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  1. There are times when you may need to calculate a standard deviation across a time-range using the data within a number of signals. Consider the below example. When a calculation like this is meaningful/important, the straightforward options in Seeq may not be mathematically representative to calculate a comprehensive standard deviation. These straightforward options include: Take a daily standard deviation for each signal, then average these standard deviations Take a daily standard deviation for each signal, then take the standard deviation of the standard deviations Create a real-time standard deviation signal (using stddev($signal1, $signal2, ... , $signalN)), then take the daily average or standard deviation of this signal While straightforward options may be OK for many statistics (max of maxes, average of averages, sum of totalizes, etc), a time-weighted standard deviation across multiple signals presents an interesting challenge. This post will detail methods to achieve this type of calculation by time-warping the data from each signal then combining each individually warped signal into a single signal. Similar methods are also discussed in the following two seeq.org posts: Two different methods to arrive at the same outcome will be explored. Both of these methods share the same Step 1 & 2. Step 1: Gather Signals of Interest This example will consider 4 signals. The same methods can be used for more signals, but note that implementing this solution programmatically via Data Lab may be more efficient when considering a high number of signals (>20-30). Step 2: Create Important Scalar Constants and Condition Number of Signals: The number of signals to be considered. 4 in this case. Un-Warped Interval: The interval you are interested in calculating a standard deviation (I am interested in a Daily standard deviation, so I entered 1d) Warped Interval: A ratio calculation of Un-Warped Interval / Number of Signals. This metric is detailing what the new time-range will be for the time-warped signals. I.e. given I have 4 signals considering a days worth of data of, each signal's day worth of data will be warped into 6 hour intervals Un-Warped Periods: This creates a condition with capsules spanning the original periods of interest. periods($unwarped_interval) Method 1: Create ONE Time-Shift Signal, and move output Warped Signals The Time Shift Signal will be used as a counter to condense the data in the period of interest (1 day for this example) down to the warped interval (6 hours for this example). 0-timeSince($unwarped_period, 1s)*(1-1/$num_of_signals) The next step is to use this Time Shift Signal to move the data within each signal. Note there is an integer in this Formula that steps with each signal applied to. Details can be viewed in the screenshots. $area_a.move($time_shift_signal, $unwarped_interval).setMaxInterpolation($warped_interval).move(0*$warped_interval) The last step is to combine each of these warped signals together. We now have a Combined Output that can be used as an input into a Daily Standard Deviation that will represent the time-weighted standard deviation across all 4 signals within that day. Method 2: Create a Time-Shift Signal per each Signal - No Need to move output Warped Signals This method takes advantage of 4 time-shift signals, one per signal. Note there is also an integer in this Formula that steps with each signal applied to. Details can be viewed in the screenshot. These signals take care of the data placement, where-as the data placement was taken care of using .move(N*$warped_interval) above. 0*$warped_interval-timeSince($unwarped_period, 1s)*(1-1/$num_of_signals) We can then follow Method 1 to use the time shift signals to arrange our signals. We just need to be careful to use each time shift signal, as opposed to the single time shift signal that was created in Method 1. As mentioned above, there is no longer a .move(N*$warped_interval) needed at the end of this formula. The last step is to combine each of these warped signals together, similar to Method 1. $area_a.move($time_shift_1, $unwarped_interval).setMaxInterpolation($warped_interval) Comparing Method 1 and Method 2 & Calculation Outputs The below screenshot shows how Methods 1 & 2 arrive at the same output Note the difference in calculated values. The Methods reviewed in this post most closely capture the true time-weighted standard deviation per day across the 4 signals. Caveats and Final Thoughts While this method is still the most mathematically correct, there is a slight loss in data at the edges. When combining the data in the final step, the beginning of $signal_2 falls at the end of $signal_1, and so on. There are some methods that could possibly address this, but this loss in samples should be negligible to the overall standard deviation calculation. This method is also heavy on processing, especially depending on the input signals' data resolution and as the overall number of signals being considered increases. It is most ideal to use this method if real-time results are not of high importance, and better fitting if the calculation outputs are input in an Organizer that displays the previous day's/week's/etc results.
  2. This method demonstrates how to apply time warping to a signal which can shorten the time between sample points while retaining the signal’s characteristic shape. This is useful for batch processes where batches may have different durations or for aligning data from multi-step processes with different durations. Note that this method is distinct from the more complex Dynamic Time Warping. The following example is based upon the Area A Compressor Power signal available in the Example Data. A single condition was created to capture each compressor run, as shown in the following image. Step 1: Specify a Time Normalization Factor The user uses the Formula tool to specifiy a time duration (scalar value), set to 4 hours for this example. The compressor power signal for each compressor run will be normalized to this time duration. There is no single correct value; the value needs to be shorter than the minimum time duration for all signals to be normalized. // User specified time duration (scalar value). 4 hours Step 2: Create the Normalized Condition Use Formula to create the normalized Compressor Run condition based on the user-specified time normalization factor. This condition will be used later when the calculated signal delay is used for normalization. $CompressorRuns.afterStart($nF) Step 3: Calculate the Run Duration Use the Signal from Condition tool to calculate the duration for each compressor run. This value will be used later for determining the calculated signal delay applied to each compressor run. Step 4: Calculate the Elapsed Time During Each Run Use the Formula tool to calculate the elapsed time during each compressor run. This value will be used later for determining the calculated signal delay applied to each compressor run. timeSince($CompressorRuns, 0.25min).convertUnits('h') Step 5: Calculate the Signal Delay Factor Needed for Time Warping Each sample (timestamp) for compressor power will be shifted to the left by a calculated amount to time warp the power signal from its original time period (Compressor Runs) to the normalized time period (Compressor Runs Normalized). The first sample point in each run will have no delay, and the last sample point will have the greatest delay. For example, if the original time period is 10 hours and we are normalizing to a time period of 4 hours, then the last sample point in the run will be shifted to the left by 6 hours (Delay Factor = -6 hrs). // This Formula first creates a signal with a value of 0 (default delay), then splice in the calculated delay during each compressor run. 0.toSignal(0.25min).convertUnits('hr').splice($ElapsedTime*($nF/$RunDuration-1),$CompressorRuns) At this point we zoom in to a single compressor run and use the Capsule Time view to better visualize the results of our intermediate calculations. For this compressor run lasting 10.9 hours, the Compressor Run Elapsed Time finishes at the correct value (10.9 hours) and the Delay Factor correctly decreases from 0 hours (beginning of run) to -6.9 hours (end of run). Step 6: Apply the Signal Delay to Time Warp the Signal Now that the appropriate delay factor is calculated for each sample point during the compressor runs, we apply it to the Area A Compressor Power signal using the delay() function in Formula. This generates the time warped signal called Compressor Power Normalized. $CompressorPower.delay($delayFactor,24h).within($CompressorRunsN) When applying the signal delay, we are required to specify a maximum delay. This is important for the Seeq calculations going on in the background, so that the queries know how far back and forward to go when requesting input data. The maximum delay also provides a convenient way for the user to limit the applied delay, if they have some reason to do so. In our case, we just want the chosen value to be longer than the longest expected compressor run duration. Results Now that the compressor power signal has been normalized, Capsule Time view gives a nice comparison of the power signal behavior across the 3 runs contained in the Display Range:
  3. Hi all, Based on a conditions, I have create 3 capsules (trend value > 0.1) for three different equipment. What I want is to align these 3 capsules (and all the follow) to have the same start time.... #howto ??
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