Full Text:   <2527>

Summary:  <1459>

CLC number: O231

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2019-09-06

Cited: 0

Clicked: 6456

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Mitar Simić

http://orcid.org/0000-0002-8300-022X

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.3 P.476-490

http://doi.org/10.1631/FITEE.1900112


Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware


Author(s):  Mitar Simić, Zdenka Babić, Vladimir Risojević, Goran M. Stojanović

Affiliation(s):  Faculty of Electrical Engineering, University of Banja Luka, Banja Luka 78000, Bosnia and Herzegovina; more

Corresponding email(s):   mitar.simic@etf.unibl.org

Key Words:  2R-1C model, Embedded systems, Parameter estimation, Non-iterative methods, Quadratic interpolation


Share this article to: More <<< Previous Article|

Mitar Simić, Zdenka Babić, Vladimir Risojević, Goran M. Stojanović. Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(3): 476-490.

@article{title="Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware",
author="Mitar Simić, Zdenka Babić, Vladimir Risojević, Goran M. Stojanović",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="3",
pages="476-490",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900112"
}

%0 Journal Article
%T Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware
%A Mitar Simić
%A Zdenka Babić
%A Vladimir Risojević
%A Goran M. Stojanović
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 3
%P 476-490
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900112

TY - JOUR
T1 - Non-iterative parameter estimation of the 2R-1C model suitable for low-cost embedded hardware
A1 - Mitar Simić
A1 - Zdenka Babić
A1 - Vladimir Risojević
A1 - Goran M. Stojanović
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 3
SP - 476
EP - 490
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900112


Abstract: 
parameter estimation of the 2R-1C model is usually performed using iterative methods that require high-performance processing units. Consequently, there is a strong motivation to develop less time-consuming and more power-efficient parameter estimation methods. Such low-complexity algorithms would be suitable for implementation in portable microcontroller-based devices. In this study, we propose the quadratic interpolation non-iterative parameter estimation (QINIPE) method, based on quadratic interpolation of the imaginary part of the measured impedance, which enables more accurate estimation of the characteristic frequency. The 2R-1C model parameters are subsequently calculated from the real and imaginary parts of the measured impedance using a set of closed-form expressions. Comparative analysis conducted on the impedance data of the 2R-1C model obtained in both simulation and measurements shows that the proposed QINIPE method reduces the number of required measurement points by 80% in comparison with our previously reported non-iterative parameter estimation (NIPE) method, while keeping the relative estimation error to less than 1% for all estimated parameters. Both non-iterative methods are implemented on a microcontroller-based device; the estimation accuracy, RAM, flash memory usage, and execution time are monitored. Experiments show that the QINIPE method slightly increases the execution time by 0.576~ms (about 6.7%), and requires 24% (1.2~KB) more flash memory and just 2.4% (32 bytes) more RAM in comparison to the NIPE method. However, the impedance root mean square errors (RMSEs) of the QINIPE method are decreased to 42.8% (for the real part) and 64.5% (for the imaginary part) of the corresponding RMSEs obtained using the NIPE method. Moreover, we compared the QINIPE and the complex nonlinear least squares (CNLS) estimation of the 2R-1C model parameters. The results obtained show that although the estimation accuracy of the QINIPE is somewhat lower than the estimation accuracy of the CNLS, it is still satisfactory for many practical purposes and its execution time reduces to 1/45−1/30.

适于低成本嵌入式硬件的2R-1C模型非迭代参数估计

Mitar SIMIĆ1, Zdenka BABIĆ1, Vladimir RISOJEVIĆ1, Goran M. STOJANOVIĆ2
1巴尼亚卢卡大学电气工程学院,波黑巴尼亚卢卡,78000
2诺维萨德大学技术科学学院,塞尔维亚共和国诺维萨德,21000

摘要:2R-1C模型的参数估计常运用需要高性能处理单元的迭代方法,从而激励我们研究更省时且更节能的参数估计方法。这些低复杂度的算法将更适于便携式微机设备的运行。本文提出二次插值非迭代参数估计方法(QINIPE);该方法基于测量阻抗虚部的二次插值,能够更精确地估计特征频率。运用一组封闭表达式从测量阻抗的实部和虚部计算2R-1C模型的参数。对仿真和测量获得的模型阻抗数据作对比分析;结果表明,相较于我们早前提出的非迭代参数估计方法(NIPE),QINIPE能减少80%测量点,且所有估计参数的相对估计误差低于1%。两种非迭代方法均基于一个微机设备实施;检测了估计精度、RAM、闪存使用以及运行时间。实验结果表明,相较于NIPE,QINIPE轻微增加了0.576ms运行时间(约6.7%),且需要多24%(1.2KB)闪存及多2.4%(32字节)RAM。然而,QINIPE的阻抗均方根误差分别降低至NIPE对应的42.8%(实部)和64.5%(虚部)。此外,比较了QINIPE和复杂非线性最小二乘法(CNLS)对2R-1C模型参数的估计。结果表明,虽然QINIPE估计精度稍低于CNLS,其依然适合许多实际应用,且运行时间降至原来的1/45至1/30。

关键词:2R-1C模型;嵌入式系统;参数估计;非迭代方法;二次型

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Abbasbandy S, 2005. Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method. Appl Math Comput, 170(1):648-656.

[2]Al-Ali AA, Elwakil AS, Maundy BJ, et al., 2018. Extraction of phase information from magnitude-only linebreak bio-impedance measurements using a modified Kramers-Kronig transform. Circ Syst Signal Process, 37(8):3635-3650.

[3]Babolian E, Biazar J, Vahidi AR, 2004. Solution of a system of nonlinear equations by Adomian decomposition method. Appl Math Comput, 150(3):847-854.

[4]Barsoukov E, Macdonald JR, 2005. Impedance Spectroscopy: Theory, Experiment, and Applications. John Wiley & Sons, Inc., USA.

[5]Bertrand CA, Hopfer U, 2002. Measurement of membrane capacitance in epithelial monolayers. In: Wise C (Ed.), Epithelial Cell Culture Protocols. Humana Press, p.315-327.

[6]Blad B, 1996. Clinical applications of characteristic frequency measurements: preliminary in vivo study. Med Biol Eng Comput, 34(5):362-365.

[7]Boinet M, Condolf C, Goulet R, et al., 2016. Parameter identification in electrochemical impedance spectroscopy applications: analysis of sensitivity. Meet Abstr, MA2016-02:1707.

[8]Bondarenko AS, 2012. Analysis of large experimental datasets in electrochemical impedance spectroscopy. Anal Chim Acta, 743:41-50.

[9]Boukamp BA, Rolle A, 2018. Use of a distribution function of relaxation times (DFRT) in impedance analysis of SOFC electrodes. Sol State Ion, 314:103-111.

[10]Cordero A, Torregrosa JR, 2007. Variants of Newton’s method using fifth-order quadrature formulas. Appl Math Comput, 190(1):686-698.

[11]Darvishi MT, Barati A, 2007. A third-order Newton-type method to solve systems of nonlinear equations. Appl Math Comput, 187(2):630-635.

[12]de Lorenzo A, Andreoli A, Matthie J, et al., 1997. Predicting body cell mass with bioimpedance by using theoretical methods: a technological review. J Appl Physiol, 82(5):1542-1558.

[13]Dong TK, Kirchev A, Mattera F, et al., 2011. Dynamic modeling of Li-ion batteries using an equivalent electrical circuit. J Electrochem Soc, 158(3):A326-A336.

[14]Ferreira J, Seoane F, Ansede A, et al., 2010. AD5933-based spectrometer for electrical bioimpedance applications. J Phys, 224(1):012011.

[15]Ferreira J, Seoane F, Lindecrantz K, 2013. Portable bioimpedance monitor evaluation for continuous impedance measurements. Towards wearable plethysmography applications. Proc 35th Annual Int Conf of the IEEE Engineering in Medicine and Biology Society, p.559-562.

[16]Freeborn TJ, Elwakil AS, Maundy B, 2017. Variability of cole-model bioimpedance parameters using magnitude-only measurements of apples from a two-electrode configuration. Int J Food Prop, 20(S1):S507-S519.

[17]Gheorghe AG, Marin CV, Constantinescu F, et al., 2012. Parameter identification for a new circuit model aimed to predict body water volume. Adv Electr Comput Eng, 12(4):83-86.

[18]Golbabai A, Javidi M, 2007. A new family of iterative methods for solving system of nonlinear algebric equations. Appl Math Comput, 190(2):1717-1722.

[19]Holevinsky KO, Nelson DJ, 1998. Membrane capacitance changes associated with particle uptake during phagocytosis in macrophages. Biophys J, 75(5):2577-2586.

[20]Hotka M, Zahradnik I, 2014. Membrane capacitance changes due to temperature increase in rat cardiac myocytes. Biophys J, 106(2 Suppl 1):121A-122A.

[21]Kern R, Sastrawan R, Ferber J, et al., 2002. Modeling and interpretation of electrical impedance spectra of dye solar cells operated under open-circuit conditions. Electrochim Acta, 47(26):4213-4225.

[22]Kyle UG, Genton L, Slosman DO, et al., 2001. Fat-free and fat mass percentiles in 5225 healthy subjects aged 15 to 98 years. Nutrition, 17(7-8):534-541.

[23]Lazović G, Vosika Z, Lazarević M, et al., 2014. Modeling of bioimpedance for human skin based on fractional distributed-order modified cole model. FME Trans, 42(1):74-81.

[24]Manjakkal L, Cvejin K, Kulawik J, et al., 2014. Fabrication of thick film sensitive RuO2-TiO2 and Ag/AgCl/KCl reference electrodes and their application for pH measurements. Sens Actuat B, 204:57-67.

[25]Manjakkal L, Djurdjic E, Cvejin K, et al., 2015a. Electrochemical impedance spectroscopic analysis of RuO2 based thick film pH sensors. Electrochim Acta, 168:246-255.

[26]Manjakkal L, Cvejin K, Bajac B, et al., 2015b. Microstructural, impedance spectroscopic and potentiometric analysis of Ta2O5 electrochemical thick film pH sensors. Electroanalysis, 27(3):770-781.

[27]Maundy BJ, Elwakil AS, Allagui A, 2015. Extracting the parameters of the single-dispersion cole bioimpedance model using a magnitude-only method. Comput Electr Agric, 119:153-157.

[28]Moss P, Au G, Plichta EJ, et al., 2008. An electrical circuit for modeling the dynamic response of Li-ion polymer batteries. J Electrochem Soc, 155(12):A986-A994.

[29]Noor MA, 2007. Fifth-order convergent iterative method for solving nonlinear equations using quadrature formula. J Math Contr Sci Appl, 1:241-249.

[30]Ortega JM, Rheinboldt WC, 1970. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, USA.

[31]Pena AA, 2009. A feasibility study of the suitability of an AD5933-based spectrometer for EBI applications. University of Boras, Boras, p.2009-2010.

[32]Qiao GF, Wang W, Duan W, et al., 2012. Bioimpedance analysis for the characterization of breast cancer cells in suspension. IEEE Trans Biomed Eng, 59(8):2321-2329.

[33]Ramírez-Chavarría RG, Quintana-Carapia G, Müller MI, et al., 2018. Bioimpedance parameter estimation using fast spectral measurements and regularization. IFAC-PapersOnLine, 51(15):521-526.

[34]Sanchez B, Schoukens J, Bragos R, et al., 2011. Novel estimation of the electrical bioimpedance using the local polynomial method. Application to in vivo real-time myocardium tissue impedance characterization during the cardiac cycle. IEEE Trans Biomed Eng, 58(12):3376-3385.

[35]Sanchez B, Rojas CR, Vandersteen G, et al., 2012. On the calculation of the D-optimal multisine excitation power spectrum for broadband impedance spectroscopy measurements. Meas Sci Technol, 23(8):085702.

[36]Sanchez B, Bandarenka AS, Vandersteen G, et al., 2013. Novel approach of processing electrical bioimpedance data using differential impedance analysis. Med Eng Phys, 35(9):1349-1357.

[37]Sánchez Terrones B, Louarroudi E, Pintelon R, et al., 2013. Modeling the non-stationary behaviour of time-varying electrical bioimpedance. Proc 19th IMEKO Symp Measurements of Electrical Quantities, p.378-384.

[38]Santos-Sacchi J, 2004. Determination of cell capacitance using the exact empirical solution of δY/δCm and its phase angle. Biophys J, 87(1):714-727.

[39]Schulz H, Teske D, Penven D, et al., 2006. Fat-free mass from two prediction equations for bioelectrical impedance analysis in a large German population compared with values in Swiss and American adults: reasons for a biadata project. Nutrition, 22(9):973-975.

[40]Seoane F, Ferreira J, Sanchéz JJ, et al., 2008. An analog front-end enables electrical impedance spectroscopy system on-chip for biomedical applications. Physiol Meas, 29(6):S267-S278.

[41]Simić M, 2014. Complex impedance measurement system for environmental sensors characterization. Proc 22nd Telecommunications Forum Telfor, p.660-663.

[42]Simić M, Stojanović GM, 2017. Compact electronic system for complex impedance measurement and its experimental verification. Proc European Conf on Circuit Theory and Design, p.1-4.

[43]Simić M, Babić Z, Risojević V, et al., 2016. A novel non-iterative method for real-time parameter estimation of the Fricke-Morse model. Adv Electr Comput Eng, 16(4): 57-62.

[44]Simić M, Babić Z, Risojević V, et al., 2017a. A novel approach for parameter estimation of Fricke-Morse model using differential impedance analysis. Proc Int Conf on Medical and Biological Engineering, p.487-494.

[45]Simić M, Manjakkal L, Zaraska K, et al., 2017b. TiO2-based thick film pH sensor. IEEE Sens J, 17(2):248-255.

[46]Vargas-Bernal R, de la Cruz Blas CA, G‘omez-Polo C, 2018. Electrical circuit modeling of sensor magneto-impedances with a square-root frequency dependence. IEEE Sens J, 18(2):623-628.

[47]Wang CS, Nehrir MH, Shaw SR, 2005. Dynamic models and model validation for PEM fuel cells using electrical circuits. IEEE Trans Energy Conv, 20(2):442-451.

[48]Wang Z, Luo M, Geng Y, et al., 2018. A model to compare convective and radiant heating systems for intermittent space heating. Appl Energy, 215:211-226.

[49]Ward LC, Heitmann BL, 1998. Multiple frequency bioelectrical impedance analysis (MFBIA) and R-X plots in the assessment of obesity. Proc Aust Soc Study Obesity, 7:20.

[50]Ward LC, Heitmann BL, Craig P, et al., 2000. Association between ethnicity, body mass index, and bioelectrical impedance: implications for the population specificity of prediction equations. Ann N Y Acad Sci, 904(1):199-202.

[51]Yousri DA, AbdelAty AM, Said LA, et al., 2017. Biological inspired optimization algorithms for cole-impedance parameters identification. AEU-Int J Electron Commun, 78:79-89.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE