Here for the downsampling process we use a low-pass Bessel digital filter of order 6, normalized cut-off frequency = 0.1. In the plot presented below we compare the results with downsampling ratio = 1, 2, 4.

We can see that increasing the downsampling ratio, we increase the error of the filter. Moreover, the error at some particular frequency f seems to depend on the ratio f/Fs, where Fs - sampling frequency (2048 Hz) devided by downsampling ratio. Error is the same for all curves below 1 Hz but then begins to increase as we increase the sownsampling ratio. In order to figure out what the problem is - mistake in the filter code, inaccurate upsample algorithm or this is NLMS particularity, I've changed sampling frequency in the chans/daq/C1PEM.ini and C1IOO.ini files from 2048 Hz to 512 Hz for corresponding channels. Now, we compare the error from the filter working with 2048 Hz frequency, downsampling ratio = 4, low-pass filter = Bessel of order 6, normalized cut-off = 0.1 and filter working with 512 Hz sampling frequency, without downsampling and with corresponding Bessel low-pass filter with normalized frequency 0.4.

MC_F measurement at 2048 Hz was done during the day, for that reason red curved is slightly higher then green in the resonance frequencies. But still we can see that these two cases are very much alike. For this reason, it seems that NLMS filter works better with higher sampling frequencies.

 In order to figure out what downsampling ratio we can take, we need to determine the running time of the fxlms_filter() function. If the filter length is equal to 5000, downsampling ratio is equal to 1, number of witness channels is 1 then with ordinary compilation without speed optimization one call runs for 0.054 ms (milli seconds). The test was done on the 3 GHz Intel processor. With speed optimization flags the situation is better

-O1 0.014 ms, -O3 0.012 ms

However, Alex said that speed optimization is not supported at RCG because it produce unstable execution time for some reason. However, by default the kernel should optimize for size -Os. With this flag the running time is also 0.012 ms. We should check if the front-end machine compilers indeed use -Os flag during the compilation and also play with speed optimization flags. Flags -O3 and -Os together might also give some speed improvement.

But for now we have time value = 0.012 ms as running time for 5000 coefficient filter, 1 witness channel and downsample ratio = 1. Now, we need to check how this time is scaled if we change the parameters.

5000 cofficients - 0.012 ms

10000 coefficients - 0.024 ms

15000 coefficients - 0.036 ms

20000 coefficients - 0.048 ms

We can see that filter length scaling is linear. Now we check downsampling ratio

ratio=1 - 0.048 ms

ratio=2 - 0.024 ms

ratio=4 - 0.012 ms

Running time on the dependance of downsample ratio is also linear as well as on the dependence of the number of witness channels and degrees of freedom. 

If we want to filter 8 DOF with approximately 10 witness channels for each DOF, then 5000 length filter will make 1 cycle for ~1 ms, that is good enough to make the downsample ratio equal to 4.

Things get a little bit complicated when the code is called for the first time. Some time is taken to initialize variables and check input data. As a result the running time of the first cycle is ~0.1 ms for 1 DOF that is ~10 times more then running time of an ordinary cycle. This effect takes place at this moment when one presses reset button in the c1oaf model - the filter becomes suspended for a while. To solve this problem the initialization should be divided by several (~10) parts.

In order to prevent different DOF from redetermining static variables in the adaptive code, I've created a separate code for each DOF with the name ADAPT_XFCODE_{$DOF}.c

I've provided the links for these files in the c1oaf.mdl, compiled and run it. Now there are no conflicts between DOFs.

I tried to filter MC_F from seismic noise measured by GUR1 seismometer. I've used 8000 tap filter, downsample ratio=8, delay=1. In the Figure the output of the filter is presented with MC_F signal.

We can see that output is close to the MC_F, but the phase for some reason is not zero. It should not be at 1 Hz - 10 Hz due to the actuator. But below these frequencies I do not see any reasons for the output phase to differ from MC_F phase. But it is possible, the phase of the actuator is evaluated very rough and the adaptive filter can't match it.

 Just to be clear what I said at the meeting, I write all this down here. Adaptive filtering of real signals (MC_F and GUR1_X) with all noises inside is 

This is offline filtering but with real signals and with the C-code that is compiled at the 40m now. We can reduce the MC_F signal by ~100 below 10 Hz, but  the problem is that reducing the adaptation gain, the error increases. As a result when we move towards FxLMS algorithm with AA, AI and downsampling, we have to take the gain equal to ~1e-2 and we do not reduce any noise. 

The second demonstration of this problem is static Wiener filtering. This is the result

We can see that adaptive filtering outperforms the "optimal" filtering. This is because an adaptive filter can follow the changes of coefficients immediately while the Wiener filter averages them. This is the mathematical formulation:

mcl_real = coeff _real* seismic_noise_real + other_noise

mcl_real - the real length of the MC,

coeff_real - real coefficients, that represent the transfer function between seismic noise and MC length,

other_noise - noise uncorrelated to the seismic noise seismic_noise_real

But in the world of our measured signals we have the equation

mcl_measured = coeff * seismic_noise_measured + other_noise

mcl_measured = TF_mcl * mcl_real

seismic_noise_measured = TF_seis * seismic_noise_real

where TF_mcl and TF_seis - transfer functions from the real world to measurements.

It seems to me that TF_mcl or TF_seis are not constants and for that reason the TF between measured seismic noise and mcl is not constant. But it is exactly what an adaptive or Wiener filter tries to define:

coeff(time) = average(coeff(time)) + delta(coeff(time))

The result of applying average(coeff) is the green line in the Figure 2 - error after applying the Wiener filtering.

delta(coeff) - the changing part of the transfer function is caught by the adaptive filtering. The lower the gain, the lower is the capability of adaptive filter to catch these changes. Theoretically. the error after applying adaptive filter can be presented like this:

E(error*error) = E(other_noises*other_noises) + 1/(2-mu)*mu*E(other_noises*other_noises)  + 1/ {mu*(2-mu)} * Tr(Q) * A

where mu = adaptation gain

Q - covariance matrix of delta(coeff)

A - norm of the seismic signal

The first term in this equation is the dispersion of other noises, the second term is the error of the adaptive filter due to non-zero gain, the third term is due to the changes in the transfer function - we can see that it is proportional to 1/mu. This term explains why the error increases while mu decreases.

Now I'm looking for the part in the path of the signals where the transfer function can change. As I mentioned above, this is not a change in the real world, it is the change in the measured signlals. My first guess is the quantization error - we do not have not enough counts. If this is not the case, I'll move to other things of the signal path.

Today I tried to make the lms filter to work online. I played around with the signals (GUR1_X and MC_F) to pre-whiten them and in the end the following configuration worked out:

1. mu = 0.03, tau = 1e-5, downsample=8, nCoeff = 4000, delay = 5 (sample-and-hold delay is not included in the new code, it should be added here!)

2. witness pass: AA32 = cheby1("LowPass", 4, 1, 32) AND 0.1:0

3. witness adaptation path: AA32 AND AI32 = cheby1("LowPass", 4, 1, 32) AND 0.1:0

4. error path: AA32 AND 0.1:0 AND anti_1Hz. Before I added anti_1Hz filter oaf did nothing. This filter tries to approximate the actuator transfer function. Note, it is not in the witness adaptation path. This is some sort of whitening.

5. correction path: AI32, gain = -1

Convergence time ~ 5 mins. The performance of the filter is far not perfect compared to the offline implementation. But it deals with a stack though.

I made static filter to work to evaluate the actuator TF.. Here is the result of static filtering:

 What I did:

 I did offline simulation of the MC_F Wiener filtering using 2 witness signals - GUR1X and GUR1Y. I've downsampled the data from 2048 to 128 Hz and applied the Wiener filter with 10000 for each witness channel:

                                            Result of the filtering                                                                                     Filter coefficients for gur1x and then gur1y

                                         Gur1x -> MC_F transfer function                                                                          Gur1y -> MC_F transfer function

Then using vectfit I approximated obtained transfer functions in the region 0.5 - 20 Hz. I used a window function and then weights to get a more precise result in this range using only 8 poles and zeros.

I obtained the zpk-model for each witness channel and entered it into the FOTON splitting it into 2 parts before that because FOTON does not like too long filters. These zpk-models are at the C1:OAF-STATIC_STATMTX_8_8 and C1:OAF-STATIC_STATMTX_8_9 filter banks.

GUR1X:

z =

  7.527339430029315 +31.603999069997801i
  7.527339430029230 -31.603999069997823i
 27.897703898191267 + 0.000000000000071i
 -6.437806394766186 + 9.893955654289517i
 -6.437806394766159 - 9.893955654289510i
  1.114401249545640 + 5.479278396987240i
  0.176877296954015 + 0.000000000000006i
  1.114401249545616 - 5.479278396987245i


p =

 -0.407251778925379 + 6.263247012022007i
 -0.407251778925379 - 6.263247012022007i
 -0.230672968859081 + 6.846868757063707i
 -0.230672968859081 - 6.846868757063707i
 -2.871419857491615 +13.707864827517826i
 -2.871419857491615 -13.707864827517826i
 -2.134260618362721 +18.319129999777648i
 -2.134260618362721 -18.319129999777648i


k =

     4.113285626223658e-04

GUR1Y

z =

 17.961416874092624 +13.631821252434328i
 17.961416874092642 -13.631821252434353i
 -8.788634771726304 + 7.653357335975781i
 -8.788634771726285 - 7.653357335975777i
 -0.037906973323273 + 5.133348020858679i
 -0.164348392996182 + 3.588803405511463i
 -0.164348392996187 - 3.588803405511474i
 -0.037906973323277 - 5.133348020858679i


p =

 -0.027577318242359 + 5.174655410828068i
 -0.027577318242359 - 5.174655410828068i
 -0.500384298611703 + 6.310552036591990i
 -0.500384298611703 - 6.310552036591990i
 -0.237055716999485 + 6.881204941979009i
 -0.237055716999485 - 6.881204941979009i
 -1.408223271160550 +14.874570175309771i
 -1.408223271160550 -14.874570175309771i


k =

    -2.723835471763049e-04

 Then I approximated the reversed actuator TF  and placed it to the C1:OAF-SUS_MC2_OUT filter bank. The gain to the static filter output is -1.

P.S. Also the static matrix was filled with 1 for some reason. Here is the script to fix it if if will be bad again

for i in {1..8}
do
    for j in {1..28}
    do
        element="C1:OAF-STATIC_STATMTX_"$i"_"$j"_GAIN"
        ezcawrite $element 0
    done
done

I've run static and adaptive filters simultaneously. AA32 filters rotate the phase of the witness signals GUR1X and GUR1Y and now the performance of the static filter is worse. Next time I'll recalculate Wiener filter coefficients taking this into account. But still 2 filters together can deal with a stack better.

 This is super awesome!  I'm totally excited!!

 Here are the issues that I found not quite accurate in the old oaf code:

1. There is no need to calculate the norm of the witness signal every time from zero: 

norm += (*pBufAdapt) * (*pBufAdapt); // add to the norm 

Every step the witness signal vector is the same except the first and last values

wit[i].norm += histAdpt[nCoeff]*histAdpt[nCoeff] - histAdpt[0]*histAdpt[0];

 This step will reduce the number of multiplications and summations from 3*M/k to 2*M/k, M - filter length, k - downsample ratio.

2. Old code filter corrects filter coefficients with a delay equal to k=downsample ratio (pretty big):

witness       o o o o o o o o o o o o o o o o o o o o o

error           o o o o o o o o o o o o o o o o o o o o o

We want the filter to work at green points and skip red points computing output and correcting coefficients at this time (downsample ratio in this example is 4). Old code

• grabs error signal
• calculates output during next k-1 red points and 1 green point
• corrects coefficients using this error during next k-1 red points and 1 green point

But LMS algorithm should correct coefficients according to the latest error. As we calculate output and correct coefficients before the latest error signal will be available, we should change the order:

• grabs error signal
• corrects coefficients using this error during next k-1 red points and 1 green point
• calculates output during next k-1 red points and 1 green point

This scheme is completely equivalent to the ordinary LMS algorithm, as now we correct coefficients according to the latest error signal and so do not add any delay.

3. So long soft start is probably not needed for the LMS filter, it makes the filter to converge longer 

// modify adaptation gain for soft start

    if( state.iWait < state.nFIR )

    {

      adaptGain = 0.0;

      decayRate = 1.0;  // clear FIR coeffs after reset

    }

As far as I understand this is done to prevent the filter from huge coefficients variations in the beginning when norm is not calculated yet. Instead we can just introduce some small

epsilon = 10.0;

to prevent the filter from divergence in the beginning 

delta = mu * error / (wit[i].norm + epsilon);

Though some soft start might be needed by not so long - it will take several minutes before the adaptation gain will take it's specified value. 

 DFT-LMS is a frequency domain adaptive filter that demonstrates faster convergence compared to the time-domain LMS filter. I've tested Discrete Fourier Transform (DFT-LMS) filter. It converts witness signal to the frequency domain using DFT and corrects the eigenvalues of the covariance matrix to make them as equal to each other as possible (does pre-whitenning of the witness signal).

Left plot compares learning curves for time domain LMS and DFT-LMS algorithms on the simulated data from seismometers and mcl (number of averages  = 30) Right plot shows the evolution of the filter coefficients norm (Euclidean norms of the coefficient vector). Though LMS algorithm works in the time domain and DFT-LMS in the frequency domain, the coefficient vectors must have the same length, because we Fourier Transform is achieved by applying a unitary operator => vector norm must not change.

Plots show that both algorithms converge to the same coefficients vector norm, but DFT-LMS does it much faster then LMS. 

Online realization: 

Good news: algorithm complexity is linear in filter length. Though the algorithm does Fourier transform, its complexity is still O(M), M - number of coefficients. Simulations show that DFT-LMS is ~8-9 times slower then LMS. This is not so bad, may be we can do even slightly better.

Bad news: downsample process is not simple. Due to Fourier transform, the filter needs the whole witness signal vector before calculating the output. This is sad and in contrast with LMS algorithm where we could start to calculate the new output immediately after computing the previous output. We either need to calculate the whole output immediately or introduce delay in the output or approximate Fourier transform with some previous witness signal values.

Realization in the kernel: I asked Alex about complex numbers, exponents, sin and cos functions in the kernel c and he answers that we do not have complex numbers, about exp, cos, sin he is not sure. But for DFT-LMS algorithm we are able to get round of these difficulties. Complex numbers will be presented as  2 real numbers. Then exp (a) = cos(a) + i*sin(a). All what we need for DFT-LMS are sin(2 * pi * k / M) and cos(2 * pi * k / M), k=0,1,2,...,M-1. Fortunately, M - (filter length) is big enough, typical value pi/M ~ 0.001 and we can calculate sin(2*pi/M) and cos(2*pi/M) using Taylor series. As the argument is small, 5-6 terms will be enough to get precision ~1e-20. Then we build the whole table of cos and sin according to induction cos(2*pi/M*k) = cos(2*pi/M*(k-1))cos(2*pi/M) - sin(2*pi/M*(k-1))sin(2*pi/M), sin(2*pi/M*k) = cos(2*pi/M*(k-1))sin(2*pi/M) + sin(2*pi/M*(k-1))cos(2*pi/M). We should do it only once, so the algorithm will build these values in the beginning during first several iterations, then will use them.

The main problem is downsampling. I need to think more about it.

I've compared offline Wiener filtering with online static + adaptive filtering for MC_F with GUR1_XYZ and GUR2_XYZ as witness signals

Note: online filter works up to 32 Hz (AI filter at 32 Hz is used). There is no subtraction up from this frequency, just MC_F was measured in different times for online and offline filtering. This difference in MC_F in frequency range 20-100 Hz showed up again as before with microphone testing.  One can see it in 1 minute. Smth is noisy.

Reasons why online filter is worse then offline:

1. FIR -> IIR conversion produces error. Now I'm using VECTFIT approximation with 16 poles (splitting into 2 filter banks), this not enough. I tried to use 50 and split them into 5 filter banks, but this scheme is not working: zpk -> sos conversion produces error and the result filter works completely wrong.

2. Actuator TF. VECTFIT works very good here - we have only 1 resonance. However, it should be measured precisely.

3. Account for AA and AI filters that rotate the phase at 1-10 Hz by ~ 10 degrees.

I've implemented online frequency domain filter and applied it to MC_F.

+

Magnitude of the filter output at 1 Hz is the same as MC_F. This means that it is not hard for FIR to match the resonance. The problem is with the phase. We can not match the resonance exactly. If the resonance is at f₀ and we match at f₀ +/- df then in the frequency range (f₀, f₀ +/- df) the phase is not matched for 180. I guess the filter does not diverge because df is small but also the filter can not account for this huge phase lag. We need to slightly change the simulated actuator TF and see how the filter will react.

Static filter was adjusted to filter 1 Hz resonance in MCL and it could do it. Stack is not great in this experiment due to the phase mismatch. I'll fix it.

Jenne and I did adaptive filtering of MC_L and measured how X and Y ARM control signals change compared to non-filtered MC_L. We did the test during 1.5 Hz seismic noise activity and adaptive filter was able to subtract it. However, it adds noise at high frequencies, It is not seen in MC_L but it is present in the ARMs control signals.

I'll investigate this problem. May be we need to reduce adaptation gain. In this experiment it was 0.1 and adaptive filter convergence time was equal to 1-2 mins.

I will do some experiments on acoustic noise canceling during my stay.
Now I am planning to cancel acoustic noise from PMC and see how the acoustic noise work and how we should place microphones.

First, I measured the noise in microphones and its circuit.

-blue, green, red, solid lines; microphone signals
-blue, green, red, dashed lines; un-coherent noise in signals
-yellow, black, solid lines; circuit noise (signal input is open, not connected to the microphones)

We can see the acoustic signal above 1 Hz, and the circuit does not seem to limit its sensitivity. But I do not know why yellow and black is so different. I will check it tomorrow.

Hi, Ayaka.  It would be good if you could give a little bit more detail about this plot:

• What exactly are the "signals"?  Are you making a sound somehow?  If so, what is producing the sound?  What is it's spectrum?
• Are the blue/green/red traces from three different microphones?
• Coherence usually implies a comparison between two signals.  Is something being compared in the dashed traces?
• Are the yellow and black traces from different amplifiers?
• What are the units of the Y axis?

 Sorry for my poor explanation.

I measured this by the same way as you measured the instrumental noise of seismometers.
I put the three microphones at the same place so that the three can hear the same sound. I did not make any sounds, just put them in the lab.
The signals from microphones are all amplified by the circuit.
And I took the correlations of each signals and two others and got the noise (dashed lines) by subtracting the correlated signal from the original signal.

So,
-The signal is the acoustic sound in the lab, amplified by the circuit.
-Three lines are from three different microphones.
-Dashed lines are subtraction of coherent signal from the original.
-Yellow and black lines are from different amplifiers in the same circuit box. The circuit has 6 channels.
-I did not calibrate the signals I got by DTT since I do not know the calibration factor now. It is just the number I got from the real time system.

Previous results
I am measuring the noise level of the microphones. The circuit does not seems to limit their sensitivities but the circuit's noise seems to be different from other channels.

Measurement
I measured the circuit noise of all 6 channels. (input open)
(mic_open.png)
The noise level is about 10 times different from the others.

Comparing the acoustic signal, microphone+circuit noise, and ADC noise;
(mic_noise.png)
- blue; acoustic signal
- green; microphone+circuit noise
- red; circuit (the data was not took simultaneously.)
- sky blue; ADC noise

To do
I will remake the circuit though the circuit does not limit the sensitivity. I would like to make sure that the circuit does not affect badly and to make the circuit noise level the same.
At the same time, I will get the PMC control signal and see coherence between it and acoustic sound.

  We have to change the sample rate and AA filter for the mic channels before going too far with the circuit design.

 To save the mic channels at higher than 2k (which we should do), we either have to move them to a different model, change the rate of the PEM model, or see if you can save data faster than the model runs (which I can't imagine is possible).

 PEM model is running at 64K now. It turned out to be tricky to increase the rate:

• BLRMS are computationally expensive and original pem model did not start at any frequency higher then 16k ( at 16k cpu meter readings were 59/60 ). Also when we go higher then 16k, front-end gives the model less resources. I guess it is assumed that this model is iop and won't need too much time. So in the end I had to delete BLRMS blocks for all channels except for GUR2Z and MIC1.
• Foton files are modified during model compilation: lines with sampling rate and declaration of filters in the beginning of the file are changed only. Sos-representation and commands are the same. I hoped that filter commands will let me change sos-representation quickly. I've opened Foton and saved the file. However, Foton modified commands in such a way that the ratio of poles and zeros to sampling rate is preserved. I guess all filters have to be replaced or this process should be done in another way.
• BLRMS block uses low-pass filters below 0.01 Hz, increasing the sampling rate by a factor of 32 might make calculations incorrect. I'll check it.

We should also increase cut off frequency of the low-pass filter in the microphone pre-amplifier from 2 kHz up to ~20-30 kHz.

 Thank you for changing the sample rate!
Also we have to change the Anti-Aliasing filter, as Jamie said.

Now my question is, whether S/N ratio is enough at high frequencies or not. The quality of EM172 microphone is good according to the data sheet. But as you can see in previous picture, the S/N ratio around 1kHz is not so good, though we can see some peaks, e.g. the sound that a fan will make. I have to check it later.
And, is it possible to do online adaptive noise cancellation with a high sampling rate such that computationally expensive algorithms cannot be run?

  That's no good - we need BLRMS channels for many PEM channels, not just two. And the channel names should have the same name as they had in the past so that we can look at long term BLRMS trends.

I suggest:

1. Have a separate model for Mics and Magnetometers. This model should run at 32 kHz and not have low frequency poles and zeros. Still would have acoustic frequency BLRMS.
2. Have a low frequency (f_sample = 2 kHz) model for seis an acc. Seismometers run out of poop by 100 Hz, but we want to have the ACC signal up to 800 Hz since we do have optical mount resonances up to there.
3. Never remove or rename the BLRMS channels - this makes it too hard to keep long term trends.
4. Do a simple noise analysis to make sure we are matching the noise of the preamps to the noise / range of the ADCs.
5. Immediately stop using bench supplies for the power. Use ONLY fused, power lines from the 1U rack supplies.

Ayaka, Den

 C1PEM model is back to 2K.

We created a new C1MIC model for microphones that will run at 32K. C1SUS machine is full, we have to think about rearrangement.

For now, we created DQ channels for microphones inside iop model, so we can subtract noise offline.

We provided 0-25 kHz bandwidth noise to AA board and saw the same signal in the output of ADC in the corresponding channel. So cut-off frequency is higher then 25 kHz. There is a label on the AA board that all filters are removed. What does this mean?

We've turned off AA bench power supply, prepare to use fused from 1U.

[Raji, Ayaka]

Thanks to Den, power supplies for microphone circuit are changed.
So I measured the microphone noise again by the same way as I did last time.

  solid lines: acoustic noise
 dashed lines: un-coherent noise
black line: circuit noise (microphone unconnected)

The circuit noise improves so much, but many line noises appeared.
Where do these lines (40, 80, 200 Hz...) come from?
These does not change if we changed the microphones...

Anyway, I have to change the circuit (because of the low-pass filter). I can check if the circuit I will remake will give some effects on these lines.

I do not think that 1U rack power supply influenced on the preamp noise level as there is a 12 V regulator inside. Lines that you see might be just acoustic noise produced by cpu fans. Usually, they rotate at ~2500-3000 rpm => frequency is ~40-50 Hz + harmonics. Microphones should be in an isolation box to minimize noise coming from the rack. This test was already done before and described here. 

I think we need to build a new box for many channels (32, for example, to match adc). The question is how many microphones do we need to locate around one stack to subtract acoustic noise. Once we know this number, we group microphones, use 1 cable with many twisted pairs for a group and suspend them in an organized way.

 I do not think they are acoustic sounds. If so, there should be coherence between three microphones because I placed three at the same place, tied together. However, there are no coherence at lines between them.

For a last few days I've been working on oaf and simulink model to simulate it. First I did online subtraction from MC when MC_L path was enabled. Inside my code I've added a sum of squares of filter coefficients so we can monitor convergence of the filter.

To to this I've measured path from OAF output to input without AA and AI filters. Then made a vectfit using 2 poles and zeros. Foton command

zpk( [-2.491928e+03;5.650511e-02], [-4.979872e+01;-3.278776e+00], 6.011323e+00)

My simulink model consists of 3 parts:

• cavity with seismic noise at low frequencies, 1/f^2 noise at medium frequencies and white noise at high frequencies
• this cavity is locked using feedback compensation filters that we use to lock arms
• locked cavity with adaptive filter

Adaptive filter in the model uses online c-code. It is connected to simulink block through an S-function. Sampling frequency of the model is 10 kHz. It works fairly fast - 1 sec of simulation time is computed in 1 sec.

I've tested FxLMS algorithm and MFxLMS algorithm that is faster. I plan to test 2 iir adaptive algorithms that are already coded.

I've applied FIR adaptive filter to YARM control. Feedback signal of the closed loop was used as adaptive filter error signal and OAF OUT -> IN transfer function I assumed to be flat because of the loop high gain at low frequencies. At 100 Hz deviation was 5 dB so I've ignored it.

I've added a filter bank YARM_OAF to C1LSC model to account for downsampling from 16 kHz to 2 kHz and put low-pass filter inside.

I've used GUR 1&2 XYZ channels as witnesses. Bandpass filters 0.4-10 Hz we applied to each of them. Error signal was filters using the same bandpass filter and 16 Hz 40 dB Q=10 notch filter. As an AI filter I used 32 Hz butterworth 4 order low-pass filter. Consequently, AI, bandpass and notch filters were added to adaptive path of witness signals.

I've used an FIR filter with 4000 taps, downsampling = 16, delay = 1, tau = 0, mu = 0.01 - 0.1. Convergence time was ~3 mins.

This is interesting. I suppose you are acting on the ETMY.
Can you construct the compensation filter with actuation on the MC length?
Also can you see how the X arm is stabilized?

This may stabilize or even unstabilize the MC length, but we don't care as the MC locking is easy.

If we can help to reduce the arm motion with the MCL feedforward trained with an arm sometime before,
this means the lock acquisition will become easier. And this may still be compatible with the ALS.

Why did you notched out the 16Hz peak? It is the dominant component for the RMS and we want to eliminate it.

 I actuate on ETMY for YARM and ETMX for XARM. For now I did adaptive filtering for both arms at the same time. I used the same parameters for xarm as for yarm.

I've notched 16 Hz resonance because it has high Q and I need to think more how to subtract it using FIR filter or apply IIR.

I'll try MC stabilazation method.

 Adaptive filtering was applied to MC and X,Y arms at the same time. I used a very aggressive (8 order) butterworth filter at 6 Hz as an AI filter for MC not to inject noise to ARMS as was done before

Mu for MC was 0.2, downsample = 16, delay = 1. I was able to subtract 1 Hz. Stack subraction is not that good as for arms but this is because I used only one seismometer for MC that is under the BS. I might install accelerometers under MC2.

EDIT, JCD, 18Feb2013:  Den remembers using mu for the arms in the range of 0.01 to 0.1, although using 0.1 will give extra noise.  He said he usually starts with something small, then ramps it up to 0.04, and after it has converged brings it back down to 0.01.

[Jenne, Raji]

We replaced the MC Refl path BS with the Y1, as usual, so that the full ~100mW goes to the REFL PD, so we don't have WFS or MC refl camera. 

The MC spots were all outside of 1mm, and some were beyond 2mm (for MC1,3, P,Y....MC2 is of course free since we have more DoFs than we need), so we touched (very, very slightly) the zigzag mirrors on the PSL table.  We realigned the MC, and now the spots are centered to my satisfaction.

MC1,2,3 Pit,    MC1,2,3 Yaw (in mm):

[0.46444020918749457, 8.2634316545130009, -0.41417975237831089, -0.89401481457980592, -0.9323196976382162, -1.543145765853893]

MC2 is way off in pitch, according to this measurement, and it's been consistently going down as we move the MC2 spot in the same direction (up on the monitor), but since we started at +15mm and are now at +8, and we've gone quite a ways, I'm not sure that we really want to go all the way to 0.  Anyhow, MC1 and MC3 are the ones which define our input pointing, so we're quitting for tonight.

We will turn on the PZTs and begin with the official vent list for dummies tomorrow.

We went into the vertex today to see about fixing the alignment.  The in-air access connector is in place, and we took heavy doors off of BS, ITMY, and ETMY chambers.

We started by looking at the pointing from the PZTs.  Manasa and Raji hooked up HV power supplies to the PZTs and set them to the middle of their ranges (75 V).

We installed a target on the BS cage, and new "free standing" targets made special by Steve for the SOSs on ITMY and ETMY.

Using a free-standing aperture target we looked at the beam height before PZT2.  It was a little high, so we adjusted it with PZT1.  Once that was done we looked at the beam height at PR2, and adjusted that height with PZT1.

We then tried to use the hysteresis in PR2 to adjust the beam height at ITMY.  Pushing just a little bit at the top or bottom of PR2 would repoint the beam in pitch.  This sort of works, but it's stupid.  Using this method we got the beam more or less centered vertically at ITMY.

We moved on to ETMY with the idea that we would again use the hysteresis in PR3 to get the vertical pointing to the ETM correct.  This was a good demonstration of just how stupid the tip-tilts really are.  Just touching slightly at the top or bottom or PR3 we could completely change the pointing at ETMY, by mili-radians (~4 cm over 40m).

At this point I cried foul.  This is not an acceptable situation.  Very little stimulation to the tip-tilts can repoint the beam inside the PR cavity.

Steve says that the TT weights, which will attach to the base of the TT mirror mounts and should help keep the mirrors vertical and not hysteretic, are being baked now and should be available tomorrow.  We therefore decided to stop what we were doing today, since we'll have to just redo it all again tomorrow once the weights are installed.

 [Raji, Manasa]

The high-voltage power supply from the OMC was removed to replace one of the PZT power supplies. The power supply terminals were connected to the rear connection ports as per instructions from the manual (TB1 panel: port 3 - (-)OUT and port7 - (+)OUT). They were both switched  on and set to deliver (75V) to the PZTs.

 We also wrote down the serial numbers (top center of each TT, inscribed by hand) for what tip tilt is installed where.  I then went through the elog to determine which TT was suspended with what kind of wire (thick or thin).  Summary: all installed tip tilts have thick wire, 0.0036" diameter.

As noted in elog 3295, we had found that there was similar hysteresis whether we used the thick or the thin wire, so we had decided not to go back and re-suspend every optic.

Also, since we will redo the pitch balance tomorrow with the new hardware tomorrow, I think we should put in the new LaserOptik mirrors at the same time.  We have not yet gotten phase maps of them, but we might as well do this rebalancing once, rather than twice.

 This means that the low voltage dual supply which was wired in series (so could supply a max of 63V = 2*31.5V) has been replaced with the OMC power supply.  This is okay since we haven't turned on the OMC PZTs in a long, long time.  This is *not* the power supply for the output pointing PZTs.  When she says "both", she means the new HV supply, as well as the HV supply that was already there, so both pitch and yaw for PZT2 are being supplied with 75V now.

Jamie has arranged for phase map measurements this afternoon, so I will take the 6 dichroic LaserOptik optics over to Downs at 1:15 this afternoon.

Team Jamie+Nic will lead the effort to clamp down dog clamps as placement markers for all 4 in-vac passive TTs, and then pull all 4 TTs out of the chambers.  They plus Den will move the TTs to the Cleanroom, and will start to install the new pitch alignment hardware. 

When I return with the optics, we will install them in the TTs and re-balance them.  Then we can put them back in the chambers and get back to work on alignment.  

After we re-install the TTs, we will need to check the leveling of all 3 corner tables, just to be sure.

 Raji took the optics over. They were all measured at 0 deg incidence angle, although we will use them at the angles required for the recycling folding mirrors.  Here's the summary from GariLynn:

In general all six pieces have a radius of curvature of around -700 meters.

I measured the transmitted power @1064nm on one of the LaserOptik mirrors labled SN6

Here is the data

The mirror is not a good reflector at 0 deg.

[Raji, Jenne]

After lunch we began where Raji and Jamie had left things.  PR2 was unfortunately pitched down so far that it was almost hitting the table just in front of PR3.  I loosened the 4 clamp screws that hold the wire clamp assembly to the mirror holder, and tapped it back and forth until I was within hysteresis range, re-tightened, then tapped the top and bottom until we were at the correct beam height just in front of PR3.  I also had to unclamp it from the table and twist the base a tiny bit, since the beam was closer to hitting the beam tube than the optic.  Finally, however, PR2 is adjusted such that the beam hits the center of PR3.

Moving on to PR3, the pitch looked good while we were looking at the aperture placed near the face of ITMY, so we left that alone.  The beam is off in yaw though.  Several times I unclamped the tip tilt from the table, and twisted it one way or another, but every time when I tighten the dog clamps, I'm too far off in yaw.  The beam points a little too far south of the center of ITMY, so we were putting the beam a little north of the center before I clamped it, but even tightening the screws in the same order, by the same amount each time, causes a different amount of slipping/twisting/something of the TT mount, so we never end up directly in the center of the ITM.  It seems a little like a stochastic process, and we just need to do it a few more times until we get it right. 

We left it clamped to the table, but not in it's final place, and left for JClub.  On Monday morning we need to go back to it.  As long as we're pretty close to centered, we should probably also have someone at ETMY checking the centering, because we need to be centered in both ITMY and ETMY.

We have not touched the SR tip tilts, so those will obviously need some attention when we get to that point.

 Maybe we have already discarded this idea, but why not do the alignment without the MC?

Just lock the green beam on the Yarm and then use the transmitted beam through the ITMY to line up the PRC and the PZTs? I think our estimate is that since the differential index of refraction from 532 to 1064 nm is less than 0.01, using the green should be OK. We can do the same with the Xarm and then do a final check using the MC beam.

In this way, all of the initial alignment can be done with green and require no laser Goggles (close the shutter on the PSL NPRO face).

[Jamie, Jenne, Raji, with consultation from Nic, Ayaka and Manasa]

We went back and re-looked at the input alignment, and now we're "satisfied for the moment" (quote from Jamie) with the PRC alignment.  Also, by adjusting the PR folding mirrors, we are almost perfectly aligned to the Yarm.

What we did:

Set PRM DC biases to 0 for both pitch and yaw.

Aperture was attached to PRM cage, double aperture was attached to BS cage, free-standing aperture was placed in front of PR2. 

Adjusted PZT1, PZT2 such that we were centered on PZT2, and through apertures at PRM and PR2.   This was mainly for setting beam height in PRC.

Checked centering on PZT1, MMT1, MMT2, PZT2.

Adjusted PRM pitch bias and PZT2 yaw such that REFL beam was retro-reflected from PRM.

Checked that REFL beam came nicely out of Faraday.

Checked that beam was still going through center of PRM aperture, and pitch height at PR2 was good.

Moved PR2 sideways until beam hit center in yaw of PR2.

Twisted PR2 such that beam was hitting center of PR3.

Moved and twisted PR3 (many times) so that beam went through BS input and output apertures, and through center of ITMY aperture.

Found that beam was just getting through black glass aperture at ETMY, top left corner, if looking at the face of ETM from ITM.

Locked down dog clamps on PR2.

This required some re-adjustment of PR3.  Re-did making sure going through BS apertures and ITMY aperture, locked down PR3 dog clamps.

Found that we are centered in yaw at ETMY, a little high in pitch on ETMY.

Replaced all of the light doors, to take a break.  4 hours in bunny suits seemed like enough that we earned a break.

This all sounds more straighforward than it was.  There was a lot of iteration, but we finally got to a state that we were relatively happy with.

What we will do:

Tweak PZT2 a *tiny* bit in pitch, ~0.5 mrad, so that the beam goes through the ETMY aperture.

See if we can align EMTY and ITMY to get multiple bounces through the Yarm.

Remove ETMX heavy door, steer BS such that we're getting through the center of an aperture at ETMX.

Align ETMX and ITMX such that we get multiple bounces through the Xarm.

Check SRM, AS path alignment.

Check REFL out of vac alignment.

Check other pickoffs.

Check all oplevs.

Check IPPOS/IPANG

We have a open-sided 2" mirror mount that we are considering using for the POY pick-off mirror.  This might help us get a little more clearance in the Y-arm of the Michelson.  Problem is the mount is not steerable, so we need to determine if that's doable or not.

[Raji, Jenne]

We tweaked PZT2, PZT1 (yaw only), and PR3 (pitch only) to get the beam ~centered on the BS aperture, the ITMY aperture, and the ETMY aperture.

After lunch I'll tweak up the MC alignment, since, although the spots are in the right places, the transmitted beam could be higher power.  This will make it easier to check our pointing, especially since the ETMY spot is larger than our aperture, but the beam is dim.

We're getting there!

 Jenne, Den

We looked at beam spots on ITMY and ETMY. We switched to smaller apertures on the other side of the rulers. For ITMY beam spot was 1mm below and 1mm south (right if you look in the direction ITMY -> ETMY) from the aperture center, for ETMY - 4 mm up and 3mm north from the aperture center. We made a correction for this using PZT 1 and 2. Now beam spots are in the middle of the apertures on ITMY and ETMY.

We tried to look at reflected beam from ETMY but it was hard to see the dependence between ETMY DC offset and reflected beam. We'll continue tomorrow.

 More data on the transmission. Measured the tranmission as a funtion of incidence angle at 1064nm

jamie, nic, jenne, den, raji, manasa

We were doing pretty well with alignment, until I apparently fucked things up.

We were approaching the arm alignment on two fronts, looking for retro-reflection from both the ITMs and the ETMs.

Nic and Raji were looking for the reflected beam off of ETMY, at the ETMY chamber.  We put an AWG sine excitation into ETMY pitch and yaw.  Nic eventually found the reflected beam, and they adjusted ETMY for retro-reflection.

Meanwhile, Jenne and I adjusted ITMY to get the MICH Y arm beam retro-reflecting to BS.

Jenne and I then moved to the X arm.  We adjusted BS to center on ITMX, then we moved to ETMX to center the beam there.  We didn't both looking for the ETMX reflected beam.  We then went back to BS and adjusted ITMX to get the MICH X arm beam retro-reflected to the BS.

At this point we were fairly confident that we had the PRC, MICH, and X and Y arm alignment ok.

We then moved on the signal recycling cavity.  Having removed and reinstalled the SRC tip-tilts, and realigning everything else, they were not in the correct spot.  The beam was off-center in yaw on SR3, and the SR3 reflected beam was hitting low and to the right on SR2.  I went to loosen SR3 so that I could adjust it's position and yaw, and that when things went wrong.

Apparently I hit something BS table and completely lost the input pointing.  I was completely perplexed until I found that the PZT2 mount looked strange.  The upper adjustment screw appeared to have no range.  Looking closer I realized that we somehow lost the gimble ball between the screw and the mount.  Apparently I somehow hit PZT2 hard enough to separate from the mirror mount from the frame which caused the gimble ball to drop out.  The gimble ball probably got lost in a table hole, so we found a similar mount from which we stole a replacement ball.

However, after putting PZT2 back together things didn't come back to the right place.  We were somehow high going through PRM, so we couldn't retro-reflect from ITMY without completely clipping on the PRM/BS apertures.  wtf.

Jenne looked at some trends and we saw a big jump in the BS/PRM osems.  Clearly I must have hit the table/PZT2 pretty hard, enough to actually kick the table.  I'm completely perplexed how I could have hit it so hard and not really realized it.

Anyway, we stopped at this point, to keep me from punching a hole in the wall.  We will re-asses the situation in the morning.  Hopefully the BS table will have relaxed back to it's original position by then.

Here is a two hour set of second trends of 2 sensors per mirror, for BS, PRM, ITMY and MC1.  You can see about an hour ago there was a big change in the BS and PRM suspensions, but not in the ITMY and MC1 suspensions.  This corresponds as best we can tell with the time that Jamie was figuring out and then fixing PZT2's mount.  You can see that the table takes some time to relax back to it's original position.  Also, interestingly, after we put the doors on ~10 or 20 minutes ago, things change a little bit on all tables. This is a little disconcerting, although it's not a huge change.

...Looks like the coating is out of spec at any angle for 1064nm. E11200219-v2