An Influence Diagram for An Influence Diagram for Management of Mildew Management of Mildew

in Winter Wheatin Winter WheatAllan Leck JensenAllan Leck Jensen

Danish InformaticsDanish Informatics

Network in the Network in the Agricultural Sciences Agricultural Sciences

Research CenterResearch Center

Finn Verner JensenFinn Verner Jensen

Department ofDepartment of

Computer ScienceComputer Science

Aalborg UniversityAalborg University

-presented by Bingyu Zhu and Sen -presented by Bingyu Zhu and Sen XuXu

AbstractAbstract• A prototype of A prototype of a decision support systema decision support system

for management of the fungal disease for management of the fungal disease powdery mildew in winter wheatpowdery mildew in winter wheat

• An influence diagramAn influence diagram which is used to which is used to determine the determine the optimaloptimal time and dose of time and dose of mildew treatmentsmildew treatments

• Practical and theoretical problemsPractical and theoretical problems during during the construction of the influence diagram, the construction of the influence diagram, and also the and also the experienceexperience with the prototype with the prototype

BackgroundBackground

• In Denmark, environmental impacts of In Denmark, environmental impacts of agricultural production must be agricultural production must be reduced.reduced.

• Findings of pesticides and nitrogen Findings of pesticides and nitrogen residues in drinking water have induced residues in drinking water have induced the government to take actions for a the government to take actions for a significant reduction of the consumption significant reduction of the consumption of fertilizers and pesticides.of fertilizers and pesticides.

Dilemma of farmersDilemma of farmers

• Agricultural input factors: fertilizers Agricultural input factors: fertilizers and pesticides—very expensiveand pesticides—very expensive

• Reductions in these input factors can Reductions in these input factors can cause inadequate effects and hence cause inadequate effects and hence economical losseseconomical losses

• Farmers: apply excessive amounts of Farmers: apply excessive amounts of input factors to avoid inadequate input factors to avoid inadequate effects of input factors.effects of input factors.

How to solve …How to solve …

• Reduce the consumption of input Reduce the consumption of input factors and save money if they can factors and save money if they can get the get the recommendations that when recommendations that when it is safe to reduce the doses.it is safe to reduce the doses.

• These recommendations could come These recommendations could come from from decision support systemsdecision support systems

• Insurance farming Insurance farming Precision Precision farmingfarming

Decision Support SystemDecision Support System

• MIDAS – Mildew Influence Diagram MIDAS – Mildew Influence Diagram for Advice of Sprayings.for Advice of Sprayings.

• Influence diagram: Influence diagram: Case-specific Case-specific recommendations of recommendations of timing and timing and dosagedosage of mildew treatments. of mildew treatments.

The Ph.D. thesis can be downloaded from http://www.sp.dk/~alj/

The Disease-Powdery The Disease-Powdery MildewMildew

• Weather condition—temperature, Weather condition—temperature, humidity and windhumidity and wind

• Under favorable conditionsUnder favorable conditions– Spread rapidlySpread rapidly

• Under unfavorable conditionsUnder unfavorable conditions– Not spread, the present disease may Not spread, the present disease may

disappear with time due to the disappear with time due to the emergence of new, uninfected leaves emergence of new, uninfected leaves and the death of old, infected leavesand the death of old, infected leaves

MIDASMIDAS

• Based on the field observations and Based on the field observations and the expectations to the future the expectations to the future

• Determine the Determine the optimaloptimal treatment treatment decision for the current disease decision for the current disease problemproblem

• Assumption: all future decisions will Assumption: all future decisions will be made optimally according to the be made optimally according to the available information at the timeavailable information at the time

Decision OptimizationDecision Optimization

• Affected by uncertainty ofAffected by uncertainty of – StochasticityStochasticity

•Weather and disease infections with Weather and disease infections with elements of unpredictabilityelements of unpredictability

– Inaccurate observationsInaccurate observations

•Field recordings of disease level are Field recordings of disease level are difficult and error pronedifficult and error prone

– Incomplete knowledgeIncomplete knowledge

• Interpretations of relations in domain Interpretations of relations in domain involves uncertaintyinvolves uncertainty

Dynamic Influence Dynamic Influence DiagramDiagram

• A sequence of time steps.A sequence of time steps.

• Each time stepEach time step– Information variablesInformation variables– A single treatment decision variableA single treatment decision variable– Chance variablesChance variables

• Time is an important parameterTime is an important parameter

Variable typesVariable typesStatic Static informatioinformationn

Winter wheat variety, Soil type, Winter wheat variety, Soil type, Nitrogen fertilization strategy, Nitrogen fertilization strategy, Plant densityPlant density

Dynamic Dynamic informatioinformationn

Weather, Disease incidence, Weather, Disease incidence, Remaining time to harvest, Cost of Remaining time to harvest, Cost of fungicide and spraying, Label dose fungicide and spraying, Label dose of fungicide, Expected price of of fungicide, Expected price of grain and yieldgrain and yield

DecisionDecision Dose of treatment (0 possible)Dose of treatment (0 possible)

UtilitiesUtilities Value of yield, Cost of treatment, Value of yield, Cost of treatment, Value of disease induced yield lossValue of disease induced yield loss

Thermal Time ScaleThermal Time Scale• Three influentialsThree influentials

– Chronological timeChronological time– TemperatureTemperature– Crop development stageCrop development stage

• Thermal time scaleThermal time scale– Definition: The expected temperature sum Definition: The expected temperature sum

remaining to crop maturityremaining to crop maturity– Divided into thermal time periods, each Divided into thermal time periods, each

corresponding to a time step of the decision corresponding to a time step of the decision model.model.

– Length of a time step is called Length of a time step is called a thermal weeka thermal week..– Farmers give their estimates of the number of Farmers give their estimates of the number of

weeks to crop maturityweeks to crop maturity

The Initial Influence The Initial Influence DiagramDiagram

• GDM moduleGDM module

• Case-specific time Case-specific time step modulesstep modules

• Decision modelDecision model

Tn

Ti

Time

Field

T2 T1

T2 T1Tn

The GDM moduleThe GDM module

Dynamic Programming Dynamic Programming

• First, the final decision is consideredFirst, the final decision is considered• For each information scenario at that For each information scenario at that

time, the decision alternative with time, the decision alternative with optimal expected utility is determined. optimal expected utility is determined.

• The preceding decisions are considered The preceding decisions are considered in reverse order, and each of them is in reverse order, and each of them is optimized under assumption of optimal optimized under assumption of optimal decision making in the future.decision making in the future.

Computation Complexity Computation Complexity ProblemProblem

• The set of information scenarios at the time of The set of information scenarios at the time of a decision consists of all configurations of a decision consists of all configurations of observed variables which are d-connected to observed variables which are d-connected to a utility node influenced by the decision. a utility node influenced by the decision.

• DiseaseLevel in initial GDMDiseaseLevel in initial GDM

the current state of the disease depends the current state of the disease depends on not only the current value of on not only the current value of DiseaseObser, but also all the previous, DiseaseObser, but also all the previous, together with all previous treatment together with all previous treatment decisions.decisions.

Information Blocking Information Blocking ConditionCondition

• The local information of the system The local information of the system overwrites all previous information.overwrites all previous information.

• P(Y | IP(Y | Ikk, D, Dkk, X) =P(Y | I, X) =P(Y | Ikk, D, Dkk))

for X for X єє U T U Ti i (i=1,…,k-1), (i=1,…,k-1),

Y Y єє U T U Ti i (i=k+1,…,n).(i=k+1,…,n).

• P(Y | TP(Y | Tkk, X) =P(Y | T, X) =P(Y | Tkk) )

Change the structureChange the structure

DiseaseObserv_1

DiseaseLevelB_1 DiseaseLevelA_1

DiseaseObserv_1

DiseaseLevelB_1 DiseaseLevelA_1

Figure3: Left: The initial causal structure of the relationships between the DiseaseObserv and the DiseaseLevel nodes. Right: The modified structure to achieve a blocking of the past by the observed nodes(DiseaseObserv).

A Decision Model with 3 Time A Decision Model with 3 Time StepStep

Experience--QuantitativeExperience--Quantitative

• Single model clique size 27388 probabilities, Single model clique size 27388 probabilities, 83196 for each additional time step. 83196 for each additional time step.

• 1.6 Million for a model with 20 time steps, 1.6 Million for a model with 20 time steps, 14.8M to store.14.8M to store.

• Performance on SUNPerformance on SUNAssemblage 1 secAssemblage 1 secCompilation 100 secsCompilation 100 secsLoading Loading 25 secs 25 secsPropagation 25 secsPropagation 25 secs

Experience--QualitativeExperience--Qualitative

• Evaluation of the predictions of DiseaseLevelEvaluation of the predictions of DiseaseLevel

• True and Approximate StructuresTrue and Approximate Structures– True structure are good.True structure are good.– Approximate Structure less satisfactoryApproximate Structure less satisfactory

underestimate high disease levels and underestimate high disease levels and overestimate low disease levels.overestimate low disease levels.

– Predicted probability distributions are too narrow.Predicted probability distributions are too narrow.– DiseaseObserv was intended to be a simple DiseaseObserv was intended to be a simple

measure for DiseaseLevel.measure for DiseaseLevel.

Future Work--ImprovementFuture Work--Improvement

• Several Different Prior Distribution for P(DLB) Several Different Prior Distribution for P(DLB) in order to fit actual situation.in order to fit actual situation.

• Additional information node introduced, in Additional information node introduced, in order to improve the calibration of order to improve the calibration of DeseaseLevel.DeseaseLevel.

• Relaxation of the information blocking Relaxation of the information blocking condition.condition.

• Approximative for decision, true for reasoning.Approximative for decision, true for reasoning.

• Other problems.Other problems.