A Resonant Pressure Sensor Capable of Temperature Compensation with Least Squares Support Vector Machine Academic research paper on "Materials engineering"

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Procedía Engineering 168 (2016) 1731 - 1734

Procedía Engineering

www.elsevier.com/locate/procedia

30th Eurosensors Conference, EUROSENSORS 2016

A Resonant Pressure Sensor Capable of Temperature Compensation with Least Squares Support Vector Machine

Lin Zhua,b, Bo Xiea,b, Yonghao Xinga,b, Deyong Chenb,*, Junbo Wangb,f, Yanshuang Wanga,b, Qiuxu Weia,b, Jian Chenb

aUniversity of Chinese Academy of Sciences, No.80, Zhongguancun East Road, Haidian District,Beijing 100190, China bState Key Laboratory of Transducer Technology, Institute of Electronics, Chinese Academy of Sciences, No.19, North 4th Ring Road, Haidian

District, Beijing 100190, China

Abstract

Resonant pressure sensors are widely used in pressure monitoring due to high accuracies, long-term stabilities and quasi-digital outputs, which, however, suffers from the key issue of temperature drifts. This paper presents a resonant pressure sensor capable of temperature compensation leveraging the compensation algorithm of least squares support vector machine. Double "H" type resonators were arranged in a differential output pressure sensor where the pressure under measurement was translated to resonant frequency output. In comparison to two conventional algorithms which are support vector machine and polynomial fitting, the new algorithm based on least squares support vector machine can effectively improve the precision of temperature compensation for the developed micro sensors. Experimental results showed that the maximum temperature drift was reduced from 8901.4 Pa (without compensation) to 2.0 Pa (with compensation) in the full temperature and pressure scale (temperature range of -40 °C to 70 °C and pressure range of 20 kPa to 260 kPa), validating the effectiveness of the new algorithm in temperature compensation. © 2016 The Authors.PublishedbyElsevierLtd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: resonant pressure sensor, temperature compensation, least squares support vector machine;

* Corresponding author. Tel.: +86-10-58887182; fax: +86-10-58887182.

E-mail address: dychen@mail.ie.ac.cn f Corresponding author. Tel.: +86-10-58887191; fax: +86-10-58887191. E-mail address: jbwang@mail.ie.ac.cn

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference doi:10.1016/j.proeng.2016.11.501

1. Introduction

Resonant pressure sensors offer the advantages of high accuracy, long-term stability and quasi-digital output compared with other types of pressure sensors [1, 2]. However, temperature drift is a key concern for resonant pressure sensors where temperature variations can cause stress changes in resonators leading to frequency drifts, and thus compromised performances in pressure measurement. To address this issue, polynomial fitting has been used for temperature compensation [3], which relies on the fitting functions between inputs of two resonant frequencies and outputs of pressure under measurement. However, the compensated precision of the method is questionable. As a machine learning algorithm, support vector machine based statistical theories were also proposed to address the issue of temperature compensation, which also leads to compromised results in term of compensation accuracy.

Compared to support vector machine, least squares support vector machine add the sum value of error squares in the target function [4], which can significantly improve the compensation accuracy. However, no previous work was conducted on temperature compensation of resonant pressure sensors with least squares support vector machine and the compensation performances of polynomial fitting, support vector machine and least squares support vector machine have not been previously compared.

In this study, we proposed a differential output resonant pressure sensor with double "H" type resonators. Based on the double resonator structure, a compensation approach leveraging the least squares support vector machine was put forward in this study, which reported the maximum temperature drift of 2.0 Pa over the full pressure and temperature scale (temperature range of -40 °C to 70 °C and pressure range of 20 kPa to 260 kPa), validating the effectiveness of the new algorithm in temperature compensation.

2. Device structure

Fig. 1. Top view (a) and back view (b) of the resonant pressure sensor.

In this study, we proposed a differential output resonant pressure sensor with double "H" type resonators (see Fig. 1) where the pressure under measurement was translated to resonant frequency output. In order to obtain a high Q factor of the resonators, the resonators were vacuum packaged through anodic bonding. Through-via-holes were formed on the handle layer of the SOI wafer for wire interconnection.

The proposed resonant pressure sensor consisted of two resonators and a pressure sensitive diaphragm. Each resonator contained an "H" type resonant beam immobilized on the pressure-sensitive diaphragm. In this device, the stress of the diaphragm was transferred to the resonant beams through the anchor after the pressure was applied to the diaphragm. The tensile stress was produced in the central beam (near the center of the diaphagm) and the compressive stress was produced in the side beam (near the border of the diaphragm), leading to a differential output featured with an increase in the resonant frequency of the central beam and a frequency decrease in the side beam [5].

Due to the uncertainties of the microfabrication, the dimensions of the two resonant beams cannot match each other exactly, and thus a difference in the temperature drift of two beams was noticed. The maximal error due to temperature variations was quantified as 8901.4 Pa (see Fig. 2) when the sensor worked in the differential mode. Thus, temperature compensation is necessary to address the issue of temperature drift.

Fig. 2. Measurement errors of full pressure scale before compensation.

3. Least squares support vector machine for temperature compensation

The temperature compensation process of resonant pressure sensors with least squares support vector machine was described in Fig. 3. Initially, all the measured data in the full pressure and temperature scales were divided into training data and test data where a proper model was chosen to form a connection between measured data and calibration data. The training data were then used to obtain the parameters of the model which was used to compensate the pressure under measurement using the test data.

Normalize all the measured data

Divide all the data into training data and test data

Train the model with

optimized parameters --

Test the test data with the training model

Initialize the model with the default parameters

Search for optimized

parameters of the model using training data

Anti normalize the predicted value

C Compensated \ pressure J

Fig. 3. Flow chart of temperature compensation with least squares support vector machine.

4. Experimental results

Fig. 4. (a) Measurement errors with three-order polynomial fitting after compensation. (b) Measurement errors with support vector machine after

compensation, which contains both training data and test data.

The error is the difference of the experimental results and the compensated pressure values. The 3D surface plot of this error with two conventional temperature compensation algorithms which are support vector machine and polynomial fitting is shown in Fig. 4.

Fig. 4(a) shows the temperature compensation based on three-order polynomial fitting. The average error was 3.1 Pa and the maximal error was -14.3 Pa in the full pressure scale. Fig. 4(b) shows the temperature compensation based on support vector machine where the averaged error was 18.2 Pa and the maximal error was -42.0 Pa in the full pressure scale. Thus, two conventional algorithms can address the issue of temperature compensation to an extent, with compromised results in term of compensation accuracy.

The result of temperature compensation with least squares support vector machine is shown in Fig. 5. The average error was quantified as 0.56 Pa and the maximal error was 2.0 Pa of the full temperature and pressure scale (20 kPa ~ 260 kPa, and -40 °C ~ 70 °C), which was largely reduced compared with the results relying on support vector machine and polynomial fitting. These results confirm that least squares support vector machine can function as an effective approach to address the issue of temperature drift during the measurement.

Fig. 5. Measurement errors with least squares support vector machine after compensation, which contains both training data and test data.

5. Conclusions

This paper presents a resonant pressure sensor capable of temperature compensation with least squares support vector machine. Compared with two conventional algorithms which are support vector machine and polynomial fitting, the new algorithm based on least squares support vector machine can effectively improve the precision of temperature compensation. Experimental results showed that the maximum temperature drift was less than 2.0 Pa of the full pressure and temperature scale (temperature range of -40 °C to 70 °C and pressure range of 20 kPa to 260 kPa), validating the effectiveness of the new algorithm in temperature compensation.

Acknowledgements

This work is supported by the National Basic Research Program of China (Grant No. 2014CB744600), the National Sciences Foundation of China (Grant No. 61431019 and 61372054), and the National Key Foundation for Exploring Scientific Instrument (No.2013YQ12035703) and Natural Science Foundation of Beijing (4152056).

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T/°C -40 50 p/kpa

References