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Mathematics and Computers in Simulation 65(2004)49–57

Design of a virtual combine harvester

K.Maertens ?,J.De Baerdemaeker

Laboratory for Agro-Machinery and Processing,Kasteelpark Arenberg 30,B-3001Leuven,Belgium

Abstract

Separation processes in agricultural machinery are typically non-linear,complex and uncertain.On-line mea-surements of input and output data are not available.Therefore,black-box modelling is not applicable and other techniques to describe the system must be used.In this paper,a dynamic separation model is constructed to predict the input–output behaviour of the separation section based on a combination of physical process knowledge and experimental results.

When the hybrid separation model is implemented in a framework to simulate the total harvesting process,a virtual combine harvester is obtained,ready to process virtual ?elds that are created with standard software programs.?2003IMACS.Published by Elsevier B.V .All rights reserved.

Keywords:Separation process;Virtual experiments;Combine harvester

1.Introduction

Combine harvesters are confronted with varying feed rate characteristics and therefore have to operate well in a wide range of conditions.One important task is to separate grain kernels from other particles as straw and chaff.In conventional machines different drums are installed together with a set of walkers (Fig.1).The ?rst drum processes about 65–80%of the available grain kernels.The second and third drum separate both about 10%.A small Straw Flow rotor is installed to ensure a good distribution on the ?rst walker section.

During the design of the individual machine sections,experiments are carried out to analyze their performance under different feed rate conditions.In literature,different separation models can be found for these tangential separation drums [1].Here,a method is proposed to combine those section models into a total separation behaviour.By implementing the dynamic and static separation model into a more general framework,a virtual harvesting system is achieved,which makes it possible to analyze the behaviour of the global harvester on changing feed rate conditions and to design automatic tuning and yield mapping systems.

?

Corresponding author.Tel.:+32-163-21444;fax:+32-163-28590.E-mail address:koen.maertens@agr.kuleuven.ac.be (K.Maertens).

0378-4754/$30.00?2003IMACS.Published by Elsevier B.V .All rights reserved.doi:10.1016/j.matcom.2003.09.007

50K.Maertens,J.De Baerdemaeker /Mathematics and Computers in Simulation 65(2004)

49–57

Fig. 1.Con?guration of separation section in a conventional New Holland TX60combine harvester.Mass ?ows ˙m SE (t),˙m walkers (t)and ˙m presieve (t)correspond,respectively,to the incoming feed rate,material ?owing across the rear end of the walkers and the separated ?ow arriving on the presieve.

2.Hybrid separation model

As starting point,a framework is set up based on analytical relations between individual machine elements [2].Subsequently,results from design experiments are included and ?nally a dynamic model is achieved,predicting how the incoming ?ow is processed.2.1.Analytical framework

The way grain kernels and MOG are separate in a crop processing unit can be expressed by a probability function.This function expresses the probability of the location where grain kernels are separated.For the con?guration of Fig.1,four probability functions have to be determined for both grain and MOG separation.Fig.2shows the con?guration of the threshing drum.A rubber ?ap is installed behind the concave to avoid the separated ?ow from being spread too far on the grain pan.

x G

(m)

x c (m )

Fig.2.Projection of concave distribution on grain pan with corresponding inverse projection function F TD (x G ).Coordinates x G and x c correspond,respectively,to the distance (m)from the front of the grain pan and distance (m)from the begin of the concave.Parameter V G denotes the transport speed (m/s)on the grain pan.

K.Maertens,J.De Baerdemaeker /Mathematics and Computers in Simulation 65(2004)49–5751

Based on geometrical measures and assumptions concerning the speed of separated grain kernels,a nonlinear function can be found between the coordinate on the grain pan x G (m)and separation length x c (m).The dynamic relation between the separate grain ?ow ˙m G TD (t),and the total incoming feed rate ˙m SE (t)through the exit of the straw elevator (Fig.1)can be approximated by

˙m G TD (t)=

L G

P G

TD [˙m SE (t ? t(x G )),x c ,t ? t(x G )]˙m SE (t ? t(x G ))d x G ,(1)where the x G -dependent time delay t (x G )(s)can be written as

t(x G )=

L G ?x G

V G

+ T sep

(2)

Later delay expresses the transport time for the speci?c in?nitesimal ?ow to get from the straw-elevator exit to the rear of the grain pan.Fixed delay T sep denotes the mean time (s)to pass the threshing concave and L G the full length (m)of the grain pan.

Probability function P G

TD [˙m SE (t),x c ,t ]corresponds to the distribution of the locations where grain kernels are separate along the threshing concave.The explicit dependency on ˙m SE (t)makes this system nonlinear.In fact,this function is dependent on more variables than only total incoming mass ?ow (moisture content,grain/straw ratios,etc.).Later ones can not be measured accurately or their in?uence is

not consistent enough to analyze their behaviour and are therefore added to the stochastic part σP G TD

(x c ,t)of distribution P G TD

:P G TD

[˙m SE (t),x c ,t ]=(P G

TD )0[˙m SE (t),x c ]+σP G TD (x c ,t)(3)

The surface under P G

TD

corresponds to the fraction of mass ?ow separated by the threshing drum.To design the stochastic part of the threshing separation,no extra information is available but the model error.Maertens and De Baerdemaeker [3]have estimated the stochastic properties of the separation variability based on results from stationary threshing experiments and suppositions about the time behaviour of these uncertainty terms.

An analogous relation can be set for the MOG-separation,the other two separation drums and walker sections.The partial mass ?ow,not separated by any of the four units leaves the walkers as separation losses ˙m G walkers or other material ˙m M walkers .

2.2.Implementation of experimental results

Once the model framework is constructed,the individual probability functions can be included.Fig.3shows the resulting grain kernel distribution for different feed rates of material.The experiments are carried out on a New Holland TX 64-Threshing drum.For each run,the optimal parameters of the model of Trollope [4]are estimated:

θ= x c

P G

TD (x)d x =α0 1+c e ?kP 0ψ(θ)kP 0?c ?kP 0e ?cψ(θ)kP 0?c (4)

with

θthe normalized cumulative separation and α0the initial concentration of grain kernels as part of the total incoming ?ow.Parameters kP 0and c are determined by mass ?ow and concave properties.Function ψ(θ)is quadratic in terms of concave angle θ(Rad)and some geometric variables.

52K.Maertens,J.De Baerdemaeker /Mathematics and Computers in Simulation 65(2004)49–57

Concave Angle (Rad)

C u m u l a t i v e S e p a r a t e d F r a

c t i o n

Concave Angle (Rad)

P r o b a b i l i t y D e n s i t y (1/R a d )

Fig.3.Experimental separation data (x )and the separation model of Trollope (?)for different feed rates of material (straw +grain)(20,25,28,30,32,35t/h)in function of concave angle θ(Rad).The left ?gure shows the cumulative separation functions θ.

Right ?gure corresponds to its derivative P G

TD (x c ).

The variation of c and kP 0for six different feed rates is given in Fig.4.By regressing the parameter variations in function of measurable ?ow properties,a method is found to incorporate the nonlinear

characteristic of P G

TD [˙m SE (t),x c ,t ]into the analytical framework discussed under Section 2.1.Note that the ?nal result consists of two local optimal regression.Since two subsequent local optimizations do not guarantee a global optimal solution,an extra step of global optimization is necessary.Similar plots as Figs.3and 4can be constructed for MOG-separation and other separation units.

18202224262830323436

0.005

0.01

0.015

0.02k P 18

202224262830323436

012

3x 103

c

Total Mass flow (Ton/h)

Fig.4.Optimal model parameters for test series of Fig.3.

K.Maertens,J.De Baerdemaeker/Mathematics and Computers in Simulation65(2004)49–5753

Fig.5.Con?guration of virtual harvesting system.Site-speci?c information is integrated by means of bitmap?les and trans-formed into instantaneous feed rate properties by using the virtual Machine Trajectory and the calculated Ground Speed/Cutting Width combination.The Virtual Combine Harvester processes the applied feed rate sequences.A control system calculates the appropriate actions while a log?le is automatically generated.

3.Integration into a virtual harvesting process

Once all processing units are modelled and connected via the analytical connections,a model of the input–output behaviour of the harvester is achieved.Fig.5illustrates how the harvester model can be implemented in a simulation tool that describes the harvesting process of one?eld.Other important parts are discussed as given below.

3.1.Control system

A control unit is necessary to interpret the signals in the harvester and to determine appropriate control signals as ground speed and cutting width.In a more advanced control scheme,extra parameters can be tuned.

3.2.Log-?le

To evaluate the control system and behaviour of the harvester,a log-?le must be generated.This?le will depend on the type of virtual experiment.

3.3.Machine trajectory

The strategy that determines the machine trajectory within the?eld plays an important role when the site-speci?c information is explicitly used as input for control algorithms[5]or in case yield mapping errors are analyzed or new yield estimation algorithms are developed[6].

3.4.Site-speci?c information

The easiest way to incorporate information on the within?eld distribution of crop properties is to create virtual?elds.This data format of site-speci?c information can be designed with standard software tools.

54K.Maertens,J.De Baerdemaeker /Mathematics and Computers in Simulation 65(2004)49–57

F e e d r a t e (T o n /h )

02

4

6

8

10

12

14

S e p a r a t e d F l o w (T

o n /h )Time (s)

S e p . L o s s e s (T o n /h )https://www.wendangku.net/doc/5a10971305.html,parison between two equally shaped feed rate sequences.

4.Results

4.1.Time domain analysis of hybrid separation model

With above model,simulations are carried out in Simulink .Fig.6illustrates simulation results for two feed rate sequences.The second signal is exactly the half of the ?rst one.The sequence con-sists of a step input of 30t/h in addition to a uniform noise sequence in a band of ±10t/h.In Fig.6,the resulting separation losses and separated grain ?ow are plotted.The smoothing in?uence and pro-cess non-linearities are obvious.In case of a feed rate of about 15t/h,almost no grain kernels ?ow across the rear end of the walkers.For a doubled feed rate,the separation losses increase more than proportionally.

Cross correlation ?R yu (τ)(t 2/h 2)between the separate grain ?ow and the incoming feed rate ˙m SE (t)gives

a good indication of the process dynamics:

?R

yu (τ)=1N ?τN ?τ

k =1

y(k)u(k +τ)(5)

The extra factor 1/(N ?τ)makes the estimation unbiased for increasing τ.By using the product of the standard deviation of input and output signal as reference,a correlation coef?cient is achieve that is

K.Maertens,J.De Baerdemaeker /Mathematics and Computers in Simulation 65(2004)49–57

55

Lag (s)

C o r r . C o e f f .

Fig.7.Correlation coef?cient ?ρ(τ)for two feed rates in function of time lag τ/F s .

dynamically rescaled:

?ρ(τ)=

?R

yu (τ)?σu ?σy

(6)

The results for both feed rates are shown in Fig.7.In both correlation sequences,a peak is visible for time

lags of 6.75s.This shape is cause by the rubber ?ap behind threshing concave due to a local accumulation of separated material.For lower feed rates,the distribution of grain kernels lies mainly in the ?rst part of the threshing concave (see Fig.3).By this,a smoothed peak around 9.5s is visible.For higher feed rates,the mean kernel distribution shifts to the back,resulting in a higher deal of the sharp peak around 6.75s and a higher correlation around 4.5s due to grain kernel separation in the rotary separator.Although the separation losses are rather low (0.5%)for the highest feed rate,an important dynamic variation is already visible,illustrating the nonlinear character of the processing units.4.2.Site-speci?c analysis with virtual harvesting system

A straightforward application of the full simulation tool is the evaluation of yield mapping systems.In contrast with real life experiments,both the original and reconstructed yield distributions are available.By comparing both,a direct measure is found for the yield map accuracy.Fig.8shows the result of a comparative study between two yield estimation algorithms [6].The colour variation of both maps is cropped in the error band between ?1.5and 1.5t/ha to accentuate the contrast in both ?gures.In the left plot,a smoothed overview is given of an error map that is calculated by an optimal time shift (14s)for the grain ?ow signal.The right map shows the difference between a yield map that is constructed with this ?xed time delay and an algorithm that makes use of a linear approximation of the harvester https://www.wendangku.net/doc/5a10971305.html,tter ?gure gives a clear indication of the spots where the model based algorithm introduces correction terms.Especially at the start an end of each harvest run,the algorithm produces more accurate yield estimations.

56K.Maertens,J.De Baerdemaeker/Mathematics and Computers in Simulation65(2004)49–57

https://www.wendangku.net/doc/5a10971305.html,parison between two different techniques of local yield estimation:Error map(t/ha)of a yield map base on an optimal timeshift(a)and the local differences(t/ha)with a model based yield estimation algorithm(b).

5.Conclusions

In this study,a method is presented to combine both experimental data and analytical insight on the harvesting process.The?nal product,a virtual harvesting system,offers new opportunities for constructors of combines.

?During the design of machine elements,experiments are necessary to analyze the impact of the new unit on the behaviour of the total harvester.The modularity of the virtual combine makes it possible to reduce these experiments.

?Although position systems are commercially available on all types of harvesters,the accompanying cost is still an important drawback for farmers and contractors.By means of the virtual harvesting process,it is possible to evaluate the need for position accuracy and to explore new applications of the available site-speci?c information.

?Repeatability is an important issue to compare and to evaluate different control and processing algo-rithms.With this virtual system,different strategies can be used to harvest the same?eld several times. Hence,real?eld experiments can be prepared profoundly and experimental costs can be scaled down.

Acknowledgements

The authors gratefully acknowledge the I.W.T.(Instituut voor Wetenschappelijk Technologisch onder-zoek)for the?nancial support through doctoral grant(no.001249).This study is made possible through cooperation of New Holland Belgium.

References

[1]F.Beck,Simulation of Threshing Processes in Combine Harvesters,Ph.D.Thesis,Universit?t Hohenheim,1999.

K.Maertens,J.De Baerdemaeker/Mathematics and Computers in Simulation65(2004)49–5757 [2]K.Maertens,J.De Baerdemaeker,H.Ramon,R.De Keyser,An analytical grain?ow model for a combine harvester.Part1:

Design of the model,J.Agric.Eng.Res.79(1)(2001)55–63.

[3]K.Maertens,J.De Baerdemaeker,Flow rate based prediction of threshing process in combine harvesters,Appl.Eng.Agric.

19(2003)383–388.

[4]J.R.Trollope,A mathematical model of the threshing process in a conventional combine-thresher,J.Agric.Eng.Res.27

(1982)119–130.

[5]H.Schneider,P.Reitz,P.Wacker,H.D.Kutzbach,Automat.Machine Setting,Landtechnik51(1996)202–203.

[6]K.Maertens,M.Reyniers,J.De Baerdemaeker,A virtual combine harvester as a design tool for yield mapping systems,

Precision Agric.(in press).

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