A phase calibration method for memoryless nonlinear systems

In certain applications, e.g. Coriolis flow meters, phase measurements are used to meter the mass flow rate of expensive fluids (oil and gas). These accurate devices apply sinusoidal forces and measure the relative phase on curved pipe sections with 0.01% accuracy. Clearly, precise phase calibration or estimation is a routine task with such instruments and it seems straightforward. Unfortunately, as will be shown, any nonlinear behavior of the sensor and the measured system can lead to systematic errors, no matter how much data is collected and can therefore lead to significant money loss over time. The present paper proposes a new phase calibration (or time delay estimation) method that operates without modification in the presence of some nonlinear distortions and non-sinusoidal periodic vibrations of the measured surfaces. The method computes the area entrapped in a Lissajous-like curve using Green's theorem and it does not employ Fourier-based analysis. Described in this paper is the mathematical background, illustrative case studies and an experimental study. The method is computationally efficient and it employs a non-parametric approach which operates directly on the raw measured data and does not need to model the system or the nonlinear distortions.