A Neural Network for Setting Target Corn Yields

J. Liu, C. E. Goering, L. Tian

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Published in Transactions of the ASAE Vol. 44(3): 705-713 (© 2001 American Society of Agricultural Engineers ).

Article was submitted for review in December 1999; approved for publication by the Information & Electrical Technologies Division of ASAE in January 2001. Presented at the 1999 ASAE Annual Meeting as Paper No. 99-3040.

The authors are Jing Liu, ASAE Student Member , Research Associate; Carroll Goering , ASAE Fellow , Professor; and Lei Tian , ASAE Member Engineer , Associate Professor; Agricultural Engineering Department, University of Illinois, Urbana. Corresponding author: Carroll Goering, University of Illinois, 1304 W. Pennsylvania Ave., Urbana, IL 61801; phone: 217-333-7534; fax: 217-244-0323; e-mail: ceg@sugar.age.uiuc.edu.

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Abstract. Setting a realistic yield goal in each part of the field is one of the critical problems in precision agriculture. Factors affecting crop yields, such as soil, weather, and management, are so complex that traditional statistics cannot give accurate results. As an automatic learning tool, the artificial neural network (ANN) is an attractive alternative for processing the massive data set generated by precision farming production and research. A feed-forward, completely connected, back-propagation ANN was designed to approximate the nonlinear yield function relating corn yield to factors influencing yield. By stratified sampling based on rainfall, some of the data were excluded from the training set and used to verify the yield prediction accuracy of the ANN. The RMS error for 60 verification patterns was about 20%. After the ANN was developed and trained, three aspects of the input factors were investigated: (1) yield trends with 4 input factors, (2) interaction between nitrogen application rate and late July rainfall, and (3) optimization of the 15 input factors with a genetic algorithm to determine maximum yield. The model was then used on another field, and preliminary results of the latter study are given.

Keywords . Neural network, Yield prediction, Genetic algorithm, Data mining.

Setting a realistic yield goal in each part of the field is one of the critical problems in precision agriculture. Once yield goals are set, agronomic recommendations are available to determine the correct amount of seed, fertilizer, etc., to produce target yields. If less fertilizer is applied, the yield may be reduced; if too much is applied, money will be wasted and the environment may suffer. The first step in setting yield goals is developing a relationship model between soil, weather, and management factors and yield with high accuracy. This model could be used to predict yields within fields with some weather, soil, and management conditions, and analyze these influencing factors. In this research, an artificial neural network (ANN) was used to build a corn yield prediction model for precision farming applications.

Crop yield history suggests that crop production systems are very complex. Both process-oriented crop growth models and traditional statistical methods can be used to study crop growth and yield response to environment and management. For example, Paz et al. (1999, 1998) developed a technique to characterize corn yield variability using the CERES-Maize process-oriented crop growth model, and to characterize soybean yield variability using the CROPGRO-Soybean process-oriented crop growth model.

Drummond et al. (1995) compared several methods for predicting crop yield based on soil properties. They noted that the process of understanding yield variability is made extremely difficult by the number of factors that affect yield. They used several multiple linear regression methods --- such as multiple linear regression (MLR), R ² = 0.42; stepwise MLR (SMLR), R ² = 0.43; partial least squares regression (PLSR), R ² = 0.43; projection pursuit regression (PPR), R ² = 0.73; and back-propagation neural network (BPN), R ² = 0.67 --- for modeling the relationship between corn yield or soybean yield and soil properties. They concluded that less-complex statistical methods, such as standard correlation, did not seem to be particularly useful in understanding yield variability. The correlation matrices described each factor's linear relationship to yield. However, when complex nonlinear relationships between factors exist, correlation may provide inaccurate and even misleading information about these relationships.

Data mining tools are beginning to show value in analyzing massive data sets from complicated systems and providing high-quality information (White and Frank, 2000). An artificial neural network (ANN) is an attractive alternative for building a knowledge-discovery environment for a crop production system. An ANN can use yield history with measured input factors for automatic learning and automatic generation of a system model. In the past few years, several yield simulation models have been built. Ambuel et al. (1994) used a fuzzy logic expert system to predict corn yields with promising results. The functional relationship using the fuzzy logic expert system was expressed linguistically instead of mathematically. The authors suggested the use of a neural network to predict within-field yields.

Prediction capabilities were highest for the nonlinear, non-parametric methods. One method Drummond et al. (1995) tried to use was a feed-forward, back-propagation ANN for corn and soybean yield prediction. They included soil properties, such as phosphorus (P), potassium (K), pH, organic matter, topsoil depth, and magnesium saturation as inputs and compared the results with other statistical models. The ANN showed promise as aid in understanding yield variability, although their network model needed further improvements for increasing accuracy. They did not include weather information and other factors in their ANN.

An ANN trained to relate crop yield to the factors that affect yield could be very useful in setting more realistic target yields within fields for precision agriculture. Crop yields are highly dependent upon weather, which cannot be predicted. However, all inputs except weather could be specified for a trained ANN. Many years of past weather records could then be input to calculate yield variation with weather. From such calculations, it would be possible to calculate probabilities of achieving crop yields at various levels. In selecting target yields, a producer would then be able to estimate the probabilities of achieving those yields.

An ANN trained to predict yield accurately in one field might not be accurate in another field. If some unmeasured factors influenced yields, the training process might set weights that compensated for the omissions in the field used for training. If the level of those unmeasured factors differed in another field, the neural network trained in the first field would be inaccurate in the second field. However, an advantage of the ANN is that it may be practical to do initial training on a field with a large database, and then retrain the network for other fields with much smaller databases. The ANN topology could be the same for all fields, but through retraining, ANN weights could be specific to each field. Moreover, the weights for each field could be updated through retraining each time a new crop was harvested.

Objective

The objective of this research was to build up an ANN model to approximate a nonlinear function relating corn yield to soil, weather, and management factors, and to evaluate this model.

ANN Development

The neural network used in this research is a back-propagation, fully connected, feed-forward neural network. The reader is referred to Neural Networks: A Comprehensive Foundation (Haykin, 1994) for details on how an artificial neural network works.

Input Factors Analysis

Before building the neural network, the number of inputs must be determined. All the important factors should be included in the input layer. Selecting the input factors was based on agronomic knowledge and trial and error through running the network. Analyzing corn development is the first step in understanding the input factors.

Temperature

The accumulated heat unit, metric Growing Degree Day (GDD), an important factor for corn development, is often computed by:

(1)

where

high temp. = Daily maximum temperature ( = 30 ? C)

low temp. = Daily minimum temperature ( = 10 ? C).

In Central Illinois, the metric GDD requirement for corn maturing is about 1000. This depends on the planting date and growing season temperature. Corn yield may be reduced 95 kg per hectare for each day that the temperature reaches 35 ? C or higher during pollination and grain-fill, so the maximum temperature during pollination and grain-fill is important. During germination, if the soil temperature is less than 10 ? C, germination is delayed. Thus, the May mean temperature is also an important factor affecting germination (Hollinger et al., 1997; Pepper, 1996).

Rainfall

The water requirement of corn varies according to the stage of development. Corn reaches its peak water use during pollination when the plants are silking. During the two weeks before and two weeks following pollination, corn is very sensitive to drought. Dry soils during this period may cause serious yield losses. Thus, in the neural network, rainfall during this period should be partitioned into critical periods (Pepper, 1996).

Soil Texture

Soil texture refers specifically to the relative proportions of sand, silt, and clay in a mass of soil. Silt soils are highly desirable for plant growth because of optimum soil water availability. An important difference between sands, silts, and clay is in their ability to supply plant nutrients and to hold water (Drallmeier et al., 1996).

Soil pH

Soil pH influences availability of soil nutrients for plant uptake. Many of the organisms involved in nitrogen transformations in the soil have their function impaired in soil with a low or high pH. For instance, soil pH has a pronounced effect on P (phosphorus) reactivity and its availability to the plant. Soils with high base saturation and a near neutral pH allow greater plant absorption of K+ from the soil solution (Drallmeier et al., 1996).

Management

Most soils cannot supply all the essential nutrients for continuously cropped soils, so they must be supplemented with fertilizers. The measurement of available P and K and yield goal information are used to make P and K fertilizer recommendations. Soil nitrogen levels generally are not tested because nitrogen is mobile in the soil and the nitrogen cycle is complex. Recommendations for N are made based on expected yield and the subsequent N removal that has been estimated for different crops. In Illinois, available Bray P ₁ levels of 0.00448 ppm, 0.00504 ppm, and 0.00560 ppm in high, medium, and low P-supplying regions, respectively, are recommended to maximize crop yields. Available K levels of 0.0291 ppm and 0.0336 ppm in low and high CEC regions, respectively, are recommended. Nitrogen fertilizer needs are estimated as follows (Drallmeier et al., 1996; Hollinger et al., 1997) :

N = 0.07 ׍ Y (2)

where

N = Amount of N needed (kg/ha)

Y = Corn yield (Mg/ha).

Before developing the neural network, we express the yield as a function of the factors affecting yield. For convenience, we group these inputs into four categories:

Yield = f ( SF , WF , MF , RF ) (3)

where

SF = Inherent soil factors, including:

Topsoil depth

Soil texture

Soil slope

Soil P

Soil K

Soil pH.

WF = Normal weather factors, including:

Precipitation, especially during critical periods

Temperatures during the month of May

No. of days temperature exceeds 95 ? F during pollination and grain fill periods

Growing Degree Days during the growing season.

MF = Management factors, including:

Seed selection (i.e., genetic yield potential of the seedcorn)

Pest control (weeds, insects, diseases)

Nitrogen fertilizer applied

Planting density

Crop residue management

Crop rotation

Irrigation

Drainage.

RF = Random factors (i.e., unpredictable, unusual events), including:

Damaging hail storms

Damaging winds

Sudden introductions of new insects or diseases (e.g., southern corn leaf blight)

Unusual, untimely frost.

Date Source

The Morrow Plots data were used to build up the ANN model. The Morrow Plots, located on the campus of the University of Illinois at Urbana-Champaign, are the oldest agronomic research plots in the United States and include the oldest continuous corn plot in the world. The average corn yield has ranged from 2 Mg/ha on the continuous-corn plot that received no fertilizer treatment to approximately 10 Mg/ha on plots that were planted to a corn-soybean rotation and received generous soil treatments (Morrow Plots, 1984). The Morrow Plots data were divided in four periods according to the soil and management treatments (Aref and Wander, 1998). Data from the fourth period (1967-1997) were employed in this research. In this phase, high amounts of NPK were added to a previously manured plot (SA). In addition, the Morrow Plots were subdivided into three parts from north to south. Only Plot 3 (continuous corn) and Plot 4 (a corn-soybean rotation) were used for developing the ANN. Plots 3 and 4 are further divided into a total of 16 subplots, each 10 m ׍ 10 m. Plots 3 and 4 of the Morrow Plots are shown in figure 1.

The soil type in the Morrow Plots is Flanagan silt loam. Although the soil type was invariant, each part received different fertilizer treatments. Plot 3, with 8 records per year and 30 years of records, and Plot 4, with 8 records per year and 15 years of corn yield records, provided the total set of 360 examples for the ANN. For the Morrow Plots data set, the temporal distribution was much larger than the spatial distribution. Plot treatments are summarized in tables 1 and 2.

Figure 1 . The Morrow Plots and an aerial image in early July of 1997.

Table 1 . Plot 3, Continuous corn ^{[a] .}

3 NA U 20,000 ^[b]	3 NB U-NPK 20,000	3 NC U 20,000	3 ND U 20,000
3 SA H-NPK 60,000	3 SB M-NPK 60,000	3 SC MPS 40,000	3 SD M 30,000
^[a]NA = Western sub-subplot remained untreated after 1955. NB = Eastern sub-subplot, NPK added in 1955. NC = Western sub-subplot remained untreated after 1955. ND = Eastern sub-subplot remained untreated after 1955. SA = Western sub-subplot received high-level NPK from 1967. SB = Eastern sub-subplot; NPK added in 1955. SC = Western sub-subplot remained manured. SD = Eastern subplot remained manured. U = Untreated plots. M = Manure-treated plots. MPS = Manured plots with higher planting density. U-NPK = NPK treatment applied to previously untreated plots. M-NPK = NPK treatment applied to previously manured plots. H-NPK = High-level NPK treatment applied to previously manured plots. ^[b]Numbers are seeding rate in seeds per hectare.

Table 2 . Plot 4, Corn-soybean rotation ^{[a] .}

4 NA U 30,000 ^[b]	4 NB U-NPK 60,000	4 NC U 30,000	4 ND U 30,000
4 SA H-NPK 60,000	4 SB M-NPK 60,000	4 SC MPS 40,000	4 SD M 30,000
^[a]NA = Western sub-subplot remained untreated after 1955. NB = Eastern sub-subplot, NPK added in 1955. NC = Western sub-subplot remained untreated after 1955. ND = Eastern sub-subplot remained untreated after 1955. SA = Western sub-subplot received high-level NPK from 1967. SB = Eastern sub-subplot; NPK added in 1955. SC = Western sub-subplot remained manured. SD = Eastern subplot remained manured. U = Untreated plots. M = Manure-treated plots. MPS = Manured plots with higher planting density. U-NPK = NPK treatment applied to previously untreated plots. M-NPK = NPK treatment applied to previously manured plots. H-NPK = High-level NPK treatment applied to previously manured plots. ^[b]Numbers are seeding rate in seeds per hectare.

Training and Test Set Preparation

Data preprocessing can greatly assist ANN learning, and it may sometimes be essential to enable an ANN to detect patterns contained in the learning data set (Lacroix et al., 1997). Before they were entered into the neural network, each of the 15 data input sets was normalized from 0 to 1 based on the maximum value of each input.

Stratified random sampling was used to select a test data set, based on the growing season total rainfall. Rainfall was grouped into three patterns: low, medium, and high. We first sampled the test set from each of the three rainfall levels, and each rainfall pattern included at least one subplot of each plot. In the same rainfall pattern, there might be several subplots, randomly chosen. The test set was withheld from training and used only to verify the prediction accuracy of the ANN. The remaining data were used as the training set. The total set included 360 patterns, of which 300 were used for training. During the neural network training, the training set was re-randomized after each epoch. Thus, in each training epoch, the training set was presented to the ANN in a new order.

Hybrid Yield Potential and Rotation Factor

All the inputs for the ANN must be numeric. Hybrid selection is an important factor for corn yield, so we developed a means for expressing hybrid selection numerically. The hybrid genetic potential is defined as the yield that would be produced if weather, soil, and fertility were all optimum. Actual yields are below the genetic potential to the extent that the various input factors differ from their optimum levels. Our initial approach to finding the genetic potential was to identify the corn hybrids that were used in the Morrow Plots over the 30-year period to be used to train the neural network. Data from the Illinois corn hybrid trials at Urbana (Corn Hybrid Test Results in Illinois, 1967 - 1997) were used to find the actual yields for each of these years. Next, a linear regression line was fit through these data. The annual yields in the trials varied considerably with annual weather conditions. Assuming weather as a random variable, however, the slope of the line (126 kg/ha or 2 bu/acre per year) was used as the annual increase in the genetic yield potential. The maximum yields in the trials were well below corn yields noted in yield contests reported, suggesting that conditions in the Illinois hybrid corn yields trials were not optimum. Therefore, the regression line was shifted upwards to more nearly approximate genetic yield potential. The equation for the resulting line was used to calculate the genetic yield potential in the year the hybrid was used in the Morrow Plots. Some hybrids were used for multiple-year periods, and the genetic potential was held constant during those periods.

A rotation factor was selected based on an observation of corn yields in a corn-soybean rotation compared to those from continuous corn. We observed that the corn yields in the rotation plots averaged about 50% higher than those in continuous corn plots. Thus, we used a rotation factor of 1.0 for continuous corn and 1.5 for corn in the rotation. We tried several other rotation factors, but using 1.5 gave the most accurate yield predictions.

Neural Network Model and Network Topology

Many computational models can map numerical input vectors to numerical outputs without knowing the mathematical function describing the actual process that generates the outputs. Function approximation is the task of learning or constructing a function that generates approximately the same outputs from input vectors as the process being modeled, based on available training data (Mehrotra et al., 1997).

The back-propagation neural network is a universal approximator (Haykin, 1994). Given sufficient hidden units, multi-layer feed-forward network architectures can approximate virtually any function of interest to any desired degree of accuracy (White et al., 1992).

The network training used data from the Morrow Plots. The input factors assumed to influence corn yield and for which data were available from the Morrow Plots included:

Soil:

· pH

· P

· K

· Organic matter

Weather:

· Growing season GDD

· May rainfall

· June rainfall

· Early July rainfall

· Late July rainfall

· August rainfall

· Previous year rainfall

Management:

· Genetic yield potential of the hybrid

· N fertilizer applied

· Planting density

· Rotation factor

Random factors were not modeled because we had no data on their effects. Input data that were invariant across the total experiment do not contribute to the ANN model and were excluded.

The segmentation of rainfall during the growing period was based on the planting date. May rainfall was the rainfall in the 30 days following planting, June rainfall was the rainfall in the next 30 days, early July rainfall in the next 15 days, and late July rainfall in the next 15 days.

The final model included 15 elements in the input vector, 20 elements in the hidden layer and one element (corn yield), in the output vector. The transfer function for each neuron in the hidden layer and output layer was the sigmoid function.

Parameter Selection

For a feed-forward, back-propagation network, the important parameters include initial weights, learning rate, number of hidden elements, and number of training epochs. Trial and error was used to select the parameter values that would give the most accurate predictions.

The most successful back-propagation structure was 15-20-1 and a constant learning rate of 0.01. Initial weights were generated randomly, and 5000 epochs were used in training. Thus, with 300 examples in each epoch, 1.5 million examples were used in training the ANN. Matlab version 5.2 was used to implement the model, which ran on a Sun workstation. Training required less than 10 minutes of computer time.

ANN Performance Evaluation

After the ANN was trained, its performance was evaluated in several aspects. First, the effect of each input factor on output yield was evaluated. A test example was randomly selected. One by one, each input was varied over its actual range while all other inputs were held constant at their values found in the test example. Output yield was plotted versus each input factor. Next, the ability of the ANN to handle interactions was evaluated. The plot of output yield versus late July rainfall was augmented by calculating and plotting yields for nitrogen fertilizer amounts equal to 20%, 67%, and 100% of that used in the test example.

The next performance evaluation was to determine whether the trained ANN could predict a yield higher than the 12.6 Mg/ha (200 Bu/acre) maximum yield used in training. A genetic algorithm (GA) was used to search the range of each of the 15 input factors to determine the combination that would produce the theoretically maximum yield. As described by Book (1996), the GA is an optimization procedure that finds global, not local, maximums. The GA is an adaptive search method that is modeled after the genetic evolutionary process. Briefly, one combination of input variables is a string, and a collection of strings is a population. At each iteration, known as a generation, each of three GA operators --- reproduction, crossover, or mutation --- is applied to each string. The reader is referred to Book (1996) for a fuller description of the GA.

The 15 input factor ranges from the Morrow Plots data were each divided into 8 levels, generating a possible 8 ¹⁵ different input factor combinations. The 15 input parameters were constructed using a 45-bit binary string, with each 3-bit group in that string representing a parameter with 8 levels (2 ³ = 8). Each parameter was assigned a fixed location in a string. Based on the input parameters, the string was organized in the following order: pH, nitrogen, P, K, soil organic matter, GDD, yield potential, May rain, June rain, early July rain, late July rain, August rain, previous year rain, planting density, and rotation factor.

Goldberg's (1989) rule of thumb was used in setting the population size. It calls for a population size approximately equal to the string length (i.e., 45), but the population size also depends on the problem. After experimentation, we used a population of 100.

The selection scheme implemented for reproduction was a binary tournament selection with replacement, which selected the better of two randomly picked strings. The best, in this case, was the parameter string that produced the highest calculated yield.

A single point crossover among the selected strings was utilized to generate a new population for each generation. In De Jong's (1975) study of genetic algorithms in function optimization, it was suggested that good GA performance required the choice of a high crossover probability. The probability of crossover was chosen to be 0.7 in this case.

Goldberg (1989) recommended a mutation rate inversely proportional to the population size. This criterion predicted a rate of 0.02 for this problem. However, since tournament selection would tend to encourage convergence of the GA, a higher mutation rate might be necessary. A mutation rate of 0.04 was used in this application.

The trained ANN was applied for function evaluation. After each generation with three operators, the 15 input parameters were fed into the model for computing the yield. The process stopped if the generation number was greater than 100.

The final step in evaluating the trained ANN was to perform a sensitivity analysis. A base-case yield was calculated with each input factor set at the midpoint of its observed range. Then the first input factor was incremented by 10% of its range and the yield was calculated while all other input factors were held constant at their range midpoint. The base-case yield was subtracted from the incremented yield to determine the sensitivity of the calculated yield to the first input factor. This process was repeated for each of the other input factors.

Results

Figure 2 illustrates the ANN that was developed to relate corn yield to the factors shown in the input layer. The ANN has 15 input nodes, 20 hidden-layer nodes, and one output node.

Figure 1 . The final feed-forward, back-propagation neural network for calculating corn yields.

The accuracy of the trained ANN was evaluated by calculating an individual modeling error for each of the 60 examples reserved for testing. Individual prediction errors were calculated as:

(4)

Using equation 4, positive errors indicate over-predictions, while negative errors indicate under-predictions. To obtain an overall accuracy measure for the 60 test examples, the RMS error was calculated:

(5)

where N = 60 (i.e., the number of reserved test examples). As shown in figure 3, a histogram of the test set errors, the RMS error was approximately 20%. The RMS error is the result of three separate trials, since the random selection of the initial weights had some influence on the RMS error. As expected, the histogram approached a normal distribution, except that there was one very large over-prediction of yield.

Figure 3 . Error histogram for the trained ANN.

Figure 4 illustrates calculated yield variation with several of the input factors. The curves for fertilizer and rain show the expected classic shape, i.e., the calculated yield increases to a maximum and then decreases as the input factor is applied in excess. As expected, yield flattened but did not decrease with continuing increase in growing degree days. No explanation was found for the puzzling decrease in calculated yield as the yield potential input approached its maximum.

Figure 4 . Calculated yield trends with selected input factors: (a) yield vs. nitrogen, (b) yield vs. growing degree days, (c) yield vs. yield potential, and (d) yield vs. late July rain.

Figure 5 shows the interactive effect of nitrogen fertilizer and late July rain on the calculated yield. Calculated yield declined when rainfall exceeded an optimum amount, and the optimum amount increased with increasing applications of nitrogen fertilizer.

Figure 5 . Interactive effect of nitrogen fertilizer and late July rain.

Table 3 lists the results of the GA analysis to determine the calculated yield when all factors were optimized. The actual minimum and maximum (i.e., the range) of each input variable is also shown. The bottom line of table 3 shows that the calculated yield was 0.974 Mg/ha when all inputs were at their minimum, 6.91 Mg/ha when all were at their maximum, and 22.2 Mg/ha when all were at their optimum. The interactions captured by the ANN allowed it to calculate an optimum yield that was 75% larger than the largest observed yield used in training the ANN.

Results of the sensitivity analysis are in the last column of table 3. The calculated yield showed the greatest sensitivity to the late July rain. The next greatest sensitivity was to nitrogen fertilizer, followed closely by early July rain and August rain. Soil phosphorous ranked fifth in influencing yield. May rain and June rain were tied in sixth place in influencing yield. The calculated yield showed considerably less sensitivity to the remaining eight input factors.

Table 1 . Summary of input variable ranges and optimization results.

Factors	Units	Minimum Value	Yield Maximizing Value	Maximum Value	Sensitivity ^[a](Mg/ha)
pH	--	5.0	6.8	6.8	2.60
Nitrogen	kg/ha	0	192	336	7.69
P	kg/ha	7.84	228	228	7.52
K	kg/ha	179	241	612	4.00
Carbon	g/kg soil	14.7	17.27	22	2.44
GDD	--	1280	1560	1930	2.57
Yield potential	Mg/ha	21.2	25.1	25.1	2.87
May rain	cm	1.22	1.22	23.6	7.32
June rain	cm	0.838	16.4	21.2	7.32
Early July rain	cm	0.051	18.6	18.6	7.62
Late July rain	cm	0.406	8.92	20.1	7.82
August rain	cm	1.27	24.4	24.4	7.58
Antecedent rain	cm	30.2	80.0	80.0	3.16
Planting density	seeds/ha	20,000	60,000	60,000	3.15
Rotation factor	--	1	1.5	1.5	2.37
Prediction yield	Mg/ha	0.974	22.2	6.91
[a] To a 10% change in the input factors.

The results of the yield potential determinations are illustrated in figure 6. Initially, the trend line through the observed yields of the seed corn trials was shifted upwards to pass through the highest observed yield, and the resulting shifted line was used in selecting yield potentials while training the ANN. However, the optimum yield as determined by the genetic algorithm was nearly double the highest observed yield. Thus, the trend line was shifted further upward to pass through the optimum yield, and the ANN was retrained. The equation for the final trend line was:

(6)

where

PY = potential yield of the hybrid seed corn (Mg/ha)

Y = year of introduction of the hybrid.

Figure 6 . Illustration of yield potential calculation.

Application on Another Field

The ANN was 80% accurate when tested using the reserved data set from the Morrow Plots. The same ANN, without retraining, was tested on another University of Illinois field --- the Dudley Smith farm. Field 7 of this farm was in a soybean-corn rotation. The 32-hectare field includes five soil types: Herrick silt loam, Virden silt loam, Virden silty clay loam, Oconee silt loam, and Harrison silt loam. The field was divided into 1041 grid points with 18.3 m ׍ 18.3 m spacing Compared with the Morrow Plots, the Dudley Smith farm had much greater spatial distribution but only two years of temporal data were available. When used on the Dudley-Smith farm without retraining, the ANN gave an RMS yield prediction error of 41.3%, i.e., the prediction accuracy fell to 58.7%. Through re-training, the prediction accuracy was increased to 83% for the Dudley-Smith farm field. Details of the Dudley-Smith farm study are too voluminous to be included here, but they are the subject of a forthcoming paper.

Discussion

As previously mentioned, one point in figure 3 was a yield over-prediction error of about 90%. There are two reasons for this large over-prediction. First, like traditional regression analyses, an ANN is not good at predicting extremes. By definition, all of the training examples lie in the range between the minimum and maximum observed yields. Thus, there are no training examples below the minimum nor above the maximum observed yield. The consequent reduction in numbers of training examples near the observed yield limits reduces the ability of the ANN to predict yield extremes. It is also significant that the largest prediction error was an over-prediction of the yield in a plot in the northwest corner of the Morrow Plots. This plot had been in continuous corn with no fertilizer applied for nearly a century, and the observed yield was very low. As a result, the base of the error percentage was also very low. If we ignored that plot, the RMS prediction error would fall from 20% to about 16.5%.

The 1993 observed yields in two plots in the northwest corner of the Morrow Plots were abnormally low. Aref and Wander (1998) studied the data and found the low yields were not due to weather, soil, or management factors. Instead, gray squirrels damaged those plots in 1993. Because we had decided to eliminate random input factors, the examples with squirrel damage were eliminated from the training data set.

The trained ANN was able to capture expected interactions between input factors. In figure 4, no amount of rainfall was able to produce high yields with low nitrogen fertilizer application. Calculated yield rose sharply with increasing rainfall when a normal amount of nitrogen fertilizer was applied, but began to fall when rainfall became excessive. As expected, the peak of the yield vs. rainfall curve moved to the right with increasing fertilizer application, i.e., the more nitrogen, the more yield could increase with rainfall before rainfall became excessive.

Using a genetic algorithm, and with appropriate normalization of the ANN variables as discussed below, we were able to find a combination of input variables that predicted a yield of 22.2 Mg/ha (table 3). This calculated yield was 75% larger than the highest observed yield used in training the network and was possible because of interactions captured by the ANN.

The network parameters affected the ANN significantly. For the BP model, the important parameters were learning rate, number of training epochs, and number of hidden layer elements. We tried 10, 20, 30, 40, 50, 70, 100, and 200 hidden layer elements. The RMS errors generally declined with increasing numbers of hidden-layer elements, but training time increased. For example, training required one hour when 200 hidden-layer elements were used with 5000 epochs and 0.01 learning rate. Twenty hidden elements were used in the final BP network. We also tried a topology with two hidden layers, but the results were no better than with one hidden layer.

We tried 3000, 5000, 8000, and 10,000 training epochs. After 8000 epochs, the network was over-trained; the training set error went down, but the test-set RMS error went up. In the final BP network, 5000 epochs were used.

We tried constant learning rate parameters of 0.1, 0.01, and 0.001 before choosing 0.01 as the best one. In addition, the dynamic learning rate was varied from 1 to 0.1 to 0.01, but the results differed little from using a constant learning rate of 0.01. The dynamic learning rate was large for initial epochs and was made smaller for later epochs.

All input variables were normalized, i.e., each was divided by its observed maximum value before being presented to the network. Initially, each observed yield was divided by the maximum observed yield for training the network, but the neuron design then prevented prediction of yields larger than the maximum observed yield. This problem was solved by dividing each observed yield by twice the maximum observed yield.

The approach used to calculate the genetic yield potential of the corn hybrid, i.e., calculating the linear regression from hybrid yield trials and then shifting it upwards, is of questionable accuracy. However, no better method for calculating yield potential was available, and the method used was thought to be better than simply ignoring changes in yield potential. Fortunately, experimentation with the ANN showed that the intercept value of the yield potential line had minimal effect on the results.

Approaches to yield prediction include microprocess models, regression models, and automatic learning models. A producer with fertilizer spreaders capable of mapping variable rate applications and with a combine equipped for yield mapping can accumulate much of the data needed for training an ANN. Additional training data must come from soil type information and from weather stations. By subdividing each field into cells, the producer could use the data from each cell in training a separate ANN for each individual field. This approach can defeat the degradation in accuracy that often occurs when a model is applied over wider areas. The work reported in this paper is only a first step in the approach to training an ANN for each field. Few producers have the 30 years of record that were available from the Morrow Plots. Further work is planned to test and then retrain the ANN for a new field of larger size and with a variety of soil types. Additional research may be required to deal with problems encountered in the first two steps. Hopefully, these steps will lead to an accurate ANN capable of modeling the yield variation in a specific field based on the input factors influencing yield.

Because corn yields are heavily dependent on weather, and future weather is unpredictable, some may question the value of an ANN for setting target yields. However, the trained ANN could be used in further work on calculating yields based on historical weather patterns. From such calculations, the probability of achieving any given yield level from a specific field could be calculated. Then, for any selected probability level, a producer could choose target yield levels with some confidence. Before using the ANN with such weather records, however, it should be used with data from a wider variety of fields. Again, the work on the ANN reported in this study is viewed as only an initial step toward the final goal of modeling yield variation in individual fields.

Summary and Conclusions

Setting a realistic yield goal in each part of the field is one of the critical problems in precision agriculture. In this research, an artificial neural network (ANN) was employed to model the relationship between yield and the factors influencing yield. The influencing factors included soil factors, weather factors, and management factors. Random factors were excluded. The ANN parameters tested included network type, network topology, learning rate, initial weights, type of transfer function, and number of training epochs. A portion of the data set, selected by stratified sampling, was withheld from training and used to verify the accuracy of the yield predictions. The following conclusions were drawn:

· The back-propagation, feed-forward neural network predicted corn yields with 80% accuracy. When an example with abnormally low yield was discarded, accuracy rose to 83.5%.

· Calculated yield trends were realistic, i.e., yields showed the expected increase, flattening, and then decrease as various input factors were increased.

· The network was able to capture the expected interaction between rainfall and amount of applied nitrogen fertilizer.

· An optimum combination of input factors was found that allowed the ANN to predict a yield 75% larger than the maximum observed yield used in training the ANN.

· The calculated yields were most sensitive to rainfall (especially late July rainfall), nitrogen fertilizer, and soil phosphorous.

Acknowledgements

The authors gratefully acknowledge Dr. Susanne Aref for providing data from the Morrow Plots, Mr. Robert Dunker for providing information on hybrid seed corn, and Dr. Jim Angel for providing Urbana weather data. This research has been supported by the Illinois Council of Food and Agricultural Research (C-FAR), Project Number 99I-113-3.

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