Structural engineering projects require reliable information about parameters of the designed systems that convey precise predictions about the behavior of the system under different load cases. These predictions are derived from numerical engineering models containing real structure geometry and parameters, resulting in responses using the well-established Finite Element Method (FEM). However, due to the presence of uncertainties and assumptions made during the construction of the model, the resulting response may not well represent the real structural behavior. Thus, the established approach involves supplying the numerical model with experimental data to reduce numerical-experimental error, improving the correlation between numerical and observed structural behavior of the system, in a process called Finite Element Model Updating (FEMU). Overall, engineers have developed many different approaches to solve this problem, mainly consisting of sampling or optimization algorithms, applying these methods in FEMU, damage detection, and optimization of sensor placement. The focus of this paper is on the implementation of the Bayesian Optimization Algorithm (BOA) to solve FEMU problems. BOA is a derivative-free optimization algorithm that aims to minimize the number of evaluations of the objective function by trading some computational resources for the construction and optimization of a cheaper auxiliary function, which evaluates the best point to evaluate next. This can be beneficial when heavy sampling of the optimization function can be very time-consuming or when limited evaluations are available, rendering sampling methods and some heuristic algorithms inefficient. To assess the behavior of the algorithm, many cases are analyzed from lower evaluation time to higher complexity cases and then compared with other methods, such as Bayesian Inference, Particle Swarm Optimization, and Genetic Algorithm. The first case is to optimize test functions, followed by some FEMU applications on an uncertain boundary condition beam and finally, a honeycomb plate, in which evaluation of the objective function is more expensive. Results show that BOA can attain good results in a short amount of time when applied to FEMU for low dimensionality problems compared with well-established methods. Overall, this paper reviews FEMU methods and proposes the implementation of a novel approach, demonstrating its effectiveness in solving model updating problems.
Read full abstract