Algorithm for local nonlinear error calibration of displacement sensor based on C2 continuous interpolation

Abstract

The laser displacement sensor based on the triangulation method has the advantages of large range, high precision, and strong anti-interference. Due to the limitation of the measurement principle, although the laser displacement sensor has high repeated measurement accuracy, it has serious high-order nonlinear system errors. Considering that in some measurement occasions, only a few local measurement intervals within the range are used. In this paper, a local nonlinear error calibration algorithm based on C2 continuous interpolation was proposed. A nonlinear calibration model was established by intensive calibration data acquisition in the local interval of the measurement application. The model can be smoothly connected with the original linear calibration model. At the same time, the measurement accuracy of the local area is greatly improved without affecting the accuracy of other intervals.

Novel Information-Driven Smoothing Spline Linearization Method for High-Precision Displacement Sensors Based on Information Criterions

“…However, the second step regarding nonlinearity reconstruction has remained insufficiently explored in terms of how to construct a linearization model that best reveals the nonlinear characteristics of the displacement sensors from small amounts of nonlinearity measurement data while also adequately addressing the noise. Conventionally, polynomial models (PL) are adopted as standard methods for linearization [9,[27][28][29]. For example, Mao et al employed a third-order PL with a C2 continuity to linearize two separated intervals of interest for a laser displacement sensor, improving its measurement accuracy by up to 70% compared to linear interpolation [28]; Pereira et al introduced an adaptive selfcalibration method via progressive polynomial interpolation, which dynamically updates the model coefficients with new measurement results [27].…”

“…Conventionally, polynomial models (PL) are adopted as standard methods for linearization [9,[27][28][29]. For example, Mao et al employed a third-order PL with a C2 continuity to linearize two separated intervals of interest for a laser displacement sensor, improving its measurement accuracy by up to 70% compared to linear interpolation [28]; Pereira et al introduced an adaptive selfcalibration method via progressive polynomial interpolation, which dynamically updates the model coefficients with new measurement results [27]. The polynomial linearization models can achieve an adequate linearization result for smooth nonlinearities.…”

“…Devised a Fabry-Perot interferometer to calibrate nanometer sensors up to a 300 µm range, with picometer resolution and nanometer uncertainty. [28] PL Laser displacement sensor Adopted a third-order PL for linearizing two non-contiguous intervals, reducing nonlinearity by up to 70% compared to linear interpolation.…”