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相关向量机核函数研究及其在污水系统中的应用

Study on Kernel Function of Relevance Vector Machine and Its Application in Wastewater System

【作者】 刘莉

【导师】 许玉格;

【作者基本信息】 华南理工大学 , 控制理论与控制工程, 2016, 硕士

【摘要】 污水系统复杂,具有参数时变,多变量耦合、强非线性,严重滞后等特点,采用传统的测量方法难以满足精确性、环保、经济测量等要求,导致污水处理质量难以得到保障,且投入成本偏高,因此建立测量精度高且经济环保的污水软测量模型,对污水处理具有重要的意义。软测量技术是一种新型智能检测技术,本文以污水处理为应用背景,结合相关向量机软测量建模的优势,以及对不同核函数性能的分析,提出了基于多属性高斯核函数的相关向量机软测量模型,并将其成功的用于污水系统出水参数的预测。本文主要研究如下:1.研究了相关向量机的原理,并在EM(Expectation Maximization)迭代估计的基础上对相关向量机算法的收敛性进行分析。针对相关向量机污水软测量模型的预测效果受核函数影响的问题,本文重点研究了核函数的性能和参数的学习,发现多属性高斯核的特点和良好性能适合作为污水软测量模型的核函数。2.考虑到相关向量机的建模优势,以及多属性高斯核的特点和良好性能,提出了一种基于多属性高斯核函数相关向量机的软测量模型来预测污水参数生物需氧量BOD、化学需氧量COD。针对多属性高斯核的学习问题,采用遗传算法来优化核参数,实验表明该模型能较好的实现BOD预测,但COD预测还有待改善。针对遗传算法在COD预测上难以获得合适的核参数的问题,采用梯度下降法来学习核参数,实验表明,该模型在COD的预测效果上较基于遗传算法的多属性高斯核函数相关向量机有所改善,并且模型具有较低的敏感性,鲁棒性较强。3.为了进一步提高污水重要参数的预测精度,本文提出基于自优化的多属性高斯核相关向量机污水软测量模型。针对多属性核参数的学习问题,提出自优化学习方法,并给出具体实现步骤,通过实验表明,该模型不仅敏感度低,鲁棒性好,而且在保证模型稀疏性和收敛性的同时获得较高的输出精度,对污水出水参数具有良好的预测效果。4.离线模型在长时间后难以保证对后序的工况点的预测效果,在一些工况点处表现出较差的适应性,针对这一问题,本文提出多属性高斯核快速相关向量机在线软测量模型。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,并引入快速边际似然算法来加快模型的更新速度。实验表明这种模型不仅能有效跟踪出水指标BOD、COD的变化,而且模型更新速度较快,能较好实现污水处理中出水水质的在线实时测量。

【Abstract】 Wastewater treatment is becoming more and more complex and has the characteristics of parameter time-varying, multi-variable, strong coupling, nonlinear, and serious lag, etc. In face of these characteristics, important variables can’t be measured by traditional method in an accurate, environment-friendly and economical way, resulting in that sewage treatment quality is difficult to be guaranteed and cost much. In order to solve this problem, it is necessary to establish economical and environmentally friendly sewage soft measurement model which has high predictor accuracy. Soft measurement technology is a new intelligent detection technology. Based on wastewater treatment process and the advantages of Relevance Vector Machine and the analysis of kernel function, this paper proposes a kind of soft measurement model by combining Multi-attributes Gaussian kernel with Relevance Vector Machine, and the proposed model is successfully used to predict the sewage system effluent parameters. Main content of this paper is as follows:First, study the principle of Relevance Vector Machine, and focus on analysis of its convergence on the basis of EM iterative estimation. In view of the fact that Relevance Vector Machine wastewater soft measurement model is affected by kernel function, this paper also focuses on the learning kernel function performance and parameters, then finds Multi-attributes Gaussian kernel which has good features and performance is suitable as kernel function of the sewage soft measurement model.Secondly, taking into account the advantages of Relevance Vector Machine and the analysis of kernel function, a soft measurement model based on Multi-attributes Gaussian kernel Relevance Vector Machine is proposed to predict sewage parameters BOD and COD, and the genetic algorithm is used to optimize the kernel parameter in the study of the Multi-attributes Gaussian kernel. Experiments show that the model can achieve better BOD prediction, but the COD prediction is still to be improved. Aiming at the problem that the genetic algorithm is difficult to obtain the suitable kernel parameters in COD prediction, the gradient descent method is used to study kernel parameter. Experiments show that the model has better accuracy than the model based on genetic algorithm in COD prediction, and it has low sensitivity and robustness.Then, in order to further improve the prediction accuracy of the important parameters of the wastewater, this paper proposes Multi-attributes Gaussian kernel Relevance Vector Machine model based on self-optimization. In view of the learning problem of kernel parameter, the self-optimization learning method is proposed, and its implementation steps are given. Experiments show that the model not only has low sensitivity and good robustness, but also can obtain high output accuracy while ensuring the sparse and convergence of the model and can better predict effluent parameters of sewage.Finally, offline model is difficult to guarantee the prediction effect of the subsequent operating point after a long time. It exhibits poor adaptability in some operating point. In order to solve this problem, this paper proposes an online soft measurement model based on Multi-attributes Gaussian kernel fast Relevance Vector Machine. The model uses the Relevance Vector Machine in the Bayesian framework to predict the output index, and introduces the fast marginal likelihood algorithm to speed up the update rate. Experiments show that the model not only can effectively track the change of BOD and COD, but also has faster update speed, and it can achieve the online real-time measurement of effluent quality of sewage treatment.

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