造纸废水处理过程的高斯过程回归软测量建模

针对造纸废水处理系统的时变性、非线性和复杂性等特点，本文提出一种基于高斯过程回归的软测量模型.基于平方指数协方差、线性协方差和周期性协方差函数组合构建了7种高斯过程回归模型，分别对出水化学需氧量和出水悬浮固形物浓度进行回归预测.此外，还对比了多元线性回归模型、主成分回归模型、偏最小二乘模型、人工神经网络模型和高斯回归模型的预测效果.对比计算结果表明无论是对输出变量的训练拟合还是预测，高斯过程回归模型的拟合效果均优于非高斯过程回归模型.高斯过程回归模型的预测结果表明：对于出水化学需氧量，线性协方差函数与周期性协方差函数的组合模型可以取得最好的预测结果；对于出水悬浮固形物，平方指数协方差函数与线性协方差函数组合模型可以取得最好的预测结果.

Soft-sensor modeling of papermaking wastewater treatment process based on Gaussian process

Considering the time-varying, nonlinear, and complex characteristics of papermaking wastewater treatment processes, an advanced soft-sensor model was proposed based on Gaussian process regression (GPR). Seven GPR models, consisting of the combinations of squared exponential covariance, linear covariance, and periodic covariance function were built and compared for the prediction of the effluent chemical oxygen demand (COD) and effluent suspended solids (SS). The GPR-based prediction results are also compared with those of multiple linear regression, principle component regression, partial least square, and artificial neural network. The results showed that the prediction accuracy of GPR models were better than other models. Furthermore, with regard to the prediction of the effluent COD, the GPR model with the combination of linear covariance function and periodic covariance function achieved the best performance. In terms of the prediction of the effluent SS, the best GPR model is the one with the combination of squared exponential covariance function and linear covariance function.