Biosystems Engineering (2002) 83(3), 299–306doi:10.1016/S1537-5110(02)00201-5, available online at http://www.idealibrary.com onPA}Precision Agriculture

1

An Information Table for Yield Data Analysis and Management

Q. Zhang1; S. Han2

1Department of Agricultural Engineering, 338 Sc. Building, University of Illinois at Urbana-Champaign, 1304 W pennysywania Avenue,Urbana, IL 61801, USA; e-mail of corresponding author: qinzhang@uiuc.edu

2John Deere Ag Management Solutions, Urbandale, IA 50322, USA; e-mail: hanshufeng@johndeere.com

(Received 9 October 2001; accepted in revised form 16 August 2002)

The lack of standard methods for processing and managing yield data is an obstacle for farmers to utilise yielddata effectively and efficiently. This paper presents a formal method of using an information table foranalysing and managing raw yield data in a format of information subsets for a manageable block in the field.An ordinary procedure for developing such an information table was introduced. A case study was performedto demonstrate the use of this method to support decision-making in precision agricultural operations. Thisformal method provided a standard technique for yield data analysis and management in real-time, and can beeasily programmed in a ‘transparent-to-farmer’ data management tool. The case study demonstrated theapplication of this model in managing the yield data obtained from an actual field in Central Illinois during aperiod of 5 yr. The results indicated that the model was capable of achieving its design goal. # 2002 Published by

Elsevier Science Ltd. on behalf of Silsoe Research Institute

1. Introduction

Recent advances in precision agriculture technology,such as site-specific management and variable-rateapplications, have promised farmers a means of moreefficient and more profitable production. For example,farmers are now capable of fertilising different zones oftheir fields at different rates to have the maximum yield(Yang et al., 1998). Yield mapping, a measure of thecrop production integrated over space and time,provides the fundamental information to adjust theinputs to identified areas to optimise farming profit-ability. However, precision agriculture practices requirespecial skills to deal with the enormous amount of yielddata to obtain the necessary information to supportoptimising production efficiency and profitability. Lackof standard methods for yield data analysis andmanagement is an obstacle for farmers utilising yielddata effectively and efficiently to support their precisionproduction.

Numerous studies have been reported in the areas ofyield monitoring, site-specific natural resources manage-ment, and geographical information system (GIS) basedfarming systems for storing site-specific production datain a map form (Graham et al., 1997; Payne et al., 1997;Plant, 2001; Robert et al., 1996; Walley et al., 2001). The

537-5110/02/$35.00 299

challenge in utilising a yield map is how to convert themassive site-specific data into the knowledge to supportthe decision-making which often requires some specialskills. Many researchers have put great effort intodeveloping technologies to address this issue. Examplesinclude the development of integrated informationmanagement system for agriculture (Thiel et al., 1999),finding a proper way of integrating multiple-year yielddata into a single map (Panneton et al., 2001),developing a field-level geographic information system(FIS) for analysing agricultural data relevant to preci-sion agriculture (Runquist et al., 2001), classifying yieldlevels using fuzzy logic (Stafford et al., 1998), anddeveloping an automated and analytical procedure todelineate information management zones for variableapplication management based on the yield map(Fraisse et al., 1999). While technologies being devel-oped can effectively collect, analyse and utilise thespatial and/or temporal data, more efforts are nowfocused on how to integrate those technologies andrepresent it in a standard way so that the integratedtechnology can be easily implemented in a ‘transparent-to-farmer’ format.

The focus of this paper is to develop a formal methodof using an information table to represent the spatialand temporal yield data. The information table will

# 2002 Published by Elsevier Science Ltd. on behalf of

Silsoe Research Institute

Q. ZHANG, S. HAN300

Notation

C a measured yield level subset of UD a block average yield subset of UIb information subsetSb influential factor sub-subsetU a finite and non-empty set of yield data%XX the average yield from the field of interest

M number of raw data within a block in thefield

N number of raw data within an area of interestP number of years of historic data being usedQ number of blocks defined in a fieldxi a raw yield data element in set U%xxd the average yield from a block in the fieldyj a yield level in subset C, represented in

natural language

a an arbitrary valve for cut-off confidence levelmyj

ð�Þ the confidence level of a yield level within ablock in the field

myj jUkð�Þ the confidence level of a yield level within a

block in the field in year ksd the standard deviation of the yield from a

block in the fieldsU the standard deviation of the yield within the

field of interestSup symbol of fuzzy union operation

SubscriptsA average levelH High levelL Low level

provide a formal approach for raw data processing,massive yield data classification and site-specific yieldclass presentation. To present the developed methodclearly, this paper is organized as follows. Section 2provides the formal presentation of the informationmodel, the detailed procedures for using the informationtable approach to represent the massive yield data,and the use of this information table to supportdecision-making. Section 3 uses an actual sample of5 yr yield data to evaluate the effectiveness andaccuracy of this developed information table methodin sorting and representing the massive raw yield data.Finally, a brief summary is given based on the case studyresults.

2. Information table model

2.1. Formal presentation

The information table model, consisting of a con-fidence measure of the yield levels, was developed forconverting massive yield data into knowledge. Theformal presentation of the information table modelcan be described as follows.

Let U be a finite and non-empty set, called theuniverse of discourse, covering a definite range of yielddata obtained from a field over a number of years. Let D

be a subset of U containing the average yield from aspecific block within the field, and C be anothersubset of U containing all the possible yield levelsrepresented using natural language. Each element %xxd inD can be mapped into at least one element yj in C

associated with a confidence factor between 0 and 1,where 0 means no confidence at all and 1 meanscompletely confident.

An information table presents the complete list ofpossible yield levels with an associated confidence factorfor each block in a field, and prepares the massive rawyield data in a format suitable to support automateddecision-making.

To ensure the information table (Table 1) modelcontaining adequate information, the following fourproperties should be held:

8 %xxd 2 D; 9 at least one yi 2 C; such that

yj ¼ %xxd ¼P

D xi

m

� �;myj

%xxdð Þ 2 0; 1½ �� �

ð1Þ

8 %xxd 2 D;Xn

j¼1

myj%xxdð Þ ¼ 1 ð2Þ

8 %xxdi U1;8 %xxdi

U2; y jjU1�U2

¼ sup myjjU1%xxdi

� �;myjjU2

%xxdi

� � ð3Þ

where: sup indicates a logic operation of finding themaximum value, and myj

ð�Þ is a fuzzy membership usedto describe the confidence level of an estimated yieldlevel for an interested block in the field.

The first property indicates that the average yield dataobtained from each block in the field can be mappedinto at least one fuzzy yield level, and its confidencelevel, described using a fuzzy membership, can bebetween 0 and 1. A confidence level of 0 means thatthe particular yield level does not reflect the average

Table 1General presentation of yield information table

Block identity Confidence level myiof a defined yield level

Yield level L Yield level A Yield level H

1 mLð %xx1Þ mAð %xx1Þ mH ð %xx1Þ2 mLð %xx2Þ mAð %xx2Þ mH ð %xx2Þ

. . . . . . . . . . . . . . . . . . . . . . . .q mLð %xxqÞ mAð %xxqÞ mLð %xxqÞ

%xx, average yield of block.

YIELD DATA ANALYSIS AND MANAGEMENT 301

yield data in the block of interest, and 1 means the yieldlevel strongly reflects the average yield data. Aconfidence level between, but not including, 0 and 1indicates that this yield level partially reflects the averageyield from the block of interest.

The second property indicates that the yield from theblock of interest can be classified into more than oneyield level. However, the total membership, a measure ofthe confidence on those possible yield levels, should be 1.This property prevents the same information from beingover-counted.

The third property is used to handle multi-year datafrom the same block. When yields from multiple yearsare being considered, a separate universe of discourseshould be used because the distribution of the yield datamay be totally changed from year to year due to theinfluence of many factors, including many unknownones. To solve this problem, the first and the secondproperty should be held in preparing yield data for eachyear. Based on all single year results, this propertyprovides the yield potential from each block.

0

0.2

0.4

0.6

0.8

1.0

Average

Fuzz

y m

embe

rshi

p

X−3σU

AveraLow yield

X−2σU X−σU

Fig. 1. Definition of fuzzy membership functions for low, averagefrom the entire field: %XX ; average yield of the en

2.2. Model development procedure

To develop an informative site-specific productioninformation table based on massive yield data, thefollowing six procedural steps should be followed forensuring that all three properties are held.

(1) Determine the average yield %XX and its standarddeviation sU based on the sample size n of themassive raw yield data obtained from the field ofinterest:

%XX ¼X

U

xi ð4Þ

sU ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1 xi %XX� �2n 1

sð5Þ

(2) Define a manageable size of blocks for the field ofinterest. It is recommended to define 50–150 blocksha 1 to keep the table within a manageable size

block yield

ge yield High yield

X+σU X+2σU X+3σUX

and high yield from a block in field relation to the average yieldtire field; sU standard deviation of the yield.

Q. ZHANG, S. HAN302

while still being capable of representing reasonabledetails of the yield distribution within a field.

(3) Collect the raw data of sample size m from eachblock, and calculate its average yield %xxd andstandard deviation sd within that block:

%xxd ¼X

D

xi ð6Þ

sd ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPmi¼1 xi %xxdð Þ2

m 1

sð7Þ

(4) Define the yield level from the block of interest for aparticular year by placing the average yield of theblock related to the overall average yield of the fieldusing the following fuzzy membership functions. Itis recommended to represent the yield variation inthe block of interest using three levels of low,average and high yield. To be able to restore theoriginal average yield, some overlap of these yieldlevels were defined using fuzzy memberships. Threefuzzy membership functions were used to describethe degree of overlap. If a yield from a block wasbetween plus/minus two standard deviations of theaverage yield from the field, it was defined as anaverage yield. If the yield was below or above theaverage yield of the field, it was defined as a low orhigh yield. Fig. 1 illustrates the domains of thesefuzzy membership functions:

mL %xxdð Þ ¼

1;

1 2%XX 2sU

� � %xxd

2sU

!2

;

2%XX %xxd

2sU

� �2

;

0;

8>>>>>>>>>><>>>>>>>>>>:

%xxd4 %XX 2sU

%XX 2sU5 %xxd4 %XX sU

%XX sU5 %xxd4 %XX

%xxd > %XX

(8)

mA %xxdð Þ ¼

0;

2%XX 2sU

� � %xxd

2sU

!2

;

1 2%XX %xxd

2sU

� �2

;

2%XX þ 2sU

� � %xxd

2sU

!2

;

0;

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

%xxd4 %XX 2sU

%XX 2sU5 %xxd4 %XX sU

%XX sU5 %xxd4 %XX þ sU

%XX þ sU5 %xxd4 %XX þ 2sU

%xxd > %XX þ 2s

ð9Þ

mH %xxdð Þ ¼

0;

2%XX %xxd

2sU

� �2

;

1 2%XX þ 2sU

� � %xxd

2sU

!2

;

1;

8>>>>>>>>>><>>>>>>>>>>:

%xxd4 %XX

%XX5 %xxd4 %XX þ sU

%XX þ sU5 %xxd4 %XX þ 2sU

%xxd > %XX þ 2sU

ð10Þ

where mL, mA and mH are the confidence levelsfor the low, average and high yield levels, respec-tively.

(5) Determine the yield potential for each block ofinterest based on p multiple-year data using thefollowing fuzzy union operation equation. Thefuzzy union operation screens the yield level withthe highest fuzzy membership out from all applic-able levels:

myjjU1�U2�����Uk¼ sup myjjU1

%xxdð Þ;myjjU2%xxdð Þ; � � �yjjUk

%xxdð Þ

¼ [p

i¼1myjjUl

%xxdð Þ ð11Þ

(6) List the obtained block yield levels (both formultiple-year and for a particular year of interest)from the field in the information table. Theinformation table can be extended by includingother factors of influence, such as the soil type, fieldelevation and slope, as well as the amount offertiliser being applied and the precipitation of theyear of interest. The only requirement is that theinfluence of all factors should be represented in theform of fuzzy memberships using the methodintroduced in steps (1)–(5).

2.3. Application of the information table

After the information table has been completed, theyield-related information for a block of interest isrepresented in a form of information subset Ib: Thenumerator of each element in the subset represents theyield level, and the denominator represents the con-fidence level for the obtained yield level:

Ib ¼yL

myL

yA

myA

yH

myH

yUL

myUL

yUA

myUA

yUH

myUH

� � �� �

ð12Þ

To support decision-making effectively for optimisingthe production, it is important to retrieve only theinformation which influences the yield significantly. An

YIELD DATA ANALYSIS AND MANAGEMENT 303

a-cut method, which eliminates all the elements withassociated fuzzy membership less than an arbitraryvalue of a from the subset (Passino & Yurkovich, 1998),is used to create a new sub-subset from the informationsubset by selecting only the influential factors using anappropriate threshold value for a. Normally, it isrecommended to use a value greater than 0.5 to pickthe influential factors from a subset.

Sb ¼yi

myi

;myi5a

( ) Ib ð13Þ

The influential factor sub-subset Sb of the informationsubset carries only a few selected influential factorsbased on the objective of optimisation in support of thedecision-making. Therefore, this information tablemodel can reduce a complicated and tedious massiveyield data analysis and management into a standard andsimple fuzzy mapping problem and prepare the data in a‘ready-to-use’ format for further applications.

3. Case study of information table development andapplication

To demonstrate the development and application ofthis information table model without loss of generality,a yield information table for a small portion of a field inCentral Illinois was created based on a 5-yr yield data.

The field of interest covers an area of 475m by 800m.The crop follows a rotation of maize and soya bean.Due to the influence of numerous factors, the yieldvariation is very large from year to year. Table 2 lists theyields from the blocks of interest, the average yield ofthe entire field, the standard deviation of the yield, andthe total number of yield points collected from the field

Tab

Yield from blocks of interest, average yield of the entire field, sta

obtained from the field of

Variables Maize

1997 1

Yield of block 1, kg ha 1 11223 7Yield of block 2, kg ha 1 10910 6Yield of block 3, kg ha 1 13162 6Yield of block 4, kg ha 1 10599 9Yield of block 5, kg ha 1 11058 9Yield of block 6, kg ha 1 8754 6Yield of block 7, kg ha 1 11372 8Yield of block 8, kg ha 1 11056 9Yield of block 9, kg ha 1 11089 6Average yield, kg ha 1 10425 1Standard deviation, kg ha 1 1193 1Total number of yield points 27466 2

of interest from 1996 to 2000. All the yield points werecollected using a commercial yield monitor. Yield datawere recorded at a 1 s time interval from 1996 to 1999,and at a 3 s interval in 2000.

One important step in developing an efficient infor-mation table is the definition of a manageable andinformative base information block. To demonstrate thetechnique without loss of generality, a small portion of a35�56m by 35�56m area (a square of three-header widthsof the combine harvester used on this farm) wasrandomly selected from the field. Therefore, the squarearea of one header width (9�14m by 9�14m) was definedas the base block in this case study with a total numberof nine blocks.

Due to the uneven distribution of sampling points inthe field, the results indicate that the number of yieldsamples obtained from those blocks vary from 1 to 17.Figure 2 shows the distribution of yield data samplescollected from the nine base blocks in the portion beingstudied within the 5-yr period.

To handle the variation in sampling size within ablock, it is strongly recommended to use the averageyield data from a particular block as the base informa-tion. By applying the fuzzy membership functionsdefined in the previous section based on the overallaverage yield, the overall standard deviation, and theblock average yield data, Table 3 gives the annual yieldlevels from the study blocks for year 2000 and thepotential yield levels estimated based on yields of 1996–2000.

Each line in Table 3 defines an information subsetregarding the particular block in the field of interest. Forexample, the content in the first line and the sixth line ofTable 3 defined information sublets for blocks 1 and 6.Table 2 indicates that the yields from blocks 1 and 6

le 2

ndard deviation of the yield, and the number of sampling points

interest in a 5-yr period

Soya bean

999 1996 1998 2000

348 3028 2824 2879774 1470 2624 1864573 2428 3167 2530685 2837 2896 2734624 3027 2867 3044289 1792 1858 1807665 2708 2639 2575392 2563 2881 2865985 2612 3582 25621430 3042 3372 2726382 505 545 5056975 21768 23670 7667

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Number of samples obtained from one block

Num

ber

of b

lock

s

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Fig. 2. Frequency of yield data samples collected inside a base block from a portion of the study field located in Central Illinoisbetween years 1996 and 2000.

Table 3

Fuzzy yield levels from individual base information blocks for the year 2000 and for the period 1996-2000 (the numbers in the tableare confidence levels for the corresponding yield levels)

Block identity Year 2000 yield Past 5 yr yield

Low Average High Low Average High

1 0 0�95 0�05 1�00 1�00 0�222 0�96 0�04 0 1�00 0�92 0�083 0�07 0�93 0 1�00 0�93 1�004 0 1�00 0 0�72 1�00 0�015 0 0�80 0�20 0�75 1�00 0�206 0�98 0�02 0 1�00 0�15 07 0�04 0�96 0 1�00 0�96 0�318 0 0�96 0�04 0�86 0�96 0�139 0�05 0�95 0 1�00 0�95 0�15

Q. ZHANG, S. HAN304

were 2879 and 1807 kg ha 1, respectively, while theaverage yield for the field was 2726 kg ha 1 with astandard deviation of 505 kg ha 1 for year 2000.Substitute these values to Eqns. (8)–(10); it results inconfidence levels of 0�95 and 0�05 for average and highyield levels, respectively. Similarly, substitute the blockyields, the field average yields and the standarddeviations for years from 1996 to 1999 to appropriateequations, and then apply Eqn. (11) to determine thehighest confidence levels for different yield levels fromthese blocks; it results in the following informationsubsets:

Ib1 ¼yL

0

yA

0�95yH

0�05yUL

1�0yUA

1�0yUH

0�22

n oð14Þ

Ib6 ¼yL

0�98yA

0�02yH

0

yUL

1�0yUA

0�15yUH

0

n oð15Þ

As defined in Eqn (12), the first three informationagents indicate the fuzzy yield level of the most recentyear (year 2000 in this case), and the second threeinformation agents indicate the fuzzy levels of potentialyield based on historic data (5 yr data in this case). Thetotal fuzzy membership of 1 for the first threeinformation agents provides yield distribution informa-tion based on the most recent year’s productioncondition. The total fuzzy memberships of the secondthree information agents are always greater than 1,which provides a measure on the consistency of the yieldfrom the block of interest under various productionconditions. As an example, the first three elements insubset Ib1 represented that the confidence levels for low,average, and high yield levels of the most recent year inblock 1 were 0, 0�95 and 0�05, respectively. The secondthree elements indicated that the confidence levels for

-250

-200

-150

-100

-50

0

50

100

150

0 5 10 15 20 25

Ordinal number of the evaluated block

Err

or in

yie

ld, k

g-1 ha

Fig. 3. Error distribution of yield data back-calculated from the fuzzy yield levels in the evaluated blocks; the base values were theraw yield data obtained from those blocks (year 2000 data)

YIELD DATA ANALYSIS AND MANAGEMENT 305

having low, average and high yield levels were 1�0, 1�0,and 0�22 based on the 5-yr historic yield data. It meansthat the yield level from this block is more likely to be oflow–average range than to be high. The inconsistency inthe confidence factors for low yield between the mostrecent year data and the five-yr average data indicatedthat there might be some unusual factors contributing tothe yield variation during the most recent year. All thesecould provide important information for determiningfertilising rate in the block.

Similarly, the elements in subset Ib6 indicated con-fidence levels of 0�98, 0�02, and 0 for low, average, andhigh yield for the most recent year, and 1�0, 0�15, 0 forlow, average and high yield potential from this block.The consistency in the confidence levels between themost recent year’s yield and the yield potential providedadditional useful information that this block was locatedin a low-yield area compared to the rest of the field.

One advantage of applying fuzzy mapping approachto classify the yield levels related to the average yield isits capability of back-calculating the real-valued yieldbased on the fuzzy memberships. Fig. 3 shows the errorbetween the real-valued yield back-calculated from thefuzzy yield levels and the original raw yield datasampled from the evaluated blocks. It indicated thatthe maximum error was 211 kg ha 1, and the root meansquare (RMS) error was 13 kg ha 1. Further analysisfound that such an error was mainly caused by theuneven readings of the raw yield data within a blocksince the fuzzy yield levels were defined based on themean yield from the block.

More elements can be included in the informationsubset if more related information becomes available.Some of the elements recommended to be included arethe field topography, the soil type, and the fertilisingrate for the block for the most recent year. The moreelements included in this information subset, the moreinformative this subset will become.

However, the information subset will become morecomplicated if dealing with a large number of informa-tion agents, especially when it needs only part of theprocessed information to make an optimal productiondecision. To solve this problem, an information-reduc-tion method is introduced to eliminate the irrelevantinformation agents using an a-cut method. Thisapproach would create a sub-subset which containsonly the most relevant attributes to the decision-making.For example, when the optimisation goal in a particulardecision-making process is to apply less fertiliser inconsistently high-yield blocks, average amounts offertiliser in average-yield areas, and more fertiliser inthe consistently low-yield zones, a threshold value a of0�5 can be used to eliminate the irrelevant agents to thisoptimisation. Based on this method, the new sub-subsetsfor blocks 1 and 6 will be represented as follows:

Sb1 ¼yA

0�95yUL

1�0yUA

1�0

n o Ib1 ð16Þ

Sb6 ¼yL

0�98yUL

1�0

n o Ib6 ð17Þ

The first sub-subset indicates that block 1 in this fieldhad an average yield for the most recent year.

Q. ZHANG, S. HAN306

Historically, the yield level from this block is betweenlow and average. Based on the defined optimisationcriterion, the available information suggests an averageto high fertilising rate to this particular block. Similarly,the remaining information agents in the sub-subset ofblock 6 indicate that yield from this block is always low,and a high fertilising rate should be applied to block 6 tobring the yield in this block up to a higher level.

By this information table approach, the yield variationin a field and its consistency over the years in the fieldcould be represented using 322 information subsetsinstead of over 100,000 raw data points for a 5-yr period.It not only reduced the size of the base information unitsby 99�7%, but more importantly organized the processeddata in an ‘easy-to-understand’ and ‘ready-to-use’format. As the number of years increased in the yielddistribution database, this feature of the informationtable approach would be more attractive.

4. Conclusions

This paper presents a method of using an informationtable model to process and manage yield data in aformat of information subset based on a manageablenumber of blocks within a field. This model provides aformal method to treat the unevenly distributed andwidely variable yield data, converts the massive rawyield data into informative and manageable fuzzy levels,and represents the resulting fuzzy levels in such a waythat it can be easily connected with other relevantproduction information to support site-specific decision-making. This formal method can be easily programmedso that it can be used to process the yield informationautomatically and lead to the development of a‘transparent-to-farmer’ precision farming information-supporting tool. The case study demonstrates theapplication of this model in managing the yield dataobtained from an actual field in Central Illinois during aperiod of 5 yr. It could reduce over 99�7% data pointsand provide more informative yield distribution infor-mation. The results indicate that the model is capable ofachieving its design goal.

Acknowledgements

This research was supported by the Strategic Re-search Initiative in Information Systems and Technol-ogy of the Illinois Council on Food and Agricultural

Research (CFAR-SRI-IT) and the United States De-partment of Agriculture (Hatch Project 10-306 AE). Allmentioned supports are gratefully acknowledged.

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