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The best option for your case would be to create an AF Analysis (whether an analysis data reference attribute or outputting the values to PI tags is up to your scenario).
The name "client side" is a little misleading when referring to data sets, and I'm not personally a fan of us using it. The data set exists on the client, meaning that you create it within ProcessBook and it lives within ProcessBook, therefore its existence is "client side". But the calculation itself is done on the data archive directly. ProcessBook ships off the equations to the server, receives a value object back, and renders the values according to which column you selected (value, pctgood, total, etc); it's not performing the calculation itself. So the term "client side" is not accurate when referring to the calculation engine. (Side note: this is also why the columns don't appear in the column list until the equation has been verified by the server.)
What this means in regards to your question, is that the data archive is not aware of the context of the display, nor is the data archive AF aware in general, so there's no way to add this to the dataset calculation or to automatically switch the calculation when you switch the display. With an AF analysis attribute, however, you can have this attribute on all of your elements and then add this attribute to your trend (or value symbol, etc). Then when you switch the context of the display, it will switch to showing the new element's analysis attribute value.
If this were done within data sets, you'd need to have a new data set for each reactor hardcoded with its tags, and then either manually switch them or use something like VBA to switch it, but I would not recommend either of those approaches over the use of an analysis attribute due to how seamless that approach would work.
You can follow below steps and tweak as per your requirement. I'm using PI AF, Analysis and PI Vision
1) Create template in AF for pump if not already exists e.g. My hierarchy contains Test with Pump 1, 2, 3 mapped to template "Pump Template"
2) Template contains Bearing attribute(Input) and child attribute "Bearing Tempature Average" to store output.
Note : IF you want to historise data you can create Bearing Temperature Average as PI Point
3) In Analysis tab, Create Analysis with 10 min avg and map to "Bearing Tempature Average" attribute.
Schedule calculation to run every 10 min
Preview results :
4) PI Vision, Trend and Attribute mapping
Asset Switch in PI Vision from Pump 1 to Pump 2
Convert to Collection - If required by selecting all symbols and right click and convert to collection.
Final Output if you are using collections.