STUDY OF SENSITIVITY ANALYSIS AND MODEL APPROXIMATION TECHNIQUES IN PROCESS OPTIMIZATION (REDUCED HESSIAN).

摘要

The quantitative influence of models on the optimization of a process flowsheet has been studied in two parts. In the first part the sensitivity of the optimal solution to parametric and model variations has been analyzed. In the second part the effect of model approximations on the convergence characteristics of an optimization procedure is investigated with regard to robustness and efficiency.; An efficient and rigorous strategy is presented for evaluating the first order sensitivity of the optimal solution to changes in process parameters or process models. An algorithm that constructs a reduced Hessian in the null space of the equality constraints is used to solve the sensitivity equations; the resulting effort to solve these equations depends only on the space of the decision (independent) variables. Consequently, large computational savings can be realized because the solution procedure eliminates the need for obtaining second partial derivatives with respect to tear (dependent) variables explicitly. The method is applied to several flowsheeting examples in order to determine efficiently the sensitivity of the optimal solution to parametric and physical property model changes.; A theoretical framework has been developed that ensures convergence to the correct optimal solution in a model approximation based optimization procedure. The procedure is based on reducing the rigorous model exact penalty function in a simplified model based search direction. If a reduction is not achieved, a rigorous model based search direction is computed. An approximation based algorithm is developed that incorporates this framework. The application of this algorithm to several flowsheet optimization problems demonstrates its robustness by converging to the correct solution, even under poor approximation schemes. The examples also show the potential of the method to register savings in computing time.