Introduction to Integrated Data Analysis

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1 7th Workshop on Fusion Data Processing, Validation and Analysis Introduction to Integrated Data Analysis R. Fischer Max-Planck-Institut für Plasmaphysik, Garching EURATOM Association Frascati, Mar 26-28, 2012

2 Outline Why do we need Integrated Data Analysis (IDA)? Implementation of IDA Applications at W7-AS JET TJ-II stellarator ASDEX Upgrade tokamak Integrated Diagnostics Design (IDD) is closely related to IDA talk A. Dinklage

3 IDA for Nuclear Fusion Different measurement techniques (diagnostics: LIB, DCN, ECE, TS, REF,...) for the same quantities (ne, Te, ) and parametric entanglement in data analysis Redundant data: reduction of estimation uncertainties (combined evaluation, super fit ) detect and resolve data inconsistencies (reliable/consistent diagnostics) Complementary data: resolve parametric entanglement resolve complex error propagation (non-gaussian) synergistic effects (parametric correlations, multi-tasking tools (TS/IF, CXRS/BES)) automatic in-situ and in-vivo calibration (transient effects, degradation,...) Goal: Coherent combination of measurements from different diagnostics replace combination of results from individual diagnostics with combination of measured data one-step analysis of pooled data in a probabilistic framework (unified error analysis!)

4 Conventional vs. Integrated Data Analysis conventional Thomson Scattering data ECE analysis analysis ne(ρ), Te(ρ), mapping ρ(x) ne(x), Te(x) data ne(x),te(x) mapping ρ(x) IDA (Bayesian probability theory) Te(x) mapping ρ(x) linked result Parametric entanglements DTS(ne(x)),Te(x)) DECE(ne(x)),Te(x)) Thomson Scattering data dts ECE data dece addl. information, constraints, model params,... result: p(ne(ρ),te(ρ) dts,dece) estimates: ne(ρ) ± Δne(ρ), Te(ρ) ± ΔTe(ρ)

5 Conventional vs. Integrated Data Analysis (2) Drawbacks of conventional data analysis: iterative (self-)consistent results? (cumbersome; do they exist?) information propagation? (Single estimates as input for analysis of other diagnostics?) data and result validation? (How to deal with inconsistencies?) non-gaussian error propagation? (frequently neglected: underestimation of the true error?) difficult to be automated (huge amount of data from steady state devices: W7X, ITER,...) often backward inversion techniques (noise fitting? numerical stability? loss of information?) result: estimates and error bars (sufficient? non-linear dependencies?) Probabilistic combination of different diagnostics (IDA) uses only forward modeling (complete set of parameters modeling of measured data) additional physical information easily to be integrated systematic effects nuisance parameters unified error interpretation Bayesian Probability Theory result: probability distribution of parameters of interest IDA offers a unified way of combining data (information) from various experiments (sources) to obtain improved results

6 Probabilistic (Bayesian) Recipe Reasoning about parameter θ: (uncertain) prior information + (uncertain) measured data + physical model + Bayes theorem p d = p prior distribution d = D D= f } p d likelihood distribution p d p p d posterior distribution + additional (nuisance) parameter β p d = d p, d = d marginalization p d, p p (integration) p d generalization of Gaussian error propagation laws + parameter averaging (model comparison) p d M = d p, d M = d p d, M p prior predictive value

7 Bayesian Recipe for IDA: LIB + DCN + ECE + TS Reasoning about parameter ne, Te: (uncertain) prior information p n e, T e + experiment 1: d LiB = D LiB n e, T e ; p d LiB n e, T e + experiment 2: d DCN = D DCN ne ; p d DCN n e + experiment 3: d ECE = D ECE T e ; p d ECE T e + experiment 4: d TS =D TS n e, T e ; p d TS n e,t e prior distribution likelihood distributions + Bayes theorem p n e, T e d TS, d ECE, d LiB, d DCN p d TS ne, T e p d ECE T e p d LiB n e,t e p d DCN n e p n e, T e posterior distribution

8 Application: W7-AS W7-AS: ne, Te: Thomson scattering, interferometry, soft X-ray R. Fischer, A. Dinklage, and E. Pasch, Bayesian modelling of fusion diagnostics, Plasma Phys. Control. Fusion, 45, (2003) Using synergism: Combination of results from a set of diagnostics Thomson Scattering dte = Soft-X-ray Electron density 30% reduced error synergism by exploiting full probabilistic correlation structure

9 Application: JET JET: ne, Te : Interferometry, core LIDAR and edge LIDAR diagnostics O Ford, et al., Bayesian Combined Analysis of JET LIDAR, Edge LIDAR and Interferometry Diagnostics, P-2.150, EPS 2009, Sofia ne : Lithium beam forward modelling D. Dodt, et al., Electron Density Profiles from the Probabilistic Analysis of the Lithium Beam at JET, P-2.148, EPS 2009, Sofia

10 Application: TJ-II TJ-II: ne : Interferometry, reflectometry, Thomson scattering, and Helium beam B. Ph. van Milligen, et al., Integrated data analysis at TJ-II: The density profile, Rev. Sci. Instrum. 82, (2011) Full forward model for Interferometry Reflectometry (group delay) Partial forward model for Thomson scattering Helium beam

11 Application: ASDEX Upgrade (1) ne, Te : Lithium beam impact excitation spectroscopy (LiB) Interferometry measurements (DCN) Electron cyclotron emission (ECE) Thomson scattering (TS) Reflectometry (REF) Equilibrium reconstructions for diagnostics mapping R. Fischer et al., Integrated data analysis of profile diagnostics at ASDEX Upgrade, Fusion Sci. Technol., 58, (2010) (2) Zeff : Bremsstrahlung background from various CXRS spectroscopies Impurity concentrations from CXRS S. Rathgeber et al., Estimation of profiles of the effective ion charge at ASDEX Upgrade with Integrated Data Analysis, PPCF, 52, (2010)

12 LIB + DCN: Temporal resolution #22561, s, H-mode, type I ELM LIN: Lithium beam only IDA: Lithium beam + DCN Interferometry density profiles with temporal resolution of 1 ms (routinely written) 50 μs (on demand)

13 IDA: LIB + DCN + ECE simultaneous: full density profiles (partly) temperature profiles pressure profile n > 0.95*n e e,cut-off masking of ECE channels opt. depth ~ n T e e masking of ECE channels

14 Summary: IDA Probabilistic modeling of individual diagnostics forward modeling only (synthetic diagnostic) probability distributions: describes all kind of uncertainties multiply probability distributions, marginalization of nuisance parameters parameter estimates and uncertainties Probabilistic combination of different diagnostics systematic and unified error analysis is a must for comparison of diagnostics error propagation beyond single diagnostics more reliable results by larger (meta-) data set (interdependencies, synergism) redundant information resolve data inconsistencies advanced data analysis technique software/hardware upgrades Applications at W7-AS, JET, TJ-II, and ASDEX Upgrade

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