- Email: [email protected]
In-situ non-linear calibration of grain-yield sensor
EAEF 2(3) : 78-82, 2009
Research Paper
In-situ non-linear calibration of grain-yield sensor* ̆ Optimization of parameters for flow rate of grain vs. force on the sensor ̆ Koichi SHOJI*1, Hiromichi ITOH*2, Tsuneo KAWAMURA*2 Abstract In-situ calibration of a mini-yield sensor (mounted on a five-row grain combine) with a non-linear relation to the flow rate was examined. Instead of measuring or controlling the flow rate of grain for calibration purposes, 10 or 12 pairs of grain weights and signal recordings were collected directly in the fields; three such data sets (weights and signals) were obtained. Two parameters of the relation were optimized so as to minimize the standard error. The relative error of validation was 3% to 5% with data sets of a wide range of flow rates, whereas it was up to nearly 10% with a data set of low flow rates. The optimized parameters varied with each data set, but those yielding low errors were common in the response surface of error, regardless of the data sets. [Keywords] Grain weight, flow rate, standard error, response surface, cross-validation
I
calibration can be as simple as the following:
Introduction
Calibration of grain-yield sensors is requisite for ensuring their accuracy for specific varieties of crops and under specific operating conditions of combines. Efforts have therefore been made to fabricate reliable testing stands for calibration. Arslan and Colvin (1998) have constructed a testing stand with an electronic scale to verify yield sensors with the weight of accumulated grain, and have conducted indoor experiments by changing the flow rate of grain (Arslan and Colvin, 1999). Burks et al. (2003, 2004) have constructed indoor weighing and metering devices for grain and have conducted similar experiments. Al-Mahasneh and Colvin (2000) have mounted an electronic scale on a combine, and Arslan and Colvin (2002) have therewith then conducted field experiments. Loghavi et al. (2008) have developed a portable testing stand that controls the flow rate of grain, so that the sensors can be calibrated directly on the combine where they are mounted. Their main focus was to observe the performance of the yield monitor under various flow rates, sudden
changes
(step
response),
and
under
various
inclinations of the combine, specifically in terms of elapsed time. They have not, however, directly shown the relation between flow rate of grain and output of sensors.
(2)
where q is the flow rate of grain, F the output of the sensor, k a parameter to be calibrated, and w the weight of the accumulated grain. Equation (2) shows that only continuous recordings of the output and the weights of the accumulated grain are needed for the linear calibration. This linear relation is, however, limited to a specific combine (Shoji et al., 2009). The output of the sensor is generally non-linear to the flow rate (Schrock et al., 1999); very low output is usually observed under low flow rates and vice versa. A similar procedure with Eq. (2) is no longer valid and, therefore, devices and innovation are needed for precise control of the flow rate of grain, as reviewed above, in order to carry out reliable calibrations. The present paper proposes an alternative and simple method of calibrating grain-yield sensors with a potentially non-linear relation, specifically, by using only several pairs of recording of the output and the weight of the accumulated grain, similar to those we have suggested for linear sensors (Shoji et al., 2009). Without relying on devices controlling the flow rate of grain, combine operators will be able to easily calibrate the sensor-combine system in the field according to
If a linear relation is assumed such that: q kF ,
w qdt k Fdt
(1)
the varieties or the conditions of the crop grown.
then by taking the integral form of Eq. (1) with time, the * Partly presented at ISMAB2008, Taichung, Taiwan (ROC), May 2008 *1 JSAM Member, Corresponding author, Graduate School of Agriculture, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan; [email protected] *2 JSAM Member, Graduate School of Agriculture, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan
SHOJI, ITOH, KAWAMURA: 79 In-situ non-linear calibration of grain-yield sensor -Optimization of Parameters for Flow Rate of Grain vs. Force on the Sensor-
II
Materials and Methods
1. Yield sensor and signal processing The sensor consists of a ring load cell and an impact plate (Fig. 1), totaling only 0.021 kg, as described by Shoji et al. (2009). The reduced mass is intended to minimize the influence of external vibration on the output of the sensor. The output of the sensor is amplified and processed through a low-pass filter (cut-off frequency of 200 Hz) and recorded at a sampling rate of 1 kHz into a compact flash card. In offline processing, one-second average of the output is calculated and stored in another file, with the instantaneous zero-point of the output being updated every one second (self-compensation for zero-point) as proposed by Shoji et al. (in press); signals with absolute value exceeding a threshold of Fth are regarded as impact, and other signals are averaged to calculate the instantaneous zero-point.
of dry grain (13.5% w.b.) being poured directly into the grain pan of the combine. Five kilograms of grain were poured manually at as constant a rate as possible, and the average flow rate calculated by dividing the weight by the duration of pouring ranged between 0.19 and 1.85 kg/s. The average force on the sensor was calculated without the self-compensation and compared with the average flow rate. The purpose of this preliminary experiment was to find a rough relation between the average force and the flow rate, for possible use as a model for calibration in field experiments. Field experiments were conducted in two seasons (2005 and 2007, Table 1) at the Food-Resource Education and Research Center of Kobe University (Kasai City, Hyogo, Japan). Portions of 0.5-ha paddy fields (Oryza sativa L., cultivars: Hinohikari) were harvested with the combine. Each recording of signals was continued until the grain was unloaded from the grain tank (every 2 or 4 paths), and the total amount of grain was weighed manually. The flow rate of the grain was varied mainly by changing the operating speed
Auger blade
Yield sensor
Rotational direction of auger
of the combine. The cutting width of the combine was either 4 or 5 rows (1.2 or 1.5 m). A total of three data sets consisting of 10 or 12 pairs (weights and recordings) were obtained.
Diffuser
Fig. 1 The yield sensor mounted on the combine inside the grain tank.
Table 1
Summary of the field experiments
Data set
2005-1
2005-2
Moisture content of 20.2±0.8 20.2±1.2 grain (%) Average operating 0.37~1.45 0.31~0.62 speed* (m/s) Average flow rate of 0.23~0.99 0.34~0.58 grain* (kg/s) Total grain weight 1825 1950 (kg) Pair of data (weight 10 10 and recording)
2007 21.6±0.8 0.38~1.60 0.35~1.01 1878 12
* Traveled distance or grain weight divided by actual operating time
III
Results and Discussion
1. Rough relation between flow rate and average force Unlike the linear relation reported for a two-row combine (Shoji et al., in press), the stationary trial, here, showed that the average force on the sensor was not proportional to the flow rate of grain (Fig. 3); the output was very low at a low Fig. 2 The five-row jidatsu combine in operation. 2. Combines and experiments The sensor was mounted inside the grain tank of a 5-row jidatsu grain combine (KUBOTA, R1-551, Fig. 2) near the upper exit of the vertical grain auger to receive a portion of the grain accelerated by the auger blade (Fig. 1). Stationary trials were conducted by changing the flow rate
flow rate, as reported by Loghavi et al. (2008) and Schrock et al. (1999). Not only the incidence of the impacts, but also the amplitude of the impacts was affected by the flow rate (Fig. 4). One of the possible reasons for this non-linearity is that the diffuser near the auger blade hindered the grain flow to the sensor. At a low flow rate, a considerable portion of grain may have escaped from the open space around the auger blade (Fig. 1).
80
Engineering in Agriculture, Environment and Food Vol. 2, No. 3 (2009) where wi is the actual grain weighed manually at the end of
Average flow rate of grain q (kg/s)
2.0
i-th recording, ti the duration of the recording, and n the
q = 1.15 F 0.71 R2 = 0.996
number of pairs (10 or 12) in the data set for the calibration. Parameters a and b were determined to minimize SEC for each data set. Equations (4) and (5) were executed on Microsoft Excel ™ using the one-second average of the
1.0
output and the weighed grain, and “the solver tool” was used for the optimization of the parameters. The relative error of calibration, REC, was then calculated. 2
0
1.0
REC
2.0
Average output of sensor F (N)
Fig. 3
(6)
REC was not used as the objective function for the
Relation between average flow rate of grain and
average output of the sensor in the stationary experiment with batch input of dry grain.
optimization (i.e. calibration), however, since a pair of data of small grain weight tends to yield a high REC. Cross-validation was carried out with the rest of the data sets that were not used for the calibration. The standard error
(a)
of predication SEP and the relative error of prediction REP were similarly calculated.
10 Output of sensor (N)
1 n wi wˆ i 100 n 2 i 1 wi
S EP
1 n (wi wˆ i )2 n i 1
REP
1 n wi wˆ i 100 n i 1 wi
0
(7)
2
(b) 10
(8)
where n is the number of pairs in the data sets for validation (10 or 12). 3.
0
Calibration and validation in the field experiments
From the relation obtained in the stationary experiment (Fig. 3), the following model was adopted for this combine-sensor system tested in the field: (3)
q aF b
where q is the flow rate, F the one-second average of the output, a and b parameters to be calibrated. Calibration was carried out using each pair of the three data sets, instead of directly measuring the flow rate of grain. For each pair (weight and recording), total weight wˆ i was estimated, and the standard error of calibration SEC was calculated as below: ti
ti
0
0
wˆ i qdt aF b dt S EC
1 n (wi wˆ i )2 n 2 i 1
of the sensor was stabilized at threshold Fth = 1Frms to 2Frms (Fig. 5), where Frms is the root-mean square output of the sensor during the no-throughput of grain (0.057N on the average, with the tested combine). This range of threshold did not necessarily give the minimum standard error, but 20
SEC
2.0
10
a 1.0.
b Uncompensated
0
0
Standard error of calibration SEC (kg)
Fig. 4 Waveforms at the average flow rate of grain of: (a) 1.45 kg/s; (b) 0.37 kg/s
Calibrated parameters a (kg s-1N-1) and b (-)
Time (0.1 s/div)
2.
Threshold of compensation for zero-point
The algorithm of the self-compensation for the zero-point
(4)
0.1 1 10 Threshold Fth (in multiplier of Frms = 0.057 N)
(5)
Fig. 5 Effect of threshold Fth on calibrated parameters (a and b) and standard error of calibration SEC with data set 2007.
SHOJI, ITOH, KAWAMURA: 81 In-situ non-linear calibration of grain-yield sensor -Optimization of Parameters for Flow Rate of Grain vs. Force on the Sensoroptimized parameters a and b remained almost constant,
those from its own set. This repeatability is due mainly to the
similar to the one reported with a small combine of linear
similarity in the range of flow rate and moisture content of the
relation (Shoji et al., in press). With an Fth greater than 4Frms,
grain in these data sets. Figure 6 (2005-1) and Fig. 6 (2007)
parameter b decreased significantly (i.e. showed greater
also show that the response surfaces of standard error SEC
non-linearity) because of small signals of impact that were
were similar to each other. With threshold Fth of 8Frms,
cut-off by the threshold, so that the output at a low flow rate
relative errors were generally lower than 5%.
could be adjusted. It is not clear, however, whether further
In contrast, data set 2005-2 yielded significantly different
reduction in SEC at a high Fth in data set 2007 is due to the
parameters (Table 2). The flow rate in this data set was
stabilization of the self-compensation or to the removal of
concentrated within a small range (0.43r0.11s.d. kg/s) where
trivial signals.
the incidence of impact was scarce and for which the
4. Stability of the parameters Cross-validation (Table 2) showed that the calibrated
non-linear model had to compensate. Therefore, the lower
parameters were interchangeable between data sets 2005-1
near the origin of the relation of force vs. flow rate (Fig. 3).
value of parameter b was calibrated to yield a greater slope
and 2007. Not only were the calibrated values of one data set
As a result, applying the parameters from 2005-2 to other data
similar to those of the other, but also the errors associated
sets resulted in up to two times the errors and vice versa.
with the parameters from the other set remained as low as Table 2 Cross-validation expressed by standard errors (SEC and SEP) and relative errors (REC and REP) Threshold
Calibrated parameters
Calibration set
diagonal (Fig. 6), signifying that non-linearity (parameter b) and amplitude (parameter a) were interrelated to some extent
2005-2
2007
in the same combine and under the same crop conditions. This
1.62 0.69
9.01) 5.6%2)
18.0 10.1%
6.8 4.2%
property may be beneficial in practical applications; even if
2005-2
1.32 0.59
15.7 7.8%
9.8 7.3%
14.5 8.2%
sub-optimum parameters belonging to such a trough would
2007
1.66 0.71
8.2 5.4%
19.7 10.7%
7.4 4.6%
a
2005-1
2005-1 8Frms 0.456N
parameters were located along a common trough along the
2005-1
Fth
2Frms 0.114N
Evaluation set
Nonetheless, the response surface of the standard error was still similar to that of the others, where the optimized
2005-2 2007
b
1.70 0.55
9.3 4.6%
19.2 10.6%
5.0 3.4%
1.41 0.47
15.0 7.6%
12.7 8.5%
9.8 5.1%
1.65 0.54
9.7 4.7%
16.9 9.7%
5.1 3.1%
Errors in bold font are SEC or REC, whereas those in normal font SEP or REP Superscripts 1) and 2) are standard error (kg) and relative error, respectively, applied similarly throughout the table
(2005-1)
30
40 30
20
20
40
(2005-2)
b 0.8 0.7 0.6
20
the parameters had not been precisely optimized, the not cause a significant reduction in the accuracy of the sensor. 5.
Implications for further studies
The accuracy of the sensor on the five-row combine in this study was not as high (Table 2) as that on the two-row combine showing REP as low as 1.5% (Shoji et al., 2009). This is mainly attributed to the non-linear relation between flow rate and output here, whereas a linear relation was observed with the two-row combine. Not only the choice of function of the calibration model [Eq. (3)] affected the accuracy, but also did the use of the one-second average of the output as the source data for optimizing (calibrating) the parameters. Strictly speaking, this averaging procedure, which was intended to reduce computational load, is permitted only if the output of the sensor is linearly related to flow rate of grain. Even when receiving a steady flow of grain, the amplitude of each impact varied significantly (Fig. 4a),
1.2
40 30 20
1.4
1.6
1.8
a
(2007) 10 10
indicating that the one-second average partly invalidated the non-linearity that had been determined as the calibration model. The averaging procedure also affected the accuracy at low flow rates of grain, specifically on data set 2005-2 (Table 2). Figure 4b indicates that the one-second interval may have
Fig. 6 Response surface of standard error of calibration SEC (kg) with respect to parameters a and b: optimized point at calibration; threshold of self-compensation for zero-point Fth = 2 Frms
caused variability in the average output under such infrequent incidences of impact, which were eventually incorporated into the non-linear model to predict unexpected flow rates.
82
Engineering in Agriculture, Environment and Food Vol. 2, No. 3 (2009)
Although the evidence is not sufficient, the difference in the
Arslan, S. and T. S. Colvin. 1998. Laboratory test stand for combine
calibrated parameters for 2005-2 can be attributed partly to
grain yield monitors. Applied Engineering in Agriculture 14(4):
this variability at low flow rates, as well as to the limited number (only two) of parameters taken into account in the calibration model.
369-371. Arslan, S. and T. S. Colvin. 1999. Laboratory performance of a yield monitor. Applied Engineering in Agriculture 15(3): 189-195.
Therefore, the algorithm for data processing needs to be
Arslan, S. and T. S. Colvin. 2002. An evaluation of the response of
further improved, preferably by avoiding the averaging
yield monitors and combines to varying yields. Precision
procedure before the optimization, while not increasing the
Agriculture 3: 107-122.
computational load for optimizing the parameters.
Burks, T. F., S. A. Shearer, J. P. Fulton, C. J. Sobolik. 2003. Combine yield monitor facility development and initial monitoring test.
IV Summary and Conclusions 1. A very small grain-yield sensor mounted on a five-row grain combine showed a non-linear relation between its output (F) and flow rate of grain (q), expressed as q = aFb. 2. To simplify the procedure of calibration, the amount of grain accumulated in the grain tank was weighed and coupled with the one-second average of the output as a data set, instead of directly measuring the flow rate of grain. Parameters a and b were then calibrated to minimize the standard error between the estimated and actual weights of the grain. 3. Self-compensation for the zero-point of the sensor was adopted in data processing. The threshold for detecting the impact of grain (Fth) was practical between 1 and 2 times the
root-mean
square
of
the
output
during
the
no-throughput of grain (Frms). The calibrated parameters were stabilized within that range, although in some cases the standard error was even lower at higher settings of Fth. 4. The relative error was around 5% in data sets of a wide range of flow rates of grain (at threshold Fth = 2Frms), whereas it was up to 10% in the data set of low flow rates. The lowest relative error was 3.1% (at Fth = 8Frms). 5. Parameters a and b were optimized at different points between the data set of the low flow rate and the sets of wide flow rates, although the low-error regions were commonly located in the response surface of error, regardless of the data sets. 6. The high relative errors in the data set of low flow rates suggest that further improvement in data processing and calibration is needed. Acknowledgement We are thankful to the Food-Resource Education and Research Center of Kobe University for technical assistance and for lending us the combine. References Al-Mahasneh, M.A. and T. S. Colvin. 2000. Verification of yield monitor performance for on-the-go measurement of yield with an in-board electronic scale. Transactions of the ASAE 43(4): 801-807.
Applied Engineering in Agriculture 19(1): 5–12. Burks, T. F., S. A. Shearer, J. P. Fulton, C. J. Sobolik. 2004. Effects of time-varying inflow rates on combine yield monitor accuracy. Applied Engineering in Agriculture 20(3): 269–275. Loghavi, M., R. Ehsani and R. Reeder. 2008. Development of a portable grain mass flow sensor test rig. Computers and Electronics in Agriculture 61: 160–168. Schrock, M. D, D. L. Oard, R. K. Taylor, E. L. Eisele, N. Zhang, Suhardjito, J. L. Pringle. 1999. A diaphragm impact sensor for measuring
combine
grain
flow.
Applied
Engineering
in
Agriculture 15(6): 639-642. Shoji, K., H. Itoh and T. Kawamura. 2009. A mini- grain yield sensor compensating for the drift of its own output. Journal of EAEF 2(2): 44-48. (Received : 5. December. 2008, Accepted : 17. February. 2009)
Research Paper
In-situ non-linear calibration of grain-yield sensor* ̆ Optimization of parameters for flow rate of grain vs. force on the sensor ̆ Koichi SHOJI*1, Hiromichi ITOH*2, Tsuneo KAWAMURA*2 Abstract In-situ calibration of a mini-yield sensor (mounted on a five-row grain combine) with a non-linear relation to the flow rate was examined. Instead of measuring or controlling the flow rate of grain for calibration purposes, 10 or 12 pairs of grain weights and signal recordings were collected directly in the fields; three such data sets (weights and signals) were obtained. Two parameters of the relation were optimized so as to minimize the standard error. The relative error of validation was 3% to 5% with data sets of a wide range of flow rates, whereas it was up to nearly 10% with a data set of low flow rates. The optimized parameters varied with each data set, but those yielding low errors were common in the response surface of error, regardless of the data sets. [Keywords] Grain weight, flow rate, standard error, response surface, cross-validation
I
calibration can be as simple as the following:
Introduction
Calibration of grain-yield sensors is requisite for ensuring their accuracy for specific varieties of crops and under specific operating conditions of combines. Efforts have therefore been made to fabricate reliable testing stands for calibration. Arslan and Colvin (1998) have constructed a testing stand with an electronic scale to verify yield sensors with the weight of accumulated grain, and have conducted indoor experiments by changing the flow rate of grain (Arslan and Colvin, 1999). Burks et al. (2003, 2004) have constructed indoor weighing and metering devices for grain and have conducted similar experiments. Al-Mahasneh and Colvin (2000) have mounted an electronic scale on a combine, and Arslan and Colvin (2002) have therewith then conducted field experiments. Loghavi et al. (2008) have developed a portable testing stand that controls the flow rate of grain, so that the sensors can be calibrated directly on the combine where they are mounted. Their main focus was to observe the performance of the yield monitor under various flow rates, sudden
changes
(step
response),
and
under
various
inclinations of the combine, specifically in terms of elapsed time. They have not, however, directly shown the relation between flow rate of grain and output of sensors.
(2)
where q is the flow rate of grain, F the output of the sensor, k a parameter to be calibrated, and w the weight of the accumulated grain. Equation (2) shows that only continuous recordings of the output and the weights of the accumulated grain are needed for the linear calibration. This linear relation is, however, limited to a specific combine (Shoji et al., 2009). The output of the sensor is generally non-linear to the flow rate (Schrock et al., 1999); very low output is usually observed under low flow rates and vice versa. A similar procedure with Eq. (2) is no longer valid and, therefore, devices and innovation are needed for precise control of the flow rate of grain, as reviewed above, in order to carry out reliable calibrations. The present paper proposes an alternative and simple method of calibrating grain-yield sensors with a potentially non-linear relation, specifically, by using only several pairs of recording of the output and the weight of the accumulated grain, similar to those we have suggested for linear sensors (Shoji et al., 2009). Without relying on devices controlling the flow rate of grain, combine operators will be able to easily calibrate the sensor-combine system in the field according to
If a linear relation is assumed such that: q kF ,
w qdt k Fdt
(1)
the varieties or the conditions of the crop grown.
then by taking the integral form of Eq. (1) with time, the * Partly presented at ISMAB2008, Taichung, Taiwan (ROC), May 2008 *1 JSAM Member, Corresponding author, Graduate School of Agriculture, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan; [email protected] *2 JSAM Member, Graduate School of Agriculture, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan
SHOJI, ITOH, KAWAMURA: 79 In-situ non-linear calibration of grain-yield sensor -Optimization of Parameters for Flow Rate of Grain vs. Force on the Sensor-
II
Materials and Methods
1. Yield sensor and signal processing The sensor consists of a ring load cell and an impact plate (Fig. 1), totaling only 0.021 kg, as described by Shoji et al. (2009). The reduced mass is intended to minimize the influence of external vibration on the output of the sensor. The output of the sensor is amplified and processed through a low-pass filter (cut-off frequency of 200 Hz) and recorded at a sampling rate of 1 kHz into a compact flash card. In offline processing, one-second average of the output is calculated and stored in another file, with the instantaneous zero-point of the output being updated every one second (self-compensation for zero-point) as proposed by Shoji et al. (in press); signals with absolute value exceeding a threshold of Fth are regarded as impact, and other signals are averaged to calculate the instantaneous zero-point.
of dry grain (13.5% w.b.) being poured directly into the grain pan of the combine. Five kilograms of grain were poured manually at as constant a rate as possible, and the average flow rate calculated by dividing the weight by the duration of pouring ranged between 0.19 and 1.85 kg/s. The average force on the sensor was calculated without the self-compensation and compared with the average flow rate. The purpose of this preliminary experiment was to find a rough relation between the average force and the flow rate, for possible use as a model for calibration in field experiments. Field experiments were conducted in two seasons (2005 and 2007, Table 1) at the Food-Resource Education and Research Center of Kobe University (Kasai City, Hyogo, Japan). Portions of 0.5-ha paddy fields (Oryza sativa L., cultivars: Hinohikari) were harvested with the combine. Each recording of signals was continued until the grain was unloaded from the grain tank (every 2 or 4 paths), and the total amount of grain was weighed manually. The flow rate of the grain was varied mainly by changing the operating speed
Auger blade
Yield sensor
Rotational direction of auger
of the combine. The cutting width of the combine was either 4 or 5 rows (1.2 or 1.5 m). A total of three data sets consisting of 10 or 12 pairs (weights and recordings) were obtained.
Diffuser
Fig. 1 The yield sensor mounted on the combine inside the grain tank.
Table 1
Summary of the field experiments
Data set
2005-1
2005-2
Moisture content of 20.2±0.8 20.2±1.2 grain (%) Average operating 0.37~1.45 0.31~0.62 speed* (m/s) Average flow rate of 0.23~0.99 0.34~0.58 grain* (kg/s) Total grain weight 1825 1950 (kg) Pair of data (weight 10 10 and recording)
2007 21.6±0.8 0.38~1.60 0.35~1.01 1878 12
* Traveled distance or grain weight divided by actual operating time
III
Results and Discussion
1. Rough relation between flow rate and average force Unlike the linear relation reported for a two-row combine (Shoji et al., in press), the stationary trial, here, showed that the average force on the sensor was not proportional to the flow rate of grain (Fig. 3); the output was very low at a low Fig. 2 The five-row jidatsu combine in operation. 2. Combines and experiments The sensor was mounted inside the grain tank of a 5-row jidatsu grain combine (KUBOTA, R1-551, Fig. 2) near the upper exit of the vertical grain auger to receive a portion of the grain accelerated by the auger blade (Fig. 1). Stationary trials were conducted by changing the flow rate
flow rate, as reported by Loghavi et al. (2008) and Schrock et al. (1999). Not only the incidence of the impacts, but also the amplitude of the impacts was affected by the flow rate (Fig. 4). One of the possible reasons for this non-linearity is that the diffuser near the auger blade hindered the grain flow to the sensor. At a low flow rate, a considerable portion of grain may have escaped from the open space around the auger blade (Fig. 1).
80
Engineering in Agriculture, Environment and Food Vol. 2, No. 3 (2009) where wi is the actual grain weighed manually at the end of
Average flow rate of grain q (kg/s)
2.0
i-th recording, ti the duration of the recording, and n the
q = 1.15 F 0.71 R2 = 0.996
number of pairs (10 or 12) in the data set for the calibration. Parameters a and b were determined to minimize SEC for each data set. Equations (4) and (5) were executed on Microsoft Excel ™ using the one-second average of the
1.0
output and the weighed grain, and “the solver tool” was used for the optimization of the parameters. The relative error of calibration, REC, was then calculated. 2
0
1.0
REC
2.0
Average output of sensor F (N)
Fig. 3
(6)
REC was not used as the objective function for the
Relation between average flow rate of grain and
average output of the sensor in the stationary experiment with batch input of dry grain.
optimization (i.e. calibration), however, since a pair of data of small grain weight tends to yield a high REC. Cross-validation was carried out with the rest of the data sets that were not used for the calibration. The standard error
(a)
of predication SEP and the relative error of prediction REP were similarly calculated.
10 Output of sensor (N)
1 n wi wˆ i 100 n 2 i 1 wi
S EP
1 n (wi wˆ i )2 n i 1
REP
1 n wi wˆ i 100 n i 1 wi
0
(7)
2
(b) 10
(8)
where n is the number of pairs in the data sets for validation (10 or 12). 3.
0
Calibration and validation in the field experiments
From the relation obtained in the stationary experiment (Fig. 3), the following model was adopted for this combine-sensor system tested in the field: (3)
q aF b
where q is the flow rate, F the one-second average of the output, a and b parameters to be calibrated. Calibration was carried out using each pair of the three data sets, instead of directly measuring the flow rate of grain. For each pair (weight and recording), total weight wˆ i was estimated, and the standard error of calibration SEC was calculated as below: ti
ti
0
0
wˆ i qdt aF b dt S EC
1 n (wi wˆ i )2 n 2 i 1
of the sensor was stabilized at threshold Fth = 1Frms to 2Frms (Fig. 5), where Frms is the root-mean square output of the sensor during the no-throughput of grain (0.057N on the average, with the tested combine). This range of threshold did not necessarily give the minimum standard error, but 20
SEC
2.0
10
a 1.0.
b Uncompensated
0
0
Standard error of calibration SEC (kg)
Fig. 4 Waveforms at the average flow rate of grain of: (a) 1.45 kg/s; (b) 0.37 kg/s
Calibrated parameters a (kg s-1N-1) and b (-)
Time (0.1 s/div)
2.
Threshold of compensation for zero-point
The algorithm of the self-compensation for the zero-point
(4)
0.1 1 10 Threshold Fth (in multiplier of Frms = 0.057 N)
(5)
Fig. 5 Effect of threshold Fth on calibrated parameters (a and b) and standard error of calibration SEC with data set 2007.
SHOJI, ITOH, KAWAMURA: 81 In-situ non-linear calibration of grain-yield sensor -Optimization of Parameters for Flow Rate of Grain vs. Force on the Sensoroptimized parameters a and b remained almost constant,
those from its own set. This repeatability is due mainly to the
similar to the one reported with a small combine of linear
similarity in the range of flow rate and moisture content of the
relation (Shoji et al., in press). With an Fth greater than 4Frms,
grain in these data sets. Figure 6 (2005-1) and Fig. 6 (2007)
parameter b decreased significantly (i.e. showed greater
also show that the response surfaces of standard error SEC
non-linearity) because of small signals of impact that were
were similar to each other. With threshold Fth of 8Frms,
cut-off by the threshold, so that the output at a low flow rate
relative errors were generally lower than 5%.
could be adjusted. It is not clear, however, whether further
In contrast, data set 2005-2 yielded significantly different
reduction in SEC at a high Fth in data set 2007 is due to the
parameters (Table 2). The flow rate in this data set was
stabilization of the self-compensation or to the removal of
concentrated within a small range (0.43r0.11s.d. kg/s) where
trivial signals.
the incidence of impact was scarce and for which the
4. Stability of the parameters Cross-validation (Table 2) showed that the calibrated
non-linear model had to compensate. Therefore, the lower
parameters were interchangeable between data sets 2005-1
near the origin of the relation of force vs. flow rate (Fig. 3).
value of parameter b was calibrated to yield a greater slope
and 2007. Not only were the calibrated values of one data set
As a result, applying the parameters from 2005-2 to other data
similar to those of the other, but also the errors associated
sets resulted in up to two times the errors and vice versa.
with the parameters from the other set remained as low as Table 2 Cross-validation expressed by standard errors (SEC and SEP) and relative errors (REC and REP) Threshold
Calibrated parameters
Calibration set
diagonal (Fig. 6), signifying that non-linearity (parameter b) and amplitude (parameter a) were interrelated to some extent
2005-2
2007
in the same combine and under the same crop conditions. This
1.62 0.69
9.01) 5.6%2)
18.0 10.1%
6.8 4.2%
property may be beneficial in practical applications; even if
2005-2
1.32 0.59
15.7 7.8%
9.8 7.3%
14.5 8.2%
sub-optimum parameters belonging to such a trough would
2007
1.66 0.71
8.2 5.4%
19.7 10.7%
7.4 4.6%
a
2005-1
2005-1 8Frms 0.456N
parameters were located along a common trough along the
2005-1
Fth
2Frms 0.114N
Evaluation set
Nonetheless, the response surface of the standard error was still similar to that of the others, where the optimized
2005-2 2007
b
1.70 0.55
9.3 4.6%
19.2 10.6%
5.0 3.4%
1.41 0.47
15.0 7.6%
12.7 8.5%
9.8 5.1%
1.65 0.54
9.7 4.7%
16.9 9.7%
5.1 3.1%
Errors in bold font are SEC or REC, whereas those in normal font SEP or REP Superscripts 1) and 2) are standard error (kg) and relative error, respectively, applied similarly throughout the table
(2005-1)
30
40 30
20
20
40
(2005-2)
b 0.8 0.7 0.6
20
the parameters had not been precisely optimized, the not cause a significant reduction in the accuracy of the sensor. 5.
Implications for further studies
The accuracy of the sensor on the five-row combine in this study was not as high (Table 2) as that on the two-row combine showing REP as low as 1.5% (Shoji et al., 2009). This is mainly attributed to the non-linear relation between flow rate and output here, whereas a linear relation was observed with the two-row combine. Not only the choice of function of the calibration model [Eq. (3)] affected the accuracy, but also did the use of the one-second average of the output as the source data for optimizing (calibrating) the parameters. Strictly speaking, this averaging procedure, which was intended to reduce computational load, is permitted only if the output of the sensor is linearly related to flow rate of grain. Even when receiving a steady flow of grain, the amplitude of each impact varied significantly (Fig. 4a),
1.2
40 30 20
1.4
1.6
1.8
a
(2007) 10 10
indicating that the one-second average partly invalidated the non-linearity that had been determined as the calibration model. The averaging procedure also affected the accuracy at low flow rates of grain, specifically on data set 2005-2 (Table 2). Figure 4b indicates that the one-second interval may have
Fig. 6 Response surface of standard error of calibration SEC (kg) with respect to parameters a and b: optimized point at calibration; threshold of self-compensation for zero-point Fth = 2 Frms
caused variability in the average output under such infrequent incidences of impact, which were eventually incorporated into the non-linear model to predict unexpected flow rates.
82
Engineering in Agriculture, Environment and Food Vol. 2, No. 3 (2009)
Although the evidence is not sufficient, the difference in the
Arslan, S. and T. S. Colvin. 1998. Laboratory test stand for combine
calibrated parameters for 2005-2 can be attributed partly to
grain yield monitors. Applied Engineering in Agriculture 14(4):
this variability at low flow rates, as well as to the limited number (only two) of parameters taken into account in the calibration model.
369-371. Arslan, S. and T. S. Colvin. 1999. Laboratory performance of a yield monitor. Applied Engineering in Agriculture 15(3): 189-195.
Therefore, the algorithm for data processing needs to be
Arslan, S. and T. S. Colvin. 2002. An evaluation of the response of
further improved, preferably by avoiding the averaging
yield monitors and combines to varying yields. Precision
procedure before the optimization, while not increasing the
Agriculture 3: 107-122.
computational load for optimizing the parameters.
Burks, T. F., S. A. Shearer, J. P. Fulton, C. J. Sobolik. 2003. Combine yield monitor facility development and initial monitoring test.
IV Summary and Conclusions 1. A very small grain-yield sensor mounted on a five-row grain combine showed a non-linear relation between its output (F) and flow rate of grain (q), expressed as q = aFb. 2. To simplify the procedure of calibration, the amount of grain accumulated in the grain tank was weighed and coupled with the one-second average of the output as a data set, instead of directly measuring the flow rate of grain. Parameters a and b were then calibrated to minimize the standard error between the estimated and actual weights of the grain. 3. Self-compensation for the zero-point of the sensor was adopted in data processing. The threshold for detecting the impact of grain (Fth) was practical between 1 and 2 times the
root-mean
square
of
the
output
during
the
no-throughput of grain (Frms). The calibrated parameters were stabilized within that range, although in some cases the standard error was even lower at higher settings of Fth. 4. The relative error was around 5% in data sets of a wide range of flow rates of grain (at threshold Fth = 2Frms), whereas it was up to 10% in the data set of low flow rates. The lowest relative error was 3.1% (at Fth = 8Frms). 5. Parameters a and b were optimized at different points between the data set of the low flow rate and the sets of wide flow rates, although the low-error regions were commonly located in the response surface of error, regardless of the data sets. 6. The high relative errors in the data set of low flow rates suggest that further improvement in data processing and calibration is needed. Acknowledgement We are thankful to the Food-Resource Education and Research Center of Kobe University for technical assistance and for lending us the combine. References Al-Mahasneh, M.A. and T. S. Colvin. 2000. Verification of yield monitor performance for on-the-go measurement of yield with an in-board electronic scale. Transactions of the ASAE 43(4): 801-807.
Applied Engineering in Agriculture 19(1): 5–12. Burks, T. F., S. A. Shearer, J. P. Fulton, C. J. Sobolik. 2004. Effects of time-varying inflow rates on combine yield monitor accuracy. Applied Engineering in Agriculture 20(3): 269–275. Loghavi, M., R. Ehsani and R. Reeder. 2008. Development of a portable grain mass flow sensor test rig. Computers and Electronics in Agriculture 61: 160–168. Schrock, M. D, D. L. Oard, R. K. Taylor, E. L. Eisele, N. Zhang, Suhardjito, J. L. Pringle. 1999. A diaphragm impact sensor for measuring
combine
grain
flow.
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Agriculture 15(6): 639-642. Shoji, K., H. Itoh and T. Kawamura. 2009. A mini- grain yield sensor compensating for the drift of its own output. Journal of EAEF 2(2): 44-48. (Received : 5. December. 2008, Accepted : 17. February. 2009)