Identification of Feasible Regions Using R-Functions

Abstract: The primary objective of flexibility analysis is to identify and define the feasibility region, which represents the range of operational conditions (e.g., variations in process parameters) that ensure safe, reliable, and feasible process performance. This work introduces a novel flexibility analysis method that requires only that model constraints (e.g., defining product Critical Quality Attributes or process Key Performance Indicators) be explicitly provided or approximated by a closed-form function, such as a multivariate polynomial model. The method is based on V.L. Rvachev's R-functions, enabling an explicit analytical representation of the feasibility region without relying on complex optimization-based approaches. R-functions offer a framework for describing intricate geometric shapes and performing operations on them using implicit functions and inequality constraints. The theory of R-functions facilitates the identification of feasibility regions through algebraic manipulation, making it a more practical alternative to traditional optimization-based methods. The effectiveness of the proposed approach is demonstrated using a suite of well-known test cases from the literature.