DOI: https://doi.org/10.15587/1729-4061.2019.156959

Construction and investigation of a method for measuring the non-stationary pressure using a wavelet transform

Myroslav Tykhan, Taras Repetylo, Serhii Kliuchkovskyi, Olha Markina

Abstract


Automated control systems badly need measurements of fast-changing non-stationary physical quantities in real time, or close to that. In this area, there is a separate group of tasks on measuring the non-stationary pressure in liquids and gases.

This paper demonstrates that measuring the non-stationary pressure in real time, or close to that, represents a problem on restoring an input signal, which, in terms of mathematics, belongs to the class of ill-posed problems (according to J. Hadamard). We have derived a solution to the inverse problem of measurement that is based on a mathematical model for measuring transformation enabled by a pressure sensor. Based on this solution, we have constructed a measuring method, which implies the wavelet processing of the sensor's output signal. In this case, we suggest that such basic functions of wavelet transformation should be selected that are the modification of the pulse transition function of the sensor.

 This paper reports an experimental study into the feasibility of the developed method, based on the measurement of the simulated pressure pulse. A pressure pulse is simulated by dropping a ball of the calibrated mass onto the sensor's membrane. We have proposed a measurement scheme for determining the duration of touch between the ball and the membrane. Testing the accuracy of the method implies comparing the actual mass of the ball with that derived from the sensor's output signal. The proposed method has demonstrated high accuracy because the maximum relative error in determining the mass of the falling ball was only 0.65 %.

The proposed method for measuring the non-stationary pressure could be used in control systems that require the high-speed dynamic correction of a measurement error. Specifically, these include control system in aerospace engineering, testing complexes, military technology, scientific research

Keywords


measurement of non-stationary pressure; inverse measurement problem; real-time measurement method; wavelet transform

References


Kraft, M., White, ‎N. M. (Eds.) (2013). MEMS for Automotive and Aerospace Applications. Woodhead Publishing Limited. doi: https://doi.org/10.1533/9780857096487

Markelov, I. G. (2009). Kompleks datchikov davleniya dlya ekspluatacii na ob'ektah atomnoy energetiki. Datchiki i sistemy, 11, 24–25.

Custom Pressure Sensors for the Aerospace Industry. Merit Sensor. Available at: https://meritsensor.com

Sensors for Aerospace & Defense. PCB Piezotronics. Available at: https://www.pcb.com/aerospace

Hadamard, J. (1923). Lectures on Cauchy’s problem in linear partial differential equations. New York: Dover Publications, 338.

Tihonov, A. N., Arsenin, V. Yu. (1979). Metody resheniya nekorektnyh zadachMoscow: Nauka, 228.

Tikhonov, A. N. (1983). Regularizing algorithms and prior information. Moscow: Nauka, 197.

Solopchenko, G. N. (1986). Methods for taking into account the priori information in the correction of the measurement error in the measurement computation channel in the dynamic mode. Research in the field of evaluation of measurement errors: Digest of scientific proceedings VNIIM. Moscow, 27–31.

Burovtseva, T. I., Zvyagintsev, A. M. (1999). Correction of sensor error by the methods of fuzzy logic. Sensors and systems, 7, 14–21.

Tykhan, M. O. (2006). Pat. No. 75915 UA. Dynamic pressure transducer. No. 2003109369; declareted: 17.10.2003; published: 15.06.2006, Bul. No. 6.

Shamrakov, A. L. (2005). Perspektivy razvitiya p'ezoelektricheskih datchikov bystroperemennyh, impul'snyh i akusticheskih davleniy. Sensors & Systems, 9.

Jin, M., Li, C. (2018). Non-Stationary Wind Pressure Prediction Based on A Hybrid Decomposition Algorithm of Wavelet Packet Decomposition and Variational Mode Decomposition. IOP Conference Series: Earth and Environmental Science, 189, 052038. doi: https://doi.org/10.1088/1755-1315/189/5/052038

Park, S.-G., Sim, H.-J., Lee, H.-J., Oh, J.-E. (2008). Application of non-stationary signal characteristics using wavelet packet transformation. Journal of Mechanical Science and Technology, 22 (11), 2122–2133. doi: https://doi.org/10.1007/s12206-007-1218-z

Komissarov, A. A., Kurochkin, V. V., Semernin, A. N. (2017). Ispol'zovanie fil'tra Kalmana dlya fil'tracii znacheniy, poluchaemyh s datchikov. Elektronniy sbornik statey po materialam LIII studencheskoy mezhdunarodnoy zaochnoy nauchno-prakticheskoy konferencii. Novosibirsk, 166–170. Available at: https://sibac.info/archive/technic/5(52).pdf

Zhang, Z. G., Tsui, K. M., Chan, S. C., Lau, W. Y., Aboy, M. (2008). A novel method for nonstationary power spectral density estimation of cardiovascular pressure signals based on a Kalman filter with variable number of measurements. Medical & Biological Engineering & Computing, 46 (8), 789–797. doi: https://doi.org/10.1007/s11517-008-0351-x

Zhang, J., Liu, Q., Zhong, Y. (2008). A Tire Pressure Monitoring System Based on Wireless Sensor Networks Technology. 2008 International Conference on MultiMedia and Information Technology. doi: https://doi.org/10.1109/mmit.2008.177

Yang, L.-J., Lai, C.-C., Dai, C.-L., Chang, P.-Z. (2005). A Piezoresistive Micro Pressure Sensor Fabricated by Commercial DPDM CMOS Process. Tamkang Journal of Science and Engineering, 8 (1), 67–73.

Kistler. Measure, analyze, innovate. Available at: https://www.kistler.com

Carter, S., Ned, A., Chivers, J., Bemis, A. Selecting Piezoresistive vs. Piezoelectric Pressure Transducers. Available at: https://www.kulite.com/assets/media/2018/01/Piezoresistive_vs_Piezoelectric.pdf

Vasylenko, G. I. (1979). Theory of restoration of signals: About reduction to the ideal device in physics and technique. Мoscow: Sovetskoe Radio, 272.

Merry, R. J. E. (2005). Wavelet theory and applications: a literature study. (DCT rapporten; Vol. 2005.053). Eindhoven: Technische Universiteit Eindhoven.

Addison, P. S. (2002). The Illustrated Wavelet Transform Handbook. CRC Press, 368. doi: https://doi.org/10.1201/9781420033397

Lee, D. T. L., Yamamoto, A. (1994). Wavelet Analysis: Theory and Applications. Hewlett-Packard, 44–52.

Tykhan, M. (2007). Choice of parameters of calibrating signal for the receive of transient characteristic of pressures sensors. Sensors and systems, 9, 17–19.


GOST Style Citations


MEMS for Automotive and Aerospace Applications / M. Kraft, ‎N. M. White (Eds.). Woodhead Publishing Limited, 2013. doi: https://doi.org/10.1533/9780857096487 

Markelov I. G. Kompleks datchikov davleniya dlya ekspluatacii na ob'ektah atomnoy energetiki // Datchiki i sistemy. 2009. Issue 11. P. 24–25.

Custom Pressure Sensors for the Aerospace Industry. Merit Sensor. URL: https://meritsensor.com

Sensors for Aerospace & Defense. PCB Piezotronics. URL: https://www.pcb.com/aerospace

Hadamard J. Lectures on Cauchy’s problem in linear partial differential equations. New York: Dover Publications, 1923. 338 p.

Tihonov A. N., Arsenin V. Yu. Metody resheniya nekorektnyh zadach. 2-e izd. Moscow: Nauka, 1979. 228 p.

Tikhonov A. N. Regularizing algorithms and prior information. Moscow: Nauka, 1983. 197 p.

Solopchenko G. N. Methods for taking into account the priori information in the correction of the measurement error in the measurement computation channel in the dynamic mode // Research in the field of evaluation of measurement errors: Digest of scientific proceedings VNIIM. Moscow, 1986. P. 27–31.

Burovtseva T. I., Zvyagintsev A. M. Correction of sensor error by the methods of fuzzy logic // Sensors and systems. 1999. Issue 7. P. 14–21.

Tykhan M. O. Dynamic pressure transducer: Pat. No. 75915 UA. No. 2003109369; declareted: 17.10.2003; published: 15.06.2006, Bul. No. 6.

Shamrakov A. L. Perspektivy razvitiya p'ezoelektricheskih datchikov bystroperemennyh, impul'snyh i akusticheskih davleniy // Sensors & Systems. 2005. Issue 9.

Jin M., Li C. Non-Stationary Wind Pressure Prediction Based on A Hybrid Decomposition Algorithm of Wavelet Packet Decomposition and Variational Mode Decomposition // IOP Conference Series: Earth and Environmental Science. 2018. Vol. 189. P. 052038. doi: https://doi.org/10.1088/1755-1315/189/5/052038 

Application of non-stationary signal characteristics using wavelet packet transformation / Park S.-G., Sim H.-J., Lee H.-J., Oh J.-E. // Journal of Mechanical Science and Technology. 2008. Vol. 22, Issue 11. P. 2122–2133. doi: https://doi.org/10.1007/s12206-007-1218-z 

Komissarov A. A., Kurochkin V. V., Semernin A. N. Ispol'zovanie fil'tra Kalmana dlya fil'tracii znacheniy, poluchaemyh s datchikov // Elektronniy sbornik statey po materialam LIII studencheskoy mezhdunarodnoy zaochnoy nauchno-prakticheskoy konferencii. Novosibirsk, 2017. P. 166–170. URL: https://sibac.info/archive/technic/5(52).pdf

A novel method for nonstationary power spectral density estimation of cardiovascular pressure signals based on a Kalman filter with variable number of measurements / Zhang Z. G., Tsui K. M., Chan S. C., Lau W. Y., Aboy M. // Medical & Biological Engineering & Computing. 2008. Vol. 46, Issue 8. P. 789–797. doi: https://doi.org/10.1007/s11517-008-0351-x 

Zhang J., Liu Q., Zhong Y. A Tire Pressure Monitoring System Based on Wireless Sensor Networks Technology // 2008 International Conference on MultiMedia and Information Technology. 2008. doi: https://doi.org/10.1109/mmit.2008.177 

A Piezoresistive Micro Pressure Sensor Fabricated by Commercial DPDM CMOS Process / Yang L.-J., Lai C.-C., Dai C.-L., Chang P.-Z. // Tamkang Journal of Science and Engineering. 2005. Vol. 8, Issue 1. P. 67–73.

Kistler. Measure, analyze, innovate. URL: https://www.kistler.com

Selecting Piezoresistive vs. Piezoelectric Pressure Transducers / Carter S., Ned A., Chivers J., Bemis A. URL: https://www.kulite.com/assets/media/2018/01/Piezoresistive_vs_Piezoelectric.pdf

Vasylenko G. I. Theory of restoration of signals: About reduction to the ideal device in physics and technique. Мoscow: Sovetskoe Radio, 1979. 272 p.

Merry R. J. E. Wavelet theory and applications: a literature study. (DCT rapporten; Vol. 2005.053). Eindhoven: Technische Universiteit Eindhoven, 2005.

Addison P. S. The Illustrated Wavelet Transform Handbook. CRC Press, 2002. 368 p. doi: https://doi.org/10.1201/9781420033397 

Lee D. T. L., Yamamoto A. Wavelet Analysis: Theory and Applications // Hewlett-Packard. 1994. P. 44–52.

Tykhan M. Choice of parameters of calibrating signal for the receive of transient characteristic of pressures sensors // Sensors and systems. 2007. Issue 9. P. 17–19.







Copyright (c) 2019 Myroslav Tykhan, Taras Repetylo, Serhii Kliuchkovskyi, Olha Markina

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061