Soft-sensor modeling of papermaking wastewater treatment process based on Gaussian process
SONG Liu1, YANG Chong1, ZHANG Hui1, LIU Hong-bin1,2
1. Co-Innovation Center of Efficient Processing and Utilization of Forest Resources, Nanjing Forestry University, Nanjing 210037, China;
2. State Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou 510640, China
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.
宋留, 杨冲, 张辉, 刘鸿斌. 造纸废水处理过程的高斯过程回归软测量建模[J]. 中国环境科学, 2018, 38(7): 2564-2571.
SONG Liu, YANG Chong, ZHANG Hui, LIU Hong-bin. Soft-sensor modeling of papermaking wastewater treatment process based on Gaussian process. CHINA ENVIRONMENTAL SCIENCECE, 2018, 38(7): 2564-2571.
Maniquiz M C, Soyoung L. Leehyung. Multiple linear regression models of urban runoff pollutant load and event mean concentration considering rainfall variables[J]. 环境科学学报(英文版), 2010,22(6):946-952.
[5]
Yuan X F, Huang B, Ge Z Q, et al. Double locally weighted principal component regression for soft sensor with sample selection under supervised latent structure[J]. Chemometrics & Intelligent Laboratory Systems, 2016,153:116-125.
Ge Z Q, Chen T, Song Z H. Quality prediction for polypropylene production process based on CLGPR model[J]. Control Engineering Practice, 2011,19(5):423-432.
[10]
Wilson A G, Adams R P. Gaussian process kernels for pattern discovery and extrapolation[J]. Microtome Publishing, 2013, 13(4):129-135.
[11]
Wang B, Chen T. Gaussian process regression with multiple response variables[J]. Chemometrics & Intelligent Laboratory Systems, 2015, 142:159-165.
[12]
He Z K, Liu G B, Zhao X J, et al. Temperature model for FOG zero-Bias using Gaussian process regression[J]. Advances in Intelligent Systems & Computing, 2012,180:37-45.
Nguyen-Tuong D, Seeger M, Peters J. Model learning with local Gaussian process regression[J]. Advanced Robotics, 2009,23(15):2015-2034.
[16]
Caywood M S, Roberts D M, Colombe J B, et al. Gaussian process regression for predictive but interpretable machine learning models:An example of predicting mental workload across tasks[J]. Frontiers in human neuroscience, 2017,10,647.
[17]
Rasmussen C E, Williams C K. Gaussian processes for machine learning[M]. London:MIT Press, 2006.
[18]
Duvenaud D, Lloyd J R, Grosse R, et al. Structure discovery in nonparametric regression through compositional kernel search[A]. Proceedings of the 30th International Conference on Machine Learning[C]//Atlanta GA, USA, 2013:1166-1174.
[19]
Rasmussen C E, Nickisch H. Gaussian processes for machine learning (GPML) toolbox[J]. Journal of Machine Learning Research, 2010,11(6):3011-3015.
