Sparse Variational Bayesian Inference for Water Pipeline Systems With Parameter Uncertainties

In this paper, multi-leak identification based on a transient wave model with physical parameter uncertainties for smart water supply systems is studied. We formulate multi-leak identification under uncertain parameters (such as friction factor, wave speed, and source–end discharge oscillation) as a sparse signal recovery problem with inaccurate parameters in the measurement matrix, by using spatial sampling in leak location space. A stochastic sparse variational Bayesian inference (SSVBI) algorithm to jointly learn the spatial samples, sparse signal, and uncertain parameters is proposed for multi-leak identification. In addition, we establish the convergence of the SSVBI algorithm to an approximate minimum means squared estimate. The proposed approach can be applied to an arbitrary number of leaks, and its computational complexity is insensitive to the number of leaks. This is a significant technical improvement over existing approaches. Finally, simulations show that the SSVBI-based joint learning of uncertain parameters and sparse model can achieve a huge performance gain over existing methods.