Broad Bayesian learning (BBL), a novel probabilistic Bayesian neural network methodology with optimized architecture configuration, is proposed. It has an expandable feedforward broad learning network. Therefore, the uncertain estimates can be quantified in terms of probability distributions and network architecture augmentation can be adopted incrementally by use of the inherited information from the previously trained network. Furthermore, a learning network architecture configuration optimization scheme is proposed to determine the optimal architecture configuration. Based on the plausibilities of the concerned configurations, the most plausible one can be obtained, and it indicates the proper augmentation to develop the optimal configuration. To demonstrate the proposed methodology, three simulation examples and an application with in-field structural health monitoring measurement are presented.