基于有限测量信息的过程系统参数可估计性分析

Parameter estimability analysis for process system with finite measurement information

实时优化与过程对象模型的精确程度有关。如果过程对象模型与实际模型偏差较大,则会引起优化结果与过程实际的最优结果不一致,并导致优化的效率降低。在实时优化中应采用参数估计,调整过程对象模型的参数,从而保证过程对象模型与实际模型相一致或偏差最小。基于系统可估计性定义,本文根据有限测量信息的参数估计问题特点,提出了系统的参数可估计性定义;通过分析线性系统与非线性系统,指出系统具有参数可估计性的充分条件;并分析了如果系统不具有参数可估计性时,则需要固定哪些参数才能使得整个系统具有参数可估计性。最后分析了当测量变量有多组测量时对系统参数可估计性的影响,通过线性与非线性实例验证了分析结果的有效性。

The economic performance of real-time optimization system is influenced by the accuracy of the model.If the process model deviates from the process plant,it would lead to the offset between the true plant optimum and the predicted optimum and decrease the efficiency of real-time optimization.So it is important to use parameter estimation to make sure the least deviation of the optimum from the true plant.The definition of parameter estimability is proposed for parameter estimation problem with finite measurement information based on the definition of system estimability.The necessary conditions for parameter estimability are stated in both linear and nonlinear systems based on matrix analysis.If the parameters of system are inestimable,the parameter estimability can be changed by fixing some of the model parameters.The relationship between parameter estimability and the number of data sets is discussed.The effectiveness of the proposed analysis can be demonstrated by the results of linear and nonlinear systems.