Using a Kalman Filter to Estimate Unsteady Flow
Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa 240-8501, Japan
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.
-  S. Yokota, D.-T. Kim etc., “An Approach to Unsteady Flow Rate Measurement Utilizing Dynamic Characteristics between Pressure and Flow Rate along Pipeline,” Trans. JSME. C, Vol.57, No.541, pp. 2872-2876. (in Japanese)
-  T. Zhao, A. Kitagawa etc., “A Real Time Measuring Method of Unsteady Flow Rate and Velocity Employing a Differential Pressure,” Trans. JSME. B, Vol.57, No.541, pp. 2851-2859. (in Japanese)
-  T. Hayase, “Ultrasonic-Measurement-Integrated Simulation of Blood Flows,” J. of the Japan Fluid Power System Society, Vol.37, No.5, pp. 302-305, 2006.
-  Y. Okamoto, M. Nakao, K. Tadano, K. Kawashima, and T. Kagawa, “A Distributed Observer Based on Numerical Simulation for a Pipeline Connecting to Pneumatic Cylinder,” Proc. of the 8th JFPS Int. Symp. on Fluid Power, OKINAWA 2011, pp. 514-520.
-  K. Sanada and A. Kitagawa, “A Finite-Element Model of Pipeline Dynamics Using an Optimized Interlacing Grid System,” Trans. JSME. C, Vol.60, No.578, pp. 3314-3321. (in Japanese)
-  K. Sanada, C. W. Richards, D. K. Longmore, and D. N. Johnston, “A finite element model of hydraulic pipelines using an optimized interlacing grid system,” Proc Instn Mech Engrs, Part I: J. of Systems and Control Engineering, Vol.207, pp. 213-222, 1993.
-  A. Ozawa, B. Gao, and K. Sanada, “Estimation of Fluid Transients in a pipe using Kalman Filter based on Optimized Finite Element Model,” SICE Annual Conf. 2010, FA10.01, 2010.
-  A. Ozawa and K. Sanada, “An Indirect Measurement Method of Transient Pressure and Flow Rate in a Pipe,” Proc. of the 8th Int. Symp. on Fluid Power, Okinawa 2011, Oct. 25-28, 2011, pp. 104-109, 2011.
-  T. Kagawa, I. Lee, A. Kitagawa, and T. Takenaka, “High speed and Accurate Computing Method of Frequency-dependent Friction in Laminar Pipe Flow for Characteristics Method,” Trans. of the JSME (Series B), Vol.49, No.447, pp. 2638-2644, 1983.
-  K. Sanada, “A Study on Simulation of Turbulent Transient Flow in Pipes using an Optimized Finite Element Model,” J. of the Japan Hydraulics & Pneumatics Society, Vol.32, No.2, pp. 46-52, 2001.