A new hybrid optimization algorithm for variational data assimilation of unsteady wake flows
Résumé
In typical variational data assimilation (DA) applications for unsteady flows the search space is large and multidimensional, while prior information about the control vector function is not available. Stochastic optimization algorithms like genetic algorithms (GA) perform global optimization but waste computational effort by doing a random search. On the other hand, deterministic algorithms like gradient descent converge rapidly but may get stuck in local minima of multimodal functions. Here, we present a new hybrid global optimization technique, where a gradient-based local search method is combined with a genetic algorithm to achieve faster convergence and better accuracy of final solution without getting trapped in local minima. The proposed methodology is applied to the reconstruction of unsteady bidimensional flows past a rotationally oscillating cylinder. More precisely, the possibility of reconstructing the rotational speed of the cylinder given observations of a reference flow was investigated via variational DA (Fig. 1). Fig. 1 Temporal mean streamwise velocity field for Reference flow, the observation domain is delineated in white lines. In order to decrease memory and computational time requirements, we used an alternative formulation of the optimization procedure proposed by Tsoulos et al. (2008). This formulation avoids the execution of the local search process each time a local minimum is found progressively by the genetic operations step (Fig. 2-left). Accordingly, the genetic algorithm was first used to approximately locate a good global minimum. Then a gradient based local search was done with the best solution found by the genetic algorithm as its starting point (Fig. 2-right). Thus, the GA was used to go near the vicinity of a good global minima and the gradient descent scheme was used to find the global minimum accurately. This approach is advantageous because it allows for exploration of new regions of the search space while retaining the ability to improve good solutions already found. The stochastic approach utilizes the grammatical evolution (GE) procedure to create trial solutions, while the GA utilizes the operations of crossover and mutation to create the evolving generations. Fig. 2 Typical convergence histories for the Hybrid approach by Tsoulos et al. (2008) (left) and present formulation (right).
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