An efficient algorithm for architecture design of Bayesian neural network in structural model updating

There has been growing interest in applying the artificial neural network (ANN) approach in structural system identification and health monitoring. The learning process of neural network can be more robust when presented in the Bayesian framework, and rational architecture of the Bayesian neural network is critical to its performance. Apart from number of hidden neurons, the specific forms of the transfer functions in both hidden and output layers are also crucially important. To the best of our knowledge, however, the simultaneous design of proper number of hidden neurons, and specific forms of hidden‐ and output‐layer transfer functions has not yet been reported in terms of the Bayesian neural network. It is even more challenging when the transfer functions of both layers are parameterized instead of using fixed shape forms. This paper proposes a tailor‐made algorithm for efficiently designing the appropriate architecture of Bayesian neural network with simultaneously optimized hidden neuron number and custom transfer functions in both hidden and output layers. To cooperate with the proposed algorithm, both the Jacobian of the network function and Hessian of the negative logarithm of weight posterior are derived analytically by matrix calculus. This is much more accurate and efficient than the finite difference approximation, and also vital for properly designing the Bayesian neural network architecture as well as further quantifying the confidence interval of network prediction. The validity and efficiency of the proposed methodology is verified through probabilistic finite element (FE) model updating of a pedestrian bridge by using the field measurement data.