A multiobjective optimization approach to filter tuningapplied to coupled hyperbolic PDEs describinggas flow dynamics

Ferdinand Evert Uilhoorn

In this work, we introduce a multiobjective optimization approach that seeks the optimal process noise statistics in the extended Kalman filter (EKF). The bi‐objective Mesh Adaptive Direct Search (BMADS) algorithm was used to minimize a performance index based on state estimate errors. The EKF estimated the gas flow dynamics in a pipeline system. Simulations were conducted with outflow boundary conditions for the flow model that contain gradual changes and discontinuities. To ensure shock‐capturing properties, the model was approximated with a semidiscrete finite volume scheme using Roe’s SUPERBEE limiter. The knee point in the Pareto front was based on normal boundary intersection approach and selected to compute the flow estimates. Numerical experiments demonstrated that BMADS is suitable for tuning the EKF and, compared to the normalized weighted sum method and nondominated sorting genetic algorithm, it showed to be superior in terms of computation time and most effective in finding Pareto optimal solutions.

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