论文部分内容阅读
提出一种利用回声状态网络(echo state network,ESN)建立复杂分布参数系统模型的灰箱建模方法。此建模方法可以充分利用已知机理模型的结构信息和回声状态网络的逼近能力,可更好地描述和解释出系统各变量之间的因果关系,使模型的“灰箱”化程度更高。首先,根据系统方程和先验知识将初始系统特征团引入ESN储备池中,赋予网络节点实际物理意义,并以此建立结构逼近神经网络模型;然后,通过逐步回归分析方法,结合递归最小二乘算法选择最优系统特征团,并对网络结构进行优化,建立起描述系统特性关系的灰箱模型。本文以实验室规模的管式聚合反应过程作为实验对象,建立以温度分布为输出的数学模型,结果表明所提出的灰箱建模方法行之有效。
A gray box modeling method based on echo state network (ESN) is proposed to establish a complex distributed parameter system model. The modeling method can make full use of the structural information of the known mechanism model and the approximation ability of the echo state network, so as to better describe and explain the causal relationship among the variables of the system so that the “gray-box” degree of the model higher. First, according to the system equations and prior knowledge, the initial system features are introduced into the ESN reserve pool, which gives the physical meaning of the network nodes and constructs the structure approximation neural network model. Then, through stepwise regression analysis, combined with recursive least squares The algorithm selects the optimal system features and optimizes the network structure, and establishes a gray box model that describes the relationship between system characteristics. In this paper, a laboratory-scale tubular polymerization process is taken as the experimental object to establish a mathematical model of temperature distribution as output. The results show that the proposed gray box modeling method is effective.