A multiobjective optimization approach to filter tuning applied to coupled hyperbolic PDEs describing gas flow dynamics. (3rd May 2019)

• Record Type: Journal Article
• Authors: Uilhoorn, Ferdinand Evert
• Is Part Of: Optimal control applications and methods. Volume 40:Number 4(2019)
• Page Start: 750
• Page End: 763
• Publication Date: 2019-05-03
• Subjects: filter tuning -- gas flow dynamics -- hyperbolic PDEs -- Kalman filter -- multiobjective optimization; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2509
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: 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 (Bi MADS) 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'sSUPERBEE 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 Bi MADS 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.