Structural Identification by Bayesian Neural Network with the Most Probable Architecture

In this work, neural networks (NNs) are used for structural identification by constructing the relationship between experimental data and structural properties. One problem is how to choose an appropriate NN architecture. It is not ideal to include as many neurons and layers as possible for a better NN ability, because limited information cannot explain the increasing NN complexity. The contribution is that a Bayesian framework and an efficient computational algorithm are proposed to design NN architecture. NN training is treated as a Bayesian inference problem, where one NN architecture with some hidden neurons and layers is considered as one candidate model class. The posterior probability density function of the NN parameters is formulated. The probabilities of competing NN architectures can then be formulated based on Bayesian model class selection. The most probable architecture is chosen as the one with the largest model class evidence. An efficient algorithm is proposed leveraging on the Laplace asymptotic approximation, NN analytical properties, and automatic differentiation to avoid the high-dimensional integral in evidence computation. The proposed efficient algorithm facilitates including high-dimensional experimental mode shapes for training. Experimental verification was conducted with a laboratory and a full-scale structure. It is found that deeper NNs (with more hidden layers) have larger evidence than the shallow ones.