Analytical Identification of Design and Multidimensional Spaces Using R-Functions

TL;DR

This paper introduces the R-DS identifier, a novel analytical method using R-functions to define design spaces in materials and process conditions, requiring minimal model evaluations and no assumptions about the underlying model.

Contribution

The paper presents a new R-DS identification method that leverages R-functions for explicit analytical representation of design spaces without relying on traditional sampling or optimization.

Findings

Successfully applied to a batch reactor system

Requires fewer model runs than traditional methods

Provides explicit geometric representation of design spaces

Abstract

The design space (DS) is defined as the combination of materials and process conditions that guarantees the assurance of quality. This principle ensures that as long as a process operates within DS, it consistently produces a product that meets specifications. A novel DS identification method called the R-DS identifier has been developed. It makes no assumptions about the underlying model - the only requirement is that each model constraint (CQA) should be approximated by a multivariate polynomial model. The method utilizes the methodology of Rvachev's R-functions and allows for explicit analytical representation of the DS with only a limited number of model runs. R-functions provide a framework for representing complex geometric shapes and performing operations on them through implicit functions. The theory of R-functions enables the solution of geometric problem such as identification of DS through algebraic manipulation. It is more practical than traditional sampling or optimization-based methods. The method is illustrated using a batch reactor system.