(390a) A Hybrid Approach for Flexible Design of Nonlinear Process Systems

Uncertainty and variability are intrinsic characteristics of any chemical process, arising from factors such as kinetic and thermodynamic correlations, raw material fluctuations, and market forecasts. In this context, a promising approach is to evaluate the system’s capacity to adapt to these uncertainties while sustaining optimal performance — known as flexibility analysis. Flexibility analysis via the seminal max–min–max optimization formulation is generally challenging due to the nested structure [1]. Existing deterministic flexibility algorithms typically transform the tri-level problem via Karush–Kuhn–Tucker conditions and solve via active set strategy [2, 3], global optimization [4], inner/outer approximation [5], etc. However, they face challenges when applied to high-dimensional, nonconvex problems. Recent advancements in data-driven and machine learning approaches for flexibility analysis have shown potential while they may present limitations imposed by the employed sampling methods [6, 7].

To address these challenges, this work proposes a hybrid approach for the feasibility analysis and flexible design of nonlinear process systems augmenting multi-parametric programming and machine learning. Given a general nonlinear process system, the feasibility function is first solved using multi-parametric programming with outer approximation created to linearize the nonlinear functions. Explicit/multi-parametric solutions can thus be obtained for the linearized feasible region boundary as piecewise affine functions with respect to uncertain parameters and design variables [8]. These explicit expressions of the linearized boundary are then exactly re-formulated as Y-Wise Affine Neural Networks (YANNs) using a rectified linear unit activation function, which has been developed in our prior work. For processes in which linearization suffices to provide a good under-estimation to the feasibility function (e.g., convex feasible region), the resulting YANNs can be directly applied to clarify the feasibility or infeasibility without requiring any additional training. For more general non-convex processes, the YANNs are further trained to characterize the nonlinear feasible region boundary by interacting with the original nonlinear process. The linearized boundary information can provide a good hot start which notably enhances sampling efficiency. The proposed approach provides a key feature to focus on identifying the feasibility/infeasibility boundary. The hybrid use of both multi-parametric programming and machine learning also enhances the algorithmic scalability, as this avoids relying on excessive boundary linearization or exhaustive sampling of the entire feasible region. The finalized YANNs classification networks can be readily integrated with mathematical programming-based process synthesis problems to achieve flexible design. This offers a generalized computational strategy for linear/nonlinear, convex/nonconvex process systems under deterministic uncertainty. The potential and efficacy of this approach are demonstrated using two case studies: (i) synthesis of a flexible heat exchanger network with convex/non-convex feasible region; and (ii) flexible design of proton exchange membrane water electrolysis based on a lab-scale experimental setup.

References

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