用序贯法对反应速率模型中的参数作精确估算

对一个确定的模型,不仅要确定参数的估算值,还必须了解其可靠性。为了缩小参数的不定性,降低参数间的相关性,以扩大模型拟合的适定性和准确度,本文讨论了参数精确估算的序贯设计过程。 文内还详细讨论了精估参数的实验设计准则——最小联合置信容积准则和形状准则,以及序贯设计的实用价值。以氨合成为例,用序贯法精确估算了反应速度模型中的参数。这一模型是在序贯判别过程中选定的。把精估结果用于拟合大型生产过程的实测数据,得到了满意的结果。

A Sequential Procedure for Precise Estimation of Parameters in Kinetic Model

For a determined mathematical model, it is not only necessary to obtain the estimates of parameters, but also their reliabilities. The present work deals with a sequential statistical design strategy for an experimental program to obtain precise parameter estimates for a nonlinear kinetic model. It aims at decreasing the indeterminatness of the parameter estimates, in reducing the correlation between parameter estimates, and in increasing the adequacy and accuracy of the model.The paper discusses the experimental design criterion for precise parameter estimates-the minimun volume design criterion and the spherical shape design criterion, and the practical value of a sequential statistical design strategy.At last, an example was performed to precise estimate the parameters in the kinetic model of ammonia synthesis reaction which was selected as being adequate in the previous work.Comparison of the results from the industrial unit and the corresponding values calculated with the model using the estimates of parameters reveals the reasonable reliability of the model.