Product Dynamic Transitions Using a Derivative-Free Optimization Trust-Region Approach

Abstract

Traditionally the optimization of processing systems has relied on the availability of an explicit model together with the corresponding gradient information. However, there are some practical scenarios such as (a) nondifferentiable systems, (b) physical experimental systems, (c) simulation environments, and (d) reduced order systems where such a model and its gradient are not available. Under these scenarios the deployment of derivative-free optimization strategies provides an alternative manner to cope with the optimization of such systems. In particular, in this work we deploy a derivative-free optimization trust region approach to deal with the product dynamic optimization problem of processing systems. To this aim, we use a closed-loop model predictive control strategy where the system to be optimized is embedded in a black-box dynamic simulation environment. The results demonstrate that black-box dynamic models can be dynamically optimized assuming that the number of decision variables is not large. The first-principles dynamic model of a binary distillation column embedded in the ASPEN dynamic simulation environment was deployed as our black-box dynamic model, to demonstrate the advantages of solving product dynamic transition problems when an explicit model of the dynamic model and/or its gradient information are not available.

A data‐driven Bayesian approach for optimal dynamic product transitions

“…To partially cope with this issue some other black-box optimization works solve the dynamic optimization problem by building an approximate surrogate (i.e., quadratic function) around the intended dynamic trajectory, turning the problem into an unconstrained optimization problem that can be solved by traditional optimization techniques. 17 Nowadays, particularly within the paradigms of Industry 4.0 and artificial intelligence, there exists a compelling imperative to address the efficient and reliable solution of optimization challenges through a predominantly data-driven methodology. 46 Within this framework, the fundamental concept revolves around the utilization of solely the measurements of process variables to both construct and address black-box optimization problems.…”

“…Finally, as done in the previous case studies, the influence of noisy measurements on the performance of the BO approach was assessed by adding 20% noise level to the objective function shown in Equation (17). The performance of the optimization scheme taking • We acknowledge the absence of a guarantee for the stability of transition trajectories in our proposed Bayesian dynamic transition approach.…”

“…For instance, in the case of the binary distillation column, these variables include the mol fractions of the distillate (x d ) and bottoms streams (x b ). These variables the basis upon which the objective function relies, as illustrated in Equation (17). It is important to clarify that the term "output" variables, as modeled by the GP, does not pertain to the controlled variables.…”

“…16 Black-box optimization represents an approach to system optimization that finds its ideal application in cases where a first-order model is unavailable. [17][18][19][20] In this method, optimization relies upon an empirical model or an approximation of the target system. Subsequently, this approximated or surrogate model can be subject to optimization.…”

Prescribing Closed-Loop Behavior Using Nonlinear Model Predictive Control

“…On the other hand, it is common to use the same process for different products in chemical plants, with the different products achieved, say via grade transition in polymerization reactors. This product transition is usually done by set point change for plant output. − In these instances, a “desired” process behavior could be specified as one where the transition to the new specification is the fastest, and a resultant optimization problem that minimizes the transition time is formulated and implemented …”