Component data assisted finite element model updating of composite flying-wing aircraft using multi-level optimization

This article studies finite element model updating of a composite flying-wing aircraft by using experimental results for both the aircraft and its components obtained in different experimental setups. A multi-level optimization approach is employed for updating the finite element models for obtaining the analysis results to match with the test results for both the global model and its components. The mass and stiffness distributions are, respectively, updated in the multi-level optimization problems. The first level optimization (Level I) updates the mass distribution, while keeping the stiffness distribution fixed. The optimal mass distribution obtained in Level I passes and are fixed in the second level optimization (Level II) for updating the stiffness related parameters. The back-and-forth iteration between these two levels continues till a convergence criteria is achieved. Both the root mean square error (RMSE) and the mean absolute error (MAE) are used as fitness functions in the optimization problems. Recognizing the nonsmooth nature of the MAE in the design domain, the optimization problem using the MAE as the fitness function is converted to a sequential linear programming problem by treating each absolute difference value as a design variable. Optimization results show that when using the MAE based optimization, some of the analysis results for the updated FEM are exactly same as the test data while RMSE based optimization distributes the errors to all responses. The multi-level optimization splits the large cost function as used in the all-at-once (AAO) optimization into two small cost functions and achieves a slightly lower fitness function than that for the AAO optimization when they have the same convergence criteria. As a result, the responses for the updated models obtained from the multi-level optimization are closer to the test results.