Calibration approach to quantify nonlinearity of MEMS pore pressure sensors using optimal interpolation

Abstract

MEMS-based instruments have become more attractive in recent years for many industries, particularly geotechnical monitoring owing to their small size and low capital cost. However, overcoming nonlinearity errors is a major concern to ensure accuracy, precision, and repeatability of measurement. Nonlinearity error in measuring instruments can be solved using polynomial function of different degree based on severity of error. In this study, Lagrange polynomial fitting method is applied for nonlinearity calibration of a newly developed MEMS pore pressure sensor by means of optimum calibration points. A procedure for optimum selection of the calibration points to get the best calibration characteristics of a pore pressure sensor is investigated. For this work, the calibration characteristics are evaluated by Lagrange interpolation using special set of Chebyshev nodes, D, A and R-optimum points. The D-A-R optimum points are constructed by Imperialist Competitive Algorithm (ICA). The value of the optimal approach is also compared with a uniform approach using equidistant points through actual readings. The results show the increased accuracy and precision of measurement using optimum approach. This increased accuracy allows the application of MEMs to sense smaller changes in pore pressure readings providing unique opportunity for passive estimation of subsurface properties.

Development of IOT-based low-cost MEMS pressure sensor for groundwater level monitoring

“…Calibration is an important step in the development of any MEMS-based instrument. It is an adjustment between the sensor's output signal and the measured quantity to reach the closest value to the truth [75,76]. Adopting a proper calibration model can significantly affect the performance of the MEMS-based instruments [32,[76][77][78][79][80].…”

“…It is an adjustment between the sensor's output signal and the measured quantity to reach the closest value to the truth [75,76]. Adopting a proper calibration model can significantly affect the performance of the MEMS-based instruments [32,[76][77][78][79][80]. A MEMS pressure sensor mainly suffer from four types of error, including offset, gain, nonlinearity, and hysteresis.…”

“…where v c is the corrected voltage after offset and gain compensation, v min is the minimum output voltage for the sensor and v r is the raw output signal, k 1 and k 2 are offset and gain coefficients, which are calculated by following equations [83,84]: In the case of the nonlinearity error, linearization models are solved by the Lagrange polynomial fitting method, by means of optimum calibration points [76].…”

“…The Lagrange interpolation method is a suitable option for a cost-effective calibration scheme due to its ability to conduct calibration with a reduced amount of data compared to other available methods [85]and [76]. An optimal Lagrange method can be achieved by ensuring that the calibration points are positioned according to the Lebesgue function criteria.…”

“…An optimal Lagrange method can be achieved by ensuring that the calibration points are positioned according to the Lebesgue function criteria. The concept is rooted in the understanding that equidistant points may not yield accurate results, and different sets of points based on Chebyshev spacing or optimality criteria can lead to better outcomes [76,86]. In this analysis, various sets of points are examined, and the best results are obtained by utilizing modified extended Chebyshev (MEC) points.…”