Non‐intrusive reduced genetic algorithm for near‐real time flow optimal control

• Published in: International journal for numerical methods in fluids Vol. 92; no. 9; pp. 1118 - 1134
• Main Authors: Oulghelou, Mourad, Allery, Cyrille
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.09.2020; Wiley
• Subjects: Algorithms; Central processing units; Chromosomes; Computational fluid dynamics; Control; CPUs; Cylinders; Dimensions; Economics; Engineering Sciences; flow past a cylinder; Fluid flow; Fluids mechanics; Genetic algorithms; Grassmann manifold; Interpolation; inverse flow problems; Lid‐driven cavity; Manifolds (mathematics); Mathematical Physics; Mechanics; optimal flow control; Optimization; Parameterization; Physics; Proper Orthogonal Decomposition; Reynolds number; Storage; subspaces interpolation; Time optimal control
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4820

Summary Most genetic algorithms (GAs) used in the literature to solve control problems are time consuming and involve important storage memory requirements. In fact, the search in GAs is iteratively performed on a population of chromosomes (control parameters). As a result, the cost functional needs to be evaluated through solving the high fidelity model or by performing the experimental protocol for each chromosome and for many generations. To overcome this issue, a non‐intrusive reduced real‐coded genetic algorithm (RGA) for near real‐time optimal control is designed. This algorithm uses precalculated parametrized solution snapshots stored in the POD (proper orthogonal decomposition) reduced form, to predict the solution snapshots for chromosomes over generations. The method used for this purpose is a economic reduced version of the Bi‐CITSGM method (Bi‐calibrated interpolation on the tangent space of the Grassmann manifold) designed specially for nonlinear parametrized solution snapshots interpolation. This approach is proposed in such a way to accelerate the usual Bi‐CITSGM process by bringing this last to a significantly lower dimension. Thus, the whole optimization process by RGA can be performed in near real‐time. The potential of RGA in terms of accuracy and central processing unit time is demonstrated on control problems of the flow past a cylinder and flow in a lid‐driven cavity when the Reynolds number value varies. We propose a non‐intrusive reduced real‐coded genetic algorithm (RGA) for flow optimal control. This algorithm relies on the Economic version of the Bi‐CITSGM (Bi Calibrated Interpolation on the Tangent Space of the Grassmann Manifold) used to evaluate the state solutions for chromosomes over generations. It is shown that RGA can perform in near‐real‐time and deliver satisfying quasi‐optimal control solutions.