A probabilistic projection of the transient flow equations with random system parameters and internal boundary conditions

ABSTRACT This paper presents a novel probabilistic approach based on the polynomial chaos expansion that can model the uncertainty propagation from the beginning of a waterhammer simulation and not as an afterthought. Uncertainties are considered in pipe diameter, friction coefficient, and wave speed, as well as internal boundary conditions of leaks and blockages. The polynomial chaos expansion solver results are in an excellent agreement with those calculated by using a model employing the traditional method of characteristics. The probabilistic polynomial chaos approach has the advantage of being robust and more efficient than other non-intrusive methods such as Monte Carlo simulation, which requires thousands of iterations for sharp solutions. The polynomial chaos approach is further extended to solve for randomness in frequency domain using the transfer matrix method with results of comparable accuracy. With further developments, this probabilistic approach can be integrated within existing network modelling software for practical hydraulic engineering problems.

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