中文摘要：

生化需氧量（biochemical oxygen demand，BOD）是评价水质好坏和污水处理效果的关键指标之一。由于污水生化处理过程复杂，在线仪表维护困难，生化需氧量无法得到快速精确地测量。针对这一问题，提出了一种基于Fast-RVM的在线软测量回归模型来实时在线预测出水指标BOD。该模型采用基于贝叶斯框架的相关向量机来在线预测输出指标，并且引入快速边际似然算法来加快模型的更新速度。通过污水数据的仿真实验，结果表明该在线模型的预测精度高于离线模型，泛化能力强，模型在线更新的快速性尤为突出，能较好地实现污水处理中出水水质的实时在线预测。

英文摘要：

Biochemical oxygen demand （BOD） is a significant indicator to evaluate the effluent quality in wastewater treatment process. Complex wastewater treatment process and high requirement for instrument maintenance make it very difficult to obtain BOD quickly and accurately. In order to solve this problem, a novel BOD on-line soft measuring model based on fast variable relevance vector machine （Fast-RVM） is proposed in this paper.Relevance vector machine algorithm with Bayesian framework is used to build up predictive model and fast marginal likelihood algorithm is applied to accelerate updating speed of the model. Simulation experiments show that the real-time on-line prediction performance and generalization ability are better by using the proposed model than those of off-line model. The online updating speed is particularly outstanding. These experimental results verify that the proposed method is very suitable for real-time on-line prediction of effluent quality in the wastewater treatment process.