and control in wastewater treatment processes. The main research objectives are as follows:

(1) Traditional neural network models often struggle to effectively capture the complex distribution structures inherent in nonlinear and high-dimensional wastewater data, resulting in suboptimal prediction performance and limited generalization capability. To address this issue, this paper proposes an Adaptive Probabilistic Modular Neural Network model (APMNN). The model divides sample space in real-time based on probability density, which not only improves the clustering quality but also enhances the adaptability of the model to time-varying data. On this basis, a probabilistic membership set is used to assign the divided working data to the corresponding subnet for learning. Finally, the learning results of each subnet are integrated by integrating weights, and the final predictive output is obtained. The experimental results show that the performance of APMNN on multidimensional data processing is significantly better than that of traditional methods, which not only have higher prediction accuracy but also have a more concise network structure.

(2) Aiming at the problem of the subnet structure of online modular neural networks being difficult to determine, Bayes' self-organizing modular neural network (ABMNN) is proposed based on (1). This method is driven by network error and combines error compensation and Bayesian inference to achieve dynamic optimization of the subnet structure. When the model learning ability is insufficient, the hidden layer neuron nodes are added adaptively, and the effective initialization of new neurons is ensured by the weight transfer strategy. When the structure is redundant, the optimal subnet structure is selected using the criterion of minimizing KL divergence by calculating the posterior probability distribution difference before and after pruning. The experimental results show that on the MG data set, the proposed method reduces the network structure by about 32.56% and improves the prediction accuracy by about 35.89%. In practical application scenarios such as sunspot prediction and sewage treatment process modeling, the model also shows excellent prediction performance and generalization ability, which verifies the effectiveness of the model.

(3) Aiming at the problem that NH3, a key parameter of sewage, is difficult to monitor in real-time, a soft-sensing system is designed and developed. Firstly, the function of the system are defined through requirement analysis, and the system is divided into several different sub-modules for development. Secondly, write code to realize each function module; Finally, the online prediction of NH3 concentration and real-time assessment of its risk level are realized, which provides a more efficient method and tool for urban sewage treatment.