data analysis for lisa pathﬁnder - max planck institute...

Data Analysis for LISA Pathfinder

M Hewitson for the LPF teamGSFC, October 11th 2011

+----------------------------------------------------+| || || **** || ** || ------------- || //// / \\\\ || /// / \\\ || | / | || ** | +----+ / +----+ | ** || ***| | |//-------| | |*** || ** | +----+ /+----+ | ** || | / | || \\\ / /// || \\\\ // //// || ------------- || ** || **** || || Welcome to the LTPDA Toolbox || || Version: 2.4.dev || Release: (R2011b Prerelease) || Date: 22-06-11 || |+----------------------------------------------------+

Wednesday, October 19, 11

M Hewitson, LPF Data Analysis, GSFC, 11th October 2011

The LTP DA Team

2

Martin HewitsonIngo DiepholzHeather AudleyPhil PetersonNatalia KorsakovaFelipe Guzman

Michele Armano

Miquel Nofrarias Marc Diaz Aguiló

Ferran GilbertNikos Karnesis

Mauro HuellerGiuseppe Congedo

Eric PlagniolLuigi Ferraioli


M Hewitson, LPF Data Analysis, GSFC, 11th October 2011 3

Activities



Activities

•DA Software• Toolbox of algorithms to act on the data• Repository for storing data products• Client for submitting and retrieving to/from repository• Documentation and testing



Activities

•DA Software• Toolbox of algorithms to act on the data• Repository for storing data products• Client for submitting and retrieving to/from repository• Documentation and testing

•DA Activities• Interpret technical descriptions of experiment• Simulate experiments• Design, build and test analyses and associated tools• Train scientists



LTPDA

4Wednesday, October 19, 11


LTPDA•Main requirement:

• provide a data analysis environment suitable for analyzing the experiment data in ‘real-time’



LTPDA•Main requirement:

• provide a data analysis environment suitable for analyzing the experiment data in ‘real-time’

•Additional requirements:• toolkit of fairly standard instrument characterisation

algorithms• results should be reproducible and accountable• reduce testing by building on a commercial product• ease of use (usable by non-experts)• simple data access for multiple users



System Architecture

5

MATLAB



System Architecture

5

MATLAB

utility functionsutility classesuser classes



System Architecture

5

MATLAB


scripting layer GUI



Objects, objects everywhere...

•LTPDA offers an object-oriented data analysis framework• we encapsulate (describe) different data analysis

concepts with classes• users instantiate (build) these classes to get ltpda

objects• DA algorithms are methods (functions) of these

different classes• users act on the objects using the methods

6

aoaoao algorithm ao



Example: Analysis Objects

•We want to encapsulate the concept of an analysis result• avoid storing images, text files, documents, etc


Analysis Object





Analysis Object




7

Numerical Data

AdditionalMeta-data

Provenance

History Tree


Analysis Object




7

Numerical Data

AdditionalMeta-data

Provenance

History Tree

- name- data vectors- creation date- units- sample rate

- name- UUID- Comments- Processing Info- Plotting Info

- creator- date- IP address- hostname- operating system- software versions

- algorithm name- algorithm version- parameter list- date- input histories



AO Algorithms



AO Algorithms

8

>> methods ao

Contents detrend hist_gauss mdc1_ifo2acc_inloop rotate std abs dft hypot mdc1_ifo2cont_utn round straightLineFit acos diag ifft mdc1_ifo2control sDomainFit string angle diff imag mdc1_x2acc save submit ao display index mean scale sum asin dopplercorr integrate median scatterData sumjoin atan downsample interp min search svd atan2 dropduplicates interpmissing minus select svd_fit bilinfit dsmean inv mode setDescription t0 bin_data dx iplot mpower setDx table bsubmit dy iplotyy mrdivide setDy tan buildWhitener1D eig isprop mtimes setFs tdfit cat eq isvalid ne setMdlfile tfe char eqmotion join noisegen1D setName timeaverage cohere evaluateModel lcohere noisegen2D setPlotinfo timedomainfit complex exp lcpsd norm setProcinfo times compute export le normdist setT0 timeshift confint fft len nsecs setUUID transpose conj fftfilt linSubtract offset setX type consolidate filtSubtract lincom optSubtraction setXY uminus conv filter linedetect phase setXunits unwrap convert filtfilt linfit plot setY update copy find lisovfit plus setYunits upsample corr firwhiten ln polyfit setZ validate cos fixfs log polynomfit sign var cov fngen log10 power simplifyYunits viewHistory cpsd fromProcinfo lpsd psd sin whiten1D crbound fs lscov psdconf sineParams whiten2D created gapfilling lt pwelch smallvector_lincom x creator gapfillingoptim ltfe quasiSweptSine smallvectorfit xcorr csvexport ge ltp_ifo2acc rdivide smoother xfit ctranspose get max real sort xunits curvefit getdof mcmc rebuild spectrogram y delay gnuplot md5 removeVal spikecleaning yunits delayEstimate gt mdc1_cont2act_utn report split zDomainFit demux heterodyne mdc1_ifo2acc_fd resample spsd zeropad det hist mdc1_ifo2acc_fd_utn rms sqrt



Don’t touch me with that AO, I don’t know where it’s been!

9

ao




9

ao

name

history

version

data




9

ao

name

history

version

data

name

input histories

version

params




9

ao

name

history

version

data

name

input histories

version

params

name

input histories

version

params




9

ao

name

history

version

data

name

input histories

version

params

name

input histories

version

params

name

input histories

version

paramsWednesday, October 19, 11


I love my mouse!



Where can I stick my AO?

11

MATLAB

LTPDA Toolbox




11

MATLAB

LTPDA Toolbox

Server

LTPDA Repository




11

MATLAB

LTPDA Toolbox

Server

LTPDA Repository

MATLAB


scripting layer GUI




11

MATLAB

LTPDA Toolbox

Server

LTPDA Repository

MATLAB


scripting layer GUI

mysql




11

MATLAB

LTPDA Toolbox

Server

LTPDA Repository

MATLAB


scripting layer GUI

mysql

php interface




11

MATLAB

LTPDA Toolbox

Server

LTPDA Repository

MATLAB


scripting layer GUI

mysql www browser

php interface

apache/httpd



LTPDA Repository



LTPDA Repository

12

Manage User Accounts

Manage Databases

Browse/Query Databases

Submit/Retrieve Objects



Extension modules

•LTPDA allows for extension modules• create your own user-classes• extend existing classes with new methods• add models, functions, etc

•Examples• LTP_DA_Module

• methods and functions directly for LTP DA• models of the system

• STOC_DA_Module• methods and function for use in the STOC

• Others used by labs etc



Documentation

•Documentation• user-manual alone ~700 pages• ~1500 documented m-files (methods/functions)

14

ao analysis object class constructor. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DESCRIPTION: ao analysis object class constructor. Create an analysis object. Possible constructors: a = ao() - creates an empty analysis object a = ao('a1.xml') - creates a new ao by loading a file a = ao('a1.mat') a = ao('a1.mat') - creates a new ao by loading the 2-column data .MAT file. a = ao('file.txt') - creates a new ao by loading the data. a = ao('file.dat') a = ao('file',pl) (Set: From ASCII File) a = ao(data) - creates an ao with a data object. a = ao(constant) - creates an ao from a constant a = ao(specwin) - creates an ao from a specwin object a = ao(pzm) - creates an ao from a pole/zero model object a = ao(pzm,nsecs,fs) a = ao(smodel) - creates an ao from a symbolic model object a = ao(pest) - creates an ao from a parameter estimates object a = ao(x,y) - creates an ao with xy data a = ao(y, fs) - creates an ao with time-series data a = ao(x,y,fs) - creates an ao with time-series data a = ao(x,y,pl) - creates an ao depending from the PLIST (Set: From XY Values). a = ao(plist) - creates an ao from a parameter list Examples Parameters Description VERSION: $Id: ao.m,v 1.348 2011/05/16 07:15:37 hewitson Exp $ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



Testing

•Unit-level tests• we run ~6000 unit tests every 3 hours

• some of these tests are dynamic (variable)•System level tests

• continuous system level testing in STOC exercises and Labs

• Some releases are system tested by professionals (FBK)• ~300 hand-run system tests• 10’s of thousands of automated tests

•Acceptance testing• each delivery to ESA is formally acceptance tested



The size of it

•224396 lines of MATLAB source code• not including extension

modules•60198 lines of HTML

documentation•~ 40000 CVS commits

since the beginning•~15 man years of effort



LTPDA

17

•First serious release in April 2008•Last release May 2011•Next release August 2011•We have made three formal deliveries to

ESA• version 1.0, 2.0 and 2.4

•We have run a few dedicated training sessions at different institutions

•LTPDA is heavily used in different labs



Infrastructure

18

DataConverter

LTPDARepository

LTPDAClient

LTPDAClient



Data Analysis Activities

•Modelling of LPF•Simulating the system•Noise projections•Simulating and analysing experiments



Modelling LPF: goals

•Template generator• fast, containing only parameters which we want to

estimate•Simulations

• detailed models, can be slower and have more parameters

• aim to accurately reproduce observed noise



Models in LTPDA

•Models are built as factory constructors of the different user classes• building a model produces an object of a particular

class•The template for making built-in models allows

for:• versioning• built-in documentation• easier testing

•Example:

21

% statespace model of LTPltp = ssm(plist('built-in', 'LTP'));



Modelling LPF



Modelling LPF

•We model LPF parts using different schemes• matrix models, symbolic models, statespace models



Modelling LPF


•For simple experiments and/or validation, we can use simple 1D models



Modelling LPF


•For simple experiments and/or validation, we can use simple 1D models

•For more realistic experiments (or in the mission) we need a full 3D description of LTP• for that we use statespace models



What can you do with an SSM?




•Measure bode plots




•Measure bode plots•Run time-domain simulations




•Measure bode plots•Run time-domain simulations•Both of these allow us to generate parameter

dependent templates in time and frequency domain• we can use these for parameter estimation

• fitting to measured data


x = Ax+Bu

y = Cx+Du


How SSM models work



Parts of LTP

25

Controllers

SensingDynamics

Actuators



Full system (current)



More advanced model

•We want to improve the model by making it more modular• Include more realistic sub-

system models• Include more physical features



Parts of LTP (1)

OBCm

easu

rem

ent p

roce

ssingST

GRS

IFO

sens

or m

appi

ngDFACS

cont

rolle

rs

deco

uplin

g m

atrix

FEEP

Salg

orith

mCa

p Ac

talg

orith

m

Data

pro

cess

ing

guidance inputs

actuation inputs[m

,rad

]

[N,N

m] ActuationCapac Act

FEEPs

FEE

Mea

sure

men

t Pr

oces

sing

Actu

ator

M

odel

Mea

s.

Proc

essin

g



Parts of LTP (1)

OBCm

easu

rem

ent p

roce

ssingST

GRS

IFO

sens

or m

appi

ngDFACS

cont

rolle

rs

deco

uplin

g m

atrix

FEEP

Salg

orith

mCa

p Ac

talg

orith

m

Data

pro

cess

ing

guidance inputs

actuation inputs[m

,rad

]

[N,N

m] ActuationCapac Act

FEEPs

FEE

Mea

sure

men

t Pr

oces

sing

Actu

ator

M

odel

Mea

s.

Proc

essin

g

+n +n dT+n dT

+n dT

+n dT

+n



Parts of LTP (1)

29

FEEP

Salg

orith

mCa

p Ac

talg

orith

m

Data

pro

cess

ing

ActuationCapac Act

FEEPs

FEE

Actu

atio

nM

odel

Mea

sure

men

t Pr

oces

sing

Actu

ator

M

odel

Com

pute

Forc

es/T

orqu

es

Dynamics

[N,N

m]

[N,N

m]

[m,r

ad]

Equa

tions

ofM

otio

n

Mea

s.

Proc

essin

g

+n dT



Parts of LTP (1)

29

FEEP

Salg

orith

mCa

p Ac

talg

orith

m

Data

pro

cess

ing

ActuationCapac Act

FEEPs

FEE

Actu

atio

nM

odel

Mea

sure

men

t Pr

oces

sing

Actu

ator

M

odel

Com

pute

Forc

es/T

orqu

es

Dynamics

[N,N

m]

[N,N

m]

[m,r

ad]

Equa

tions

ofM

otio

n

Mea

s.

Proc

essin

g

+n dT

+n dT +n

+n

+n dT



Full System

30

OMS

GRS

ST



Full System

30

OMS

GRS

ST

LTPDFACS



Full System

30

OMS

GRS

ST

LTPDFACS

Cap. Act.

FEEPs



Full System

30

OMS

GRS

ST

LTPDFACS

Cap. Act.

FEEPs

Dynamics



Full System

30

OMS

GRS

ST

LTPDFACS

DRSDFACS

Cap. Act.

FEEPs

Dynamics



Full System

30

OMS

GRS

ST

LTPDFACS

DRSDFACS

Cap. Act.

FEEPs

Colloids

Dynamics



Simulating the system

•We have two simulators at our disposal• The linear SSM model• The industry-provided, non-linear simulator (OSE)



What is the OSE?



What is the OSE?

•The OSE is the DFACS simulator produced by Astrium to verify performance of DFACS



What is the OSE?


• It is a full 3D, non-linear, fairly detailed simulator of LPF



What is the OSE?



• It is used as one of the ‘engines’ in the STOC simulator (LSS)



What is the OSE?




• It produces the closest data we can get to actual LPF data



What is the OSE?




• It produces the closest data we can get to actual LPF data

• It is not really designed for use by end-users• reasonably difficult to use/configure• difficult to understand how it works, or why it does

some things the way it does



Noise projections



Noise projections

•Aim to explain the noise of the STOC Simulator (OSE) using our statespace linear model of LPF• iterative process to bring our model as close as

possible to the OSE• this closely resembles what we will do during the mission



Noise projections

•Aim to explain the noise of the STOC Simulator (OSE) using our statespace linear model of LPF• iterative process to bring our model as close as

possible to the OSE• this closely resembles what we will do during the mission

•Simulator configured with:• M3 all-optical• Star Tracker noise switched on/off• nominal cross-couplings• All other noises nominal• test-mass 1 total stiffness = -1e-6• test-mass 2 total stiffness = -2e-6



Making the SSM prediction



Making the SSM prediction1. We use our linear statespace model of LPF

1.1. The version used is using the same DFACS controllers as the OSE




1.1. The version used is using the same DFACS controllers as the OSE 2. Inject a single noise source, e.g., capacitive actuation noise

for TM1





for TM13. Run simulation (~10000s)





for TM13. Run simulation (~10000s)4. Save time series





for TM13. Run simulation (~10000s)4. Save time series5. Make spectral density estimates of two longitudinal IFO

outputs (o1,o12)






outputs (o1,o12)6. Convert these to acceleration (a1, adelta) and make spectral

density estimates







density estimates7. Repeat for other noise sources







density estimates7. Repeat for other noise sources8. Make correlated sum of all time-series

8.1.also convert this to acceleration and make spectral density estimates







density estimates7. Repeat for other noise sources8. Make correlated sum of all time-series

8.1.also convert this to acceleration and make spectral density estimates9. Make projection plots



SC x position noise



TM differential displacement noise



SC Residual Acceleration



Differential Test-mass Acceleration



Understanding the model




• Strategy:• get data out of the simulator at all possible points in the

loop• measure the (open-loop) transfer functions of individual

elements in the loop, wherever possible• non-linear blocks can’t be done this way• blocks which mix many inputs to one output need special

treatment• inspect the simulator code to validate the measurements

and expectation








and expectation• We focus only on the IFO signal loops as a first step








and expectation• We focus only on the IFO signal loops as a first step• Aim:

• validate and understand the model• use the model to develop our own model of LTP• produce new noise projections and compare



Experiments

40

•Technical studies are broken down in to investigations

•These investigations are then packed in to the time-line

Measurement of Parasitic Voltages

Measurement of differential acceleration noise on LISA Pathfinder

Measurement of cross-talk between the y-axis and the x-axis on the LTP

Measurement of LTP dynamical coefficients by system identification

Analysis of Data from the Radiation Monitor on LISA Pathfinder

Thermal experiments on board the LTP

Magnetic experiments on board the LTP

OPD noise investigations for LTP

Laser frequency noise characterisation for LTP

Laser Amplitude Noise Characterisation for LTP

The Drift Mode for LISA Pathfinder



Estimating external forces

•we want to estimate:• the residual acceleration on the spacecraft• the differential residual acceleration of the two test-

masses

41

o =�D · S�1 +C ·A ·Hdcpl ·H

��1 �gi +C ·A ·Hdcpl ·H · oi + gn +D · S�1 · orn

�





masses

41



�control chain control chain





masses

41



�

outputs input forces

guidance inputs

external forces readout noise

control chain control chain





masses

41



�

outputs input forces

guidance inputs

external forces readout noise

control chain control chain

o =DS

�1

1 +G

(gi + gn) +G

1 +G

oi +1

1 +G

o

ro



1D system model

42

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



1D system model

42

o1

o12

�12

interferometer

1s2 + �2

3

1s2 + �2

1Cdf

Asus

Adf

SC Force

Noise

TM

Differential

Force

Noise

Sensing

Noise

Sensing

Noise

Csus

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



Compute acceleration

43

⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi




43

Modelled

⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi




43

Modelled

Given⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi




43

Modelled

Given

Result

⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi




43

Modelled

Given

Result

Unknown⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi




43

Modelled

Given

Result

Unknown⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi

Injections




43

Modelled

Given

Result

Unknown⇥DS

�1 +C

⇤o = a = DS

�1

o

ro

+A+Coi

Injections

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



System identification



System identification•Many optimisation steps require measurement of

physical parameters of the system




physical parameters of the system•Dedicated experiments aim at determining small

sets of these physical parameters• e.g. stiffness of TM-SC coupling, IFO X-talk




physical parameters of the system•Dedicated experiments aim at determining small

sets of these physical parameters• e.g. stiffness of TM-SC coupling, IFO X-talk

•Example: x-axis system identification• injecting signals in x-axis control loops we can

measure:• stiffness of the two test-masses, actuator gains, IFO X-talk,

loop delays



Parameter estimation

•Employ different estimation methods to work with multiple inputs, multiple outputs

•All methods require a parametric model of the system



Linear fit

46

Signal Data pre-processing

Compute whitening filtersWhiten data

Generate test signals

Generate system model

Linear fitCompute residuals

Noise Data pre-processing


M Hewitson, LPF Data Analysis, GSFC, 11th October 2011 47Wednesday, October 19, 11


Results using mission simulator

•We can simulate experiments using the mission simulator• 3D, non-linear, time-domain simulation

•We can recover the parameters with high precision• very dependent on having a good model



LPF Mission Aims



LPF Mission Aims

• Noise hunting and system optimisation to reach free-fall level of 3×10-14 ms-2 / √Hz• iterative process through experiments, system

identification, loop optimisation• reduce noise sources• reduce noise couplings



LPF Mission Aims

• Noise hunting and system optimisation to reach free-fall level of 3×10-14 ms-2 / √Hz• iterative process through experiments, system

identification, loop optimisation• reduce noise sources• reduce noise couplings

• Develop detailed system and noise model for LPF• goes hand in hand with system optimisation and

identification• will enable us to fully explain the observed residual

force noise• model can then be used to project the performance

towards LISA



Requirements Differential Force Noise Budget

50

Total

Cap. Act

uN Thru

sters

OMS Sen

sing

Direct Forces

Star Tracker

OMS Angular

Spectral

Den

sity

[fms�

2/pHz]

Frequency [Hz]



Improvements

•Due to the extensive ground testing campaigns we have a better understanding of the system• better noise models• more realistic coupling factors

51

Input from Bill Weber, UTN

From laboratory experiments to LISA Pathfinder: achieving LISA

geodesic motionCQG 28, 2011, 094002

LISA Pathfinder: an experimental analysis of the LPF free-fall

performanceBill Weber, Moriond Proceedings,

2011



Other improvements

52

measured performance

+ lab environment

measured performance

system optimisation

system identification



Best Estimate Differential Force Noise Budget

53

SpectralDensity

[fms�

2/pHz]

TotalCap. Act

uN ThrustersOMS Sensing

Direct Forces

Star Tracker

OMS Angular

Frequency [Hz]



Free-flight experiment




•Capacitive actuation will be close to limiting around 1mHz





•Do an experiment with the actuation off (more representative of a LISA-like configuration)• must be short otherwise the TM will drift too far• repeat many times





•Do an experiment with the actuation off (more representative of a LISA-like configuration)• must be short otherwise the TM will drift too far• repeat many times

•Experiment:• kick test-mass away• turn off actuation• let the test-mass drift (in parabola)• repeat


M Hewitson, LPF, AMALDI, 15th July 2011

Simulation



Data Analysis

•Need to analyse the multiple short (200s) drift segments to estimate the spectrum at 1mHz

•One approach: window the data, and proceed with normal PSD estimate



PSD Estimate

57

Simulation with requirement-level noises but x3 reduced direct TM

force noise



Towards s/LISA/%s

58

Frequency [Hz]

SpectralDen

sity

[fms�

2/pHz]



Conclusions

59

•Always expect the unexpected!• analysis tools need to be flexible and robust• modelling system needs to be highly configurable• operations science team needs to be well trained and

familiar with all aspects of the system•We will be ready through:

• on-ground unit- and system-level hardware testing• mock data challenges• operational exercises• training sessions• rigorous testing


data analysis for lisa pathﬁnder - max planck institute...

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