(347e) A Novel Methodology for the Identification of Complex Process Feasibility Regions
AIChE Annual Meeting
2023
2023 AIChE Annual Meeting
Computing and Systems Technology Division
Data-driven and Surrogate Optimization in Operation II
Wednesday, November 8, 2023 - 1:54pm to 2:15pm
Feasibility analysis is used to determine the operability region within which all process and quality constraints are met, i.e., the design space (DS) of the process. The description of the DS is particularly relevant in highly regulated chemical engineering sectors, such as the pharmaceutical industry, where assurance of manufacturability and quality of the product is a key step of process development (Destro and Barolo, 2022). The accurate reconstruction of the feasible operation range may be challenging, particularly for nonconvex problems and in presence of disjoint operability regions. When available process models are computationally expensive or include various black-box constraints, the use of surrogate-based approaches for feasibility analysis has been demonstrated to effectively identify the feasibility region (Wang and Ierapetritou, 2018). However, the selection and performance of a suitable candidate surrogate strongly depends on the specific case study and the dataset that is available for training. In this context, the following issues need to be addressed:
• How is it possible to reconstruct the feasibility shape based on the available dataset? Is there a minimum number of datapoints that are necessary to obtain a complete knowledge of the problem complexity? How does the inclusion of new samples affect the results?
• How can we compare the performance of different candidate surrogate models, while improving the prediction accuracy?
To answer the questions above, we propose a novel framework to uncover knowledge about the feasible space and predict the feasibility boundaries based on a predetermined level of accuracy with the minimum requirement of training data. Topological analysis (Smith and Zavala, 2021) and data interrogation (Sun and Braatz, 2021) are firstly combined to reconstruct the dataset complexity and narrow down a number of candidate surrogates to be trained. The Bayesian information criterion (BIC) (Schwartz, 1978) is used to assess quality of fitting and compare predictive performances. If none of the trained surrogates allows to attain the preset level of accuracy (i.e., stop criterion), new sampling points are added. The implementation of an adaptive algorithm locates additional samples in the feasible region, which are then included in the dataset for training. The scheme is iteratively repeated up to achieve the required accuracy.
The implementation of the methodology is critically tested on a number of numerical problems with complex feasible regions, showing the effectiveness of the approach and the benefits of the proposed techniques. Results demonstrate that although the initial number of points and sampling technique strongly influence the reconstruction of the problem complexity, the inclusion of adaptive points promotes a fast identification of all (eventual) disjointed operability regions and significant accuracy improvement. In this framework, the original use of topological descriptors is proved to effectively characterize complex data structures. Finally, the effectiveness of the proposed workflow will be demonstrated in a case study concerning pharmaceutical manufacturing, where the accurate description of the DS is key to process development and optimization.
• How is it possible to reconstruct the feasibility shape based on the available dataset? Is there a minimum number of datapoints that are necessary to obtain a complete knowledge of the problem complexity? How does the inclusion of new samples affect the results?
• How can we compare the performance of different candidate surrogate models, while improving the prediction accuracy?
To answer the questions above, we propose a novel framework to uncover knowledge about the feasible space and predict the feasibility boundaries based on a predetermined level of accuracy with the minimum requirement of training data. Topological analysis (Smith and Zavala, 2021) and data interrogation (Sun and Braatz, 2021) are firstly combined to reconstruct the dataset complexity and narrow down a number of candidate surrogates to be trained. The Bayesian information criterion (BIC) (Schwartz, 1978) is used to assess quality of fitting and compare predictive performances. If none of the trained surrogates allows to attain the preset level of accuracy (i.e., stop criterion), new sampling points are added. The implementation of an adaptive algorithm locates additional samples in the feasible region, which are then included in the dataset for training. The scheme is iteratively repeated up to achieve the required accuracy.
The implementation of the methodology is critically tested on a number of numerical problems with complex feasible regions, showing the effectiveness of the approach and the benefits of the proposed techniques. Results demonstrate that although the initial number of points and sampling technique strongly influence the reconstruction of the problem complexity, the inclusion of adaptive points promotes a fast identification of all (eventual) disjointed operability regions and significant accuracy improvement. In this framework, the original use of topological descriptors is proved to effectively characterize complex data structures. Finally, the effectiveness of the proposed workflow will be demonstrated in a case study concerning pharmaceutical manufacturing, where the accurate description of the DS is key to process development and optimization.
References
Destro, F., Barolo, M. 2022. A review on the modernization of pharmaceutical development and manufacturing – Trends, perspectives, and the role of mathematical modeling. Int. J. Pharm., 620, 121715.
Smith, A., Zavala, V. M., 2021. The Euler characteristic: A general topological descriptor for complex data. Comput. Chem. Eng., 154, 107463.
Sun, W., Braatz, R. D., 2021. Smart process analytics for predictive modeling. Comput. Chem. Eng., 144, 107134.
Schwarz, G., 1978. Estimating the dimension of a model. Ann. Stats., 6, 461–464.
Wang, Z., Ierapetritou, M., 2018. Global sensitivity, feasibility, and flexibility analysis of continuous pharmaceutical manufacturing processes. Comp. Aid. Chem. Eng., 41, 189–213.