The operability of nonlinear high-dimensional processes is a difficult task because of the immense number of calculations. This motivates the development of a new methodology for solving such problems. Here we propose a new approach motivated by the well established design of experiments procedure that has been successful in enabling the calculation of operating sets from the steady-state point of view.;The combination of design of experiments methods and response surface models enables the calculation of approximate mathematical models with a much reduced number of calculations. The approximate models can replace the complex ones without any significant loss of accuracy. Consequently they are very efficient for the calculation of the achievable output set (AOS) from the available input sets (AIS). The applicability of the developed method is illustrated with two motivating examples and a plant-wide industrial process, the Tennessee Eastman challenge problem. For all the examples considered, it is shown that the AOS obtained from the approximate models are able to describe the exact ones with satisfying accuracy.;A particular interest is the examination whether the response surface models are able to accurately describe the phenomenon of input multiplicity, which causes the output map of the boundary of the AIS to be different from the boundary of the AOS. This is a substantial limitation of the method that just tries to map boundaries. It is shown here that the response surface model is able to represent such challenging shape of the AOS.;This is achieved by searching the maximal and minimal values within the limits of the AIS along the boundaries of the approximate AOS. If the maximal or the minimal values are outside the AOS, the input multiplicity could happen in this place. The effectiveness of this method is shown in given examples.
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