Mech Resonance Wiki

I've updated the wiki by trawling the elog for violin entries. Please keep it up to date so that we can make violin notches.

AIC Wiki updated to latest stable version of DokuWiki: 2017-02-19b "Frusterick Manners" + CAPTCHA + Upgrade + Gallery PlugIns

The most up to date pictures of the AP table and ETMX table that Steve took have been uploaded to the relevant page on the wiki. It seems like the wiki doesn't display previews of jpg images - by using png, I was able to get the thumbnail of the attachment to show up. It would be nice to add beam paths to these two images. The older versions of these photos were moved to the archive section on the same page.

ETMX table layout uploaded with beam paths to the wiki.   

The pdf file is uploaded into the wiki.

LiYuan has kindly done some Total Integrating Sphere (TIS) measurements on ITMU01 and ITMU02. A summary of the measurement is attached. I uploaded the measurements and some analysis script to nodus at /home/export/home/40m_TIS. I created a Wiki page for the measurements and linked to it from the core optics page.

These TIS measurements look very similar to the TIS of the LIGO optics. Further analysis shows that the scatter loss is 10+/-1.7 ppm for ITMU01 and 8.6+/-0.4 ppm for ITMU02.

In this calculation, a gaussian beam the same size bouncing off the 40m ITMs is assumed to scatter from the mirrors. The error is calculated by moving the beam around randomly with STD of 1mm.

In LiYuan's setup, TIS is measured for scattering angles between 1 and 75 degrees. If we go further and assume that the scatter is Lambertian we can extrapolate that the total loss is 10.9+/-1.9 ppm for ITMU01 and 9.2+/-0.5 ppm for ITMU02.

These measurements complete the loss budget nicely since with the 6ppm loss predicted from the phase maps, the total loss in the arm cavities would be 6+10+10=26ppm which is very close to the 28ppm loss that was measured after the arm cavity optics were cleaned.

I updated the mime.local.conf file for the AIC Wiki so as to allow attachments with the .txz format. THis should be persistent over upgrades, since its a local file.

Measured the PZT beatnote using the setup mentioned in elog post 17031. Attached is the data taken from 10kHz to 1MHz, decadewise data was also taken that I'm not including in this post. A_R refers to the transfer function taken of channel A wrt the voltage reference (the swept sine we are inputting which has an IF of 30kHz). A and B correspond to the I and Q components of the signal taken from the DFD, respectively. I am currently working on plotting the data, and will shortly update this post with plots. Next steps - 

- quantify the uncertainty in the signal (I think)

- vectfit the data to find poles and zeroes

(and possibly find a better way to print/obtain data)

Edit: first pass of data plotted

cosmic rays in cars

Came in, found all front-ends down.

Keyed a bunch of crates, no luck:

Requesting coeff update at 0x40f220 w/size of 0x1e44
No response from EPICS 

Powered off/restarted c1dcuepics.  Still no luck.

Powered off megatron.  Success!  Ok, maybe it wasn't megatron.  I also did c1susvme1 and c1susvme2 at this time.

BURT restored to Nov 26, 8:00am

But everything is still red on the C0_DAQ_RFMNETWORK.adl screen, even though the front-ends are running and synced with the LSC.  I think this means the framebuilder or the DAQ controller is the one in trouble--I keyed the crates with DAQCTRL and DAQAWG a couple of times, with no luck, so it's probably fb40m.    I'm leaving it this way--we can deal with it tomorrow.

Requesting coeff update at 0x40f220 w/size of 0x1e44
No response from EPICS 

 I found the red sea when I came in this morning.

I tried several things.

1. ssh into fb40m: connection refused
2. telnet fb40m 8087: didn't respond
3. shutdown fb40m by physically pushing the power button: it worked and the FB came back to life but still with a red light on the MEDM DAQ_DETAIL screen;
4. powercycled fb40m AND C0DAQCTRL: no improvement
5. shutdown fb40m, C0DAQCTRL, C1DCUEPICS and pushed the reset button on the RF network crate; then I restarted the computers in this order: fb40m, C1DCUEPICS, C0DAQCTRL: it worked: they came back to life and the lights eventually turned green on the MEDM montior screen

I'm now going to restart the single front -ends and burtgooey them if necessary.

Requesting coeff update at 0x40f220 w/size of 0x1e44
No response from EPICS 

Everything is back on.

Restarted all the front ends. As usual c1susvme2 was stubborn  but eventually it came up.

I burt-restored all the front-ends to Nov 26 at 8am.

The mode cleaner is locked.

Taking  a cue from entry 2346, I immediately went for the nuclear option and powered off fb40m.  Someone will probably need to restart the backup script.

 Backup script restarted.

Looks like there was a power outage. The control room workstations were all off (except for op440m). Rosalba and the projector's computer came back, but rossa and allegra are not lighting up their monitors.

linux1 and nodus and fb all appear to be on and answering their pings.

I'm going to leave it like this for the morning crew. If it

The monitors for allegra and rossa's seemed to be in a weird state after the power outage.  I turned allegra and rossa on, but didn't see anything.  However, I was after awhile able to ssh in.  Power cycling the monitors did apparently got them talking with the computers again and displaying.

I had to power cycle the c1sus and c1iscex machines (they probably booted faster than linux1 and the fb machines, and thus didn't see their root and /cvs/cds directories).  All the front ends seem to be working normally and we have damped optics.

The slow crates look to be working, such as c1psl, c1iool0, c1auxex and so forth.

Kiwamu turned the main laser back on.

I checked the vacuum system and judged there is no apparent issue.

The chambers and annulus had been vented before the power failure.
So the matters are only on the TMPs.

TP1 showed the "Low Input Voltage" failure. I reset the error and the turbine was lift up and left not rotating.
TP2 and TP3 seem rotating at 50KRPM and the each lines show low pressur (~1e-7)
although I did not find the actual TP2/TP3 themselves.

One of the possibilities that we see a large low-frequency digital noise is due to Foton. I've checked the SOS coefficients that saves Foton with a Matlab coefficients. I used a 3 order low-pass cheby1 filter cheby1("LowPass",3,0.1,3) 

In matlab I generated SOS model using 3 approaches 

[A,B,C,D]=cheby1(3,0.1,3/1024) % create SS form

[sos,g]=ss2sos(A,B,C,D)  % convert to SOS form

[z, p, k]=cheby1(3,0.1,3/1024) % create ZPK form

[sos,g]=zp2sos(z,p,k)  % convert to SOS form

[b, a]=cheby1(3,0.1,3/1024) % create TF form

[sos,g]=tf2sos(b,a)  % convert to SOS form

As this is a 3 order filter, in the SOS representation we'll get 2 by 6 SOS - matrix. It is presented below. In each matrix place there 4 numbers - from the Foton file and obtained using these 3 methods.

GAIN

1.582261654653329e-07

1.582261654653329e-07

1.582261654653329e-07

1.582261655030947e-07

SOS-MATRIX

1              1.0000000000000000      #           0                                              #       1      #         -0.9911172660954457     #       0

1              1.0005663179617605      #           0                                              #       1      #         -0.9911172660954457     #       0

1              1.0000000000000000      #           0                                              #       1      #         -0.9911172660954457     #       0

1              0.9999894976396830      #           0                                              #       1      #         -0.9911172660997303     #       0

############################################################################################################

1              2.0000000000000000      #          1.0000000000000000         #       1      #        -1.9909750803252266      #      0.9911175825477769

1              1.9994336820732397      #          0.9994340026283055         #      1       #       -1.9909750803252262       #     0.9911175825477765

1              2.0000000000000000      #          1.0000000000000000         #      1       #       -1.9909750803252262       #     0.9911175825477765

1              2.0000105023603174      #          1.0000105024706190         #      1       #       -1.9909750803209423       #     0.9911175825434912

It seems that smth analog to zp2sos is used in Foton. We can see that due to representation error we have derivations in the 4 and 6 digits for SS and TF forms. This means that a pretty big mistake can run due to digital transforms even using double precision as in the Matlab test.

Alex Ivanov said that he'll fix that single precision problem and in the 2.5 release we won't have any FLOAT variables. Though we still do not understand how that variables declared as FLOAT can cause filter calculations. 

 In the previous elog we've compared Matlab and Foton SOS representations using low-order filter. Now we move on to high order filters and see that Foton is pretty bad here.

We consider Chebyshev filter of the first type with cuf off frequency 12 Hz and ripple 1 dB. In the table below we summarize the GAINS obtained by Matlab and Foton for different digital filter orders.

We can see that for high orders the gains are completely different (ORDER of 2!!!). Interesting that besides of very bad GAIN, SOS-MATRIX Foton calculates pretty well. I checked up to 5 digit - full coincidence. Only GAIN is very bad.

The filter considered is cheby1("LowPass",6,1,12) and is a part of the bad Cheby filter where we loose coherence and see some other strange things.

 I tried to understand what part of the signal is corrupted while passing through a digital straight line without any filters. From here we can figure out what precision is used.

I analysed coherence between C1:SUS-MC3_LSC_EXCMON and C1:SUS-MC3_LSC_OUTMON without any filters between them. 

I did the simulation in Matlab using single and double precision. Basically, I took a random signal, made some operations with it to obtain some digital error:

signal1 = randn(1e6, 1);          signal2 = randn(1e6, 1);         signal3 = signal1+signal2;          signal4 = signal3 - signal2;

Then I plotted coherence between signal1 and signal4 that are actually the same signal but signal4 has some digital error. This was done both for single (left red plot) and double (right blue plot) precision.

From here we make a conclusion that C1:SUS-MC3_LSC_EXCMON and C1:SUS-MC3_LSC_OUTMON has single precision. The signal might be converted from double to single in the dtt tools but if dtt works with double precision then the problem is with signals.

 In the previous elog we've proved that signals C1:SUS-MC3_LSC_EXCMON and  C1:SUS-MC3_LSC_OUTMON are in single precision. Now we try to understand if the precision is lost when the signals enter dtt tools or in the online code. For this measurement we just switch on one of the filters between the signals. By this we add mathematical operations inside the online code. If double precision is used there, then we'll see the same error as before, because the real error is still very small (~10^-15) and dtt tools add this 10^-7 error. But if the digital error will increase then no matter what kind of precision use dtt, online code uses single precision. At least at some points.

Test 1.   cheby1("LowPass",6,1,12) 

Test 2.  cheby1("Lowpass",2,0.1,3)

 Test 3. butter("LowPass",8,10)

Test 4.  butter("LowPass",2,10)

We can see that coherence become worse. And longer filter - more digital error. This means that single precision is used in calculations.

Foton Matlab Error     

We investigated some more the discrepancy between Matlab and Foton numbers. The comparison of cheby1(k, 1, 2*12/16384) was done between versions implemented in Matlab, R and Octave. Filters created by R and Octave agree with Foton.

Also, we found that Matlab has gross precision errors for cutoff frequencies just smaller than used in our fitler, for example cheby1(6, 2*3/16384) fails miserably.

It would be useful to see some plots so we could figure out exactly what magnitude and phase error correspond to "gross" and "miserable".

In order to verify our theory about coherence corruption in linear systems due to the line

if((new_hist < 1e-20) && (new_hist > -1e-20)) new_hist = new_hist<0 ? -1e-20: 1e-20;  

in the /opt/rtcds/caltech/c1/core/release/src/include/drv/fm10Gen.c in the iir_filter function I've changed -20 to other numbers and watched at the coherence input and output of the digital filter cheby1("LowPass", 3, 0.1, 0.5)cheby1("LowPass", 6, 1, 1.5). The sampling rate was 2K. The frequency responce of the filter presented in this figure.

The next plot shows psd and coherence of the signal for different numbers in the if-statement line : 1e-20 , 1e-25, 1e-100.

We can see that for present value coherence between input and output signals is small even for low frequencies. The psd of the output signal is also corrupted because at low frequencies it should have the same psd as input signal. For 1e-25 and 1e-100 we can see that coherence is close to 1 at low frequencies so if-statement does not work and we have a first order transition from bad to good filter performance with discontinious jump of coherence.

However, for 1e-25 and 1e-100 data is still corrupted by the round-off error. Lack of coherence for high frequencies can be explained by the fact that dtt tools use single precision for data analysis and output is too small to plot a right coherence. But the coherence is also not precisely 1 for low frequencies. Actually, it is 0.99 for this aggresive filter. We use double precision in the real-time code but still for such kinds of filters round-off error is present. As wrote Daniel Sigg for Cheby filter:  "You need a lot more digits than you may naively suspect. In the 8th order example, the output of each SOS is amplified by ~10⁶. This regardless of the fact that the coefficients are all of order 1. If you require a level of 10^-3 attenuation in the stop band, you would have lost 9 digits already. Then, add the fact that you have to do of order 10⁴ subtractions to get from 16kHz to 12Hz, loosing another ~2 digits. On top, the high Q section is probably 10 worse than the others and you lost 12 digits. In a real example this may stack up even worse."

Next we need to figure out what effects does round-off error introduce in the performance of the interferometer.

To show why Matlab is bad in filtering at small cut-off frequencies we did the same thing in Matab, Octave and R: we've taken the low-pass chebyshev filter of the type 1, order 6, ripple 1 dB, the sampling frequency was 16384 Hz and cut-off frequency varied from 1 to 1000 Hz. Here is the plot for the gain of the zpk model versus to cut-off frequency.

We can see that Matlab's gain shows surprising gains for low cut-off frequencies through for > 100 Hz it is fine. In the next table we compare gain from Foton, Matlab, R and Octave for the same filter. So Foton is also good

I'm trying to get some intuition how digital noise due to quantization shows up in iir filters. I decided to do tests in C using Python to calculate psd and visualize. I've implemented Direct Form 1, 2, "Biquad" and "Low Noise" forms of realization of second-order iir filter from Matt's presentation. There is a typo in the "Low Noise Form" scheme - a₁ and a₂ gains should be switched. Other then that schemes correctly implement 2 order iir. 

The input signal to each filter was a sine wave plus white noise with small amplitude x[n] = sin(2*pi*f*t[n]) + g*random( [-1, 1] ),  g << 1, f=1kHz. Sampling frequency was 16384 Hz. All 4 forms implemented 2 order low-pass butterworth filter with cut-off frequency 0.2 Hz

For g=1e-2 all implementations work fine. For g=1e-8 when quantization noise increases, all implementations give a lot of noise at low frequencies. I did not notice any significant difference between any of these implementations. I'll try to do more tests to figure out any difference in noise between the forms.

Quantization noise depends on the architecture of the processor, compiler and what not. But I do not think this can give a huge difference in results. We need to understand carefully digital noise during PSD estimation and all operations done at Matlab or Python.

 Direct Form 2 is noisy in the first test. This is the one similar to Matt's in his presentation. Input signal was a sine wave at 1 Hz with small amplitude white noise x[n] = sin(2*pi*1*t[n]) + 1e-10 * random( [-1, 1] ). It was filtered with a notch filter: f=1Hz, Q=100, depth=210dB. SOS representation was calculated in Foton. Sampling frequency is 16kHz.

DF2 output noise level is the same if I change white noise amplitude while DF1, BQF, LNF can follow it. Time series show quantization noise of DF2. I've plotted coherence of the signals relative to DF1, because non of the signals will be coherent to it at low frequencies due to fft calculations.  

In the second test the input was white noise  x[n] = random( [-1, 1] ) It was filtered with a 2 order low-pass butterworth filter with cut-off frequency f = 0.25 Hz. SOS representation was calculated in Python. Sampling frequency is 16kHz.

In this test all implementations work fine. I guess dtt works with single precision and for that reason we see disturbance in coherence when we do the same test online.

If the problem is the precision in DTT, then why would the noise change when the corner frequency of the filter is changed?

And how about checking for filter noise in the situation we saw online? 4th order low pass at 1 Hz or 8 Hz.

 This is because when we plot signals with sampling frequencies 2k and 16k with the same BW, we actually create psd/coherence using different numbers of points in FFT calculations as NFFT ~ fs/bw, fs-sampling frequency. So we secretly used 8 times more fft points for 16k signal then for 2k signal. Following plots demonstrate this effect. The first plot shows transfer function and coherence for filtering of 16k signal with butter('LowPass',4,8) and 2k signal with butter('LowPass',4,1)  when BW=0.1. There is a disturbance in coherence for 2k signal below 2 Hz. Now let's take BW=0.8 and plot transfer function and coherence for 16k signal. We can see the same effect of coherence disturbance.

The similar effect takes place when we change the cut-off frequency. The following plots show transfer function and coherence of two pairs of 2kHz signals. 4 order butterworth low-pass filter was used. For the first pair cut-off frequency was 1 Hz, for the second 10 Hz.  On the first plot BW=0.1 and there is a disturbance in coherence below 1 Hz. However on the second plot when BW=0.01, this effect is lost.

I guess my goal is to figure out when these effects come from fft calculations and when from digital filter noise.

 I've filtered a 1 Hz sin wave excitation with a notch filter inside c1sus and c1rfm models. The biquad key is switched on in the last one, c1sus uses DF2. The results are indeed different.

Still I do not like huge (2n+1) harmonics in the output of the biquad filter, I do not get them in the simulations. They are absent in the time series as well. So this is not a psd-estimation effect.

 Excitation generator created these harmonics. When I applied low-pass butterworth filter, I've got the result of online filtering close to simulations. On the second graph blue is biquad filter output spectrum, red corresponds to DF2. 1 Hz sin wave was filtered with a notch filter of Q=100, depth=300 at 1 Hz.

What is "DQF"?  Is that the biquad?  And what is the difference between DF1 and DF2?  Why don't you just write out the name, so it's more clear.

 We decided to write a script that will check online filters for digital noise. One method can be implemented using the following algorithm:

• calculate filter output using single precision
• calculate filter output using double precision and assume that it is precise
• find digital noise at the output of the filter when single precision is used
• extrapolate the result to the double precision filter dividing by 2^D-S ~ 10⁷, D - number of bits used in double precision mantissa, S - in single precision

Restriction: Single precision filter internal variables must be checked for overflows.

I applied this method to filtering a 1 Hz sine wave with a notch filter. Precise output should also be a 1 Hz wave => at other frequencies we see noise => digital noise spectrum should coincide with filter output. The plot shows the method worked out for this example.

Using this method I estimated digital noise of butter("LowPass", 2, 0.001) applied to white noise. Sampling frequency was 16 kHz. 

The script estimates digital noise produces by online filters. First version of Matlab files and complied c files are in scripts/digital_noise directory.

Algorithm for 1 filter bank (max number of filters = 10):

1.        extract sos - representation from Foton file for each filter (Matlab)
2.        download data from corresponding DQ channel using NDS (Matlab)
3.        find filters that are switched on (Matlab)
4.        filter signal using Df2 and BQF with single and double precision (C)
5.        estimate digital filter noise (Matlab)
6.        calculate power spectral density and plot the result (Matlab)

More details on (2)

Often DQ channels have reduced sampling rate. In this case the script will upsample data adding zeros.

AI filter is not applied. But in the end only the frequency range (0, DQ RATE / 2) is analyzed.

More details on (3):

• input switch ON / OFF => 4 / 0
• filters 1 - 6 ON /OFF
  • 1 => 48 / 0
  • 2 => 192 / 0
  • 3 => 768 / 0
  • 4 => 3072 / 0
  • 5 => 12288 / 0
  • 6 => 49152 / 0
  • If a switch is ON but there is no corresponding filter (one green and one red line under the switch) then the switch value is divided by 3

_SW2R channel value is the sum of the following numbers:

• decimation switch ON / OFF => 512 / 0
• output switch ON / OFF => 1024 / 0
• filters 7 - 10 ON /OFF
  
  • 7 => 3 / 0
  • 8 => 12 / 0
  • 9 => 48 / 0
  • 10 => 192 / 0
  • If a switch is ON but there is no corresponding filter (one green and one red line under the switch) then the switch value is divided by 3

Note: as for now Matlab script assumes that input, output and decimation filters are switched ON and there are no turned ON filter switches that do not correspond to any filters

More details on (5)

Digital noise using double precision is estimated by extrapolation of digital noise with single precision. The last is calculated by subtracting outputs of the filters with single and double precision. Then this noise is multiplied by 3 * 10^-7.

This extrapolation number was achieved by printf tests of the number 0.123456789012345678 with single and double precision on C. Using type 'float' variables 10 significant numbers show up, using type 'double' - 17.

I also did 'calibration tests' to achieve extrapolation number - signal was filters with an aggresive low-pass filter. At high frequencies filter output spectrum is flat => digital noise amplitude must be the same. The plot shows GUR1_X channel filtered with low-pass chebyshev type 1 filter.

However, extrapolation number is not the same for all cases. In the following example of analyzing BS_SUSPOS filter bank using extrapolation 3 * 10^-7 we get noise that is slightly overestimated. In some other examples we need to take a larger number. But in average, I think, this is a good approximation.

To avoid extrapolation problem we can use long double precision (~19 digits). I was able to do this with gcc compiler. However, in mex compiler using long double in filter calculations, I do not get any better precision then using double precision. I'll think more about it.

Matlab version of ifo digital noise estimation code is almost ready. It estimates digital noise introduced by each filter bank in each model. I'm waiting for NDS group to complete function to download online data to Matlab. Now code downloads data from the past that is not great because not all _IN1 channels are recorded and some of them are recorded at lower frequencies.

There might be some useful functions in this code for other applications as I've heard during the meetings. This is what it does

• reads model names from the input list
• for each model
  
  • finds corresponding Foton file and extracts modules with sos filters and sampling rate of the model
  • finds corresponding MDL file and makes a search for subsystems with "top_names" tag and "biquad=1" tag
  • creates _IN1 channel names using module names and subsystems with "top_names" tag
  • for each channel inside the model
    
    • reads filter bank parameters (which filters are ON, switches, limit, offset...)
    • downloads data
    • calculates output and estimates digital noise
    • checks that output is less them limit if it is on
    • reports if something is wrong

NDS group plans to release the function to download online data this week. Hopefully, it will be possible to download ~30 channels at a time. Code will need a few minutes of data for each channel. So it will be possible to check the whole ifo during the night.

At this point I've checked 40m using DQ channels. We have ~40 IN1_DQ channels with non-empty filter banks. These are osems channels. Digital noise is low for them.

On behalf of Steve and of the rest of the not-native-English community at the 40m willing to have their browser's spell checker working while editing the Elog, I fixed the Elog's feature that prevented Firefox' context menu (that one which pops up with a mouse right click) to work when using the HTML editing interface (FCKeditor).

That let also Firefox spell checker to get enabled.

To get the browser context menu just press CTRL right-clicking.

To make sure that the features works properly on your browser, you might have to fully clear the browser's cache.

Basically I modified the FCKeditor config file (/cvs/cds/caltech/elog/elog-2.7.5/scripts/fckeditor/fckconfig.js). I added this also to the elog section on our Wiki.

elog was acting up again (not running), so I restarted it. 

And again.  This makes 4 times since lunchtime yesterday....something bad is up.

We want the elog process to run in verbose mode so that we can see what's going. The idea is to track the events that trigger the elog crashes.

Following an entry on the Elog Help Forum, I added this line to the elog starting script start-elog-nodus:

./elogd -p 8080 -c /cvs/cds/caltech/elog/elog-2.7.5/elogd.cfg -D -v > elogd.log 2>&1

which replaces the old one without the part with the -v argument.

The -v argument should make the verbose output to be written into a file called elogd.log in the same directory as the elog's on Nodus.

I haven't restarted the elog yet because someone might be using it. I'm planning to do it later on today.

So be aware that:

We'll be restarting the elog today at 6.00pm PT. During this time the elog might not be accessible for a few minutes.

 I tried applying the changes but they didn't work. It seems that nodus doesn't like the command syntax.

I have to go through the problem...

The elog is up again.

 Zach made me notice that the elog had crashed earlier on this afternoon. 

I just restarted it with the restarting script.

Instructions on how to run the last one are now in the wiki page. Look on the "How To" section, under "How to restart the elog".

 Again, this morning Zach told me that the elog had crashed while he was trying to post an entry.

I just restarted it.

 I restarted the ELOG on NODUS just now. Our attempt to set up error logging worked - it turns out ELOG was choking on the .ps file attachment.

So for the near future: NO MORE .PS files! Use PDF - move into the 20th century at least.

matlab can directly make either PNG or PDF files for you, you can also use various other conversion tools on the web.

Of course, it would be nice if nodus could handle .ps, but its a Solaris machine and I don't feel like debugging this. Eventually, we'll give him away and make the new nodus a Linux box, but that day is not today.

 The elog was down and I ran the restart script.

I found the elog down and I restarted it.

Then, after few seconds it was down again. Maybe someone else was messing with it. I restarted an other 5 times and eventually it came back up.

When I went to use the elog this morning, it wasn't responding.  I killed the process on nodus, and then restarted, per the 40m wiki instructions.