Detecting heavy metal contamination in soil usingcomplex permittivity and artificial neural networks

J.Q. Shang, W. Ding, R.K. Rowe, and L. Josic

Abstract: The use of the complex permittivity, an intrinsic electrical property of materials, to detect the presence andtype of heavy metals in soil is investigated. The soil specimens are prepared by mixing the soil with distilled anddeionized water, NaCl solutions, and copper and zinc salt solutions and compacting at known water contents. The com-plex permittivities of the soil specimens are measured in the laboratory using a custom-developed apparatus. A data-base, which includes both contaminated and uncontaminated soil specimens, is developed, with the soil water content,density, and pore-fluid salinity varying over a relatively wide range. Two artificial neural network (ANN) models aredeveloped to (i) identify whether the heavy metals are present in the soil; and, if so, (ii) distinguish the metal type,based on the complex permittivities measured on the soil specimens. The first ANN model (identification) can correctlyidentify the presence of heavy metals in 90% of cases. The second ANN model (classification) can correctly classifythe type of the heavy metal in 95% of cases. Better performance can be achieved if more complex permittivity data areavailable for the training of the networks.

Key words: heavy metals, soil contamination, contamination detection, complex permittivity, artificial neural networks.

Résumé : On étudie l’utilisation de la permittivité complexe, propriété électrique intrinsèque des matériaux, pour détec-ter la présence et le type de métaux lourds dans le sol. Les spécimens de sol sont préparés en mélangeant le sol avecde l’eau distillée et déionizée, des solutions de NaCl, et des solutions de sels de cuivre et de zinc, et en le compactantà des teneurs en eau connues. Les permittivités complexes des spécimens de sols sont mesurées en laboratoire aumoyen d’un appareil développé sur commande. Une base de données qui inclut des spécimens de sols tant contaminésque non contaminés a été développée avec une teneur en eau, une densité et une salinité du liquide interstitiel variantdans une plage relativement large. On a développé deux modèles de réseaux de neurones artificiels (ANN) pour(i) identifier la présence de métaux lourds dans le sol, et si tel est le cas, (ii) distinguer le type des métaux sur la basedes permittivités complexes mesurées dans les spécimens de sols. Le premier modèle ANN (identification) peut identi-fier correctement la présence de métaux lourds dans 90 % des cas. Le second modèle ANN (classification) peut classi-fier correctement le type des métaux lourds dans 95 % des cas. On peut obtenir une meilleure performance si plus dedonnées de permittivité complexes sont disponibles pour le calibrage des réseaux.

Mots clés : métaux lourds, contamination des sols, détection de la contamination, permittivité complexe, réseaux deneurones artificiels.

[Traduit par la Rédaction] Shang et al. 1067

Introduction

Subsurface contamination caused by heavy metals affectshuman health and the ecosystem through a number of path-ways. The toxicity, solubility, and mobility of heavy metalsare governed by chemical equilibrium of soil–water systems

and are dependent on many factors, including soil pH, pore-fluid chemistry, mineralogy, grain size, etc. With increasedawareness of the potential health and safety implications re-lated to heavy metals, government regulation of heavy metalcontamination in soil has become significantly more strin-gent over the past two decades. The methods commonlyused to detect heavy metal contamination in the subsurfaceinvolve taking soil samples and performing chemical analy-ses on these samples. Such routine sampling and analysiscan be costly and time-consuming. Therefore, fast, reliable,and quantitative in situ monitoring techniques for heavymetals may offer significant benefits in terms of both effec-tiveness and cost savings. In any subsurface monitoring orsite assessment of heavy metal contamination, two essentialtasks need to be addressed, namely, to establish whetherheavy metals are present at the site and, if so, to identify thetypes and concentrations of the contaminants. Identificationof the presence of heavy metals and classification of theheavy metal type are difficult tasks because the solubility,

Can. Geotech. J. 41: 1054–1067 (2004) doi: 10.1139/T04-051 © 2004 NRC Canada

1054

Received 30 September 2003. Accepted 17 May 2004.Published on the NRC Research Press Web site athttp://cgj.nrc.ca on 20 November 2004.

J.Q. Shang1 and W. Ding. Geotechnical Research Centre,Department of Civil and Environmental Engineering, TheUniversity of Western Ontario, London, ON N6A 5B9,Canada.R.K. Rowe. Department of Civil Engineering, Queen’sUniversity, Kingston, ON K7L 3N6, Canada.L. Josic. AMEC Earth & Environmental Ltd., Mississauga,ON L4Z 3K7, Canada.

1Corresponding author (e-mail: jqshang@uwo.ca).

chemical speciation, and absorption of heavy metals varyover a broad range, and the structural, mineralogical, andchemical properties of soil are complex.

The objective of this paper is to examine the complexpermittivity of a site-specific soil with respect to two heavymetals as the first step towards developing an in situ sub-surface detection system for heavy metal contamination.Using these data, the paper seeks to develop, and test, artifi-cial neural networks (ANNs) that can be used to relate thecomplex permittivity of a particular natural clayey soil tosoil properties and contamination. More specifically, it seeksto identify the presence of heavy contamination and, if pres-ent, identify whether the contaminant is Cu or Zn.

Background

The complex permittivity is an intrinsic property of a ma-terial and reflects the interaction of the material with anexternal alternating electric field. The complex permittivityhas two components, the real part ( ′ε ), often known as thepermittivity or dielectric constant, and the imaginary part( ′′ε ), also known as the dielectric loss factor. The complexpermittivity is dependent on the constituents of a material.Since the soil in nature consists of air, liquid (water), andsolids, the complex permittivity of soil is a function of di-electric properties of each phase. Therefore, the complexpermittivity of soil is affected by parameters such as the soilwater content, density, degree of saturation, mineralogy,temperature, and pore-water chemistry (Kraszewski 1996).The use of the complex permittivity as an indicator for de-tection of contamination in the subsurface has certain advan-tages over other geophysical methods, such as time domainreflectometry (TDR), resistivity, and induced polarizationsurveys. The complex permittivity reflects the polarizationand conduction behaviour of soil, which are a function ofthe frequency of the electrical field. Since the complex per-mittivity is measured over a range of frequencies, a largenumber of data (typically in the order of hundreds pairs ofreal and imaginary parts) are obtained for each measure-ment. These data provide information regarding the proper-ties of the soil system, including soil pore-water chemistry,water content, density, temperature, structure, etc. Further-more, since a large quantity of data are collected, modellingtools such as multiple linear regression and ANNs can be

employed to predict and detect heavy metal contaminationin the subsurface.

Experimental studies of the complex permittivity of soilhave been conducted by a number of investigators. For ex-ample, Santamarina and Fam (1997) measured the complexpermittivity of bentonite and kaolinite in the frequency rangefrom 0.2 to 1.3 GHz at various soil moisture contents andsolution concentrations; Klein and Santamarina (1997) dis-cussed the methods of complex permittivity measurement;Kaya and Fang (1997) reported the complex permittivity ofbentonite and kaolinite mixed with methanol or aniline; andThevanayagam (1994) discussed the interaction effects ofparticle shape, orientation, porosity, and relative disparitybetween electrical parameters (conductivity and dielectricconstant) of soil particles and pore fluid on the electrical re-sponse of bulk soil.

The present paper forms part of an extensive study of thecomplex permittivity of soil which has included the develop-ment of a complex permittivity measurement system forcompacted soil (Shang et al. 1999; Scholte et al. 2002) andsoil permeated with chemical solutions (Rowe et al. 2001);and complex permittivity measured on soil samples withvarious water contents, densities, pore-fluid compositions(including soil contaminated by heavy metals, organic com-pounds and landfill leachate), degrees of saturation, etc.(Scholte 1999; Xie 1999; Shang et al. 2000; Josic 2001;Rowe et al. 2002; Shang and Rowe 2003).

In this study, ANNs are used to relate the complex per-mittivity of a natural clayey soil and heavy metal (Cu andZn) contamination. ANNs learn from input information andhave the capability of generalization, pattern recognition,classification, prediction, simulation of sophisticated physi-cal processes, and quality control (Haykin 1994). A typicalANN structure (Fig. 1) consists of a number of processingunits, or neurons, which are usually arranged in layers: aninput layer, an output layer, and hidden layers. The inputlayer receives information (xi), which is multiplied by ad-justable connection weights (wji). The weighted inputs aresummed, a threshold value (θj) is subtracted, and then thecombined input, Ij = Σ wjixi – θj , is passed through an activa-tion function ( f(x)) to produce the output of the processingunit (yj) through the hidden layers. Both hidden and outputlayers are fully or partially connected to the units in the in-put layer, which play internal roles and produce outputs in

© 2004 NRC Canada

Shang et al. 1055

Fig. 1. Typical structure of ANNs.

the execution of the network (Shahin et al. 2001). For detailsregarding ANNs, readers are referred to texts such asHaykin (1994).

ANNs have the ability to learn from inputs and knowncorresponding outputs. ANNs then synthesize and memorizethe relationship between the inputs and outputs through atraining process that must contain sufficient representativedata to allow the ANN to recognize the underlying structureof the information involved. Once an ANN is establishedand verified, it can then be used to perform the tasks of iden-tification and (or) classification for which it has beentrained.

ANN applications in geoenvironmental engineering areunder active investigation by many researchers. For example,Dan et al. (2002) used ANNs to explore contaminant con-centration profiles observed in soils of polluted sites. Theydeveloped a polycyclic aromatic hydrocarbon (PAH) data-base to extract the most characteristic components of knowncontaminations and to identify the source type of similarpolluted sites. Lu et al. (2002) developed a neural networkmodel to forecast the pollutant levels in the downtown areaof Hong Kong. Kemper and Sommer (2002) discussed thepossibility of using an ANN approach to predict heavy met-als in soils polluted by a mining accident.

Complex permittivity measurement

The complex permittivity measurement system used forthe soil tests reported herein consists of a Hewlett-Packard8753D Automatic Network Analyzer (ANA), a sampleholder, a set of coaxial cables, and a personal computer fordata processing. Details of the apparatus can be found inShang et al. (1999) and Scholte et al. (2002).

The Halton Till, a soil recovered from Milton, Ontario,Canada, is used in this study. The major clay mineral is illitewith some chlorite and smectite. Non-clay minerals includequartz, carbonates, and feldspar. The properties of the Hal-ton Till are summarized in Table 1. Four simple salts(CuCl2, CuSO4, ZnCl2, and ZnSO4) were used to preparecopper- and zinc-contaminated soil specimens. The chemicalwas dissolved in water and the solution of known concentra-tion was mixed with dry soil to obtain a predefined watercontent. The mixture was then compacted to a known den-sity in a special sample holder prior to measurement of thecomplex permittivity. A total of 38 soil samples contami-nated with Cu and Zn were prepared and tested, including10 with CuCl2 solutions at concentrations ranging from0.125 to 31.250 g/L, 10 with ZnCl2 solutions at concentra-tions ranging from 0.123 to 41.050 g/L, 10 with CuSO4 so-lutions at concentrations ranging from 0.23 to 58.00 g/L, andeight with ZnSO4 solutions at concentrations ranging from0.26 to 64.95 g/L. The repeatability of the complex permit-tivity measurement was examined in three series of tests,and it was found that the results are highly consistent. In ad-dition, 84 soil samples mixed with distilled and deionizedwater (mega-pure water, MPW hereafter) and with NaCl so-lutions at various concentrations were prepared and tested(Scholte 1999; Xie 1999; Josic 2001), including 61 samplesmixed with MPW and 23 samples mixed with NaCl solu-tions at concentrations ranging from 0.5 to 15.0 g/L. Table 2

summarizes the details of soil samples that form the data-base in this study.

The soil physical properties (Table 2) vary over a rela-tively wide range, with the water content varying from 6.0%to 21.7%, the dry density varying from 1.60 to 2.08 Mg/m3,the degree of saturation varying from 36.7% to 100.0%, andthe electrical conductivity varying from 0.028 to 0.704 S/m.The complex permittivity of soil specimens was measured inthe frequency range of 0.3–1300 MHz. Details on the mea-surement procedure can be found in Shang et al. (1999) andScholte et al. (2002). Figures 2–5 show examples of thecomplex permittivity measurement, including the real andimaginary parts, versus frequency for Halton Till mixed withCuCl2, CuSO4, ZnCl2, and ZnSO4 solutions and MPW. Themetal concentrations at 10, 100, and 500 µg/g are presentedalong the MPW trace for comparison. The figures show thatdielectric dispersion (the real part of the complex permit-tivity) decreases with increasing frequencies, approaches �2,and then remains constant. The traces vary significantly forsoil specimens contaminated with different heavy metals andcontaining different anions in the pore fluid, as shown inFigs. 2–5. This reflects the effects of multiple factors in ad-dition to the presence of heavy metals (e.g., the soil watercontent, degree of saturation, density, and pore-fluid salinity)and highlights the need for a numerical tool for data analy-sis.

The selection of the frequency range in which the com-plex permittivity data are processed takes several factors intoaccount. First, the complex permittivity measured at lowerfrequencies is dominated by the electrode and soil electricaldouble layer polarizations and the soil static electrical con-ductivity. This can be observed in Figs. 2–5 as the highvalues of both real and imaginary parts of the complexpermittivity at frequencies below 200 MHz (Shang et al.1999). Second, as shown in Figs. 2–5, the complex permit-tivity data of contaminated soil specimens in the frequencyrange of 200–500 MHz can be distinguished from the soilspecimen mixed with MPW. When the frequency increasesto above 600 MHz, however, the complex permittivity traces

© 2004 NRC Canada

1056 Can. Geotech. J. Vol. 41, 2004

Sand (%) 16Silt (%) 57Clay (%) 27Plastic limit (%) 19.1Plasticity index (%) 10.9Specific gravity, Gs 2.79Carbonate content

Dolomite (%) 3.5Calcite (%) 12.7Total (%) 16.2

Pore-fluid chemistrypH 7.6Chloride (mg/L) 290Sulphate (mg/L) 3640Sodium (mg/L) 290Potassium (mg/L) 60Calcium (mg/L) 530Magnesium (mg/L) 610

Table 1. Summary of properties of Halton Till.

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Shang et al. 1057

Mixing fluid

SampleNo. Test No. Sourcea

w(%)

θv

(%)ρb

(Mg/m3)ρd

(Mg/m3)S(%)

κ(S/m) Chemical

Concn.(g/L)

1 SHTMP1 Scholte 21.7 35.4 1.98 1.60 85.1 0.095 — —2 SHTMP2 Scholte 9.8 19.7 2.21 2.01 70.5 0.075 — —3 SHTMP3 Scholte 15.2 28.9 2.19 1.90 90.3 0.098 — —4 SHTMP4 Scholte 12.6 25.3 2.26 2.00 90.6 0.089 — —5 SHTMP5 Scholte 17.3 31.5 2.14 1.83 91.0 0.102 — —6 SHTMP6 Scholte 8.5 17.4 2.22 2.04 65.1 0.073 — —7 SHTMP7 Scholte 11.2 23.1 2.29 2.06 87.7 0.090 — —8 SHTMP8 Scholte 14.4 28.1 2.23 1.96 93.1 0.098 — —9 SHTMP9 Scholte 12.0 21.8 2.03 1.81 62.2 0.073 — —10 SHTMP10 Scholte 11.6 21.4 2.06 1.84 63.0 0.073 — —11 SHTMP11 Scholte 11.7 21.9 2.09 1.86 66.1 0.075 — —12 SHTMP12 Scholte 11.5 21.9 2.12 1.90 69.0 0.082 — —13 SHTMP13 Scholte 16.6 30.8 2.16 1.85 91.9 0.106 — —14 SHTMP14 Scholte 16.9 31.2 2.16 1.85 92.6 0.107 — —15 SHTMP15 Scholte 16.6 30.5 2.15 1.84 90.1 0.107 — —16 SHTMP16 Scholte 16.7 31.0 2.17 1.86 93.3 0.107 — —17 SHTMP17 Scholte 16.8 31.0 2.16 1.85 91.9 0.109 — —18 SHT-15-1 Scholte 13.3 26.2 2.23 1.98 89.2 0.290 NaCl 15.019 SHT-15-2 Scholte 16.4 30.5 2.17 1.87 91.7 0.352 NaCl 15.020 SHT-15-3 Scholte 9.9 19.3 2.15 1.95 64.5 0.196 NaCl 15.021 SHT-15-4 Scholte 19.1 33.8 2.11 1.77 92.6 0.405 NaCl 15.022 SHT-15-5 Scholte 21.0 35.6 2.05 1.70 91.0 0.446 NaCl 15.023 SHT-15-6 Scholte 9.3 19.3 2.27 2.08 75.6 0.214 NaCl 15.024 SHT-15-7 Scholte 10.7 22.4 2.31 2.08 89.0 0.269 NaCl 15.025 SHT-15-8 Scholte 14.2 27.5 2.21 1.94 89.8 0.323 NaCl 15.026 SHT-15-9 Scholte 16.5 30.6 2.16 1.84 90.9 0.364 NaCl 15.027 SHT-15-1 Scholte 7.6 14.1 2.01 1.86 42.4 0.116 NaCl 15.028 SHT-1-1 Scholte 6.0 11.5 2.03 1.92 36.7 0.049 NaCl 1.029 SHT-1-2 Scholte 9.2 18.0 2.13 1.96 59.8 0.082 NaCl 1.030 SHT-1-3 Scholte 10.9 22.1 2.25 2.02 80.6 0.121 NaCl 1.031 SHT-1-4 Scholte 13.5 26.1 2.19 1.93 85.0 0.116 NaCl 1.032 SHT-1-5 Scholte 10.5 19.7 2.08 1.87 60.3 0.084 NaCl 1.033 SHT-1-6 Scholte 7.9 14.6 1.99 1.85 43.2 0.065 NaCl 1.034 SHT-5-1 Scholte 9.9 18.8 2.09 1.90 59.0 0.036 NaCl 5.035 SHT-5-2 Scholte 7.8 14.4 2.00 1.85 42.9 0.030 NaCl 5.036 SHT-05-1 Scholte 10.2 19.4 2.10 1.91 61.1 0.034 NaCl 0.537 SHT-05-2 Scholte 7.8 14.7 2.02 1.87 44.5 0.028 NaCl 0.538 SHT-10-1 Scholte 10.1 19.1 2.09 1.90 59.6 0.166 NaCl 10.039 SHT-10-2 Scholte 9.3 16.9 2.00 1.83 49.1 0.031 NaCl 10.040 SHT-10-3 Scholte 10.5 19.7 2.07 1.87 59.9 0.156 NaCl 10.041 XS1B-1 Xie 14.4 27.7 2.20 1.93 89.1 0.104 — —42 XS1B-2 Xie 14.4 27.7 2.20 1.93 89.1 0.103 — —43 XS1B-3 Xie 14.4 27.9 2.21 1.94 90.4 0.102 — —44 XS1B-4 Xie 14.4 27.6 2.19 1.92 87.8 0.103 — —45 XS1B-5 Xie 14.4 27.8 2.20 1.93 89.1 0.104 — —46 XS1B-6 Xie 14.4 27.7 2.20 1.93 89.1 0.104 — —47 XS1B-7 Xie 14.4 27.7 2.20 1.93 89.1 0.104 — —48 XS1B-8 Xie 14.4 27.9 2.21 1.94 90.4 0.103 — —49 XS2B-1 Xie 14.6 27.8 2.18 1.91 87.3 0.103 — —50 XS2B-2 Xie 14.6 28.1 2.19 1.92 88.6 0.106 — —51 XS2B-3 Xie 14.6 27.8 2.17 1.91 86.0 0.105 — —52 XS2B-4 Xie 14.6 27.5 2.15 1.89 83.6 0.105 — —53 XS2B-5 Xie 14.6 27.7 2.17 1.90 86.0 0.110 — —54 XS2B-6 Xie 14.6 27.8 2.17 1.91 86.0 0.112 — —55 XS2B-7 Xie 14.6 27.9 2.18 1.91 87.3 0.102 — —

Table 2. Summary of soil sample properties.

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1058 Can. Geotech. J. Vol. 41, 2004

Mixing fluid

SampleNo. Test No. Sourcea

w(%)

θv

(%)ρb

(Mg/m3)ρd

(Mg/m3)S(%)

κ(S/m) Chemical

Concn.(g/L)

56 XS2B-8 Xie 14.6 27.8 2.17 1.90 86.0 0.102 — —57 XS3B-1 Xie 14.5 27.7 2.19 1.91 88.2 0.108 — —58 XS3B-2 Xie 14.5 27.7 2.19 1.91 88.2 0.108 — —59 XS3B-3 Xie 14.5 27.9 2.20 1.92 89.5 0.113 — —60 XS3B-4 Xie 14.5 27.7 2.19 1.91 88.2 0.112 — —61 XS3B-5 Xie 14.5 27.5 2.17 1.90 85.7 0.105 — —62 XS3B-6 Xie 14.5 27.5 2.18 1.90 86.9 0.106 — —63 XS3B-7 Xie 14.5 27.3 2.16 1.89 84.5 0.105 — —64 XS3B-8 Xie 14.5 27.4 2.16 1.89 84.5 0.103 — —65 XS4B-1 Xie 14.6 27.6 2.17 1.90 86.0 0.102 — —66 XS4B-2 Xie 14.6 27.7 2.18 1.90 87.3 0.107 — —67 XS4B-3 Xie 14.6 27.7 2.18 1.90 87.3 0.108 — —68 XS4B-4 Xie 14.6 27.7 2.18 1.90 87.3 0.107 — —69 XS4B-5 Xie 14.6 27.7 2.17 1.90 86.0 0.107 — —70 XS4B-6 Xie 14.6 27.7 2.18 1.90 87.3 0.109 — —71 XS4B-7 Xie 14.6 27.5 2.16 1.89 84.8 0.106 — —72 XS4B-8 Xie 14.6 27.6 2.17 1.90 86.0 0.107 — —73 XS5B-1 Xie 14.3 27.4 2.19 1.92 87.5 0.094 — —74 XS5B-2 Xie 14.3 27.5 2.20 1.92 88.8 0.098 — —75 XS5B-3 Xie 14.3 27.5 2.20 1.92 88.8 0.095 — —76 XS5B-4 Xie 14.3 27.4 2.19 1.92 87.5 0.099 — —77 XS5B-5 Xie 14.3 27.4 2.19 1.92 87.5 0.096 — —78 XS5B-6 Xie 14.3 27.5 2.20 1.93 88.8 0.096 — —79 XS5B-7 Xie 14.3 27.3 2.18 1.91 86.2 0.098 — —80 XS5B-8 Xie 14.3 27.4 2.19 1.92 87.5 0.098 — —81 HTMPW-1 Josic 17.0 32.6 2.17 1.85 94.1 0.065 — —82 HTMPW-2 Josic 18.2 34.9 2.16 1.83 96.4 0.058 — —83 HTMPW-3 Josic 17.0 32.6 2.16 1.85 92.8 0.067 — —84 HTMPW-4 Josic 16.5 31.7 2.16 1.85 91.2 0.084 — —85 HTCuCl2-5 Josic 17.0 32.6 2.16 1.84 92.1 0.091 CuCl2 0.12586 HTCuCl2-6 Josic 16.9 32.5 2.17 1.86 93.7 0.096 CuCl2 0.12587 HTCuCl2-7 Josic 16.5 31.7 2.10 1.80 84.0 0.081 CuCl2 0.12588 HTCuCl2-8 Josic 17.0 32.6 2.18 1.86 94.7 0.112 CuCl2 1.25089 HTCuCl2-9 Josic 17.5 33.6 2.16 1.84 94.3 0.096 CuCl2 1.25090 HTCuCl2-10 Josic 17.3 33.2 2.15 1.83 92.4 0.167 CuCl2 6.25091 HTCuCl2-11 Josic 17.0 32.6 2.16 1.85 92.8 0.236 CuCl2 12.50092 HTCuCl2-12 Josic 17.0 32.6 2.17 1.85 94.1 0.255 CuCl2 12.50093 HTCuCl2-13 Josic 17.5 33.6 2.15 1.83 93.0 0.426 CuCl2 31.25094 HTCuCl2-14 Josic 17.0 32.6 2.17 1.85 94.1 0.345 CuCl2 31.25095 HTZnCl2-25 Josic 16.9 32.4 2.16 1.85 92.8 0.114 ZnCl2 0.12396 HTZnCl2-26 Josic 17.0 32.5 2.17 1.86 94.3 0.126 ZnCl2 0.60097 HTZnCl2-27 Josic 17.0 32.5 2.16 1.85 92.4 0.106 ZnCl2 1.23098 HTZnCl2-28 Josic 16.7 32.1 2.17 1.86 93.1 0.170 ZnCl2 4.11099 HTZnCl2-29 Josic 16.3 31.2 2.16 1.86 90.8 0.214 ZnCl2 8.210100 HTZnCl2-30 Josic 17.3 33.2 2.16 1.84 93.4 0.278 ZnCl2 12.300101 HTZnCl2-31 Josic 17.4 33.4 2.31 1.97 100.0 0.335 ZnCl2 21.550102 HTZnCl2-32 Josic 18.1 34.8 2.16 1.83 96.1 0.448 ZnCl2 30.750103 HTZnCl2-33 Josic 17.1 32.7 2.16 1.85 92.9 0.338 ZnCl2 30.750104 HTZnCl2-34 Josic 16.5 31.7 2.18 1.87 93.2 0.704 ZnCl2 41.050105 HTCuSO4-15 Josic 16.9 32.5 2.19 1.87 95.7 0.103 CuSO4 0.23106 HTCuSO4-16 Josic 17.4 33.4 2.15 1.83 92.7 0.100 CuSO4 0.23107 HTCuSO4-17 Josic 17.0 32.6 2.16 1.85 92.8 0.105 CuSO4 2.32108 HTCuSO4-18 Josic 16.9 32.5 2.16 1.85 92.5 0.092 CuSO4 2.32109 HTCuSO4-19 Josic 16.7 32.1 2.16 1.85 91.8 0.104 CuSO4 11.59110 HTCuSO4-20 Josic 16.8 32.3 2.17 1.86 93.4 0.105 CuSO4 23.18

Table 2 (continued).

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Shang et al. 1059

Mixing fluid

SampleNo. Test No. Sourcea

w(%)

θv

(%)ρb

(Mg/m3)ρd

(Mg/m3)S(%)

κ(S/m) Chemical

Concn.(g/L)

111 HTCuSO4-21 Josic 17.5 33.6 2.15 1.83 93.0 0.104 CuSO4 23.18112 HTCuSO4-22 Josic 17.1 32.8 2.13 1.82 89.4 0.088 CuSO4 58.00113 HTCuSO4-23 Josic 17.1 32.9 2.13 1.82 89.4 0.104 CuSO4 58.00114 HTCuSO4-24 Josic 17.5 33.6 2.15 1.83 93.0 0.099 CuSO4 58.00115 HTZnSO4-35 Josic 16.9 32.4 2.17 1.85 93.0 0.098 ZnSO4 0.26116 HTZnSO4-36 Josic 17.0 32.6 2.20 1.88 97.3 0.097 ZnSO4 2.60117 HTZnSO4-37 Josic 16.5 31.7 2.17 1.86 92.5 0.068 ZnSO4 2.60118 HTZnSO4-38 Josic 16.3 31.3 2.16 1.85 90.1 0.103 ZnSO4 12.95119 HTZnSO4-39 Josic 17.0 32.6 2.16 1.85 92.6 0.107 ZnSO4 12.95120 HTZnSO4-40 Josic 16.9 32.5 2.16 1.85 93.0 0.091 ZnSO4 25.95121 HTZnSO4-41 Josic 16.6 31.9 2.16 1.85 91.6 0.112 ZnSO4 25.95122 HTZnSO4-42 Josic 16.6 31.9 2.16 1.85 91.4 0.097 ZnSO4 64.95

Note: Mixing fluid indicates the fluid mixed with the soil samples. w, water content; θv, volumetric water content; ρb, bulk density; ρd, dry density; S,degree of saturation; κ, electrical conductivity.

aSamples 1–40 tested by Scholte (1999), 41–80 by Xie (1999), and 81–122 by Josic (2001).

Table 2 (concluded).

Fig. 2. Examples of complex permittivity traces. Soil mixed with mega-pure water (MPW) and CuCl2 solutions at concentrationsshown in the legends: (a) real part; (b) imaginary part.

converge due to dielectric dispersion. Lastly, the selection ofcomplex permittivity data at specific frequencies within therange of 200–500 MHz is based on the stability of data. Forexample, Figs. 2–5 show that some traces have notable rip-ples, especially at higher metal concentrations, and themodel needs to be trained to deal with this experimentalvariability. Taking these factors into account, complex per-mittivity values in the frequency range between 200 and500 MHz were selected for use in developing the ANN.

Modelling of neural networks

Multiple linear regression models were adopted in theanalysis of complex permittivity data (Scholte et al. 2002;Shang et al. 2000). Because the complex permittivity de-pends on soil parameters that are not linearly correlated,however, the models can predict one soil property only whenother properties vary in a narrow range. The ANN is usedas a modelling tool to relate the complex permittivity andheavy metal contamination. The software, Trajan version 4.0(Trajan Software Ltd. 1999), allows the programmer to con-struct linear or nonlinear models to solve multivariable re-

gression and classification problems. To achieve the specificgoal of predictive modelling, there must be a relationshipbetween the proposed inputs and outputs in the training dataand the data must be representative of the likely range ofconditions that can be encountered, as discussed in the pre-vious section.

DatabaseThe ANN modelling database includes the complex

permittivities of 122 soil samples measured from 200 to500 MHz, with various water contents, degrees of saturation,dry densities, and mixing fluids, as summarized in Table 2.In the development of the ANN, the complete set of data isdivided into three subsets (i.e., training, verification, andtesting subsets). The training subset is used to train the net-works, and the verification subset is used to check the per-formance of the networks during training. The presence ofacceptable and consistent errors for both training and verifi-cation does not guarantee good network performance at thetests stage, however. Thus, it is necessary to assign a testingdata subset, which is not used in the training process and isdedicated to testing the network performance after training.

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Fig. 3. Examples of complex permittivity traces. Soil mixed with MPW and CuSO4 solutions at concentrations shown in the legends:(a) real part; (b) imaginary part.

Based on the general principles of ANN modelling (TrajanSoftware Ltd. 1999), the soil data are assigned randomly inan approximate ratio of 2.5:1:1 among the training, verifica-tion, and testing subsets during each modelling process. Insome cases, the soil data available are not enough for model-ling, and then the verification dataset was omitted to ensureadequate data in the training and testing sets, as illustrated inthe next section.

Input and outputThe output of an ANN model is selected based on the

application. In this study, two tasks are set for heavy metaldetection: (i) identify the presence of two heavy metals (Cuand Zn); and (ii) classify the type of heavy metal if it ispresent in the soil. It was found that two separate ANN mod-els, each handling one task with a single output, gave thebest performance.

The inputs are selected from the soil complex permittivitymeasured in the frequency range of 200–500 MHz. For eachsoil sample, there are 94 inputs available, including 47 realparts, ′ε , and 47 imaginary parts, ′′ε . It is found in the model-ling process that the inputs must be reduced because it is

very difficult for ANNs to analyze the relationships betweena large number of inputs ( ′ε and ′′ε ) and a single output. Fur-thermore, too many inputs will result in a complex ANNarchitecture, resulting in slow execution and poor perfor-mance. Therefore, it is critically important to choose themost representative and significant inputs that are most sen-sitive to the output and to make the ANN architectures assimple as possible. In this study, the input selection wasbased on a trial-and-error procedure (Ding 2002).

Modelling procedureThe modelling procedure for neural networks depends on

specific application. In this study, the ANN modelling proce-dure is designed based on the nature of the database (i.e., thelarge number of soil complex permittivity data as inputs)and limited soil contamination data (i.e., presence and typeof heavy metals) as target outputs. The ANN modelling pro-cedure includes the following steps.

(1) Selection of network typeMultilayer perceptrons (MLP) networks were selected for

the heavy metal identification and classification modelling

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Fig. 4. Examples of complex permittivity traces. Soil mixed with MPW and ZnCl2 solutions at concentrations shown in the legends:(a) real part; (b) imaginary part.

after a comprehensive literature review of the characteristicsof several neural networks and comparison of their perfor-mance on the complex permittivity data (Ding 2002).

(2) Selection and optimization of learning algorithmLearning algorithms are techniques used to adjust weights

and thresholds of neurons. In general, there are two types ofalgorithms commonly used in practice: supervised learningand unsupervised learning. In an unsupervised learning pro-cess, only inputs are fed into networks to conduct learning,and outputs are not required prior to the training. In a super-vised learning process, both inputs and outputs are fed intonetworks (Trajan Software Ltd. 1999). The network learns toderive the relationship between the inputs and outputs. Theweights and thresholds are adjusted throughout the learningprocess by comparing the target outputs and network actualoutputs heuristically. In this study, the back-propagation,a widely used supervised training algorithm, is adoptedbecause the target outputs, namely the presence of heavymetals and the heavy metal type, are all available. The back-propagation is expressed by

[1] ∆ ∆w t E o w ti j j i i j, ,( ) ( )= + −η β 1

where ∆w ti j, ( ) is the weight change at the end of the tth iter-ation (epoch), η is the learning rate, Ej is the local error gra-dient, β is the momentum coefficient, oi is the output of theith neuron, and ∆w ti j, ( )− 1 is the weight change at the end ofthe (t – 1)th epoch (Trajan Software Ltd. 1999). The back-propagation algorithm travels in the direction of steepest de-scent on the error surface, then takes appropriate steps downthe surface proportional to the learning rate, and picks upmomentum as it maintains a consistent direction (TrajanSoftware Ltd. 1999). In this way, weights and thresholds areadjusted based on the feedback error calculated. For each it-eration (epoch), the inputs (i.e., the complex permittivitiesmeasured at specific frequencies) are presented to the net-work, which is executed to generate the outputs such as thepresence and type of heavy metals. At the end of each train-ing epoch, the differences between outputs generated by theANNs and target outputs (from measurements) are calcu-lated. The differences are then combined by a specific errorfunction as the network error. The error in turn serves as thefeedback of the next learning process, which is used to ad-just the weights and thresholds (Bishop 1995). The trainingcontinues until the network error falls below an acceptableerror level.

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Fig. 5. Example of complex permittivity traces. Soil mixed with MPW and ZnSO4 solutions at concentrations shown in the legends:(a) real part; (b) imaginary part.

The critical component in the training process is to set ηand β, which define the rate and direction, respectively, ofsearch movement of minimum network error during thetraining process. A large learning rate tends to speed up thelearning process and converge more quickly, although it mayovershoot the global minimum of the error surface. A smalllearning rate may achieve the global minimum, but it mayalso be tedious and time-consuming. In this study, the learn-ing rate is first set at a relatively high value of 0.5 to speedup the training process. Then it is reduced gradually to avoidovershooting. The momentum coefficient guides the searchmovement on the error surface in a fixed direction. In thisstudy, the training is first implemented with a relatively lowmomentum coefficient of 0.05, and it is then increased grad-ually (Ding 2002).

(3) Selection of activation functionThe activation function of each neuron is selected based

on the recommendation of Trajan Software Ltd. (1999). Thelinear activation function is used in the input and output lay-ers in the two ANN models developed. This function passesthe inputs to neurons directly as outputs without functionalprocessing. Logistic (Sigmoid) activation function is em-ployed in hidden layers of the two models developed in thisstudy, which provides the output of each neuron in the rangeof (0, 1).

(4) Selection of error functionThe error function is used to calculate the difference be-

tween outputs of the neural network and target outputs. Thissum-squared error function (E), which is the most popularand practical error function used in regression and classifica-tion cases, is used in this study and is expressed as

[2] EN d oti ti

=× ∑ ∑ −

12 2( )

where N is the number of epochs in the training process, dtiis the desired output of the ith output neuron for the tth ep-och, and oti is the actual output of the ith output neuron forthe tth epoch. The error is the sum of squared differences be-tween the desired outputs and actual outputs on each outputneuron.

(5) Determination of stopping conditionsThe training process could last for a long time and it can

cease by specifying stopping conditions. Stopping condi-tions can be set by three methods: (i) setting up the maxi-mum number of training epochs (training stops when itcompletes the specific number of iterations), (ii) setting upthe minimum error level (training stops when the networkerror reaches the target error level), and (iii) setting up theminimum error improvement (training stops when the errorfails to improve over a given number of epochs). In thisstudy, all three conditions are adopted. For the latter twoconditions, stopping is based on the difference between thepredicted output, XP , and the experimentally measured out-put, XM, and both the minimum error level and minimum er-ror improvement are set to 0.

(6) Architecture design of ANN modelsThe two ANNs developed for heavy metal identification

and classification are designed to have a single output, one

hidden layer, and an input layer with multiple inputs. Duringthe training processes, the network architecture design startswith fewer hidden neurons, and then the number of hiddenneurons is adjusted by assessing the network error. If the er-ror decreases by adding more hidden neurons, it indicatesthat the network size might be too small. If the error in-creases by adding hidden neurons, it indicates that the net-work size might be too large. At the same time, the inputvariables are fine-adjusted to match with hidden neurons.The procedure is repeated until the error reaches an accept-able level, and then the network architecture design is com-plete.

(7) Comparison of ANN modelsDuring a modelling process, there may be a number of

models with acceptable performance and error levels. There-fore, all models are compared regarding the model perfor-mance, error level, regression statistics, network size, andarchitecture complexity. Then the best network is retainedfor the proposed prediction or classification function.

Detection and classification of Cu and Znin Halton Till

Two ANN models are developed for identification andclassification of Cu and Zn in Halton Till, namely ANN-M6for identification of the presence of any heavy metal (Cu orZn) in the soil, and ANN-M7 for classification of the type ofheavy metal (Cu or Zn) in the event of positive identificationof heavy metals from ANN-M6.

ANN-M6: identification of presence of heavy metalsANN-M6 is designed to identify the presence or absence

of Cu and Zn in soil. Two categories of outputs are definedprior to the modelling process based on the database pre-sented in Table 2: the presence of heavy metals (Cu or Zn),which includes 38 soil samples mixed with CuCl2, ZnCl2,CuSO4, and ZnSO4 solutions (samples 85–122, Table 2),forms the output for “Yes”; and the remaining 84 soil sam-ples (samples 1–84, Table 2) mixed with NaCl solutions ordistilled and deionized water form the output for “No.” Twothresholds are set to 1 and 0, which correspond to the pres-ence (Yes) and absence (No) of heavy metals. If one casehas a numerical output close to one of the thresholds, thecase is assigned to the corresponding class with a nominaloutput such as Yes or No. That means the case is assigned tothe most probable class represented by a specific threshold.

The 122 soil samples in the database (Table 2) were ran-domly divided into three subsets: 70 for training, 26 for veri-fication, and 26 for testing. During the modelling process,the nominal outputs (Yes or No) need special handling. Thesoftware built-in pre- and post-processing function (i.e., theconversion function) is employed to transfer between thenominal and numeric values required for network execution.The number of epochs is set to 1000 for training. The activa-tion functions are set based on the discussion in the previoussection.

The best network found after supervised training is anMLP model. The model consists of one input layer with 10neurons, one hidden layer with six neurons, and one outputlayer with one neuron, as shown in Fig. 6. The 10 inputs

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correspond to the real parts ( ′ε ) of the complexpermittivities measured at frequencies 201, 356, 362, and375 MHz and the imaginary parts ( ′′ε ) measured at frequen-cies 259, 265, 291, 298, 304, and 349 MHz. The selection ofthe input is based on factors such as the stability of the com-plex permittivity traces at specific frequencies and the rela-tionship between the input and output parameters in thetraining process. Once the ANN model is established, usersdo not need to change the inputs and ANN architecture if thedatabase is simply expanded. For example, if more complexpermittivity measurements are made on Halton Till soil sam-ples, ANN-M6 can be applied directly. If the data are fromanother site, however, it may be necessary to reselect theinput variables used to train the ANN model. The single out-put neuron corresponds to Yes or No, i.e., presence or ab-sence of heavy metals (Cu or Zn). Through a sensitivityanalysis, it is found that the real part ( ′ε ) measured at362 MHz is the most significant input in the model. Thesensitivities of the inputs are presented in the order of theirrelative importance, as shown in Fig. 6.

Table 3 presents the performance and statistics of themodel. The overall correct identification percentage is 90%.The correct identification percentages in the training, verifi-cation, and testing data subsets are 91%, 92%, and 85%, re-spectively. In the testing subset, 26 data are reserved for theassessment of model performance. ANN-M6 correctly iden-tified three out of four soil specimens that contained heavymetals and correctly classified 19 out of 22 that did not con-tain heavy metals. Table 4 summarizes all wrongly identifiedsoil samples. It is observed that for four misidentified soilspecimens containing heavy metals (samples 94, 99, 104,and 112), the concentrations are relatively high, i.e., in therange of 8.2–58.0 g/L, whereas none of the soil sampleswith low heavy metal concentrations (0.125–6.25 g/L) aremisidentified.

The root mean squared (RMS) error function is defined as

[3] RMSP M

=−

=∑ ( )X X

n

i ii

n2

1

where XPi is the predicted output of the ith datum, XMi is themeasured output of the ith datum, and n is the total numberof data in the dataset (Trajan Software Ltd. 1999). The RMSerrors for the training, verification, and testing datasets are0.267, 0.127, and 0.336, respectively, which indicates therelatively stable performance of this model. It is noted thatin the testing dataset, the correct identification ratio isslightly lower than those of other two datasets (training andverification datasets), which is likely due to the insufficient

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Fig. 6. Architecture of ANN-M6 for identification of presence of heavy metals. The database included samples 1–122 from Table 2.

Trainingdataset

Verificationdataset

Testingdataset

No Yes No Yes No Yes

Total 45 25 17 9 22 4Correct 42 22 15 9 19 3Wrong 3 3 2 0 3 1Unknown 0 0 0 0 0 0Correct (%) 93 88 88 100 86 75Average correct (%) 91 92 85RMS error 0.267 0.127 0.336ANN correct (%) 90

Note: The database included samples 1–122 from Table 2. Total, totalnumber of data; Correct, number of correct identifications of presence orabsence of heavy metals; Wrong, number of wrong identifications of pres-ence or absence of heavy metals; Unknown, number of unidentified heavymetals; Correct (%), percentage of correct identification for Yes or No;Average correct (%), average percentage of correct identification; RMS er-ror, root mean squared error for each dataset (eq. [3]); ANN correct (%),overall percentage of correct identification.

Table 3. Regression statistics of ANN-M6 for identification ofthe presence of heavy metals.

number of representative data in the datasets and the bias ofthe database (84 soil samples do not contain heavy metals,while only 38 soil samples contain heavy metals). More datafor heavy metal contaminated soil samples will providefurther teaching information to improve the model perfor-mance. Nevertheless, the overall correct identification ratioof 90% indicates that the model is capable of identifying thepresence of heavy metals under most circumstances for Hal-ton Till soil samples.

ANN-M7 for classification of heavy metal typeThe toxicity and environmental impact of heavy metals

depend on the metal type. In the assessment of a contami-nated site, it is necessary to classify the types of heavy met-als contained in the soil for the selection of remediationstrategy. The ANN-M7 model is developed for this purpose.Among 122 soil samples shown in Table 2, 38 are contami-nated by the heavy metals Cu or Zn, and they form the data-base for the modelling of ANN-M7. Due to the limitednumber of data, 30 points are used for the training subsetand eight for the testing subset, and the verification set isomitted to reserve learning information for the training.

An MLP network, as described earlier, is again foundto best capture the relationship between the complex permit-tivity and the heavy metal type (Cu or Zn). The MLP net-work consists of one input layer with 12 input neurons, onehidden layer with 10 hidden neurons, and one output layerwith a single output neuron corresponding to the heavymetal type (Cu or Zn), as shown in Fig. 7. In the modellingprocess, two thresholds are set to 1 and 0, which correspondto the nominal output Cu and Zn, respectively. The networkfunction parameters and network architecture are fine-adjusted to match the input variable selection to enhance theperformance of the network. The conversion function of thesoftware (Trajan Software Ltd. 1999) is employed in the in-put and output layer to ensure the inputs and outputs are in alimited range. To optimize the back-propagation, the numberof epochs is increased to 2000; the learning rate and momen-tum coefficient are set to 0.08 and 0.32, respectively (Ding2002). The training process stops when 2000 epochs arecompleted, or target error 0 or minimum error improvement0 is reached. The same error function as that in ANN-M6 isused. The activation functions are the linear function in the

input layer and logistic function in the hidden and outputlayers.

In the network architecture shown in Fig. 7, the 12 inputscorrespond to the real parts ( ′ε ) of complex permittivitiesmeasured at frequencies 311, 317, 324, 337, and 343 MHzand the imaginary parts ( ′′ε ) of complex permittivities mea-sured at frequencies 272, 278, 285, 291, 298, 304, and311 MHz. The sensitivity analysis shows that the real partmeasured at 317 MHz ( ′ε (317 MHz)) is the most significantinput dominating the network performance. Figure 7 alsopresents the relative importance of each variable, expressedas the sensitivity rankings.

The model performance and regression statistics for thetraining and testing datasets are shown in Table 5. The cor-rect classification percentages in the training and testingdatasets are 97% and 88%, respectively, and the overall cor-rect classification ratio is 95%. In the testing dataset consist-ing of eight data, ANN correctly identified all three soilspecimens containing Cu, and four out of five soil specimenscontaining Zn. Table 6 summarizes two wrongly identifiedsoil specimens (samples 104 and 109). The heavy metal con-centrations of the specimens are relatively high as comparedwith the range of heavy metal concentrations in all soil spec-imens. In this case, because of limited data available fortraining and testing ANN-M7 (38), misclassification is most

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Mixing fluid

SampleNo. Data type

w(%)

θv

(%)ρb

(Mg/m3)ρd

(Mg/m3)S(%)

κ(S/m) Chemical

Concn.(g/L)

ANNoutput Target

3 Testing 15.2 28.9 2.20 1.90 90.3 0.098 — — Yes No5 Training 17.3 31.5 2.14 1.83 91.0 0.102 — — Yes No8 Verification 14.4 28.1 2.23 1.96 93.1 0.098 — — Yes No19 Testing 16.4 30.5 2.17 1.87 91.7 0.352 NaCl 15.00 Yes No21 Training 19.1 33.8 2.11 1.77 92.6 0.405 NaCl 15.00 Yes No77 Testing 14.3 27.4 2.19 1.92 87.5 0.096 — — Yes No79 Verification 14.3 27.3 2.18 1.92 86.2 0.098 — — Yes No80 Training 14.3 27.4 2.19 1.92 87.5 0.098 — — Yes No94 Training 17.0 32.6 2.17 1.85 94.1 0.345 CuCl2 31.25 No Yes99 Training 16.3 31.2 2.16 1.86 90.8 0.214 ZnCl2 8.21 No Yes104 Training 16.5 31.7 2.18 1.87 93.2 0.704 ZnCl2 41.05 No Yes112 Testing 17.1 32.8 2.13 1.82 89.4 0.088 CuSO4 58.99 No Yes

Table 4. Properties of wrongly identified soil samples in ANN-M6.

Training dataset Testing dataset

Cu Zn Cu Zn

Total 17 13 3 5Correct 16 13 3 4Wrong 1 0 0 1Unknown 0 0 0 0Correct (%) 94 100 100 80Average correct (%) 97 88RMS error 0.049 0.458ANN correct (%) 95

Note: The database included samples 85–122 from Table 2. Correct,correct classification; Wrong, wrong classification. Other definitions as inTable 3.

Table 5. Regression statistics of ANN-M7 for classification ofthe type of heavy metal.

likely due to the insufficient training data representing vari-ous situations.

The RMS errors for the training and testing datasets are0.049 and 0.458, respectively. The RMS error in the testingdataset is considerably higher than that of the training data-set. It is also noted that the model architecture is more com-plex than that of ANN-M6, since it involves more inputs andmore hidden neurons in the hidden layer. In a sense, thecomplexity of the network architecture represents the com-plexity of the underlying relationship between the input andthe output. The more complex structure of ANN-M7 is at-tributed to two major factors, namely the smaller databaseavailable for the modelling, and the similarity of Cu and Znelements in terms of the atomic number, atomic weight, andvalence. It is anticipated that the model performance can beimproved and the errors can be reduced with more soil dataavailable for training.

Conclusions

The complex permittivities of 122 Halton Till soil speci-mens were measured in the laboratory and a database wasestablished. The properties of these soil specimens, includ-ing water content, degree of saturation, density, and pore-fluid salinity, vary over a wide range. Of the 122 soil

specimens, 38 were artificially contaminated with copperand zinc. Two ANN models, ANN-M6 and ANN-M7, weretrained to detect the presence and type of the heavy metalsin the soil based on the complex permittivity data. The mod-elling process, architectures of the networks, model perfor-mance, and errors are discussed. The results show that theANN models detected contamination by Cu and Zn in Hal-ton Till with soil properties varying over a relatively widerange. The concentration of mixing fluid ranges from 0.125to 31.25 g/L for CuCl2, 0.23 to 58.00 g/L for CuSO4, 0.123to 41.05 g/L for ZnCl2, and 0.26 to 64.95 g/L for ZnSO4.ANN-M6 correctly identified the presence of heavy metalsin 90% of cases, and ANN-M7 correctly classified the typeof heavy metal in 95% of cases. The performance of themodels can be further improved with more data. Althoughfurther study is needed, these findings suggest that the com-bined use of complex permittivity data and ANNs for inter-pretation of the data has the potential to be developed into ascreening tool for the identification of heavy metal contami-nation of soils.

Acknowledgement

The research is supported under Strategic Project GrantSTPGP 085 and Corporative Research and Development

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1066 Can. Geotech. J. Vol. 41, 2004

Fig. 7. Architecture of ANN-M7 for classification of heavy metal types. The database included samples 85–122 from Table 2.

Mixing fluid

SampleNo.

Datatype

w(%)

θv

(%)ρb

(Mg/m3)ρd

(Mg/m3)S(%)

κ(S/m) Chemical

Concn.(g/L)

ANNoutput Target

104 Testing 16.5 31.7 2.18 1.87 93.2 0.704 ZnCl2 41.05 Cu Zn109 Training 16.7 32.1 2.16 1.85 91.8 0.104 CuSO4 11.59 Zn Cu

Table 6. Properties of wrongly identified samples in ANN-M7.

Grant CRDPJ 259485 from the Natural Sciences and Engi-neering Research Council of Canada.

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