Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method

Ferraioli, L.; Porter, E. K.; Armano, M.; Audley, H.; Congedo, G.; Diepholz, I.; Gibert, F.; Hewitson, M.; Hueller, M.; Karnesis, Nikolaos; Korsakova, Natalia; Nofrarias, M.; Plagnol, E.; Vitale, S.

doi:10.1007/s10686-014-9372-7

Cited by 4 publications

(4 citation statements)

References 28 publications

(33 reference statements)

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“…( 12), we need to establish the likelihood of the set of experimental observations. A likelihood can be constructed by assuming that the experimental observations (i.e., data points) are independent and normally distributed, i.e., the experimental data points are observations drawn from normal distributions with means estimated by the reduced order model and variances, 𝝈, estimated from the experimental data of the measured indentation property at M grain orientations [23,[30][31][32].…”

Section: Estimating Intrinsic Materials Properties From Indentation M...mentioning

confidence: 99%

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

Castillo

Kalidindi

2019

Front. Mater.

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This paper presents a two-step Bayesian framework for the estimation of the intrinsic single crystal elastic stiffness parameters from the measurements of spherical indentation stress-strain responses in multiple individual grains of a polycrystalline sample, whose crystal lattice orientations have been measured using electron back-scattered diffraction technique. The first step requires the establishment of the functional dependence of the indentation elastic modulus given the lattice orientation and the intrinsic single crystal elastic stiffness parameters. Previous efforts for this step required a large database of computationally expensive finite element (FE) simulations in order to establish this function with adequate accuracy. In this paper, it is shown that the introduction of a Bayesian framework can greatly reduce the number of simulations necessary to establish this function, while introducing practically useful measures of uncertainty which can guide the selection of specific additional simulations that are expected to best improve the predictive accuracy of the function. The second step involves a Markov Chain Monte-Carlo (MCMC) sampling of the distribution of possible values for the single crystal elastic stiffness parameters based on a given set of experimentally measured elastic indentation moduli in individual grains of different lattice orientations. This second step is accomplished by calibrating the available experimental data to the function established in the first step. This novel framework is presented and demonstrated in this paper for an as-cast cubic polycrystalline Fe-3% Si sample and a hexagonal polycrystalline commercially pure (CP-Ti) titanium sample.11 12 44 Literature a 225 135 124 Previous Study b 216 132 122 Current Study 223 132 114 a. Simmons and Wang [40] b. Patel et al. [9]

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Section: Estimating Intrinsic Materials Properties From Indentation M...mentioning

confidence: 99%

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

Castillo

Kalidindi

2019

Front. Mater.

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“…The B and C j coefficients, on the other hand, were estimated using a global parameter estimation method, which included all the available measurements for all the channels at the same time. A Markov Chain Monte Carlo (MCMC) method [18][19][20] was used as the parameter estimation technique. MCMC methods are advantageous over other techniques as they are straightforward to implement and allow the estimation for the mean value of the parameters and their posterior distribution.…”

Section: B Analysis Of Datamentioning

confidence: 99%

Capacitive sensing of test mass motion with nanometer precision over millimeter-wide sensing gaps for space-borne gravitational reference sensors

Armano¹,

Audley²,

Auger³

et al. 2017

Phys. Rev. D

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Capacitive sensing of test mass motion with nanometer precision over millimeter-wide sensing gaps for space-borne gravitational reference sensors. Physical Review D, 96(6), 062004.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/148989/ We report on the performance of the capacitive gap-sensing system of the Gravitational Reference Sensor (GRS) onboard the LISA Pathfinder (LPF) spacecraft. From in-flight measurements, the system has demonstrated a performance, down to 1 mHz, that is ranging between 0.7 aF Hz −1/2 and 1.8 aF Hz −1/2 . That translates into a sensing noise of the test mass motion within 1.2 nm Hz −1/2 and 2.4 nm Hz −1/2 in displacement and within 83 nrad Hz −1/2 and 170 nrad Hz −1/2 in rotation. This matches the performance goals for LPF and it allows the successful implementation of the gravitational waves observatory LISA. A 1/f tail has been observed for frequencies below 1 mHz, the tail has been investigated in detail with dedicated in-flight measurements and a model is presented in the paper. A projection of such noise to frequencies below 0.1 mHz shows that an improvement of performance at those frequencies is desirable for the next generation of GRS sensors for space-borne gravitational waves observation. 2PACS numbers: 04.80. Nn, 95.55.Ym

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“…As already mentioned, by 'preprocessed' we mean here that the series are filtered via an algorithm that depends on some set of parameters, θ, that become free fitting parameters. Commonly for the g c 2 n, θ series, θ only includes the amplitude, A, and a delay, τ , but single pole filters that simulate the response of the actuators have also been tested in the past [14][15][16][17]. In addition to the feedback force removal, we also subtract, from the acceleration data, the forces due to the motion of both TMs within the static force gradient in the satellite (see Eq.…”

Section: Extraction Of Calibration Signalsmentioning

confidence: 99%

Data series subtraction with unknown and unmodeled background noise

et al. 2014

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LISA Pathfinder (LPF), ESA's precursor mission to a gravitational wave observatory, will measure the degree to which two test-masses can be put into free-fall, aiming to demonstrate a residual relative acceleration with a power spectral density (PSD) below 30 fm/s$^2$/Hz$^{1/2}$ around 1 mHz. In LPF data analysis, the measured relative acceleration data series must be fit to other various measured time series data. This fitting is required in different experiments, from system identification of the test mass and satellite dynamics to the subtraction of noise contributions from measured known disturbances. In all cases, the background noise, described by the PSD of the fit residuals, is expected to be coloured, requiring that we perform such fits in the frequency domain. This PSD is unknown {\it a priori}, and a high accuracy estimate of this residual acceleration noise is an essential output of our analysis. In this paper we present a fitting method based on Bayesian parameter estimation with an unknown frequency-dependent background noise. The method uses noise marginalisation in connection with averaged Welch's periodograms to achieve unbiased parameter estimation, together with a consistent, non-parametric estimate of the residual PSD. Additionally, we find that the method is equivalent to some implementations of iteratively re-weighted least-squares fitting. We have tested the method both on simulated data of known PSD, and to analyze differential acceleration from several experiments with the LISA Pathfinder end-to-end mission simulator

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Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method

Cited by 4 publications

References 28 publications

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

Capacitive sensing of test mass motion with nanometer precision over millimeter-wide sensing gaps for space-borne gravitational reference sensors

Data series subtraction with unknown and unmodeled background noise

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