Abstract

Abstract

Abstract

Abstract

Abstract
The class of subspace system identification algorithms is used here to derive new identification algorithms for 2-D causal, recursive, and separable-in-denominator (CRSD) state space systems in the Roesser form. The algorithms take a known deterministic input-output pair of 2-D signals and compute the system order (n) and system parameter matrices {A, B, C, D}. Since the CRSD model can be treated as two 1-D systems, the proposed algorithms first separate the vertical component from the state and output equations and then formulate a set of 1-D horizontal subspace equations. The solution to the horizontal subproblem contains all the information necessary to compute (n) and {A, B, C, D}. Four algorithms are presented for the identification of CRSD models directly from input-output data: an intersection algorithm, (N4SID), (MOESP), and (CCA). The intersection algorithm is distinguished from the rest in that it computes the state sequences, as well as the system parameters, whereas N4SID, MOESP, and CCA differ primarily in the way they compute the system parameter matrices {A1, C1}. The advantage of the intersection algorithm is that the identified model is in balanced coordinates, thus ideally suited for 2-D model reduction. However, it is computationally more expensive than the other algorithms. A comparison of all algorithms is presented.

Abstract
In this paper a new approach to gas leakage detection in high pressure natural gas transportation networks is proposed. The pipeline is modelled as a Linear Parameter Varying (LPV) System driven by the source node massflow with the gas inventory variation in the pipe (linepack variation, proportional to the pressure variation) as the scheduling parameter. The massflow at the offtake node is taken as the system output. The system is identified by the Successive Approximations LPV System Subspace Identification Algorithm which is also described in this paper. The leakage is detected using a Kalman filter where the fault is treated as an augmented state. Given that the gas linepack can be estimated from the massflow balance equation, a differential method is proposed to improve the leakage detector effectiveness. A small section of a gas pipeline crossing Portugal in the direction South to North is used as a case study. LPV models are identified from normal operational data and their accuracy is analyzed. The proposed LPV Kalman filter based methods are compared with a standard mass balance method in a simulated 10% leakage detection scenario. The Differential Kalman Filter method proved to be highly efficient.