Design of multi-hidden-layer Bayesian neural networks for model updating

Structural health monitoring (SHM) based on artificial neural networks (ANN) has received a lot of attention in recent decades, especially the Bayesian neural network (BNN) approach, which is more robust to noise for training and generalization. Since building a high-quality BNN architecture suitable for a specific task depends highly on user experience, the existing literature generally studies BNNs with simple single-hidden-layer architectures designed by empirical formulas or very few tailor-made algorithms. Multiple hidden layer BNN (MBNN) has a more complex architecture than single hidden layer BNN (SBNN) and is expected to achieve better generalization performance for complex problems. But the corresponding architectural design problem is much more complex, and there is no previous experience in the literature. To achieve this for MBNN, this paper proposes two feasible algorithms to optimize the number of neurons in each hidden layer simultaneously, where a logarithmic evidence metric is introduced to quantitatively characterize the performance of MBNN for a given multi-hidden-layer architecture. The feasibility and effectiveness of the proposed method are verified by the finite element (FE) model updating of both a planar truss model and a real-life pedestrian bridge. The verification results show that the second algorithm is much more computationally efficient for the optimal design of the MBNN architecture and has the potential for practical application.