Acceleration Method for Evolutionary Optimization of Variable Cycle Engine

VCE (Variable Cycle Engines) is considered as one of the best options for advanced military or commercial supersonic propulsion system. Variable geometries enable the engine to tailor performance across the flight envelope but greatly increase the design complexity of the engine. Therefore, optimization is necessary for VCE technique. As for traditional gradient-based optimization methods, the optimal result can be obtained quickly with the derivative information. But the traditional gradient-based optimization methods rely on the selection of starting point. Improper starting point leads to the local optimal solution. As a result, the performance potential of VCE cannot be fully exploited. Evolutionary algorithms (EAs) are a broad class of global stochastic optimization algorithms inspired by biology. EAs have a prominent advantage over traditional gradient-based optimization methods in terms of global optimization capability, making it more suitable to deal with complex VCE performance optimization. The Newton–Raphson method is used to solve the VCE model during evolution. Due to the stochasticity of evolution, the initial guesses inputted into the VCE model are extremely important. Without suitable initial guesses, the Newton–Raphson solver cannot reach the basin of convergence quickly or even get a convergent solution. Obviously, EAs can be used to solve the VCE model instead of the Newton–Raphson method. However, the nested optimization structure is computationally expensive making it unaffordable. To alleviate this problem, surrogate model is built using the converged information as training data. The VCE model can query this surrogate model and get reasonable initial guesses. But building a surrogate model requires a lot of training samples, and it is unrealistic to build a surrogate model for each engine design.

This paper introduces an efficient approach to generate reasonable initial guesses during evolution. Each individual in the evolutionary population is extended with initial guesses. Similar to design variables, the initial guesses will be adjusted by means of evolution. Both of them are applied at the individual level. The initial guesses are obtained by evolution before the VCE model is solved, so they influence the balance process of the VCE model. Better (encoded) initial guesses lead to faster convergence of VCE model, and these initial guesses will be propagated by surviving individual, which, in turn is more likely to generate better initial guesses in the next evolution. Differential evolution (DE), a simple yet powerful EA for global optimization, is used to verify our method. First, two single point optimizations are conducted with flight conditions at ground throttling and supersonic cruise. Then, multipoint optimization considering one on-design condition (takeoff) and one off-design condition (supersonic cruise) is performed. The result indicates that the optimization results and generation numbers of evolution are almost unchanged, but the VCE model call numbers are reduced by 45.2%, 63.4% and 63.7% respectively during ground throttling, supersonic cruise and multi-point optimizations, which means a dramatic reduction in terms of evolution time.