Development of concurrent subspace optimization method and its applications in parallel design of complex system

Concurrent Subspace Optimization (CSSO) method was modified for better convergence and was validated using a gearbox design problem and an aircraft conceptual design problem. For complex engineering design in aeronautic and astronautic field, the conventional design strategy was computational expensive, time-consuming, and was complicated in communication between subsystems. Global Sensitivity Equation based CSSO (GSECSSO) was a promising method to solve this problem due to its parallel design strategy and its ability of reducing design variables and constraints. However, GSECSSO sometimes had bad convergence. It was found that trade-off coefficients may cause divergence when it allowed too much violation of a constraint in order to obtain a reduction of the objective reduction. And an inappropriate value of parameter ρ for cumulative constraints may cause premature convergence when it was not large enough, or may cause divergence when it was too large. In this work, two strategies had been adopted to modify the original GSECSSO method as bellow: 1) The trade-off coefficients were abandoned, since all trade-offs will occur naturally with minimization of objective function. 2) To prevent the inappropriate selection of ρ, ρ was modified to start from a small value and increase with a user-defined step, which can make the design correct its search direction thus the active constraint gradually dominates the cumulative constraint. A gearbox is designed using the modified method and the original one, respectively; the results show that the oscillatory convergence is much suppressed by using the modified GSECSSO and premature convergence has not happened. Then the modified GSECSSO is applied in the conceptual design of a general purpose aircraft. This conceptual design problem was divided into three disciplines, including aerodynamics, weight and performance discipline. Because aerodynamic subsystem transferred the lift-to-drag ratio to weight subsystem and performance subsystem and weight subsystem also provided performance subsystem with design gross weight for calculating range and stall velocity, three subsystems were coupled. Besides in weight subsystem, empty weight and design gross weight was also coupled. For obtaining the value of coupling variables, the decoupling was performed by iteration among these subsystems. The optimization models were set up respectively using the modified GSECSSO. The convergence was achieved in twelve iteration steps and the convergence history was smooth. Compared with the original scenario, the design gross weight was reduced by 19.7% and the lift drag ration was increased by 4.4%. That is to say, the performance of the new scenario is improved greatly. It shows that our method is efficient and practical.