Info. Activity 212

8/10/2019 Info. Activity 212

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Hi folks,

Below is an elaboration on the ALPRO high activity model. The equations can be seen asillustrations, I doubt any customer will insist to have them explained but it may be goodto know that the algorithms are more than just, for instance, todays activity divided by

the rolling average of 5 days and it may furthermore be beneficial to get a picture onhow the alarms are generated, how the different thresholds will affect the number ofalarms and what makes us stand out from competitors.

The high activity model (the + / ++ / +++ attentions)

a. How the model worksTechnically, the high activity model is a time-series typed of adaptive filter. Here are themain attributes of the high activity model:

Extremely high confidence level (more on that onwards!)

One separate measurement/estimation model for every hour (total 24) of the dayo Each of the 24 estimations cover a block of 6 hours combined

Meaning that The activity model is quite reliable when it comes to

interferences (for example, a dog chasing the cow for a fewminutes, should not influence the total activity movementsfor six hours)

Meaning, that, for example, the measure/estimation for: Activity measure for 2am consists of data collected by

meter between 8pm and 2am Activity measure for 8am consists of data collected by

meter between 2am and 8am Activity measure for 9am consists of data collected by

meter between 3am and 9am Meaning, that, if an alarm is generated at 9am (start time is 9am)

We have a significant increase between 3am and 9am butnot a significant activity increase between 2 am and 8am.(see illustration)


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For each hour, the model looks like this:(1)

Where is the high activity measure, is the latest activity value (for a block

of six hours), is yesterdays, is the day before yesterday etc. is thekalman parameter and simply means that the formula goes on andon(recursively)

The formula can be simplified to:

or

or assuming that is constant (which nearly the case)

(2)

Or, knowing that is often quite close to 0.6

(3)


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The high activity measure is not sufficient to generate an alarm withsignificance (some competitors offer very simplified algorithms though, likeincrease in percentage). To supply a statistical result with significance, we alsomeasure the variance and standard deviations.

o The variance is calculated like this (standard definition formula): (4)o The standard deviation (or estimation error) of is

(5)

The standard deviation is pretty much normally distributed (the bell curve)around zero.

Practical implications: Thanks to the time-series analysis, the system does a fairly good job to adopt to anew activity levels (cow changing groups, going to pasture etc. in cases of bigactivity changes, like going on summer pasture, there may be or is even likely to

be- false positives for one or two days but then the system has completelyadopted)

It is the standard deviation (5) that we use to generate high activity attentions. The fact that we have one estimation model for each 24 hours of the day (al

though technically each estimation model looks at a 6 hour block) means that wecan say not only that the activity is significantly increased but also which hour itstarted. This is the only reliable way to generate an hour-resolution of an activity

alarm and this is one of our main strengths compared to competitors.

b. How the alarms are generated

The standard deviation can, by its definition (5) be interpreted in more intuitive ways. Butfirst: Lets switch to what we recognize from the ALPRO menus, the values 38, 50, 60,70. What is the correlation between them and the standard deviation?

The alarm settings can be seen as a one-decimal-up interpretation of the standarddeviation. (3.8, 5.0, 6.0, 7.0)

But the thresholds can also be interpreted as a factor as the standard deviation

definition (5) can be seen as a norm:o The values 38/50/60 in ALPRO menu 6:1:6:4:2 can be interpreted as:

If the cow moves 3.8 / 4.0 / 5.0 times more than usual for this 6-hour time frame, then generate an alarm!

As mentioned above, the standard deviation is very close to being normallydistributed, which means that we can estimate the significance level:

o The significance level is what is displayed in menu 6:1:6:4:2 3.8 99.882%


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5.0 99.996 % 6.0 99.998 %

Obviously, the significance levels are indeed quite high. To generate an alarm, thecow does not just need to move a little bit more than usual she really have to

move extremely much more than usual! One may think though, that with suchhigh significance levels, we should not receive any false positives at all! But letsdo the maths for the default + setting: Each our 99.882% of the sendings shouldnot generate an alarm. For 24 hours, this means ( ) that thereshould not be more than 3% false positives with normal cow behavior for thelowest significance level. We can check the other ones:

Significance level Theoretical # false positives / day

Theoretical false positives -/day500 animals

Theoretical false positives -/day 1000animals

3.0 99.180% 18% 90 180

3.4 99.674% 8% 40 803.8 99.882% 3% 15 304.0 99.931% 2% 10 204.4 99.977% 1% 5 105.0 99.996% 0.1% 0-1 16.0 99.998% 0.05% 0-1 0-17.0 99.999% 0.02% 0 0-1

The table above illustrates how the significance levels will (theoretically!!! -reality maydiffer slightly from theory) affect the number of false positives or even number of alarmsin general. Note: we are not concerned about too many false positive (though the 3.0 and3.4 levels above might give too many high activity alarms to deal efficiently with the highactivity alarms). We will successfully filter most of them out but well discuss that in acoming mail!

Also note: We must also accept the fact that cows may choose to run around (or bechased) and get a significantly increased activity without being in heat!

Summary: The + / + + / +++ alarms are generated whenever ALPRO finds that there is anincreased activity for a 6-hour block, using the standard deviation (5). The thresholds(38/50/60) correspond directly to the standard deviation of the activity modelsestimation. Since the standard deviation is normally distributed, it is obvious, thatchanging the threshold from, say, 4.0 to 3.0 will generate many more high activityalarms, than changing a threshold from 6.0 to 5.0 there is no linear correlation betweenthe number of expected activity alarms and the threshold level. This is what is mostimportant to know when changing the threshold levels. Also, the threshold (significance)levels should be utilized (see table above) knowing that the lowest level (+) allowsmore false positives.


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c. Strenghts/limitations

The biggest strengths with the DeLaval ALPRO high activity model are:

Separate measures/model for each hour!

o The activity tag deliver activity information filed on unique hourso ALPRO makes an estimation model for each houro Each hours model is based on a 6-hour blocko This gives us the possibility to generate an estimated start time for the

increased activity This is extremely important of particularly because of two reasons:

Breeding the cow within in the correct time frame isextremely critical. Finding the cow in heat is one thing, but

breeding her too late is a waste of time and money! And breeding her too early reduces the chances of getting her

pregnant dramatically. Most, if not all, competitors cannot supply any detailedinformation on when to breed the cow. Many just tell thatthere is a high activity attention at one milking session, butnot on the previous (meaning the activity increase startedsomewhere in between, say 1-12 or 1-8 hours ago!)Usually, this indeed means that the cows increased activitystarted between the two milking sessions, so the advicewould possible be: breed within 4 or 8 hours. But eventhough plausible for many cows, this will be too early forsome, and basically an incorrect assumption for others

(where the activity start time was actually close to one ofthe milking sessions) as it may be discovered 8 or 12hours too early or too late. Moreover: by measuringactivity just between milking sessions will reduce thechances of finding the cows that start to increase in activity

just before a milking session.

On top of that, we have the obvious advantage that theALPRO solution also works on heifers

The other way around: Not only is ALPRO instrumental in

telling when to inseminate. The start-time-hour also tells ifit is too late to inseminate which can save good money inthe long run!

Time series-model quickly adapts to changed activity patterns! Activity alarms based on statistically significant alarm levels is much more

reliable than those just based on percentage levels!


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Not only are the alarms are generated with an accurate start time, they are alsogenerated quickly.

The good-to-know limitations of the ALPRO high activity model are:

The start time is fairly accurate, but as for real (and not only fulfillingsignificant threshold) it must be considered with plus/minus (mostly minus) 1-2hours.

The fact that we look on 24 measures per day may give us slightly more false positives than if we would look on only 2-3 measures per day (on the other hand,we will also find more true positives). It is important to keep in mind though, thatthe false positives should not bother us too much (as we have means and ways tofilter those out)!

A large deal of the true positives are generated at night or in the morning (this is partly because the cows biology, partly because things are then more calm andundisturbed), but the ALPRO model (and probably everybody elses) look at each

segment of the day in the same way. In ALPROs case, it means that on occasion,we can get a false positive during the day, and since we have already generatedthat alarm, we may not generate a new one if the cow then actually becomes inheat during the following night! This is an uncommon example (yet it canhappen!) but there are ways to address that (see coming mail).

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Info. Activity 212