Signal Processing for Transient Flow Rate Determination: An Analytical Soft Sensor Using Two Pressure Signals

Signals, vol. 5, pp. 812–840

Abstract

Accurate knowledge of the flow rate is essential for hydraulic systems, enabling the calculation of hydraulic power when combined with pressure measurements. These data are crucial for applications such as predictive maintenance. However, most flow rate sensors in fluid power systems operate invasively, disrupting the flow and producing inaccurate results, especially under transient conditions. Utilizing pressure transducers represents a non-invasive soft sensor approach since no physical flow rate sensor is used to determine the flow rate. Usually, this approach relies on the Hagen–Poiseuille (HP) law, which is limited to steady and incompressible flow. This paper introduces a novel soft sensor with an analytical model for transient, compressible pipe flow based on two pressure signals. The model is derived by solving fundamental fluid equations in the Laplace domain and converting them back to the time domain. Using the four-pole theorem, this model contains a relationship between the pressure difference and the flow rate. Several unsteady test cases are investigated and compared to a steady soft sensor based on the HP law, highlighting our soft sensor’s promising capability. It exhibits an overall error of less than 0.15% for the investigated test cases in a distributed-parameter simulation, whereas the HP-based sensor shows errors in the double-digit range.

Authors 4

1. Faras Brumand‐Poor corresponding Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   Institute for Fluid Power Drives and Systems (ifas), RWTH Aachen University, 52074 Aachen, Germany

2. Tim Kotte Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   Institute for Fluid Power Drives and Systems (ifas), RWTH Aachen University, 52074 Aachen, Germany

3. Enrico Pasquini
   Affiliation as printed

   Independent Researcher, 85088 Vohburg, Germany

4. Katharina Schmitz Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   Institute for Fluid Power Drives and Systems (ifas), RWTH Aachen University, 52074 Aachen, Germany