Alternating Identification Algorithm and Its Application to a Class of Nonlinear Discrete-time Dynamical Systems
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摘要: 表征产品在工业过程加工的质量、效率、成本、能耗或物耗等的运行指标与过程控制系统的输出密切相关，它们之间的动态模型往往机理不清，具有强非线性，难以用精确数学模型描述，但运行指标的预报对运行操作具有重要意义.本文利用工业过程在工作点附近工作的特点，将过程控制系统的输出与运行指标之间的动态模型描述成线性模型与高阶非线性项即未建模动态组成，对线性模型以及未建模动态提出了一种由改进的投影算法与未建模动态估计算法组成的交替辨识算法.最后，通过数值仿真实验和电熔镁炉的真实数据进行功率预报实验，实验结果表明了所提方法的有效性.Abstract: The major operational indexes such as quality, efficiency, cost, energy and material consumptions in industrial process of product processing are closely related to the output of the process control system; their dynamic models between the operational indexes and the output of the process control system are often nonlinear and with unclear structure nature generally. Therefore, it is difficult to obtain an accurate model. However, the prediction of operational index is of great significance to the operational operations. In this paper, based upon the characteristic that complex industrial systems often work near an operating point, the dynamic model between the operational indexes and the output of the process control system is represented by a linear model plus a higher order nonlinear term (unmodeled dynamics). With the above development, an alternating identification algorithm which consists of improved projection algorithm for the linear model and an estimation algorithm for unmodeled dynamic are proposed. Finally, through simulation study and a power forecast experiment using real data of an electric-melting magnesia furnace, the effectiveness of the proposed algorithm is justified.
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图 1 BP神经网络估计$v[\varphi (k)]$的结构
Fig. 1 The structure of the estimation for $v[\varphi (\text{k})]$ by BP neural networks[
图 3 未建模动态(星线)及其估计值(圈线)
Fig. 3 The un-modeled dynamics (star line) and its estimation value (circle line)
图 4 采用BP神经网络估计未建模动态的误差
Fig. 4 Estimation error for the un-modeled dynamics which produced by BP neural networks
图 5 采用BP神经网络的估计误差(残差)的概率密度函数
Fig. 5 The probability density functions of prediction errors (residuals) by BP neural networks
图 6 BP神经网络的性能、训练状况和相关系数
Fig. 6 The performance,training state,and regression of BP neural networks
图 7 $A({z^{ - 1}})$ 中的参数和$B({z^{ - 1}})$中的参数
Fig. 7 Parameters in A(z-1) and parameters in B(z-1)
图 8 未建模动态(星线)及其估计值(圈线)
Fig. 8 The un-modeled dynamics (star line) and its estimation value (circle line) by BP neural networks
图 9 采用BP神经网络估计未建模动态的误差
Fig. 9 Estimation error for the un-modeled dynamics which produced by BP neural networks with he proposed method
图 10 采用BP神经网络的估计误差(残差)的概率密度函数
Fig. 10 The probability density functions of prediction errors (residuals) by BP neural networks
图 11 BP 神经网络的性能、训练状况和相关系数
Fig. 11 The performance, training state, and regression of BP neural networks
图 14 功率(星线) 及其估计值(圈线)
Fig. 14 The power (star line) and its estimation value (circle line) by the proposed method
图 16 估计误差(残差) 的概率密度函数
Fig. 16 The probability density functions of prediction errors (residuals)
图 17 BP 神经网络的性能、训练状况和相关系数
Fig. 17 The performance, training state, and regression of BP neural networks
表 1 辨识的平均绝对值误差、方差以及标准差
Table 1 The average absolute error,variance and the standard deviation which produced by the proposed method
平均绝对值误差 方差 标准差 432.6477 311320 557.9634 
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