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The objective of this study was to develop a flow model for grain combines based on the laboratory and field response of an impact based grain flow sensor. The grain flow model developed in this study is of first order with constant coefficients. A computer code was written to solve the model and to simulate the response of a yield sensor whose response had been determined previously for various types of flow rate inputs both in field and laboratory experiments. The computer program for the simulation can also compensate for the time delay. The simulation results of the theoretical model suited well to the experimental data and showed that the model effectively shows the input-output relationship of grain flow through a grain combine. This model could be used for periodic flow signals acquired from grain yield sensors. It was concluded that the model postulated in this study could be further developed to determine the grain yield entering the combine using the outlet flow rate measured by a yield sensor.

Amongst other research areas in precision agriculture, developing yield mapping technology is important because yield maps display crop response to the management techniques applied and help identify the causes and effects of yield variability. To generate a yield map, a combine grain flow model is needed so that the amount of grain measured by a yield sensor on a combine could be related to the location of grain in the field.

Amount of grain at a specified location in the field is measured after the crop is processed, usually on or at the exit of the clean grain elevator. Thus, there is a time delay in flow rate measurements, which addresses the time for grain to be transported from the combine head to the yield sensor [

One of the earliest studies for yield reconstruction was conducted by Searcy et al. (1989). According to Searcy et al. (1989), the major cause of error in estimating grain yield was the grain flow model. They noted that transfer function determination for each component of the combine was impractical because of the material flow complexity and the difficulty in measuring the flows through each combine component. As a result, the authors assumed a lumped-parameter system to model the grain flow from the combine head to the yield sensor. They concluded that a combine transfer function reconstruction employing a first-order transportation delay could be used to generate grain yield maps. The grain, however, is distributed during the flow of grain inside the combine. The travel time of individual grain kernels from a combine head to grain tank vary substantially as a result of threshing and separating processes [

Vansichen and De Baerdemaeker (1991) measured wheat yield continuously on a combine. The inputs of the yield measurement model are yield (YI), combine travel speed (SP), and the actual cutting width (AWI). At each time t, the machine location (x,y)(t) is used to transform the location dependent yield YI(x,y) to a time dependent variable YI(t). The authors stated that the combine acts as a dynamic system with respect to grain flow. FR_{out}, grain transported to the grain tank, is a function of FR_{in}, flow rate at the head. Reitz and Kutzbach (1996) provided an expression that readily employs grain moisture content to calculate yield based on yield YG(t), mass flow rate MG(t), combine ground speed V(t), cutting width W(t), and grain moisture content UG(t) [

It has been shown that the scheme for calculating the yield at combine head using the flow rate measured at the yield sensor is in essence the same in the referred studies so far where flow rate, ground speed, and cutting width data are incorporated to derive the yield at the combine head. The studies conducted by Searcy et al. (1989) and Birrell et al. (1996) differ from the others in that they both used paddle wheel flow sensor that does not measure flow rate periodically. The flow signal requires data processing to obtain a periodic signal necessitating further manipulation of the flow data.

Grain flow dynamics may be affected by crop conditions and may vary from one combine model to another. The flow models just reviewed use grain delay time to match the flow data to position data. In doing so, the flow signal was shifted by a constant value of the transportation time delay. These models assume that the grain enters combine and goes through combine components without being disturbed until the flow was measured by the yield sensor. They rely on the assumption that shifting of the flow signal suffices for determining the actual field coordinates of yield. Therefore, the grain mixing and its effects on yield measurements were neglected and modeling grain flow was based on linear, non-mixing grain flow.

Characterizing variation of flow rates inside the combine and how these variations relate to yield variation was studied [

The objective of this study was to develop a combine grain flow model that could be further developed to be used as another yield mapping tool for periodic grain flow rate data. Development of such a model consists of two steps. In the first step, the theoretical development of a model needs to be handled, followed by testing the model's applicability in terms of input-output relationship for the grain flow rate. In the second step, the model and the algorithm need to be improved and incorporated with relevant data such as grain moisture content, ground speed, cutting width, slope, GPS data, and clean grain elevator speed, so that it could be better used in a yield mapping tool. Thus the second step comprises the incorporation of actual field data for further development of the model. The scope of this study is limited to the model development, i.e., the first step just described above. The specific objectives of this study were to

derive a combine grain flow model that relates the input and output grain flow rates,

demonstrate through simulation the capability of the model to generate first order signals that are similar to the flow signals obtained previously in field and laboratory experiments using a commercial yield sensor.

The field experiments were previously done during corn harvest using a Case IH 2166 and an impact based yield sensor (AgLeader 2000) was used to collect the flow rate data [

It was mentioned in the previous section that first order models are practical to use while models of higher orders cause errors and noise due to the complexities of combine dynamics. In this study, another first order model was developed that could be used for grain combines. Although this model is to be used just as other first order models referred to in the previous section this postulated model differs in the way the model is derived. According to the postulated model, grain is assumed to flow into a chamber with some form of outlet port. The model is based on the system representation shown in

The following assumptions were made to explain the flow through the closed conduit or a chamber, representing a combine:

The chamber has a constant cross section with the area of the chamber, A.

The height of grain in the chamber is h and generally varies with time.

The outlet port controls the outlet mass flow with the relationship:

According to conservation of mass, the mass flow at the inlet of the chamber would be equal to the mass flow at the outlet port provided that no grain is accumulated in the chamber. Since, according to assumption 2, the height of grain generally varies with time, conservation of mass can be expressed as:

Mass accumulation in the chamber is related to the cross section of the chamber (A), density of the material flowing into the chamber (ρ), and the material height that is time-dependent. Internal rate of mass accumulation thus can be expressed as ρA(dh/dt).

Using the symbols developed so far,

In _{out}=kh the rate of change of mass flow is also related to the rate of change of material height in the chamber. This relationship then can be shown as:

Substituting the latter term into

This first order differential equation can be rearranged yielding

Thus the dynamics of mass flow may be expressed in the conventional form for a first order system:

In

A computer program was written to solve the model and various graphs were plotted to see whether grain flow signals that were obtained from grain combines could be simulated. The program can shift flow signal back in time to incorporate the time delay.

The model expressed in ^{-1}. Therefore,

Other researchers used filtering techniques when processing grain yield data from a combine harvester. Amongst these are a normal low-pass filter and a filter model based on the characteristics of the machine dynamics, after a low-pass filter [

The common feature of the graphs from the laboratory and field experiments is the exponential increases and decreases observed in the beginning and at the end of the tests. This shows that the combine itself behaves like a first order sensor due to the accumulation of grain inside the combine at the beginning of a harvest strip and at sudden yield changes as the harvest continues. Therefore the flow model should be able to simulate field or laboratory responses shown in

Thus the shapes of the graphs in

It is known that the combine transports material through various forms of conduits and this takes time. This means that a disturbance at the input will not be observed at the output until the material has had time to progress through the machine. ^{-1}, this magnitude could not be measured by the yield sensor for about 10 seconds. The magnitude of the signal increased exponentially as the grain accumulated and progressed in the combine. Laboratory experiments (

Despite the differences in the flow rate signals in the field and laboratory experiments, there are common characteristics that can be observed. As a result of careful observation of the experimental graphs, one can conclude the following: a constant flow rate input at the beginning of a harvest operation can not be measured by the yield sensor immediately, which necessitates the flow signal to be shifted back in time in accordance with the time delay. Once the yield sensor starts reading flow data points, the magnitude is very small, and hence can not be accurately correlated to the somewhat constant input flow rate. In order words, initial flow rate readings do not give accurate information on the magnitude of the grain flow rate until the grain flow signal reaches its constant value, which is another critical problem that the researchers would like to address in their efforts in generating accurate grain yield maps.

Simulation result shown in

The model seems to explain the experimental results quite satisfactorily. The program is capable of shifting quantities back in time so that the time delay can be compensated based on combine model and grain type being harvested.

This postulated grain flow model may be regarded as simplified, considering the complex dynamics of combines. The result of applying the

The application of the theoretical model that was developed in this study resulted in an acceptable dynamic response for the combine with a flexibility of altering transport delay time of flow signal based on operating conditions.

At this stage of the model development, the time delay as it relates to combine dynamics has been incorporated. The model does not compensate for potential time delays that might result from sensors' responses or monitoring and recording systems. Therefore, future study on this model shall not only focus on including other data such as grain moisture and slope data but also on the effects of monitoring and recording system as well.

The followings could be summarized and concluded as a result of this study:

A mathematical model was derived for combine grain flow dynamics that relates the input and output grain flow rate that is measured by a grain flow rate sensor.

The flow model developed is of first order with constant coefficients.

The simulation results showed that the model effectively shows the input-output relationship of grain flow through a combine.

The computer program for the simulation can compensate for the time delay.

The model and the numerical program need to be modified and developed in order to incorporate field data so that the developed model could be used to predict the inlet flow rate based on actual grain flow rate measured by a yield sensor.

The help of Prof. Dr. R. J. Smith (Emeritus), Iowa State University, is appreciated in this study.

Schematic representation of grain flow through a combine for the theoretical model.

Simulated unit step response for the theoretical model.

Grain yield sensor response to step changes in grain flow on a combine during harvest [

Grain flow signal as measured by a yield sensor for step changes in grain flow in a laboratory experiment [

Step response for the theoretical model for repeated inputs.