Using a Kalman Filter to Estimate Unsteady Flow

A Kalman filter that estimates incompressible unsteady flow in a pipe is proposed in this paper. It is a steady-state Kalman filter based on amodel of pipeline dynamics, that is, an optimized finite element model developed by the author. Pressure signals at both ends of a target section of a pipe are input to the model of pipeline dynamics, and, as an output of the model, an estimated pressure signal at a mid-point in the pipe is obtained. The deviation between a measured and an estimated pressure signal at the mid-point is fed back to the dynamic model of the pipeline to modify state variables of the model, which are pressure and flow rate along the pipe. According to the Kalman filter principle, the state variables of the model are modified as to converge to real values. The Kalman filter is examined by experiment using an oil-hydraulic circuit. The unsteady flow and unsteady pressure of a delivery port of an oil-hydraulic pump are estimated by the Kalman filter. The performance of the Kalman filter is demonstrated, and its bandwidth is discussed.