Sensors & Transducers 2015 by IFSA Publishing, S. L.

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1 Sensors & Transducers 2015 by IFSA Publishing, S. L. Improved Performance in Soil Resistivity Measurement through Nonlinear Data Fitting 2* T. Islam and 1 Z. Chik 1 Department of Civil and Structural Engineering Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia Bangi, Selangor, Malaysia 2 Department of Electrical and Electronics Engineering, Faculty of Computer Science and Engineering, PSTU, Bangladesh * Tel.: , fax: +60(3) staohidul@yahoo.com Received: 21 May 2015 /Accepted: 22 June 2015 /Published: 30 June 2015 Abstract: This paper shows the improved performance in measurement of near surface soil resistivity through nonlinear data fitting criteria. The soil electric sensors use apparent resistivity to get near surface soil properties and profiles through in field investigations. To estimate the near surface soil characteristics based on soil apparent resistivity is erroneous because of the empirical relationship between probe distances and depth of soil profile. Iteration of data fitting is used until determination of coefficient, R 2 becomes to be 1 or nearby 1. The performance of obtaining reliable soil apparent resistivity is shown through the experiment with Matlab The nobility of our research is to obtain reliable soil characteristics for a wide range of applications in geotechnical investigations. Copyright 2015 IFSA Publishing, S. L. Keywords: Electrical conductivity, Soil resistivity, Noise reduction, Data fitting. 1. Introduction Accurate soil electrical resistivity measurements are very important for determining the specific soil properties in geotechnical characteristics. Soil electric resistivity is used for hydrological applications [3] and agricultural applications [2, 10]. Soil electrical resistivity is also used to determine the dry density of soil, salinity and porosity [4, 11, 15], chemical contamination of soil [1, 6] in geotechnical investigations. The particle shape of soils, soil water contents, temperature or salt contents influence important transport properties such as electrical conductivity of soil [12]. The basic principle of the soil electrical resistivity measurements is that when a constant voltage is applied to one of the two probes placed in the soil the current that flows between the probes is inversely proportional to the resistance of the soil [7]. Using soil apparent resistivity is crucial in geotechnical characterizations because it is easy to set up in field [11]. To determine the near surface soil properties, resistivity of soil is observed and measured through electrical probes penetrated in near surface soil shown as Fig. 1. The conventional soil resistivity measurements are erroneous for including empirical relationship in surface soil profile. Moisture contents of soil also affect the soil resistivity measurements and can change interpretation of soil properties through apparent resistivity. However, very limited work has been done on the technologies to be used to obtain 157

2 accurate soil characteristics. Takahashi and Kawase [14] also uses measuring gauge conception in multilayer earth structure to obtain the matching of apparent resistivity data. Though there is consideration of multilayer soil structure, this criterion is used for matching of nonlinear apparent resistivity data. The limitation of this method is that the precision of the method is not very high due to the difficulties to cover all the situations by the gauges. I Technology and Innovation of Malaysia. The study of soil characterization through electrical resistivity and the analysis is performed using MATLAB The concept of soil properties measurement through electrical signal is developed based on the research of Friedman [5] and Islam & Chik [17]. According to fundamental Electrical equation E = gradψ (1) From the continuity condition of current, we get div J = 0 (2) v ψ ψ ψ ψ σ ψ σ ψ σ = x y z σ x x y y z z (3) z a h U1st layer 2 nd layer 3 rd layer Fig. 1. Soil resistivity measurements using four points probe. There is also previous study to match apparent resistivity data including matching of kernel function and nonlinear multivariable equation [8, 16]. This is far complex to use this above criteria for matching of apparent resistivity data based on nonlinear multivariable equation. The advancement in numerical analysis is very significant due to obtain reliable outcomes of soil resistivity measurements. Incorporating nonlinear data fitting criteria with soil resistivity measurements are important to obtain reliable outcomes in soil site investigations. Levenberg Marquardt method is included as fitting criteria of nonlinear apparent resistivity data. Experiments are carried out through data fitting in Matlab programming. Initially, matching of dataset is performed and R 2 is obtained. The programming iteration is stopped where R 2 is 1 or close to 1. Collecting soil apparent resistivity data is used in experiment of data fitting programming with Matlab Performance is observed as comparing R 2 value in fitting criteria. 2. Methodology The research study on soil apparent resistivity is carried out at University Kebangsaan Malaysia (UKM) with the cooperation of Ministry of Science, By introducing cylindrical coordinates (r,z), we obtain ψ ψ ψ ψ σ = 0 r r r z z σ z (4) A general solution on scalar potential can be written as 0 ( ) ψ = F( λ) R λ, r Z( λ, z) dλ (5) This potentiality is implemented in obtaining soil resistivity through potential gradient as E J = (6) ρ This is the Ohm s law where j is the current density, E is the potential gradient and ρ is the resistivity of the medium. For two layer model, the resistivity corresponding to probe distance is considered as apparent resistivity. Fluke 1625 is used in our research as four probes Wenner method to obtain apparent resistivity of near surface soil shown as Fig. 2. There are the nonlinear fitting criteria implemented on soil apparent resistivity data. Consideration of Levenberg- T Marquardt (LM) method as arg min d d shows ab, the fitting of nonlinear apparent resistivity data. Here and d T =[d 1,d 2,.d n ] T (7) d = [ y f( x; a, b)] (8) i i i 158

3 The LM algorithm requires the Jacobian matrix of the vector d. The Jacobian matrix of the vector d is given as d1 d1 a b d2 d2 J = a b dn d n a b (9) Figure shows the data fitting of nonlinear data of soil apparent resistivity. This apparent resistivity data is plotted corresponding to depth where depth parameter is obtained from probes distances considering empirical relationship. Statistical analysis based on determination of coefficient, R 2 is also considered to get more reliability in setting of depth corresponding soil apparent resistivity profile. This analysis is carried out using programming of Matlab Results and Discussions Probes Fluke earth ground tester, model 1625 Recent advancements in electrical and numerical study have improved the ability to collect, process, and analyze data to manifest reliable subsurface soil properties of near surface soil profile. Soil resistivity measurements are an important parameter for soil monitoring system in geotechnical investigations. Though researchers show soil apparent resistivity for multilayer soil structure, soil apparent resistivity is obtained up to now through two layer model in practical. Usually, the spacing between two adjacent probes is increased successively along a linear survey line to obtain soil apparent resistivity as shown in Fig. 3. Acquired multiple records are processed to produce a 1-D soil resistivity profile in soil investigations. Obtaining soil apparent resistivity is not more reliable for including empirical relationship between probe distances and depth in soil characterizations. Fig. 2. Soil apparent resistivity measurements in UKM. Fig. 3. Soil characterization with apparent resistivity using two-layer model. In the geotechnical investigations, soil resistivity is used to get near surface soil characteristics [4, 9]. Table 1 shows the typical soil resistivity range to show the resistivity values for several types of soil. To maximize the effectiveness of soil site investigations, the depth, thickness of layer, soil type of different layer across the field have to be obtained consistently in geotechnical characterizations. The unreliable outcomes are observed clearly at very near surface soil in graph of soil resistivity measurements shown by dot symbol in Fig. 4. Using Levenberg- Marquardt method fits nonlinear data of 159

4 soil resistivity measurements. The method of nonlinear data fitting is performed through the best-fit curve shown in Fig. 4. The processed data is used in soil profile that has the minimal sum of the deviations squared (least square error) from the given set of data. Apparent resistivity data is taken as true resistivity data and set according to depth in soil profile. Fig. 4 shows the setting of apparent resistivity data corresponding to depth. Minimization of root mean square error (RMSE) is crucial in this data fitting criteria. Table 1. Resistivity values for several types of soils and water. Types of Soil Typical Resistivity (Ohm-m ) Usual Limit (Ohm-m) Clay 50 10~ 70 Clay & sand mixtures ~150 Shale, slates, sandstone ~120 Peat, loam & mud ~250 Sand ~1000 Gritstone ~ In this analysis, final fitting shows R 2 as 0.82 which is obtained as best fit of data in the iteration. Setting of this apparent resistivity profile is useful to fit nonlinear data corresponding to depth with maximum determination of coefficient. This fitting criterion improves the performance with reduction of the feasibility of erroneous outcomes in soil apparent resistivity profile. Seedher and Arora [13] shows two layer resistivity model using four-probe Wenner method for obtaining near surface soil. Though this apparent resistivity can be used to get soil properties, these are limited to obtain accurate results when the initial values were radically different from those obtained by actual convergence. Therefore, it may be necessary to have more than one trial with different sets of initial values. Apparent resistivity (ohm-m) Resistivity profile 1st fitting 2nd fitting Final fitting Resistivity profile Data fitting Depth (m) Apparent resistivity (ohm-m) Fig. 5. Iteration of fitting of soil apparent resistivity profile. Table 2. Performance evaluation of different fitting criteria Depth (m) Fig. 4. Setting of apparent resistivity data corresponding to depth. Determination of coefficient, R 2 is also significant to fit this nonlinear data. Iteration of this fitting is also used in this study to get the best fit of soil apparent resistivity data. Fig. 5 shows the several fittings to obtain best fit in soil resistivity profile. Parameter of RMSE and R 2 are considered in comparison to select which data setting is closer to measured resistivity profile in the iteration. Table 2 shows the RMSE and R 2 value for the data fitting criteria of Fig. 5. In this iteration, 1 st data fitting shows RMSE as and R 2 as 0.79 which is very closer to the 2 nd fitting of apparent resistivity data. 3 rd fitting shows the improvement of data fitting where the R 2 is as Experiments MSE RMSE R 2 value 1 st fitting e nd fitting e rd fitting e Final fitting e Zou et al. [16] shows the better results in obtaining soil apparent resistivity considering the matching the apparent resistivity profile at various depth. This is also time consuming for consideration of several apparent resistivity profiles. This criterion is also complex for iteration of kernel function matching. In our study simple nonlinear data fitting criteria is included according to depth. Statistical parameters are included for comparison to get best fit in soil apparent resistivity profile. 4. Conclusions Nonlinear data fitting criteria is included to obtain reliable apparent resistivity profile for geotechnical 160

5 investigations. This fitting criteria is much simpler compared to other model. Nonlinear data fitting criteria with LM is also described in this study. Best fitting of apparent resistivity profile is obtained though highest coefficient of determination, R 2. This method would be enhanced in future study including more statistical parameters in data fitting criteria. Acknowledgments This research is sponsored by Research Project of Science Fund No SF0681 from Ministry of Science, Technology and Innovation of Malaysia and DPP of Universiti Kebangsaan Malaysia. References [1]. R. Clement, M. Descloitres, T. Gunther, L. Oxarango, C. Morra, J. P. Laurent, J. P. Gourc, Improvement of electrical resistivity tomography for leachate injection monitoring, Waste Management, Vol. 30, 2010, pp [2]. D. L. Corwin and S. M. Lesch, Apparent soil electrical conductivity measurements in agriculture, Computers and Electronics in Agriculture, Vol. 46, 2005, pp [3]. I. Cousin, A. Besson, H. Bourennane, C. Pasquier, B. Nicoullaud, D. King, G. Richard, From spatialcontinuous electrical resistivity measurements to the soil hydraulic functioning at the field scale, Computes Rendus Geoscience, Vol. 341, 2009, pp [4]. J. A. Doolittle, K. A. Sudduth, N. R. Kitchen, S. J. Indorante, Estimating depths to claypans using electromagnetic induction methods, J. Soil and Water Conservation, Vol. 49, 1994, pp [5]. S. P. Friedman, Soil properties influencing apparent electrical conductivity: a review, Computers and Electronics in Agriculture, Vol. 46, 2005, pp [6]. R. K. Frohlich, P. J. Barosh, T. Boving, Investigating changes of electrical characteristics of the saturated zone affected by hazardous organic waste, Journal of Applied Geophysics, Vol. 64, 2008, pp [7]. R. Herman, An introduction to electrical resistivity in geophysics, Am. J. Phys., Vol. 69, 9, 2001, pp [8]. M. Kang, C. J. Boo, H. C. Kim & J. M. Zurada, Estimating soil parameters using the kernel function, Computational Science and Its Applications ICCSA 2010, Lecture Notes in Computer Science, Vol. 6017, 2010, pp [9]. J. D. McNeill, Electromagnetic terrain conductivity measurement at low induction numbers, Technical note TN-6, Geonics Limited, Mississauga, Ontario, [10]. D. Michot, Y. Benderitter, A. Dorigny, B. Nicoullaud, D. King, A. Tabbagh, Spatial and temporal monitoring of soil water content with an irrigated corn crop cover using surface electrical resistivity tomography, Water Resources Research, Vol. 39, 5, 2003, p [11]. J. M. Sabatier, D. C. Sokol, C. K. Frederickson, M. J. M. Rdmkensb, E. H. Grissingerb, J. C. Shipps, Probe microphone instrumentation for determining soil physical properties: testing in model porous materials, Soil Technology, Vol. 8, 1996, pp [12]. A. Samouelian, I. Cousin, A. Tabbagh, A. Bruand, G. Richard, Electrical resistivity survey in soil science: a review, Soil & Tillage Research, Vol. 83, 2005, pp [13]. H. R. Seedher and J. K. Arora, Estimation of two layer soil parameters using finite Wenner resistivity expressions, IEEE Transactions on Power Delivery, Vol. 7, 3, 1992, pp [14]. T. Takahashi and T. Kawase, Analysis of apparent resistivity in a multi-layer earth structure, IEEE Transactions on Power Delivery, Vol. 5, 2, 1990, pp [15]. G. L. Yoon, J. B. Park, Sensitivity of leachate and fine contents on electrical resistivity variations of sandy soils, Journal of Hazardous Materials, Vol. 84, 2001, pp [16]. J. Zou, J. L. He, R. Zeng, W. M. Sun, G. Yu and S. M. Chen, Two-stage algorithm for inverting structure parameters of the horizontal multilayer soil, IEEE Transactions on Magnetics, 40, 2, 2004, pp [17]. T. Islam, Z. Chik, Simple equation guide for multilayer earth structure with soil electrical properties, in Proceedings of the IEEE Conference on Open Systems (ICOS), September, 2011, pp Copyright, International Frequency Sensor Association (IFSA) Publishing, S. L. All rights reserved. ( 161