Excellent pattern matching capability makes artificial neural networks (ANNs) a very promising approach for vibration-based structural health monitoring (SHM). The proper design of the network architecture with the suitable complexity is vital to the ANN-based structural damage detection. In addition to the number of hidden neurons, the type of transfer function used in the hidden layer cannot be neglected for the ANN design. Neural network learning can be further presented in the framework of Bayesian statistics, but the issues of selection for the hidden layer transfer function with respect to the Bayesian neural network has not yet been reported in the literature. In addition, most of the research works in the literature for addressing the predictive distribution of neural network output is only for a single target variable, while multiple target variables are rarely involved. In the present paper, for the purpose of probabilistic structural damage detection, Bayesian neural networks with multiple target variables are optimally designed, and the selection of the number of neurons, and the transfer function in the hidden layer, are carried out simultaneously to achieve a neural network architecture with suitable complexity. Furthermore, the nonlinear network function can be approximately linear by assuming the posterior distribution of network parameters is a sufficiently narrow Gaussian, and then the input-dependent covariance matrix of the predictive distribution of network output can be obtained with the Gaussian assumption for the situation of multiple target variables. Structural damage detection is conducted for a steel truss bridge model to verify the proposed method through a set of numerical case studies.
A hierarchical deep convolutional neural network and gated recurrent unit framework for structural damage detection