دانلود رایگان مقاله برآورد پارامتر با تحلیل توانایی برآورد اعمال شده برای فرآیند پلیمریزاسیون مقیاس صنعتی

Abstract

This paper aims to estimate the parameters of a complex model representing an industrial scale polymerization process. The estimability analysis of the parameters prior to estimation allows simplifying the optimization problem but it is usually neglected in literature when industrial data is used for estimation. In this case, though, the estimability analysis would be even more important since usually less data is available, they are associated with a higher uncertainty and the experiments might not be designed as in laboratory or pilot plant. The orthogonalization method reduced from 68 to 29 the number of parameters of the model. Polymer properties, which are measured offline with low frequency, as well as process temperatures and flow rates are used for validating the model. Small deviations, up to 5%, between model prediction and experimental data indicate the quality of fit of the model and the importance of carrying out first an estimability analysis.

6. Conclusion

This paper presents how the estimability analysis allows parameter estimation simplification of a complex phenomenological model representing an industrial scale process. Previous studies in literature have already dealt with the preliminary analysis of the parameters, but they use experimental data obtained from laboratory or pilot plants. Using experimental data obtained from process history presents some challenges notfaced with laboratory or pilot plant experiments: less information is available, the measurements have more uncertainties and the experiments might not be designed. The estimability analysis based on the orthogonalization method allowed determining the set of estimable parameters of a phenomenological model representing an industrial scale copolymerization process. The number of parameters to be estimated was reduced from 68 to 29, ensuring a successful estimation. The Hessian matrix analysis indicates that the space formed by these parameters is not strictly convex, hence a local minimum might be found. The estimability analysis was then repeated, indicating a positive definite Hessian matrix. The parameter estimation was followed by the model validation with a different data set, representative of another polymer grade. The small deviations between the model prediction and the experimental data, both from the estimation and validation data sets, indicate the quality of fit of the model.