On-line Moisture Content Measurement of Wheat

J. agric. Engng Res. (1996) 65, 287 – 296

On-line Moisture Content Measurement of Wheat P. A. Berbert;* B. C. Stenning† * Departamento de Engenharia Agrı´cola, Universidade Federal de Vic¸ osa, 36571-000 Vic¸ osa MG, Brazil † Silsoe College, Cranfield University, Silsoe, Bedford MK45 4DT, UK (Receiy ed 29 August 1995; accepted in rey ised form 28 June 1996)

A method has been developed which allows continuous measurement of the moisture content of a stream of hard winter wheat to an accuracy acceptable for normal grain drying operations. A test rig was designed and constructed to allow measurements to be made, on-line, of grain flowing through a sensing device. All sets of experiments were conducted at room temperature (19 – 248C), where the relative humidity varied from 50% to 65%. The dielectric properties were measured using wheat samples with bulk densities ranging from 625 to 891 kg / m3. A series of simultaneous measurements of capacitance and conductance at 0?5 MHz on varieties Slejpner, Mercia, and Hereward, varying in moisture content from 11?5 – 21?5%, w.b., revealed that the function [(» 9 2 1) / » 0] was practically independent of mass flow rate in the range from 2?0 – 14?4 kg s21 m22. Non-linear regression models were used to correlate moisture content with the function [(»9 2 1) / »0]. The individual calibration equations developed for each variety could estimate moisture content with standard errors of calibration of 0?5 percentage point (Slejpner), and 0?4 percentage point (Mercia and Hereward). The maximum error of moisture estimation was 1?3 percentage points, and occurred for a sample of variety Slejpner at 21?8% moisture content. The maximum error never exceeded 0?7 percentage point for varieties Mercia and Hereward. The limitation of moisture contents to the range from 11?5 to 16?3% led to a linear relation between moisture content and the function [(» 9 2 1) / » 0] , reducing the standard errors of calibration to the surprisingly low value of 0?1 percentage point moisture. ÷ 1996 Silsoe Research Institute 1. Introduction By the end of the period of forty years up to 1989, the number of grain drying installations in the UK1 0021-8634 / 96 / 120287 1 10 $25.00 / 0

287

Notation e

difference between oven and predicted moisture contents, percentage point moisture f frequency, Hz j 421, complex operator n number of samples used to derive a calibration equation p number of independent variables in a multiple regression model C capacitance, pF G conductance, m S L inductance, H M moisture content, percent wet basis R resistance, Ω SEC standard error of calibration, percentage point moisture » * complex relative permittivity, dimensionless » 9 relative permittivity, or real part of the complex relative permittivity, dimensionless » 0 loss factor, or imaginary part of the complex relative permittivity, dimensionless v angular frequency, v 5 2π f, rad / s Suffices a air e empty f fringing field m measured p parallel-equivalent value s sample 0 vacuum ÷ 1996 Silsoe Research Institute

288

P. A. BERBERT ; B. C. STENNING

had become approximately 45 000. Of these, about 10 000 units were of the continuous flow type, where the aim is, as far as possible, to produce a finished dry product after only one pass of the stock through the drier. The residence time of the material in a continuous flow drier is usually of the order of 50 to 60 min for a moisture extraction of 5 percentage points, w.b. The residence period required by the grain is influenced not only by the parameters associated with the drying air, i.e. temperature, relative humidity and flow rate, but also by the target or finished moisture content of the material and the variability of the moisture content of the grain arriving from the field. The latter may vary slowly throughout the day’s harvest, or rather rapidly perhaps as the result of rain or the combine harvester moving to another field. For many years the control of continuous flow driers was entirely manual, whereby the condition of grain leaving the drier was adjusted by the operator until the required value of moisture content was achieved. This was usually carried out by controlling the discharge rate of the drier, the other variables of airflow rate and air temperature having been predetermined, the first by the drier manufacturer and the second usually by the operator, having regard for the eventual prospective use of the grain. As the drying operation proceeded, the determination of grain moisture content was generally performed by drier operators equipped with moisture meters utilising the electrical properties of grain. In practice, these measurements were usually carried out at hourly intervals on samples of the out-flowing grain. However, observations made on the performance of typical continuous flow drying installations have demonstrated that when the adjustments required to correct a particular variation in output moisture content are based solely on the previous experience of the drier operator, there is scope for considerable error and the control procedure can be inefficient. The usual approach taken to ensure that all grain is dried to the specified target moisture content is to over-dry, but this results in excessive energy consumption by the drier, and can impair the quality of the product. It can be seen, therefore, that the manipulation of grain drier performance is a matter which can benefit greatly from the introduction of automated control technology. Apart from energy saving considerations, the other main goal would be the reduction of operational costs by lessening skilled labour requirements, provided an on-line moisture sensor could be built at an affordable cost for an agricultural market. In order to avoid time-consuming and difficult manual adjustments, and to achieve a

more homogeneously dried output product, manufacturers have indeed introduced, at various times in the past thirty years, automatic monitoring and control systems based on electrical or thermal methods for the estimation of moisture content. However, installation of these automated, unattended moisture monitoring systems has not been widespread. In any automatic control system it is the measurement of the controlled variable which is the primary key to success, and regrettably the equipment currently available has not always led to the desired accuracy of control. Where moisture content is the controlled variable there is one major difficulty associated with the use of the capacitance and microwave techniques for its estimation. It has to be remembered that, from the point of view of the instrumentation engineer, the dielectric material contained within the measurement cell comprises three main components. These are borne-dry grain, water and air. The proportions in which these are present depends on many factors including grain size and shape, grain surface friction, and grain particle density. These all contribute to the overall bulk density of the measured sample. A greater or lesser degree of compaction of the grain in the cell can have a significant effect on the indicated result. Various methods have been proposed to reduce or eliminate the bulk density effect during measurement of on-line grain moisture content but it is generally accepted that the only reliable solution is the use of density-independent functions, since it is very difficult, if not impossible, to control the bulk density of a stream of grain. Density-independent functions for estimation of moisture content have been examined in an associated paper,2 but since they were derived under static conditions, it remains to be shown whether or not they can provide satisfactory results under continuous flow conditions, where the greatest variations in bulk density of the grain are to be expected. The object of the work described here was to develop a technique which could provide a continuous measurement of the moisture content of a moving column of hard winter wheat, Triticum aestiy um L., to an accuracy acceptable for normal grain drying operations.

2. Materials and methods 2.1 . Test rig The experimental test rig for determining the dielectric properties of a moving column of wheat and to indirectly estimate its moisture content is shown in

289

ON-LINE MOISTURE CONTENT MEASUREMENT OF W HEAT

Fig. 1. On top of the outer cylindrical brass electrode (A) there was a polytetrafluoroethylene (ptfe) tube 0?13 m high (B), and surmounting this tube there was another cylindrical section (C) constructed of mild steel having a height of 0?07 m. A conical hopper (D) of 608 included angle and an orifice of 0?085 m diameter was positioned over this unit. An additional ptfe tube (E) was added below the test cell, followed by another mild steel cylindrical section 0?20 m high (F). The inner electrode was capped by a ptfe cone (G). The reason for using ptfe tubing immediately adjacent to both ends of the test cell was based on the need to guarantee proper electrical insulation, and to introduce as little disturbance as possible in the fringing electric field at the edge of the electrodes. The test rig had an effective height of 0?81 m, a free volume of 7?25 3 1023 m3, and was capable of holding approximately 5?5 kg of wheat at 14?5% moisture content. Positioned immediately below the test rig discharge point was a vibrating valve (H) which was controlled by a power oscillator. A wooden cone with 1208 apex angle (I), mounted on top of a vibrator, provided a mechanical means of controlling the grain flow rate. This system was mounted on a wooden base (J) located inside a plastic bucket (K) which collected the grain from the test rig. The whole structure described above was supported upon a wooden framework (L) of square cross section of 0?25 m2.

D

C

B G

A

E

F

L

2.2. Wheat samples

I

H

Three varieties of certified seed-quality hard winter wheat Triticum aestiy um L. were used in the present work: varieties Mercia and Hereward, obtained from Plant Breeding International (PBI Cambridge), were harvested in 1993 and kept in cool storage (58C) at 14% moisture for approximately 10 months. Samples of the third variety, Slejpner, were harvested at approximately 16?8% moisture content in 1994 from the farm at Silsoe College. The moisture content of 7 kg sub samples of each variety was artificially raised up to 22% in increments of approximately 1 percentage point moisture by adding the required amount of distilled water. Samples needing reduction of moisture content were dried at ambient temperature in a prototype laboratory drier. Determination of moisture content was made on a wet basis and was carried out according to the British Standard Methods of Test for Cereals and Pulses.3 Temperature and relative humidity of the ambient air were continuously monitored throughout the tests.

J K

Fig. 1. Experimental test rig. (A) outer brass electrode of the test cell; (B) ptfe tube 0?13 m high; (C) mild steel tube 0?07 m high; (D) conical hopper; (E) ptfe tube 0?13 m high; (F) mild steel tube 0?20 m high; (G) ptfe cone; (H) y ibrating y aly e; (I) wooden cone; (J) wooden base; (K) plastic bucket; (L) supporting wooden framework

290

P. A. BERBERT ; B. C. STENNING

2.3. Equipment and procedures

A Hewlett-Packard model 4285A Precision LCR Meter was used for measuring the dielectric properties of moving samples of wheat. In order to repeatedly measure capacitance and conductance at the two selected frequencies, 0?5 and 5?0 MHz, as a moving column of grain passed through the electrodes of the test cell, the List sweep function of the Meter was used. This function allows the simultaneous measurement of any two electrical parameters at ten sweep frequency points and partial automation of the measurement process. In this way, the equipment was programmed to measure Cp (the parallel-equivalent capacitance) and G (the conductance) five times sequentially, each time first at 0?5 MHz then at 5?0 MHz. Grain was introduced into the test rig by manually pouring it out of an ancillary bucket. During measurements on static grain, to prevent grain kernels from leaking through the clearance that exists between the lower edge of the test rig and the inclined surface of the wooden cone, a rubber ring was fastened around the clearance and held in place with ordinary parcel tape. Electrical measurements on static grain could then be made. The discharge was initiated by simultaneously activating the vibrating mechanism and releasing the rubber ring taped around the clearance. The sequence of measurements then commenced. Upon termination of the discharge, the total weight of grain collected in the bucket was measured, and the bulk density of the static column was subsequently calculated by dividing this weight by the known free volume of the test rig. After weighing the material, the test rig was refilled with the same sample and a new sequence of measurements started. Different mass flow rates could be achieved by controlling the frequency of vibration of the wooden cone. The clearance between the lower edge of the test rig and the surface of the wooden cone could also be adjusted to ensure different grain flow rates. For each series of measurements on the continuously flowing grain, the test rig was filled by hand, batchwise, i.e. there was no continuous top-up during the measurement process. Six different random combinations of amplitude of vibration and clearance were tested at each moisture content level in order to assess the influence of different grain flow rates on the dielectric properties of grain. The frequency of vibration was set at 45 Hz. Measurements of mass flow rate in kg / s were made by timing the flow of a known mass of grain through the clearance at the discharge point of the test rig. By dividing this rate by the cross sectional area at the

discharge point (5?7012 3 1023 m2), the mass flow rate in kg s21 m22 was determined.

2.4 . Measuring principle The measuring principle used in this work was similar to that discussed in a previous paper.2 The two parameters of the complex relative permittivity of the sample material, » * 5 » 9 2 j» 0 , were calculated from measurements of the parallel-equivalent capacitance (Cp) and the conductance (G ) of the sample container, both empty and filled with the grain sample. The real part of the complex permittivity, » 9 , was determined from parallel-equivalent capacitance measurements according to the following equation »s9 5

C m 2 C f 2 1?3368 6?2130

(1)

where Cm is the measured capacitance of the sample container filled with grain. The values of capacitance associated with fringing fields Cf, were calculated, at each frequency, using the following equation, where Ce is the measured capacitance of the empty sample container C f 5 Ce 2 7?5535 (2) The following equation was derived to predict the loss factor of a sample flowing in the test rig. The conductance measured with the sample container empty, Ga, also represents the conductance associated with the fringing fields and connecting cables.

» s0 5

Gm 2 Ga vC0

(3)

For a complete derivation of Eqns (1), (2), and (3), the reader is referred to an associated paper.2

3. Results and discussions Mass grain-flow rates achieved in the experiments reported here varied between 2?0 and 14?4 kg s21 m22. The lower limit of this range is above normal levels of mass flow rates used in commercial drying operations. The mass grain-flow rate in commercial driers varies according to the type of drier, its design characteristics and operational conditions such as drying air temperature, grain initial and final moisture contents, and airflow rate. Ives et al.4 reported grain flow rates of the order of 0?17 kg s21 m22 for counterflow drying of maize from 22 – 17% moisture content at 708C. Paulsen and Thompson,5 studying the effects of reversing airflow in a crossflow grain drier, reported maize

ON-LINE MOISTURE CONTENT MEASUREMENT OF W HEAT

291

flow rates varying from approximately 0?004 – 0?05 kg s21 m22 for drying air temperatures varying from 38 – 1158C, respectively. Nybrant6 investigating the modelling and adaptive control of concurrent flow driers used a mass flow rate of 0?28 kg s21 m22 to dry wheat from 20% to 16% moisture at 958C. Bruce and McFarlane7 developed a control algorithm to regulate the output moisture content in mixed-flow driers. Steady-state mass flow rates from 0?14 – 0?97 kg s21 m22 have been reported. It is appreciated that the present tests, therefore, used flow rates which significantly exceeded normally encountered values. However, it is suspected that high flow rates are attended by reduced bulk densities, so that the measurements made could be regarded as covering extreme cases in relation to normal practice.

due to the progressive reduction in the bulk density of moving grain associated with increasing mass flow rates. Analysis of similar graphs for increasing values of moisture content revealed the same trend and also showed that the variation of » 9 and » 0 with frequency was not as regular for moving grain as it was for static samples. This irregularity is not an inherent characteristic of moving grain. It results from small variations in mass flow rate during measurements. It is believed that a steady variation of » 9 and » 0 with frequency would be achieved if a stable mass flow rate could be maintained during measurements. This was clearly not the case with the vibrating valve employed in the present work, and doubt remains if such a constant mass flow rate could be achieved in any practical situation.

3.1. Relatiy e permittiy ity and loss factor of static and moy ing grain

3.2 . Uniqueness and density -independence of the function [(» 9 2 1) / » 0] for moy ing wheat

Relative permittivity and loss factor values were calculated in the frequency range from 0?5 to 5?0 MHz according to Eqns (1) and (3) for static samples and also for grain moving at two different mass flow rates. The results for the relative permittivity of grain at 12?4% moisture content, for variety Mercia, are shown in Fig. 2 , where two substantially different mass flow rates were chosen in order to observe their effect on the dielectric parameters. It was clear, from the overall results, that an increase of mass flow rate resulted in a decrease of permittivity of wheat samples at all frequencies in the range from 0?5 to 5?0 MHz. This was most probably

Results presented in a previous paper2 have shown that the function developed by Meyer and Schilz,8 [(» 9 2 1) / » 0] , is practically independent of grain bulk density for static samples of wheat. It remained to be examined whether the density-independence of this function would be maintained for considerably lower values of bulk density associated with moving grain. The results for variety Slejpner are shown in Fig. 3 , where the mass flow rate, and hence the densityindependence of this function at 0?5 MHz can be observed. Similar results for variety Mercia and Hereward were obtained and are shown in Figs 4 and 5 , respectively. The straight lines in these figures

Relative permittivity (ε')

4·6

4·4

4·2

4·0 0·1

1

10

Frequency (f), MHz

Fig. 2. Variation of the permittiy ity of hard winter wheat , y ariety Mercia , with frequency at 12?4% moisture content and indicated mass flow rates at 21 – 248C. j , static sample (761?2 kg / m 3); h , 6?4 kg s 21 m 22; m , 56?6 kg s 21 m 22

292

P. A. BERBERT ; B. C. STENNING

18

14

16 12

14

10

[(ε' – 1)/ε"]

[(ε' – 1)/ε"]

12

8

10

8 6

6

4 4

2 0

2

4

6

Mass flow rate, kg

8 s–1

10

12

m–2

2

0

2

4

6

Mass flow rate, kg s

8 –1

10

12

–2

m

Fig. 3. Comparison of the y alues of the function [(» 9 2 1) / » 0] at 0?5 MHz y ersus grain mass flow rate for hard winter wheat , y ariety Slejpner , at indicated moisture contents , and 21 – 248C. j , 11?5%; h , 12?9%; m , 15?0%; n , 15?7%; r , 16?9%; e , 17?8%; d , 18?9%; s , 19?9%; 1 , 21?0%; 3 , 21?8%

Fig. 4. Comparison of the y alues of the function [(» 9 2 1) / » 0] at 0?5 MHz y ersus grain mass flow rate for hard winter wheat , y ariety Mercia , and indicated moisture contents , and 21 – 248C. j , 11?5%; h , 12?4%; m , 14?5%; n , 15?4%; r , 16?3%; e , 17?4%; d , 18?6%; s , 19?4%; 1 , 20?4%; 3 , 21?3%

represent the mean values obtained for the function [(» 9 2 1) / » 0] at each moisture content. The uniqueness of the Meyer and Schilz function at 0?5 and 5?0 MHz for a moving column of wheat over

the moisture content range from approximately 11?5 – 21?5% is shown in Fig. 6 for variety Mercia. Points shown are mean values of six tests with grain flowing at different rates. As the rate of decrease of [(» 9 2 1) / » 0]

293

ON-LINE MOISTURE CONTENT MEASUREMENT OF W HEAT

18

18

16 14

ε' – 1 ε"

12 16

10 8 6 4

14

2 11

12

13

14

15

16

17

18

19

20

21

22

Moisture content, %w.b.

Fig. 6. Relationship between the function [(» 9 2 1) / » 0] and grain moisture content for a moy ing column of hard winter wheat , y ariety Mercia , at 21 – 248C , and mass flow rates in the range from 2?9 – 10?3 kg s 21 m 22 and indicated frequencies. j , 0?5 MHz; h , 5?0 MHz

[(ε' – 1)/ε"]

12

3.3 . Deriy ation of density -independent equations for moy ing columns of wheat according to the method described by Meyer and Schilz 8

10

Non-linear regression analyses of experimental data obtained at 0?5 MHz over the moisture content range from approximately 11?5 – 21?5% yielded the following polynomial equations for varieties Slejpner, Mercia and Hereward, respectively, all with coefficients of determination very close to unity

8

6

S» 9»20 1D 5 0?1183M 2 4?8956M 2

1 53?495;

4

[r2 5 0?9946]

(4)

S» 9»20 1D 5 0.1483M 2 6?3610M 2

1 70?981; 2

0

2

4

6

8

Mass flow rate, kg s

10 –1

12

14

–2

m

Fig. 5. Comparison of the y alues of the function [(» 9 2 1) / » 0] at 0?5 MHz y ersus grain mass flow rate for hard winter wheat , y ariety Hereward , at indicated moisture contents , and 21 – 248C. j , 11?1%; h , 12?2%; m , 14?3%; n , 15?4%; r , 16?3%; e , 17?6%; d , 18?6%; s , 19?5%; 1 , 20?3%; 3 , 21?4%

with increasing moisture content is more pronounced at 0?5 MHz than at 5?0 MHz, the development of density independent equations for moving grain will be restricted to the frequency of 0?5 MHz.

[r2 5 0?9925]

(5)

S» 9»20 1D 5 0?1565M 2 6?5044M 2

1 70?505;

[r2 5 0?9941]

(6)

The effect of variety upon the values of [(» 9 2 1) / » 0] at 0?5 MHz for moving columns of wheat can be seen more clearly in Fig. 7 , where the curves representing Eqns (4), (5) and (6) have been plotted on the same graph to allow direct comparisons. However, as pointed out by Zoerb et al. ,9 in a device intended to be used for monitoring moisture content, the sensor output signal would have to be considered the independent variable. Formulating the non-linear regres-

294

P. A. BERBERT ; B. C. STENNING

ated values predicted by the calibration equation, and is given by the following equation10,11

20 18 16

SEC 5

ε' – 1 ε"

14 12 10 8 6 4 2 10

12

14

16

18

20

22

Moisture content, %w.b.

Fig. 7. Effect of y ariety upon the Meyer and Schilz function at 0?5 MHz for moy ing columns of hard winter wheat at 21 – 248C. j , Selejpner; h , Mercia; m , Hereward

sion model with moisture content as the dependent variable yielded the following density-independent equations for varieties Slejpner, Mercia and Hereward, respectively.

S D »9 2 1 M 5 28?799S D »0 »9 2 1 M 5 28?897S D »0 M 5 30?801

»9 2 1 »0

20?3831

;

[r2 5 0?9798]

(7)

;

[r2 5 0?9813]

(8)

;

[r2 5 0?9843]

(9)

20?3088

20?3232

Equations (7), (8), and (9) were used to estimate the moisture contents of moving columns of wheat from their measured values of permittivity and loss factor, and the results were compared with the values of moisture content obtained with the standard oven method. The standard and mean errors of calibration and the worst-case errors for the three varieties are shown in Table 1. The standard error of calibration measures the scatter of the moisture contents determined by the standard oven method about the estim-

–

oni51 e 2i

n 2p 21

(10)

The mean error of calibration is the mean value of the differences between oven and predicted moisture contents. The graphical representation of the relationship between predicted and measured moisture contents for variety Mercia is shown in Fig. 8 . The straight line in this figure represents ideal agreement between predicted and measured values. The results presented in Table 1 compare well with the degree of accuracy reported by Lawrence and Nelson10 and Kraszewski and Nelson12 for static samples of wheat. In practical terms, the use of individual calibration equations for each variety would not be feasible. From the limited data collected so far, it seems that it would be possible to classify different varieties into separate groups having similar dielectric properties, and hence, to derive calibration equations for the different groups. Statistical analysis of the experimental data obtained by the authors revealed that a linear relationship between meter output and moisture content could be attained if the moisture was restricted to the range from 11?0 – 16?3%. The following linear approximations were obtained for varieties Slejpner, Mercia, and Hereward, with coefficients of correlation indicated

S» 9»20 1D 1 18?886; »9 2 1 M 5 20?4377S D 1 19?003; »0 »9 2 1 M 5 20?4355S D 1 18?620; »0 M 5 20?5837

[r2 5 0?9922]

(11)

[r2 5 0?9960]

(12)

[r2 5 0?9987]

(13)

The accuracy of Eqns (11), (12) and (13) was tested by using them to calculate moisture content from the experimental values of permittivity and loss factor,

Table 1 Performance of non-linear density-independent equations for the estimation of moisture content (11?5% < M < 21?5%) of moving columns of hard winter wheat Equation

Variety

Standard error of calibration (SEC )

Mean error of calibration

Maximum error of calibration

Number of samples

7 8 9

Slejpner Mercia Hereward

0?5 0?4 0?4

20?012 20?004 20?003

1?3 0?6 0?7

56 63 56

295

ON-LINE MOISTURE CONTENT MEASUREMENT OF W HEAT

22 21

Predicted moisture content, % w.b.

20 19 18 17 16 15 14 13 12 11

11

12

13

14

15

16

17

18

19

20

21

22

Oven moisture content, %w.b.

Fig. 8. Relationship between oy en moisture content and moisture content predicted by Eqn (8) for y ariety Mercia at 21 – 248C

and the results were compared with the original values determined by the standard oven method. The standard and mean errors of calibration and the worstcase errors for the three varieties are presented in Table 2. Despite the limited applicable range of moisture content, the results were surprisingly good if one takes into account the simplicity of the linear approximations as compared with the corresponding power equations numbered (7), (8), and (9). 4. Conclusions A series of simultaneous measurements of capacitance and conductance at 0?5 MHz made on three varieties of hard winter wheat (Slejpner, Mercia, and Hereward) varying in moisture content from 11?5 – 21?5%, revealed that the function [(» 9 2 1) / » 0] was

practically independent of grain mass flow rate in the range from 2?0 to 14?4 kg s21 m22. Non-linear regression models were used to correlate moisture content with this density-independent function, and the performances of the resulting calibration equations numbered (7), (8), and (9) were considered extremely satisfactory for the prediction of moisture content of flowing streams of grain. The individual calibration equations developed for each variety could estimate moisture content with standard errors of calibration of 0?5 percentage point (Slejpner), and 0?4 percentage point (Mercia and Hereward). The worst-case error of moisture estimation, 1?3 percentage points, occurred for a sample of variety Slejpner at 21?8% moisture content. The maximum error never exceeded 0?7 percentage point for varieties Mercia and Hereward over the whole range of moisture content. The limitation of moisture contents to the range 11?5% < M < 16?3% led to a linear response of the Meyer and Schilz function, reducing the standard errors of calibration to a surprisingly low value of 0?1 percentage point moisture. The intended application of the on-line sensor described here would be in continuous flow driers, although the minimum mass flow rate investigated was above normal levels used in commercial drying operations. However, there was an indication that the density-independence of the function [(» 9 2 1) / » 0] would be maintained for considerably lower values of mass flow rate. Another prospective use for the technique described here would be the dynamic online measurement of grain moisture content in combine harvesters. Further studies would then have to be carried out to determine the usefulness of the Meyer and Schilz function for moisture estimation at considerably higher mass flow rates than those reported in this research work. Acknowledgements The authors are indebted to the Post-Graduate Federal Agency (CAPES), Ministry of Education, Brazil, for sponsoring this research work.

Table 2 Performance of linear density-independent equations for the estimation of moisture (11?5% < M < 16?3%) content of moving columns of hard winter wheat Equation

Variety

Standard error of calibration (SEC )

Mean error of calibration

Maximum error of calibration

Number of samples

11 12 13

Slejpner Mercia Hereward

0?1 0?1 0?1

20?001 20?002 20?001

0?3 0?1 0?2

24 33 29

296

P. A. BERBERT ; B. C. STENNING

References 1

2

3

4

5

6

Ministry of Agriculture Fisheries and Food Agricultural Statistics United kingdom. H.M.S.O. London, 1989 Berbert P A; Stenning B C Analysis of densityindependent equations for determination of moisture content of wheat in the radiofrequency range. Journal of Agricultural Engineering Research 1996, 65(4): 275 – 286 British Standard Methods of Test for Cereals and Pulses. BS 4317: Part 3: 1993. Determination of moisture content of cereals and cereal products (routine method) Ives N C; Hukill W V; Black H M Corn-drying time at counterflow steady state. Transactions of the American Society of Agricultural Engineers 1968, 11: 240 – 249 Paulsen M R; Thompson T L Effects of reversing airflow in a crossflow grain dryer. Transactions of the American Society of Agricultural Engineers 1973, 16: 541 – 544 Nybrant T G Modelling and adaptive control of concurrent-flow driers. Computers and Electronics in

7

8

9

10

11

12

Agriculture 1989, 3: 243 – 253 Bruce D M; McFarlane N J B Control of mixed-flow grain dryers: an improved feedback-plus-feedforward algorithm. Journal of Agricultural Engineering Research 1993, 56: 225 – 238 Meyer W; Schilz W A microwave method for density independent determination of the moisture content of solids. Journal of Physics D: Applied Physics. 1980, 13: 1823 – 1830 Zoerb G C; Moore G A; Burrow R P Continuous measurement of grain moisture content during harvest. Transactions of the American Society of Agricultural Engineers 1993, 36: 5 – 9 Lawrence K C; Nelson S O Radio-frequency densityindependent moisture determination in wheat. Transactions of the American Society of Agricultural Engineers 1993, 36: 477 – 483 Jarret J; Kraft A Statistical analysis for decision making. Boston, Allyn and Bacon. Pp. 712, 1989 Kraszewski A W; Nelson S O Density-independent moisture determination in wheat by microwave measurement. Transactions of the American Society of Agricultural Engineers 1991, 34: 1776 – 1783