J. Kissel
I've processed yesterday's measurement suite (see LHO aLOG 55018) to the point where I've been able to add it to the collection of measurements used to produce an estimate of the unknown, frequency-dependent (but time independent) systematic error in the model (i.e. the Gaussian Process Regression of the measurement collection's residual frequency dependence after the model has been divided out of the measurement, and the measurement has been compensated for time dependence).
I've done this for four reasons:
(1) To confirm that most of the response function uncertainty in the middle frequency range (20-300 Hz) is dominated by the uncertainty in this estimate of unknown systematic error
(2) I've always been curious how much "one more data set" gathered improves the overall uncertainty (you would guess it should improve by sqrt(N), but N is different for each of the four model components -- C, A_UIM, A_PUM, and A_TST -- and the digital filtering on each of these components means that the contribute to the uncertainty in a sophisticated, frequency dependent way that is in no way easy to predict)
(3) In the event that we *do* throw away the data prior to 2020-11-12's fix to the known PCAL systematic error (aka PCALSYSERR) because it's easier than figuring out how to salvage the data prior, as alluded to in LHO aLOG 55007, then I'd like to see as much PCALSYSERR-free data included in the estimate as possible
(4) To see if adding "one more data set" would help us "resolve" the discrepancy we see between a processed GDS-CALIB_STRAIN in the presence of a broad-band PCALY injection.
The results satisfy (1) through (3) positively, but they leave (4) unresolved.
See the attached figure, which shows the two uncertainty envelopes from 2020-02-07 (i.e. LHO aLOG 55007) and 2020-02-11 (today, this aLOG) compare against the same 2020-01-13 pre-processed GDS transfer function data (from LHO aLOG 54565).
We see improvement (frequency dependent, of course) with the addition of the 2020-02-10 measurement suite. This confirms (1), and demonstrates (2) that we're still in the "winning" region of 1/sqrt(N) for the actuator, given that the number of measurements, N, is 5 to 6 for each stage. Since we measure it every week, the sensing function measurement number 13, so we don't see "as much" improvement above ~100 Hz where the sensing function's contribution to the response function is dominant.
Addressing (3) the improvement (again, it's frequency dependent -- look at the plot -- so in this sentence I'm just using "verbal" numbers to describe what I see) at ~50 Hz is about 0.5% / 0.25 deg -- and when you're talking about a budget that is achieving a 3-4% / 1-2 degree level, that's pretty substantial.
So, for the next few calibration measurement days, I might start getting actuator data too (i.e., until N gets large, increase the frequency of measuring the actuator suite from ~twice a month to once a week).
As far as (4) -- In the region that we're seeing the largest discrepancy between median predicted systematic error (plus uncertainty) and the measured systematic error between PCAL and the final product -- between 40 Hz and 150 Hz -- the uncertainty remains too large to "resolve" the discrepancy. In fact -- if we focus on exactly 100 Hz, I'm now pretty confident that we're limited by the overall PCAL uncertainty (a frequency independent 0.54%) and *not* the GPR uncertainty, so this discrepancy may never get resolved.
I still would like to see
- a different day's broad band injection process and put on this plot, and
- all of the swept sine transfer functions for which we only have CAL-DELTAL_EXTERNAL, but properly corrected for time-dependence, such that the comparison with this "reference time" envelope is valid and we can see how the envelope compares to measurement across all frequencies from 5 to 5000 Hz,
before declaring that "it won't get any better than this -- let's release this envelope!"
Stay tuned for the results of that work.
Also -- remember, this envelope will likely *not* be valid for the first 2 hours of every lock stretch.
Analysis of showing the systematic error as the IFO thermalizes (based on the data from LHO aLOG 53951) is underway.
