The First LTP Mock Data Challenge€¦ · 7th International LISA Symposium – Barcelona, Spain / June 16-20, 2008 Albert Einstein Institute Hannover, Germany LISA Group AEI Hannover,

7th International LISA Symposium – Barcelona, Spain / June 16-20, 2008 Albert Einstein Institute Hannover, Germany

LISA Group AEI Hannover, Germany LTP Data Analysis, 17/06/2008

Albert Einstein Institute

www.lisa.aei-hannover.de Max Planck Institute for Gravitational Physics

Hannover

The First LTP Mock Data Challenge

Anneke Monsky for the LTP Team


Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/

LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008

Outline

• Organisation

• Model of LTP Dynamics

• Prediction of simulated IFO Data

• Prediction of TM acceleration

• Calibration of IFO Data to TM acceleration

• Summary and Outlook




Two teams for the LTP mock data challenge:

3

Data GenerationTeam

Organisation





3

Data GenerationTeam

Organisation

Model LTP Dynamics





3

IFOMock Data

Data GenerationTeam

Organisation

Model LTP Dynamics





3

Data AnalysisTeam

IFOMock Data

Data GenerationTeam

Organisation

Model LTP Dynamics





3

Data AnalysisTeam

IFOMock Data

Data GenerationTeam

Organisation

Model LTP Dynamics





3

Data AnalysisTeam

IFOMock Data

Data GenerationTeam

Analysis Result(TM acceleration)

Organisation

Model LTP Dynamics

UTN (Trento) - simulated

IFO output data using

Mathematica




Dynamical Model (operation mode)

IFO/DMU

x

A

A 1

A2

x2

k1x1

k3x2

AN AT

Csus

CdfTM 1

TM 2

r =

0.3

m





r =

0.3

m

x

x1

x2

IFO/DMU





• TM1:

r =

0.3

m

x

x1

x2

IFO/DMU

TM 1





• TM1:– drag free

– S/C follows TM1

r =

0.3

m

x

x1

x2

IFO/DMU

TM 1






– S/C follows TM1

– drag free control loop

r =

0.3

m

x

x1

x2

IFO/DMU

CdfTM 1






– S/C follows TM1


• TM2: r =

0.3

m

x

x1

x2

IFO/DMU

CdfTM 1

TM 2






– S/C follows TM1


• TM2:– position electrostatically

relative to TM1

r =

0.3

m

x

x1

x2

IFO/DMU

CdfTM 1

TM 2






– S/C follows TM1


• TM2:– position electrostatically

relative to TM1– electrostatic control loop

r =

0.3

m

x

x1

x2

IFO/DMU

Csus

CdfTM 1

TM 2




Dynamical Model (Input force noises)

TM 1

r =

0.3

m

IFO/DMU

TM 2

Cdf

Csus

x

A

x1

x2





• AT - thruster forceTM 1

r =

0.3

m

IFO/DMU

TM 2

Cdf

Csus

x

A

x1

x2

AT





• AT - thruster force

• AN - additional force noisesTM 1

r =

0.3

m

IFO/DMU

TM 2

Cdf

Csus

x

A

x1

x2

AN AT






• AN - additional force noises

• - k1 x1 and -k3 x2 coupling between TM and S/C

TM 1

r =

0.3

m

IFO/DMU

TM 2

Cdf

Csus

x

A

x1

x2

AN AT

k1x1

k3x2






• AN - additional force noises

• - k1 x1 and -k3 x2 coupling between TM and S/C

• A1, A2 - force noises on TM1 and TM2

TM 1

r =

0.3

m

IFO/DMU

TM 2

Cdf

Csus

x

A

x1

x2

AN AT

A1

A2

k1x1

k3x2




Definitions

• Dynamics– stiffness

• TM coordinates

• Force noises

• IFO output data

D =[

s2 + ω21 0

ω2∆ s2 + ω2

3

]=

[Sω1 0ω2

∆ Sω3

]

!q =[

x1

x∆

]

!o =[

o1

o∆

]

!gn =[

AN −A1

A2 −A1

]




Equations of motion

• Result of Euqations of motion in Laplace domain:

• Relating IFO data to TM coordinates:

• Combining equations:

!o = S!q + !on

[DS−1 + C]!o = D!on S−1 + !gn

a_calibrated→ a_predicted→

D!q = C!o + !gn




Prediction of simulated Interferometer output data




Prediction of simulated X1 and X12 Interferometer Data

!o =

[1

Sω1+C10

−β(Sω1+C1)(Sω3+C2)

1Sω3+C2

] [Sω1on1 + A1 −AN

βon1 + Sω3on∆ + A2 −A1

]

β = ω2∆ − δSω3

!o = [DS−1 + C]−1 [DS−1!on + !gn]• Prediction of IFO

output data:

where




Prediction of simulated X1 Interferometer Data

AN

A1 + S−1ω1

+

on1

Sdf o1

• output data contains:

– force noise on TM1

– force noise on S/C

– X1 IFO sensing noiseo1 = Sdf on1 +

Sdf

Sω1

(A1 + AN )




Prediction of simulated X12 Interferometer Data

β S−1ω1

on1++

Sdf

Re{Sdf}

A2 ++

Sdf S−1ω1

on∆

β

−2

A1

AN

Ssus

++

2 Re

{Sdf

Sω1

}

S−1ω3

o∆




Prediction of IFO Data

10-4

10-3

10-2

10-1

100

10-12

10-11

10-10

10-9

10-8

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

o1 predicted

o! predicted

o1 generated

o! generated




Reference:Prediction of test mass

acceleration




Predicting TM acceleration

a1 = Sω1on1 + A1 + AN

ANA1

on1 a1++ ++Sω1

From Equations of motion: !apredicted = D!on S−1 + !gn




Predicting differential acceleration

a∆ = βon1 + Sω3on∆ + A2 + A1

Sω3on1

on∆

A2

A1

−δ ++

−ω2∆

Sω3

++ ++

++

a∆




Prediction of acceleration

10-4

10-3

10-2

10-1

100

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

10

10

10

10

10

10

10

10

10

10

-16

-15

-14

-13

-12

-11

-10

-9

-8

-7

a1 predicted

a! predictedThruster noise

TM noise

IFO noise TM2

IFO noise TM1




Result:Calibration of simulated IFO data to test mass

acceleration




Calibrating simulated IFO Data to TM acceleration

a1Sω1o1 S−1df

• From Lagrangian: !acalibrated = [DS−1 + C]!o

a1 = [Sω1 S−1df ] o1




Calibrating simulated IFO data to differential TM acceleration

Sω3 −δ ++

ω2∆

Sω3

++ a∆

o∆ S−1sus

o1

a∆ = [ω2∆ + Sω3 · (−δ)] o1 + [Sω3 S−1

sus] o∆




Results: calibration to acceleration

10-4

10-3

10-2

10-1

100

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

a1 calibrated

a1 predicted)

a! calibrated

a! predicted




Results of 11 Data Sets for a1

10-4

10-3

10-2

10-1

100

10-10

10-9

10-8

10-7

10-6

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

Data set 1

" 2

" 3

" 4

" 5

" 6

" 7

" 8

" 9

" 10

" 11




Results for all 11 Data Sets for a∆

10-4

10-3

10-2

10-1

100

10-14

10-13

10-12

10-11

10-10

10-9

10 -8

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

Data set 1

" 2

" 3

" 4

" 5

" 6

" 7

" 8

" 9

" 10

" 11




Average a1

10-4

10-3

10-2

10-1

100

10-10

10-9

10-8

10-7

10-6

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

a1 averaged

error

a1 predicted




Average a∆

10-4

10-3

10-2

10-1

100

10-14

10-13

10-12

10-11

10-10

10-9

10-8

Frequency [Hz]

Am

plitu

de

[ms−

2/√

Hz]

a! averaged

error

a! predicted




Calibration vs. Prediction

10-4

10-3

10-2

10-1

100

0

0.5

1

1.5

2

2.5

3

3.5

Frequency [Hz]

Rati

o

a_1 calibrated / a_1 predicted

a_! calibrated / a_! predicted




Summary / Outlook

• Verified theoretical model for LTP dynamics– predicted generated data

• Calculated theoretical reference– predicted TM acceleration

• Analysed generated data– calibrated given IFO output to TM acceleration– analysed 11 data sets and averaged

• Next MDCs– Parameter estimation (stiffness)– XY Crosstalk




Thank you!

The First LTP Mock Data Challenge€¦ · 7th International LISA Symposium – Barcelona, Spain / June 16-20, 2008 Albert Einstein Institute Hannover, Germany LISA Group AEI Hannover,

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