Azman K, Kocijan J
Jozef Stefan Institute, Department of Systems and Control, Jamova 39, 1000 Ljubljana, Slovenia.
ISA Trans. 2007 Oct;46(4):443-57. doi: 10.1016/j.isatra.2007.04.001. Epub 2007 Jun 4.
Different models can be used for nonlinear dynamic system identification and the Gaussian process model is a relatively new option with several interesting features: model predictions contain the measure of confidence, the model has a small number of training parameters and facilitated structure determination, and different possibilities of including prior knowledge exist. In this paper the framework for the identification of a dynamic system model based on Gaussian processes is shown, illustrated on a simulated bioreactor example and then applied to two case studies. The first one addresses modelling of the nitrification process in a wastewater treatment plant and the second models biomass growth in the Lagoon of Venice. Special emphasis is placed on model validation, an often underemphasised part of the identification procedure, where the Gaussian model prediction variance can be utilised.
不同的模型可用于非线性动态系统识别，高斯过程模型是一个相对较新的选择，具有几个有趣的特性：模型预测包含置信度度量，模型具有少量训练参数且便于结构确定，并且存在纳入先验知识的不同可能性。本文展示了基于高斯过程的动态系统模型识别框架，以一个模拟生物反应器示例进行说明，然后应用于两个案例研究。第一个案例涉及污水处理厂中硝化过程的建模，第二个案例是威尼斯潟湖生物量增长的建模。特别强调了模型验证，这是识别过程中经常被忽视的部分，其中可以利用高斯模型预测方差。
