Effects of A Simulated Power Cut in AMS on Milk Yield Valued by Statistics Model

Anja Gräff et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 12, (Part - 3) December 2015, pp.07-12
www.ijera.com 7 | P a g e
Effects of A Simulated Power Cut in AMS on Milk Yield Valued
by Statistics Model
Anja Gräff1
*, Sascha Wörz1
, Johannes Dietrich1
, Manfred Höld2
, Jörn
Stumpenhausen2
, Heinz Bernhardt1
1. TechnischeUniversitätMünchen, Center of Life and Food Sciences, Agricultural Systems Engineer-
ing, Am Staudengarten2, D-85354 Freising, Germany,
2. Hochschule Weihenstephan-Triesdorf, University of Applied Sciences Weihenstephan-Triesdorf,
Faculty of Agricultural and Nutritional Sciences, Am Hofgarten 1, D-85354 Freising, Germany,
SUMMARY
A statistics model was developed in order to be able to determine the effects of a simulated power cut of an
Automatic Milking System on the milk output.Measurable and relevant factors, such as power cuts, milk yield,
lactation days, average two days digestion and rumination and time were considered in the calculation tool.
Key words: Automatic milking system, milk yield, ruminant activities, statistics model
I. INTRODUCTION
A vast number of factors, such as less physical
work, higher flexibility and cow specific milking,
have led to an increase in the number ofautomatic
milking systems throughout Bavaria. In the past
years, the number of farms equipped with automatic
milking systems has risen considerably, to nearly
1,200 agricultural holdings (Sprengel and
Korndörfer, 2014).
Applying automatic milking systems leadsnot
only to organizational adjustments but alsorequires
adapting energy supplies. The energy required must
be available for24 hrs/day.
Though surveys have shown that Europe
provides quite a stable power network, there have
been diverse irregularities in supply in different
countries of the EU (Roon and Buber, 2013). The
last significant power cut, on November 25th
2005 in
North Rhine-Westphalia, Germany, left
250,000people without power for up to four days;
on November 4th
2006 10 million people in vast
parts of Europe were without power for two hours.
In this paper we will present one of the effects
of a simulated power cut in four Bavarian farms on
the frequency of use of the Automatic Milking
System, on the ruminant activities, the immediate,
intermediate and long term reaction of the cows and
possible effects on their milk output.
In order to simulate a power cut, twelverandom
cows were not admitted to the Automatic Milking
System for twohours on three consecutivedays.
Furthermore, stress reactions were examined
closely via video analysis, heart rate, pedometer and
measurements of cortisolmetabolites.
MATERIALAND METHODS
In order to be able to determine the feasibility of
milking by automatic systems, a plant independent
calculating method was developed. Measurable and
relevant factors, such as power cuts, milk yield,
lactation days, average two days digestion and
rumination and time were considered in the
calculation tool. Parameters induced by stress such
as heart rate and cortisol content may be included
any time.
The model generalises Cauchy-Link and binomial
distribution based on probability. Hence, the result
and its tendency may be influenced by the choice
and the interpretation of the variables.
The data used in this study were generated in four
different south Bavarian farms with an average herd
size of 60 milking cows in the time from 3.3. -
24.8.2014. The data gave 34,203 random samples.
Some data were deliberately not included in the
model, as they would have distorted the results. For
this reason, the parameter “minimal milking interval
not achieved” was eliminated.
The reduced data set of 19,232 was not transformed,
all data were of equal value. These are realistic and
as such closely related to practical experience.
In order to restrict complexity, only one target
variable was applied together with five variables.
The target variable is X6 = milking outcome (yes/no)
and the five chosen co-variables (X1 = simulated
power cut (yes/no); X2 = milk output, rounded; X3 =
lactation days; X4 = average two hrs activity/two hrs
RESEARCH ARTICLE OPEN ACCESS

rumination; X5 = time). Adding further variables
merely leads to collinearity and increases the
complexity of problematic instances. The developed
GLM (Generalised Linear Model) does not include
any random effects and hence can analysed easily.
Due to the low rate of error in the sample the model
proves to be very easily predictable. It satisfies
imitation of conditions, prediction and the
significance of explanatory variables.
The model was calculated using the statistics software R. The following formula was defined through stepwise
backward reduction considering the AIC Criterion:
y ~ x1 + x2 + x3 + x4 + x5 + x1:x3 + x1:x4 + x1:x5 + x2:x3 +
x2:x4 + x2:x5 + x3:x4 + x3:x5 + x4:x5 + x1:x3:x4 + x1:x3:x5 +
x1:x4:x5 + x2:x3:x4 + x2:x3:x5 + x2:x4:x5 + x3:x4:x5 + x1:x3:x4:x5 +
x2:x3:x4:x5
RESULTS
The following tables show the calculation of the coefficients (estimates) and the approximation quality
(deviance residuals) of the above model:
Deviance Residuals:
Min 1Q Median 3Q Max
-3.4296 -0.1582 0.0854 0.1111 3.1227
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.832e+00 2.463e+01 0.115 0.9085
x1 -4.593e+07 8.783e+10 -0.001 0.9996
x2 -1.637e-01 8.123e+00 -0.020 0.9839
x3 -1.088e-01 1.014e-01 -1.073 0.2834
x4 -9.929e-01 5.702e-01 -1.741 0.0816 .
x5 -6.979e-01 1.576e+00 -0.443 0.6579
x1:x3 1.088e-01 8.315e+08 0.000 1.0000
x1:x4 9.929e-01 2.315e+09 0.000 1.0000
x1:x5 6.980e-01 6.758e+09 0.000 1.0000
x2:x3 3.983e-02 3.294e-02 1.209 0.2265
x2:x4 3.173e-01 1.869e-01 1.697 0.0897 .
x2:x5 3.668e-01 5.002e-01 0.733 0.4633
x3:x4 3.649e-03 2.042e-03 1.787 0.0740 .
x3:x5 3.810e-03 6.382e-03 0.597 0.5504
x4:x5 3.637e-02 3.677e-02 0.989 0.3226
x1:x3:x4 -3.649e-03 2.177e+07 0.000 1.0000
x1:x3:x5 -3.812e-03 5.579e+07 0.000 1.0000
x1:x4:x5 -3.637e-02 1.782e+08 0.000 1.0000
x2:x3:x4 -1.307e-03 6.566e-04 -1.991 0.0465 *
x2:x3:x5 -1.609e-03 2.019e-03 -0.797 0.4254
x2:x4:x5 -1.595e-02 1.137e-02 -1.404 0.1605
x3:x4:x5 -1.307e-04 1.300e-04 -1.005 0.3150
x1:x3:x4:x5 1.307e-04 1.522e+06 0.000 1.0000
x2:x3:x4:x5 5.449e-05 4.012e-05 1.358 0.1745
Signif. codes: 0 „***‟ 0.001 „**‟ 0.01 „*‟ 0.05 „.‟ 0.1 „ ‟ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 25957.3 on 19231 degrees of freedom
Residual deviance: 2002.8 on 19208 degrees of freedom
AIC: 2050.8
Number of Fisher Scoring iterations: 25

In addition the statistical influence (Pr(>Chi)) of the coefficients is identified by the milk output.
Analysis of Deviance Table
Model: binomial, link: cauchit
Response: y
Terms added sequentially (first to last)
Df Deviance Resid. DfResid. DevPr(>Chi)
NULL 19231 25957.3
x1 1 1000.2 19230 24957.1 < 2.2e-16 ***
x2 1 22917.8 19229 2039.3 < 2.2e-16 ***
x3 1 0.3 19228 2039.0 0.5942626
x4 1 15.0 19227 2024.1 0.0001095 ***
x5 1 0.6 19226 2023.4 0.4208560
x1:x3 1 0.0 19225 2023.4 1.0000000
x1:x4 1 0.0 19224 2023.4 0.9987861
x1:x5 1 0.0 19223 2023.4 1.0000000
x2:x3 1 0.6 19222 2022.8 0.4410557
x2:x4 1 4.9 19221 2017.9 0.0262460 *
x2:x5 1 3.2 19220 2014.7 0.0737422 .
x3:x4 1 2.0 19219 2012.7 0.1556413
x3:x5 1 0.5 19218 2012.2 0.4755629
x4:x5 1 1.7 19217 2010.4 0.1872985
x1:x3:x4 1 0.0 19216 2010.4 1.0000000
x1:x3:x5 1 0.0 19215 2010.4 1.0000000
x1:x4:x5 1 0.0 19214 2010.4 0.9999309
x2:x3:x4 1 0.7 19213 2009.7 0.4024740
x2:x3:x5 1 3.7 19212 2006.0 0.0549941 .
x2:x4:x5 1 0.1 19211 2005.9 0.7357760
x3:x4:x5 1 1.2 19210 2004.7 0.2763516
x1:x3:x4:x5 1 0.0 19209 2004.7 0.9999034
x2:x3:x4:x5 1 1.9 19208 2002.8 0.1646522
---
Signif.codes: 0 „***‟ 0.001 „**‟ 0.01 „*‟ 0.05 „.‟ 0.1 „ ‟ 1
It should be mentioned that, if the null hypothesis is not rejected it is not true to say that the corresponding
coefficients do not have any influence on the milk output. As expected, the power cut (x1, p-value < 2.2e-16),
the milk output (x2, p-value < 2.2e-16), the average two hrs activity/two hrs rumination (x4, p-value =
0.0001095) and the interactions milk output:average, two hrs activity/two hrs rumination (x2:x4, p-value =
0.0262460), milk output:time (x2:x5, p-value = 0.0737422) and milk output:lactation:time (x2:x3:x5, p-value =
0.0549941) are obvious to the significance niveau 0.1. The interactions could be expressed by the linear
predictor parts.
Now the error classification matrix and rate is calculated:
y 0 1
0 7621 161
1 35 11415
It is obvious that in 7621 cases with “no milking” and in 11415 cases with “milking” the data has been classified
in the correct way. As there is a miss-classification in 196 cases we will have aerror-classification rate of
1.019135 %.
The influence of anAMS power cut on the milk output in a certain time interval is analyzedby using the standard
k-nearest-neighbor regression (knn-regression) method. As explained above, the power cut and the milk output

variables are modeled by a 0-1 sequence. All other variables are directly taken to the knn-regression by using the
R functions knn.reg:
knn.reg(train, test, y, k = 1, algorithm=c("kd_tree", "cover_tree", "brute"))
Arguments:
train matrix or data frame of training set cases.
test Matrix or data frame of test set cases. A vector will
be interpreted as a row vector for a single case.
If not supplied, cross-validataion will be done.
y reponse of each observation in the training set.
k number of neighbours considered.
algorithmm nearest neighbor search algorithm.
With theFNN-package and the plot function, the following three examples are observed:
Example 1
Power cut: 0, 0, 0, 0, 1, 1, 1, 0, 1, 0
Milk output in [l]: 9, 17, 11, 15, 0, 0, 0, 14, 0, 16 (assumed by the authors of the paper)
Lactation in [days]: 116, 79, 75, 115, 170, 170, 24, 61, 170, 52
Average two hrs activity/two hrs rumination: 38, 32, 35, 45, 32, 32, 31, 49, 32, 23
Time in [hrs]: 4.15, 4.37, 4.44, 4.54, 4.54, 4.58, 5.01, 5.07, 5.08, 5.37
Milk result: 1, 1, 1, 1, 0, 0, 0, 1, 0, 1
The knn-regression graph indicates the relationship between time and the milk output.
Figure 1: Relationship between time and milk output for example 1.
It should be noted that this first example is trivial, because it is using the origin data pool with the 19232 random
samples.The knn-regression with k = 1 has been able to reconstruct the origin data by 100 percent.
Example 2
Power cut: 0, 0, 0, 1, 1, 1, 1, 0, 0, 0
Milk output in [l]: 11, 21, 9, 0, 0, 0, 24, 22, 13 (expected by the authors of the paper)

Average two hrs activity/two hrs rumination: 38, 32, 35, 45, 32, 32, 31, 49, , 32, 23
Time in [hrs]: 6.15, 6.17, 6.24, 6.5, 6.51, 6.55, 7, 7.1, 7.18, 7.21
Milk result: 1, 1, 1, 0, 0, 0, 0, 1, 1, 1
The following correlation therefore exists between the milk output and the time:
With the knn-regression method and k = 1 the following milk output in [l] was gained: 11, 10, 5, 0, 0, 0, 0, 9, 11,
15. The above milk output graph shows that the milk output after a short power cut behaves as expected by the
authors: The milk output shows a sharp increase.
Example 3
Power cut: 0, 1, 1, 1, 0, 0, 0, 0, 0, 0
Milk output in [l]: 25, 0, 0, 0, 29, 5, 20, 9, 13, 15 (expected by the authors of the paper)
Average two hrs activity/two hrs rumination: 41, 41, 41, 38, 44, 39, 40, 15, 23, 28
Time in [hrs]: 15.03, 16.45, 16.48, 16.54, 17.09, 17.28, 17.41, 17.57, 18.08, 18.37
Milkresult: 1, 0, 0, 0, 1, 1, 1, 1, 1, 1
The following correlation therefore exists between the time and the milk output:
The estimated milk output obtained by the knn-regression with k = 1in [l] was the following: 10, 10, 10, 21, 0, 0,
0, 7, 0, 13. It can be seen that the milk output assumed by the authors (increasing) does not behave as the milk

output graph obtained by knn-regression. Probably the reason therefore could be that the cows usually visit the
AMS in the morning or in the evening times, and so there are not enough random samples available for this time
stamp. In this case, the knn-regression fails.
II. DISCUSSION AND CONCLUSION
Generalising the model allowed its adaption and
application to any method of observation. The
advantage is that the model can be applied to any
dairy farm using an automatic milking system,
regardless of its size, the cattle race and the herds
output. The model works via probability and not with
exact data. Therefore, direct consequences of
simulated core times or power cuts cannot be
analysed directly. However, due to the large amount
of data, the low rate of error classification, and the
high quality of the model, the results are so precise
that it is impossible to identify individual
probabilities.
Even though the statistical methodology was of high
quality and has a very low rate of error, when
considering good practice and interpretation of data,
one must be aware that the concept is based on
simulation. The power cut was simulated for 12 cows
from four dairy farms. Not much data needed to be
considered because only 12 animals were effected.
The consequence of a real power cut would be a lot
worse, as this would effect all animals of the herd and
not only a dozen focussed cows. Thereby, also see the
failure of the knn-regression. To improve the knn-
regresion, the random samples can be scaled and
weights of the knn-regression can be adjusted by a
genetic algorithm. But the problem, where no data
are available, is not eliminated.
Parameters such as cortisol content, heart rate
variability and paces may be included into the model
by significant additional work in order to record
individual animal reaction regarding health and stress.
In summary the model proves to be very good for
statistical surveys, the evaluation and interpretation
of possible effects of simulated power cuts of the
milking robot on milk yield. Precise observation and
examination, especially taking into account
individual animal behaviour, would require further
data and parameters.
REFERENCES
[1] Roon, S. von; Buber, T.: Versorgungsqualität
und –zuverlässigkeit als Standortfaktor (2013),
URL:
https://www.ffegmbh.de/aktuelles/veroeffentlic
hungen-und-fachvortraege/351-
versorgungsqualitaet-und-zuverlaessigkeit-als-
standortfaktor (Stand: 29.09.2014)
[2] Sprengel, D., Korndörfer, R. (2014): Eigene
Stärken und Schwächen erkennen.
Betriebsvergleich für AMS-Betriebe frei
geschaltet. In: LKV-Journal 1/14, S.20

Effects of A Simulated Power Cut in AMS on Milk Yield Valued by Statistics Model

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