Example of calculating the derivative

It can be very useful to search for periods when parameter readings increase or decrease, because variation can indicate process issues. Calculating the derivative enables you to determine a process's sensitivity to a change in a given parameter. 

Applying trendviewer's delta operator will give you the power to quickly approximate the derivative to identify meaningful variations within a process, over any tagged period. 

If the occurrence of background noise in a system prevents insightful information drawn from the delta operator, simply apply our easy to use two step method to obtain a meaningful derivative.

Go to the tag builder menu and select the aggregation submenu, to;

• Smoothen the measurement
• Calculate derivative

Smoothing the measurement

To achieve the closest approximate derivative of a chosen function, it is crucial to limit the fluctuations (i.e. noise) over the selected period. To reduce background noise, you can smooth the tagged data by selecting the aggregation option in the tag builder menu. To do this you:

1. Open the tag builder menu .
2. Click on the aggregation submenu  .
3. Select the tag you wish to aggregate.
4. Select the average as operator.
5. Set the time interval (10 minutes in this example).
6. Enter a 'Name' and 'Description'.
7. Click the 'Save' button.

Note: Filtering over shorter time periods produces fits that are closer to the original tag. However, if you select a period that is to short the undesired noise will not filter out.

The temperature of a reactor is recorded over a ten-minute period (green), see figure directly below. Once calculated, the averaged (smoothed) temperature is superimposed (pink).

Calculate derivative

The next step is to add a formula tag. You then subtract the tag from a shifted version of itself, over a small time period. The smaller this period is, the better the real derivative is approximated.

In this illustration a step size of 1 minute is selected.

1. Open the tag builder menu .
2. Click on the formula submenu  .
3. Enter the formula: 'A-B'.
4. Map your tag to both the 'A' and 'B' variables.
5. Click the options hyperlink in the 'Mapping' section.
6. Enter a timeshift (1 minute in this example) for variable 'B'.
7. Enter a 'Name' and 'Description'.
8. Click the 'Save' button.

The derivative can be calculated as follows:

• dY/dt = [Y(t+dt)-Y(t)]/dt 

 - Where Y(t) is the averaged out temperature tag as function of the time, and;

 - dt is defined as 1 minute as discussed before.

The derivative is then superimposed onto the original and smoothed data, see figure below. The figure presents:

• The temperature of the reactor (green)
• The averaged temperature (pink)
• The calculated derivative of the averaged tag (blue)

The value of each tag is highlighted in the figure above using separate scooters. When the averaged tag is constant, the derivative is zero. At the peak of the temperature spike, the derivative is also zero, because the slope at this point is zero. Where the temperature spike goes from concave to convex the derivative reaches its maximum, because the temperature rise is at its maximum.