Analytical Identification of Design and Multidimensional Spaces Using R-Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917726909366272 |
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| author | Kucherenko, Segei Klymenko, Oleksiy Shah, Nilay |
| author_facet | Kucherenko, Segei Klymenko, Oleksiy Shah, Nilay |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical Identification of Design and Multidimensional Spaces Using R-Functions Kucherenko, Segei Klymenko, Oleksiy Shah, Nilay Algebraic Geometry Numerical Analysis 14-02 (Primary) 65D99 (Secondary) 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. |
| title | Analytical Identification of Design and Multidimensional Spaces Using R-Functions |
| topic | Algebraic Geometry Numerical Analysis 14-02 (Primary) 65D99 (Secondary) |
| url | https://arxiv.org/abs/2407.13573 |