mock-data-challenges for ltp - aei.mpg.dehewitson/presentations/presentations2009/files/wed... ·...

Mock-Data-Challenges for LTP

M Hewitson for the LTP Team

Saturday, 20 June 2009

AMALDI, NY, June 09

Outline

•Why MDCs•MDC1

•calibration of IFO outputs to out-of-loop acceleration•MDC2

•parameter estimation•MDC3 and beyond

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AMALDI, NY, June 09

Mock-Data-Challenges

3

Define MDCmodel(s),

assumptions, etc

1


AMALDI, NY, June 09


3

Define MDCmodel(s),

assumptions, etc

1

Produce data sets based on 1)

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AMALDI, NY, June 09


3

Define MDCmodel(s),

assumptions, etc

1


2

Analyse data(based on some details from 1)

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AMALDI, NY, June 09

Compare results to expected

4


3

Define MDCmodel(s),

assumptions, etc

1


2

Analyse data(based on some details from 1)

3


AMALDI, NY, June 09

MDC1

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AMALDI, NY, June 09

MDC1

•Simple model of LTP (x-axis dynamics)

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AMALDI, NY, June 09

MDC1

•Simple model of LTP (x-axis dynamics)•Data generation

•Model is based on 5 parameters of the system• stiffness of two test-masses• gains of two control servos• cross-coupling in IFO from X1 to X12

•Generate two IFO output time-series

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AMALDI, NY, June 09

MDC1

•Simple model of LTP (x-axis dynamics)•Data generation

•Model is based on 5 parameters of the system• stiffness of two test-masses• gains of two control servos• cross-coupling in IFO from X1 to X12

•Generate two IFO output time-series•Data analysis

•convert the two IFO outputs to out-of-loop acceleration• convert each to in-loop acceleration• account for control forces

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AMALDI, NY, June 09

Data generation

•Frequency-domain analytical model of transfer functions•Fit sets of digital filters to the transfer functions•Filter white-noise time-series to produce simulated IFO

outputs

5

o1

o12


AMALDI, NY, June 09

Data generation

•Frequency-domain analytical model of transfer functions•Fit sets of digital filters to the transfer functions•Filter white-noise time-series to produce simulated IFO

outputs

5

o1

o12

Generation of simulated noise for LTP Mock Data ChallengesLuigi Ferraioli


AMALDI, NY, June 09

Control loops

6

TM1

TM2

o12

o1

Cdf

Csus

x1

x2

ATAN

A

k1x1

k3x2

m

m

M

m1 = m2 = 1.96 kg

M = 475 kg

IFO/DMU

A1

A2 Asus

k1

k2

!A

!A


AMALDI, NY, June 09

o1

o12

!12

interferometer

1s2 + !2

3

1s2 + !2

1Cdf

Asus

Adf

SC Force

Noise

TM

Differential

Force

Noise

Sensing

Noise

Sensing

Noise

Csus

Control loops

6

TM1

TM2

o12

o1

Cdf

Csus

x1

x2

ATAN

A

k1x1

k3x2

m

m

M

m1 = m2 = 1.96 kg

M = 475 kg

IFO/DMU

A1

A2 Asus

k1

k2

!A

!A


AMALDI, NY, June 09

Calibration procedure

7

Convert to in-loopacceleration

[m]

[m]

!m s!2

"

!m s!2

"

Generate control signals

[m]

[m]

!m s!2

"

!m s!2

"

a1(t)

a2(t)

o1(t)

o12(t)


AMALDI, NY, June 09


7


[m]

[m]

!m s!2

"

!m s!2

"


[m]

[m]

!m s!2

"

!m s!2

"

a1(t)

a2(t)

o1(t)

o12(t)

Double differentiation


AMALDI, NY, June 09


7


[m]

[m]

!m s!2

"

!m s!2

"


[m]

[m]

!m s!2

"

!m s!2

"

a1(t)

a2(t)

o1(t)

o12(t)

Double differentiation

Filter with controllertransfer functions


AMALDI, NY, June 09

Results

8

10−4 10−3 10−2 10−1 10010−14

10−13

10−12

10−11

10−10

10−9

10−8

10−7

Spectral Density [m][s−2][Hz−1/2]

Frequency [Hz]

DifferentialTM Force Noise

IFO Sensin

g Noise

Thruster Force Noise

a1

a1 ref

a2

a2 ref


AMALDI, NY, June 09

MDC2

•Model same as MDC1•Analysis team does not know exact parameter values for the

model• Instead, they must be determined from a series of

experiments where the system is excited•3 different experiments•10 different ‘noise’ runs

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AMALDI, NY, June 09

Strategy

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AMALDI, NY, June 09

Strategy

•Using ‘noise’ runs we determine the spectrum of the noise in the different channels•from these we construct whitening filters

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AMALDI, NY, June 09

Strategy


•Outputs are whitened to produce statistically independent samples

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AMALDI, NY, June 09

Strategy



•Estimate parameters from the whitened outputs

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AMALDI, NY, June 09

Strategy



•Estimate parameters from the whitened outputs•Calibrate back to acceleration

• injected signals are removed (to some extent)

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AMALDI, NY, June 09

Strategy



•Estimate parameters from the whitened outputs•Calibrate back to acceleration

• injected signals are removed (to some extent)•Look at residuals

•update whitening filter?

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AMALDI, NY, June 09

Experiments

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AMALDI, NY, June 09

Experiments

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i2

i1

Csus

CDFGDF

Gsus

D(!21)

o1

o12

!21

D(!23)

!12

interferometer

!2!


AMALDI, NY, June 09

Experiments

• Experiment 1• inject signals into both control

loops and measure at the outputs• i1->o1 and i12->o12

• Gdf, Gsus (stiffnesses?)

11

i2

i1

Csus

CDFGDF

Gsus

D(!21)

o1

o12

!21

D(!23)

!12

interferometer

!2!


AMALDI, NY, June 09

Experiments




• Experiment 2• Match stiffness of two TMs• Inject in drag-free loop, measure in

X12 loop• i1->o12

• IFO cross-coupling

11

i2

i1

Csus

CDFGDF

Gsus

D(!21)

o1

o12

!21

D(!23)

!12

interferometer

!2!


AMALDI, NY, June 09

Experiments




• Experiment 2• Match stiffness of two TMs• Inject in drag-free loop, measure in

X12 loop• i1->o12

• IFO cross-coupling

• Experiment 3• Un-matched stiffness• Same injection

• i1->o12• difference of stiffness

11

i2

i1

Csus

CDFGDF

Gsus

D(!21)

o1

o12

!21

D(!23)

!12

interferometer

!2!


AMALDI, NY, June 09

Different approaches

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AMALDI, NY, June 09


•Non-linear least-squares•time-domain:

• (fast) time-domain simulation•freq-domain:

• fit to measured transfer function

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AMALDI, NY, June 09




• fit to measured transfer function•Linear least-squares

• linearize transfer functions in the parameters•do in either frequency-domain or time-domain

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AMALDI, NY, June 09




• fit to measured transfer function•Linear least-squares

• linearize transfer functions in the parameters•do in either frequency-domain or time-domain

•MCMC•‘explore’ the full parameter space to determine posterior PDFs

for each parameter

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AMALDI, NY, June 09

Time-domain fitting

•Use models of the transfer functions with fft filtering to produce time-domain templates

•Look at experiment 1•fit 2 gains and 2 stiffness values

•Minimise χ2 to find best parameter estimates

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AMALDI, NY, June 09

Linearised model

•Taylor expand model of Transfer function around the nominal parameter values

•Solve with linear least-squares routine

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Ti1o1 ! Ti1o1 linear

= T0 +!T0

!G0(Gdf "G0) +

!T0

!"0("1 " "0)


AMALDI, NY, June 09

Linearised model

•Taylor expand model of Transfer function around the nominal parameter values

•Solve with linear least-squares routine

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Ti1o1 ! Ti1o1 linear

= T0 +!T0

!G0(Gdf "G0) +

!T0

!"0("1 " "0)

Linear Analysis of the Second Mock Data Challenge for LTPAnneke Monsky


AMALDI, NY, June 09

MCMC approach

•Find maximum of the likelihood surface using a standard simplex method

•Use Metropolis sampling to map-out the likelihood surface around this maximum

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AMALDI, NY, June 09

MCMC approach

•Find maximum of the likelihood surface using a standard simplex method

•Use Metropolis sampling to map-out the likelihood surface around this maximum

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Bayesian parameter estimation in LISA Pathfinder MDCsMiquel Nofrarias


AMALDI, NY, June 09

MDC3 and beyond

•Aim to verify the analysis in S2-UTN-TN-3045•Do full experiment campaign•Confirm parameters can be measured with the expected

accuracy•Work through other major experiments

•move in to 2D and 3D• x-y cross-talk, angular couplings, etc

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AMALDI, NY, June 09

Conclusions

•Conversion to acceleration is (mostly) understood•Tools are in place

•Parameter estimation is being studied•Some of the tools are in place•Understanding the experiments and what we can measure is

ongoing

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