Filtering and Model Reduction of PDAEs with Stochastic Boundary Data

Abstract

AbstractIn this paper we investigate state reconstruction for gas pipeline networks using model hierarchies derived from model order reduction techniques. The pipeline network is described by partial differential algebraic equations (PDAEs), for which model order reduction was extensively studied in [1]. We use and extend upon the aforementioned results to estimate the system state, when the boundary data is perturbated by an Ornstein‐Uhlenbeck process. We study the performance of state reconstruction based on the derived model hierarchy. Of special interest, hereby, is the relationship between the quality of the state estimation and the underlying reduced order model.