Two centuries ago Italian scientist Giovanni Battista Venturi (1746-1822) discovered a method for measuring a fluid flow. He developed a flow tube that introduces a pressure drop from which the mass flow of the fluid can be derived. Precision agriculture took off after the first commercially available “Yield Monitors” that measure the continuous flow of discrete particles (distinct particles that can be counted individually), such as the flow of crop seeds, peanuts, and cotton bolls. Classical measurement concepts used in yield monitors are (1) impact plates, (2) radiometric methods, and (3) optical methods.

An impact plate measures a force that is related to the product of mass and velocity of the flow. Because it is essential that the velocity of the flow remains constant, and since the velocity itself is not measured, imperceptible errors may be introduced using this technology.

The radiometric method uses a radioactive transmitter source (such as Americium 241) and a receiver. Without interruption, there is a constant amount of radiation received. The material is dropped between the transmitter and receiver and it absorbs some of the radiation. The reduction of received radiation is now proportional to the mass flow rate. A drawback of the radiometric method is that the underlying mechanism is not well understood; it is an empirical method that relies on calibration and is susceptible to errors due to changes in material properties, and environmental variables.

The optical method used in yield monitors, measures the height of the material on the paddles of an elevator. This method is not truly continuous; it needs an elevator mechanism to discretize the flow and can not be used in cases of high density continuous flows, such as found in granular fertilizer application. Another essential development in precision agriculture is the trend toward variable rate equipment to apply dry materials. It does not suffice to convert existing machinery by replacing fixed drives with variable drives without a feedback mechanism that measures the flow rate of the material.

AAES research has led to the development of a new approach to measuring the mass flow of discrete particles using a truly continuous method. It is based on a simple and well understood mechanism; a variation on the theme of counting.

In a very sparse flow regime, the diameters of all passing particles can be measured individually and, after conversion to a volume and multiplication with the true material density, the mass flow can be computed. In a dense flow regime, however, instead of measuring the diameter of each individual particle, the lengths of clusters can be obtained. The mass flow could be computed using the same principle only if the original number of particles in a cluster could be reconstructed from the measured cluster lengths. AAES research has developed both the measurement system and the reconstruction algorithm needed for this calculation.

The sensor that measures the cluster lengths (Figure 1) contains a light source and two infrared sensor arrays that are “on” when they receive light and “off” when they are blocked by the cluster. The lenses magnify the shadow of the clusters, which improves the measurement accuracy. The principle of cluster length measurement is shown in Figure 2.

The output of the sensor arrays during the cluster passage are shown in the top right graph. The velocity of the cluster is derived from the time difference between the passage of the two light-sensitive sensor arrays (Dt_f). The total time that a cluster interrupts either layer (Dt_p) combined with the velocity and the distance between the sensor arrays, yields the cluster length D as follows:

As mentioned, the mass flow measurement is a variation on the theme of counting. Assume that the particles all have identical diameters and there are N particles in an experiment. If the flow is very sparse, the diameter (D) of each particle is measured and there would be N measurements. This is shown in the top graph of Figure 3. In this case the measured diameters are translated into a volume and, multiplied by the density, a total mass is obtained.

When the flow becomes dense, clustering occurs, and instead of measuring the diameters of individual particles, the lengths of clusters are measured. This situation is shown in the bottom graph of Figure 3. Reconstruction now implies finding a relationship between the original number of particles N and the measured variables E (the total number of clusters measured in a time period) and N₀,N₁,... (number of singles, doubles, triples etc). This relationship was discovered through simulation as follows:

where:

estimated number of particles

total number of measured clusters

total number of measured Singles

total number of measured Doubles

density measure for the flow

This reconstruction scheme requires the total number of measured clusters E as well as the measured number of singles (N₀) and doubles (N₁). The first equation (or its inverse,) can be explained theoretically. Since the number of clusters detected (E) is equal to the number of gaps between clusters, the probability of a cluster arrival is equal to the probability of observing no event per time unit in a Poisson driven process with density which is e^-l. This also confirms the simulation result that this formula is independent of the diameter distribution of the particles, since the cluster arrival does not take the internal cluster structure into account.

Furthermore, Poisson theory predicts the following relationship for the number of singles and doubles in the identical diameter case:

which preserves the relationship found in simulation. Combination of these relationships gives a very simple reconstruction formula for identical diameter particles:

 

A major advantage is that this method only uses the total number of clusters E and the number of singles particles measured, N₀. An earlier reconstruction method used the Doubles as well as the Singles in the equation. Not only is it more complicated to keep track of the Singles and Doubles, but the number of Doubles also contain half of the three-particle clusters which complicates the issue even further. Alas, the formula shown above only works for identical particles, measured without error, and is not practical because there are no perfect measurement systems.

In practice, the values of the measured diameters are always distributed, even when particles have identical diameters, due to errors in the measurement system. For the distributed diameter case, a very similar reconstruction formula was found using simulation. The original first relationship

was found to be independent of the diameter distribution, and the second one was modeled with a factor a, a material distribution dependent constant.

The relationship between a and the moments of the diameter distribution is not known at this time: The value is one (unity) for identical particles, and deviates from unity for distributed diameter particles.

As in the identical diameter case, there is a reconstruction formula that only uses the number of singles be it somewhat more complicated:

where:

: estimated number of particles

: total number of measured clusters

: total number of measured singles

: density measure for the flow

a

: material specific constant

Note that if a = 1, the formula reduces to the original identical diameter particle version.

As an example, the measured cluster lengths of identical particles of 4.5 mm diameter are shown in Figure 4 (compare this to the bottom graph in Figure 3). Singles do not show up as a perfectly straight horizontal line because the sensor measures their diameters with a certain error. Apart from that, singles, doubles, and triples are easily recognized.

To validate the model

as derived earlier, the

was plotted against

as shown in Figure 5. According to theory, this must be a straight line with a formula slope equal to 1/a. The straight line was fitted with the origin as a fixed point. The reason is that this point represents a very sparse flow, where the number of observations E equals the number of particles N (every particle is measured individually). In this case there are no doubles and hence,

The slope of the line was found to be 0.99, leading to a =1.01 indeed close to one.

The normalized accuracies are presented in Figure 6.  Here, the estimated number of particles (using the reconstruction formula

with a =1.01) was divided by the number of particles in the experiment (4,000). From the plot it is clear that the system is very accurate with errors averaging less than 3%.

This newly-developed method may someday help agriculturalists, from farmers to chemical application specialists such as crop dusters, better calibrate the amount of material they are applying to land or better judge their yields by making such measurements more precise.

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Grift is Assistant Professor of Biosystems Engineering.