Design and calibration of a new compound sensor for water content and electrical conductivity in soilless substrates

Abstract

Reliable and affordable compound sensors for measuring the water content and electrical conductivity simultaneously in soilless substrates are limited. In this study, a new compound sensor based on dielectric theory and four-electrode method is presented, and the size of the sensor is determined with the help of ANSYS software. A water content calibration test is designed in vinegar residue and coconut chaff with the same electrical conductivity. Test results show that the water content calibration equation is suitable for different substrates. Similarly, an electrical conductivity calibration equation is obtained in different concentrations of salt solutions. Considering the influence of electrical conductivity to water content measurement, a two-factor (water content and electrical conductivity) orthogonal test is designed in coconut chaff. Based on the analysis of test results, two compensation models – the multiplicative model and the additive model – are proposed. To evaluate the reliability of the models, a multiple linear regression analysis is employed. The results indicate that the additive model has a relatively higher reliability, i.e. the additive model can be regarded as the compensation model. After compensation, the relative errors of the measured values (including volumetric water content and electrical conductivity) are no more than 10%, and the compound sensor is suitable for different soilless substrates without recalibration.

Keywords

Calibration electrical conductivity sensor soilless culture water content

Introduction

Human beings are facing an unprecedented challenge to produce an adequate and economically feasible food supply, especially in the underdeveloped countries of the world, because of the rapid increase in human population. As a result, there has been a significant shift in global agricultural practice, and soilless plant cultivation systems have gained increased attention in recent years (Bogena et al., 2010; Raviv and Lieth, 2008; Skierucha and Wilczek, 2010). Accurately quantifying the water content and electrical conductivity (EC, i.e. salinity) is critical for soilless cultivation (Kannan, 2010; Mortl et al., 2011; Suweis et al., 2010). In light of these observations, it is important to obtain information on water content and EC in the soilless substrates. Even if the properties of soilless substrates (such as particle size, bulk density, organic components) are very different from soils, the measurement of water content and EC for soilless cultivation is always similar to that in soil. A reliable and affordable compound sensor combining water content with EC in soilless substrates is limited in the market.

At present, ignoring the soilless substrates, several methods are considered suitable for measuring soil water content and EC. As a sensor based on time domain reflectometry (TDR) has been presented to measure the water content of soil (Topp et al., 1980), a previous study has shown that the electromagnetic pulse of the sensor probe varies with EC of solutions (Giese and Tiemann, 1975), and the relationship that can derive the EC from water content is determined with further research (Dalton et al., 1984). Another study found that water content and bulk EC can be obtained simultaneously with a TDR sensor (Huisman et al., 2008). Frequency domain reflectometry (FDR) is another method for measuring the water content of soils. On the basis of the method of FDR, complex soil dielectric permittivity, which relates to water content and EC, is measured with a high-frequency signal (Amezketa, 2006). To analyse the influence of soil water content and EC/salinity on the complex dielectric permittivity of soil measured by a developed FDR sensor, the frequency spectrum of dielectric permittivity from 10 to 500 MHz of reference liquids, and soil samples of various moisture and salinity, are studied and the performance of the analysed sensors are compared with TDR sensors of similar mechanical construction (Skierucha and Wilczek, 2010). Although the approach above needs only one sensor and has a high accuracy, a complex processing circuit and high cost make the sensors unfeasible for commercial applications.

In this paper, we developed a new compound sensor combining water content with EC, and put forward a compound compensation model. Compared with previous designs and research, the proposed sensor has the following strengths: 1) the compound sensor responds rapidly and stably, and can be used in real time detection; 2) the processing circuit is relatively simple, has low cost and is easy to realize; 3) after compensation, the compound sensor is suitable for substrates with different EC without recalibration; 4) the small dimensions of the sensor make it easy to package and apply to agricultural production.

In particular, the aim of the study was: 1) to design a compound sensor probe; 2) to design a relative simple processing circuit; 3) to test the performance of the sensor through experiments; 4) to research the relationship between the sensor output and water content and EC, and propose a compensation model.

Principles of sensor design

Model of water content measurement

Multiple methods for measuring water content are available, including TDR, capacitance, FDR, standing wave ratio (SWR) and spectrum (Mortl et al., 2011; Muñoz-Carpena, 2005; Overduin et al., 2005). Considering the high relative permittivity of water (∼80) relative to a solid matrix (∼3 to 8) and air (∼1), a planar capacitive water content sensor based on the measuring technique of capacitance (Hu and Yang, 2010) to determine cultivated media moisture was designed. Figure 1 shows a physical model of the planar capacitive water content sensor. The model includes two parts: a drive plate and a sense plate. Considering the interaction between the drive plate and the sense plate, we assume that the length of plate (L) is infinite and the edge effect is ignored. Calculating capacitance with the unit integral method (Kudryashov and Kruchinin, 1995), the increase of the tiny area (ΔF=LΔx) of the capacitor can be expressed by

Δ C \approx 2 \frac{ε_{0} ε_{r} Δ F}{π (x + a / 2)}

(1)

Δ C \approx 4 \frac{L ε_{0} ε_{r}}{π (2 x + a)} Δ x

(2)

where $ε_{0}$ is the permittivity of vacuum, $ε_{r}$ is the relative permittivity of substrate and a is the plate space.

Considering the plate width b, the total capacitance can be obtained by

C \approx \int_{\frac{a}{2}}^{\frac{a}{2} + b} \frac{L ε_{0} ε_{r}}{π (2 x + a)} dx

(3)

C \approx 2 ε_{0} ε_{r} \frac{L}{π} \ln (1 + \frac{b}{a})

(4)

Based on the dielectric theory, a change in water content of a cultivated media can result in a significant change in the relative permittivity of the media. By developing an analytical relationship between the change in the water content and the associated change of relative permittivity, the volumetric water content of cultivated media can be indirectly estimated (Kodešová et al., 2011).

Model of electrical conductivity measurement

The method for measuring EC using a four-electrode probe has been applied in soil science for almost a century and the theory of the method is well developed (Kim et al., 2011). In this paper, the four-electrode probe is employed to measure the EC. The methods introduce an electrical current into the soil through current electrodes at the soil surface and the potential is measured at potential electrodes that are placed in the vicinity of the current flow. The electric conductivity $σ$ can be calculated with the driving current I and response potential $Δ U$ by

σ = \frac{(\frac{1}{d_{JM}} - \frac{1}{d_{JN}}) - (\frac{1}{d_{KM}} - \frac{1}{d_{KN}})}{2 π} \frac{I}{Δ U}

(5)

where $d_{JM}$ , $d_{JN}$ , $d_{KM}$ and $d_{KN}$ are spaces of corresponding two electrodes, respectively, $Δ U$ is the response potential of the potential electrodes and I is the driving current.

Taking the practicality into account, the Wenner method, where $d_{JM} = d_{KN} = d_{NM} = c$ , is applied in this paper (Presuel-Moreno et al., 2013). Equation (5) is simplified to

σ = \frac{1}{2 π c} \frac{I}{Δ U}

(6)

where c is the space between any adjacent electrodes.

In the above method, a constant current source is critical. Although a stable, reliable constant current source is difficult to realized, a constant voltage source with a precise resistor is employed as a solution (Figure 2). Equation (6) is derived to

σ = \frac{1}{2 π c} \frac{U_{R}}{R Δ U}

(7)

where R is the value of precise resistor and $U_{R}$ is the voltage at the precise resistor.

Structure of sensor design

A compound probe based on above models is designed as follows: copper sheets inlayed in a long printed circuit board (PCB) plate form the plates of the planar capacitive water content sensor, four electrodes are arranged in the bottom of the PCB plate and the processing circuit is arranged on top of the PCB plate (Figure 3). The material of plate farfield region of the insulating layer is usually epoxy resin, the relative permittivity of which is usually an invariable constant of 4.7. Considering how convenience it is to use, the length of the electrodes is 20 mm, the diameter is 0.8 mm and the material is stainless steel.

Design of probe size

According to Equation (4), the total capacitance relates to the ratio of plate space and plate width (a/b), obviously. Taking the probe sensitivity into account, the size of the sensor probe is determined by simulation.

With the help of ANSYS software, the numerical solution is used to perform the two-dimensional simulation of the probe electric field (assuming the length of plate L is infinite, the thickness of plate is infinitely thin; the real length L is 70 mm and the thickness is 1.6 mm), analysing the relationship between the ratio of plate space and plate width (a/b) and probe sensitivity.

Define the element type and material properties: choose the two-dimensional solid element PLANE121 as the computing unit; define unit INFIN110 as the infinite farfield; define the relative permittivity of the plate substrate, air and substrate (the relative permittivity of the air, plate substrate and substrate are set to 1, 4.7 and 20, respectively);

Model building: define two small rectangles as plate cross-section (b=10 mm, a=5, 8 and 10 mm); define a large rectangle as the farfield region and the substrate region; mesh and generate the model (Figure 4);

Define loads: define 5 and 0 V in the two plates, respectively;

Solve and post-process: choose a STATIC type, select the equation solver JCG and invoke the CMATRIX macro command (Figure 5).

In the simulation, changing the plate space a, with relative permittivity of the substrate change 1 unit, the simulation results of the change in capacitance value (ΔC) are shown in Table 1.

Table 1.

The relationship between probe sensitivity and a/b (where b is 10 mm, a is changeable, △C is the change of capacitance with relative permittivity of the substrate change 1 unit).

Number	a (mm)	a/b	△C (pf)
1	5	0.5	19.4
2	6	0.6	18.27
3	7	0.7	17.38
4	8	0.8	16.64
5	9	0.9	16.02
6	10	1	15.48
7	11	1.1	15.02

It can be observed that plate space a and a/b decrease, while the electric field intensity and ΔC resulting from a relative permittivity change increase, i.e. the sensitivity and the action range of the probe increase.

Taking sensitivity and action range into account, the plate space a=8 mm, copper sheet width b=10 mm, plate width B=14 mm, plate length L1=55 mm, copper sheet length L2=45 mm and space between adjacent electrodes c=11 mm.

Design of sensor circuit

Processing circuit of water content measurement

To measure the capacitance of the water content sensor, a resonance method is employed. The circuit comprises a power supply module, a resonance circuit, a frequency division circuit and a frequency-to-voltage (f/V) conversion circuit (Figure 6). The power circuit employs a low dropout voltage regulator chip AMS1117 (Advanced Monolithic Systems, Inc.) to provide a stable voltage source; the resonance circuit employs an integrated voltage-controlled oscillator (VOC) chip MC1648 to produce a frequency signal, which is determined by the equivalent capacitance Cx of the probe. The frequency division circuit employs a dual modulus prescaler chip MC12017 (Motorola, Inc.) and a 12-bit high-speed asynchronous counter 74HC4040 (Philips, Inc.), respectively, to transform the high-frequency signal produced by the resonance circuit into a low-frequency signal, which can be processed by the f/V conversion chip; the f/V conversion circuit employs a precision frequency-to-voltage converter LM331 (National Semiconductor, Inc.) to convert the frequency signal into a proportional voltage signal output.

Processing circuit of electrical conductivity measurement

The processing circuit of the EC measurement comprises a power supply module, a drive signal source circuit and an amplifier circuit (Figure 7). A 300-Hz signal [produced by a JFET-input operational amplifier TL082 (Texas Instruments), a resistor and a capacitor] loads on the precise resistor R. The voltage across the resistor and the voltage across the M and N points are amplified by precision dual-channel difference amplifier AD8270 (Analog Devices, Inc.), then the two voltages are converted to a DC voltage by a low-cost, low-power, true RMS-to-DC converter AD736 (Analog Devices, Inc.). Through the last dual, low-noise, low-offset instrumentation operational amplifier OP2277 (Analog Devices, Inc.), $U_{R}$ and $Δ U$ will be obtained.

Materials and methods

Materials and instruments

The test substrate is vinegar residue and coconut chaff.

The instruments include an electronic scale (the measuring range is 0–3000 g, the accuracy is ±0.1 g); a high accuracy digital multimeter; a constant voltage source (9 V); a vacuum drying oven DZF6050 (Shanghai Jinghong Laboratory Instrument Co., Ltd); a portable conductivity meter DDB-303A [INESA Instruments, the measuring range is 0.00–100 mS/cm, the accuracy is ±1.0% (full scale)]; a portable soil conductivity meter HI98331 [Hanna, Inc., the measuring range is 0.00–4.00 mS/cm, the accuracy is ±0.05 mS/cm (0.00–2.00 mS/cm), ±0.30 mS/cm (2.00–4.00mS/cm)].

Other equipment: a beaker (1000 ml), a glass rod, some filter papers, some polyvinyl chloride (PVC) cylindrical columns (internal radius=13 cm, height=25 cm) and sodium chloride (analytical pure).

Procedures of water content calibration

All substrates were oven dried for 8 h at 100°C before sample preparation. The substrates were divided into 13 groups (each weighing 250 g). To obtain a range of water contents in each substrate, from dry to near saturation, different volumes of deionized water were added to each substrate and mixed thoroughly to obtain uniformity. A certain quality of substrate samples were then transferred into beakers and pressed to 900 ml. Different volumetric water content can be obtained according to Table 2.

Table 2.

Sample of water content calibration processing (assuming that 1 g of water=1 ml).

Coconut chaff				Vinegar residue
No.	Weight of added water (g)	Weight of measuring sample (g)	Volumetric water content	No.	Weight of added water (g)	Weight of measuring sample (g)	Volumetric water content
1	80	267	0.072	1	40	267	0.041
2	120	300	0.108	2	80	226	0.061
3	180	310	0.144	3	120	228	0.082
4	240	333	0.181	4	160	238	0.103
5	300	358	0.217	5	200	253	0.125
6	360	386	0.253	6	240	262	0.143
7	420	415	0.289	7	280	274	0.161
8	480	445	0.325	8	320	290	0.181
9	540	475	0.361	9	360	300	0.197
10	600	506	0.397	10	400	319	0.218
11	660	537	0.433	11	440	329	0.233
12	720	570	0.470	12	480	352	0.257
13	800	598	0.506	13	520	362	0.272

The sensor probe was inserted into each beaker containing the substrates. The output was recorded as $U_{sw}$ after it became stable. The measurement was repeated three times and the mean value obtained.

Procedures of electrical conductivity calibration

Considering the difficulty of preparing samples, the response of EC was studied in salt solutions. Eight salt solutions (whose volume is 500 ml, ECs are 0.34, 0.93, 1.43, 1.91, 2.62, 3.31, 3.87 and 4.33 mS/cm, respectively) were prepared. The probe was inserted into each solution. After the outputs are stable, two voltages were recorded as $U_{R}$ and $Δ U$ .

Procedures of the two-factor orthogonal test

The coconut chaff was chosen as the test substrate in the orthogonal test. All coconut chaff was divided into seven groups (each weighing 250 g) and was numbered 1 to 7, respectively. Then seven salt solutions (whose volume was 500 ml, ECs were 0.31, 1.05, 1.70, 2.45, 3.10, 3.77 and 4.51 mS/cm, respectively) were prepared. These solutions were added to each substrate and mixed thoroughly to obtain uniformity. All mixed substrates were oven dried for 8 h at 100°C.

To obtain a range of water contents in each substrate, from dry to near saturation, different volumes of deionized water were added to each substrate and mixed thoroughly to obtain uniformity. A certain quality of substrate samples was then transferred into beakers and pressed to 900 ml. Different volumetric water content can be obtained according to Table 3.

Table 3.

Table of sample of two-factor orthogonal test processing (assuming that 1 g of water=1 mL).

Weight of added water (g)	Weight of measuring sample (g)	Volumetric water content
100	214	0.068
200	278	0.137
300	338	0.205
400	401	0.274
500	462	0.342
600	524	0.411
700	588	0.481

The sensor probe was inserted into each beaker containing the substrate. The outputs (including $U_{sw}$ , $U_{R}$ and $Δ U$ ) were recorded after they became stable (Figure 8). The measurement was repeated three times and the mean value obtained.

A dry sample of 50 g was weighed, mixed with deionized water (mass ratio of substrate/water=1:10), stirred for 10 minutes and left standing for 2 h; the substrate water extract was obtained by filtering. Portable soil conductivity meters HI98331 was used to measure the EC of the substrate water extract (EC_w). The output was recorded when it became stable. The measurement was repeated three times and the mean value obtained.

Results and discussion

Water content calibration results

The previous research demonstrated that there was a fine linear relationship between the soil volumetric water content and the square root of the soil relative permittivity (Topp and Reynolds, 1998) as follows

θ = m \sqrt{ε_{s}} + n

(8)

where $θ$ is the volumetric water content, $ε_{s}$ is the soil relative permittivity, and m and n are constants.

According to Equations (2) and (3), there is a linear relationship between capacitance C_x and substrate relative permittivity ε_s . Through the processing circuit, the equation can be derived to

ε_{s} = \frac{k_{3}}{U_{sw}^{2}} + k_{4}

(9)

θ = \frac{q}{U_{sw}} + p

(10)

where $U_{sw}$ is the output voltage of water content measurement, and $q$ , $p$ , $k_{3}$ and $k_{4}$ are constants.

The relationship between the water content $θ$ and 1/U_sw are studied in this paper according to Equation (10), as shown in Figure 9.

Tests results indicate that there is a same response tendency in both vinegar residue and coconut chaff, i.e. the category of organic and inorganic makes no difference to the sensor response. The fitting equation is

θ = 0.3901 (1 / U_{sw}) - 0.4023

(11)

where the linear correlation coefficient R ²=0.9926. It is accorded with the description of Equation (10).

EC calibration results

According to Equation (7), there is a linear relationship between EC $σ$ and the ratio of $U_{R}$ to $Δ U$ , assuming that $k = U_{R} / Δ U$ . The relationship of EC $σ$ to the ratio $k$ is studied in the following. According to the test results, as shown in Figure 10, the fitting equation can be obtained as follows

σ = 0.8969 k + 0.0248

(12)

where the linear correlation coefficient R ²=0.9972.

Two-factor orthogonal test results

The two-factor orthogonal test is finished with different water contents and different ECs in coconut chaff, and the results are as shown in Figures 11 and 12.

According to the Figure 11, there is a linear relationship between the water content and 1/U_sw with the same EC_w; however, with the increasing EC_w, the slope is decreasing. Obviously, the EC will influence the measurement of the water content. Assuming that there is a relationship like

θ = f_{1} (a_{1} / U_{sw} + b_{1}) + f_{2}

(13)

where $a_{1}$ and $b_{1}$ are constants; f ₁ and f ₂ are variables determined by ratio $k$ ( $k = U_{R} / Δ U$ ).

According to Figure 12, there is a quadratic polynomial relationship between the water content and the ratio k with the same EC_w; however, with the increase in EC_w, the curvature is decreasing. Assuming that there is a relationship similar to

θ = f_{3} (a_{2} k^{2} + b_{2} k + c_{2}) + f_{4}

(14)

where $a_{2}$ , $b_{2}$ and $c_{2}$ are constants; $f_{3}$ and $f_{4}$ are variables determined by 1/U_sw .

Taking Equations (13) and (14) into account, two possible models can be obtained as follows.

Multiplicative model:

\begin{matrix} θ & = (a_{1} / U_{sw} + b_{1}) (a_{2} k^{2} + b_{2} k + c_{2}) \\ = d_{1} k^{2} / U_{sw} + d_{2} k / U_{sw} + d_{3} / U_{sw} + d_{4} k^{2} + d_{5} k + d_{6} \end{matrix}

(15)

where $d_{1}$ , $d_{2}$ , $d_{3}$ , $d_{4}$ , $d_{5}$ and $d_{6}$ are constants.

Additive model:

\begin{matrix} θ & = (a_{3} / U_{sw} + b_{3}) + (a_{4} k^{2} + b_{4} k + c_{4}) \\ = e_{1} / U_{sw} + e_{2} k^{2} + e_{3} k + e_{4} \end{matrix}

(16)

where $e_{1}$ , $e_{2}$ , $e_{3}$ and $e_{4}$ are constants.

The multiplicative model can be considered a multiple linear model including five different variables, which are 1/U_sw , k, k ², k /U_sw and k ²/U_sw , and the data of these variables shown in Table 4 are obtained according the results of orthogonal test. The method of multiple linear regression is applied in this paper, and the results shown in Table 5.

Table 4.

Variables of multiple linear models according the multiplicative and additive model.

Number	θ	1/U_sw	k	k ²	k/U_sw	k ² /U_sw
1	0.068	1.2455	0.016	0.0003	0.0203	0.0003
2	0.068	1.2479	0.019	0.0003	0.0231	0.0004
3	0.068	1.2534	0.019	0.0004	0.0238	0.0005
4	0.068	1.2708	0.020	0.0004	0.0248	0.0005
5	0.068	1.2815	0.026	0.0007	0.0332	0.0009
6	0.068	1.2863	0.030	0.0009	0.0392	0.0012
7	0.068	1.3108	0.040	0.0016	0.0530	0.0021
8	0.137	1.3889	0.060	0.0036	0.0835	0.0050
9	0.137	1.4016	0.060	0.0036	0.0843	0.0051
10	0.137	1.4249	0.087	0.0076	0.1238	0.0108
11	0.137	1.4769	0.093	0.0086	0.1368	0.0127
…	…	…	…	…	…	…
48	0.481	2.9762	1.941	3.7668	5.7762	11.2107
49	0.481	3.3213	2.657	7.0577	8.8233	23.4403

Table 5.

Results of multiplicative model regression analysis.

		df	SS	MS	F	Significance F
Regression analysis		5	0.9010	0.1802	345.0243	1.57E-33
Residual error		43	0.0224	0.0005
Total		48	0.9235
	Coefficients	Standard error	t Stat	p-value	Lower 95.0%	Upper 95.0%
Intercept	−0.5272	0.0482	−10.9361	5.33E-14	−0.6244	−0.4300
1/ U_sw	0.4801	0.0364	13.1933	1.03E-16	0.4067	0.5535
k	−0.3107	0.0844	−3.6831	0.0006	−0.4808	−0.1406
k ²	0.0116	0.1074	0.1084	0.9141	−0.2049	0.2282
k/U_sw	0.0211	0.0510	0.4143	0.6808	−0.0817	0.1240
k ² /U_sw	−0.0009	0.0229	−0.0394	0.9687	−0.0470	0.0452

The fitting equation is

\begin{matrix} θ & = - 0.0009 k^{2} / U_{sw} + 0.0211 k / U_{sw} \\ + 0.0116 k^{2} - 0.3107 k + 0.4801 / U_{sw} - 0.5272 \end{matrix}

(17)

where the linear correlation coefficient R ²=0.9728, RMSE=0.0229, the maximum residual error is −0.0467, the F value is 345.0243 and the p value is 1.57×10^–33. However, the p values of k ², k /U_sw and k ²/U_sw are very high; hence the model is unreliable.

Similarly, the additive model can be considered a multiple linear model including three different variables, which are 1/U_sw , k and k ². Afterwards, the result of multiple linear regression is as shown in Table 6.

Table 6.

Results of additive model regression analysis.

		df	SS	MS	F	Significance F
Regression analysis		3	0.9009	0.3003	598.8509	2.89E-36
Residual error		45	0.0225	0.0005
Total		48	0.9234
	Coefficients	Standard error	t Stat	p-value	Lower 95.0%	Upper 95.0%
Intercept	−0.5377	0.0284	−18.9472	4.48E-23	−0.5949	−0.4806
1/ U_sw	0.4870	0.0206	23.6533	5.07E-27	0.4456	0.5285
k	−0.2785	0.0315	−8.8364	2.16E-11	−0.3420	−0.2150
k ²	0.0215	0.0086	2.4984	0.0162	0.0042	0.0389

The fitting equation is

θ = - 0.487 / U_{sw} + 0.0215 k^{2} - 0.2785 k - 0.5377

(18)

where the linear correlation coefficient R ²=0.9739, RMSE=0.0223, the maximum residual error is −0.0475, the F value is 598.85 and the p value is 2.89×10^–36. Moreover, all p values are less than 0.05; hence, the model is more reliable than the multiplicative model and is considered a compensation model.

In order to identify the validity and adaptability of the compound sensor, the authors have carried out a comparison analysis. Considering there are few reports and productions concerning the measurement of volumetric water content and EC for soilless culture substrates, the authors compared the compound sensor performance with a portable soil conductivity meters HI98331 (Hanna, Inc.), an EC-5 small soil moisture sensor and EM50 digital/analogue data logger (Decagon Devices. Inc.) in a mixture (on volume basis) of turf, coconut chaff and vinegar residue (2:2:1). The processes of the comparison experiment are similar to that described in the section on procedures of the two-factor orthogonal test. Herein, the authors take the EC of substrate water extract EC_w as the standard value, and compare it with the measured value of the compound sensor. The measurement was repeated three times and the mean value obtained, as shown in Tables 7 and 8.

Table 7.

Results of comparison experiments for measuring volumetric water content.

Standard value	The compound sensor			EC-5 small soil moisture sensor
Standard value	Measured values	Absolute errors	Relative errors	Measured values	Absolute errors	Relative errors
0.067	0.071	0.004	5.97%	0.037	−0.030	−44.8%
0.133	0.121	−0.012	−9.02%	0.070	−0.063	−47.4%
0.200	0.189	−0.011	−5.5%	0.093	−0.107	−53.5%
0.267	0.246	−0.021	−7.87%	0.114	−0.153	−57.3%
0.334	0.306	−0.028	−8.38%	0.175	−0.159	−47.6%
0.400	0.417	0.017	4.25%	0.191	−0.209	−52.3%

Table 8.

Results of comparison experiments for measuring electrical conductivity.

Standard value	Measured values (mS/cm)	Absolute errors (mS/cm)	Relative errors
0.31	0.307	−0.003	−1.07%
0.42	0.395	−0.025	−6.01%
0.49	0.504	0.014	2.76%
0.60	0.566	−0.034	−5.61%
0.83	0.754	−0.076	−9.15%
1.08	1.144	0.064	5.93%

According to Table 7, the max absolute error of the compound sensor is −0.028 and the max relative error is −9.02%, whereas the max absolute error of EC-5 small soil moisture sensor is 0.209 and all the relative errors are about 50%.

According to Table 8, the max absolute error of the compound sensor relative to the measured value of HI98331is −0.076 mS/cm and the max relative error is −9.15%.

It is obvious that all the relative errors of the measured values (including volumetric water content and EC) are no more than 10%; consequently, the compound sensor is suitable for different soilless substrates without recalibration.

Conclusion

To obtain the water content and EC of substrates quickly and accurately, the water content and EC compound sensors for substrates were designed based on dielectric theory and the four-electrode method, and the dimensions of the sensor were determined with the help of ANSYS software. The water content calibration test was designed in vinegar residue and coconut chaff with the same EC. Test results showed that the water content calibration equation is suitable for different substrates. Similarly, the EC calibration equation is obtained in different concentrations of salt solutions. Considering the influence of EC to water content measurement, a two-factor orthogonal test was designed. Based on the analysis of test results, two compensation models – the multiplicative model and the additive model – were proposed. To evaluate the reliability of the models, a multiple linear regression analysis was employed. The results showed that the additive model had a relatively higher reliability and the maximum residual error is −0.0475. After compensation, the relative errors of the measured value (including volumetric water content and EC) are no more than 10%; consequently, the compound sensor is suitable for different soilless substrates without recalibration.

Footnotes

Conflict of interest

The authors declare that there is no conflict of interest.

Funding

This work was partly supported by the National Key Technology R&D Program (grant number 2014BAD08B04). We also acknowledged the financial supports of the Special Fund for Agro-scientific Research in the Public Interest of China (grant number 201203095) and the Innovation Project for Graduate Student Research of Jiangsu Province (grant number KYLX15_1055).

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