Real-time Data Fusion for Nuclear Fusion

Transcription

1 Real-time Data Fusion for Nuclear Fusion Chris Rapson R. Fischer, L. Giannone, M. Reich, W. Treutterer & the ASDEX Upgrade Team MPI for Plasma Physics, Garching ASDEX Upgrade This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme -8 under grant agreement No The views and opinions epressed herein do not necessarily reflect those of the European Commission.

2 ydata fusion in daily life ASDEX Upgrade Principle: combine independent measurements to improve parameter estimate hear a bang, turn to look Real-time Data Fusion for Nuclear Fusion /5

3 ydata fusion in daily life ASDEX Upgrade Principle: combine independent measurements to improve parameter estimate hear a bang, turn to look position estimation phones: GPS, WiFi, Accelerometer cars: as above, plus wheel encoders, LIDAR, Sonar, cameras, IR... [ Real-time Data Fusion for Nuclear Fusion /5

4 ydata fusion in daily life ASDEX Upgrade Principle: combine independent measurements to improve parameter estimate hear a bang, turn to look position estimation phones: GPS, WiFi, Accelerometer cars: as above, plus wheel encoders, LIDAR, Sonar, cameras, IR... [ sports refereeing player statistics entertainment [ Real-time Data Fusion for Nuclear Fusion /5

5 ydata fusion in theory A large body of work, applied to many different fields combine two independent measurements E( obs, = σ E( obs σ, = σ σ + σ + σ + σ E( obs σ + σ P( obs P( obs Real-time Data Fusion for Nuclear Fusion 3/5

6 ydata fusion in theory A large body of work, applied to many different fields combine two independent measurements E( obs, = σ E( obs σ, = σ σ + σ + σ + σ E( obs σ + σ P( obs P( obs P( obs, Real-time Data Fusion for Nuclear Fusion 3/5

7 ydata fusion in theory A large body of work, applied to many different fields combine two independent measurements E( obs, = σ E( obs σ, = σ σ + σ + σ + σ E( obs σ + σ P( obs P( obs P( obs, identify and correct systematic errors & drifts if E( obs E( obs, > large error { } fi(obs line integrated density [ 9 m 3 ] 8 #987 DCN H DCN H Thomson time [s] Real-time Data Fusion for Nuclear Fusion 3/5

8 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π obs t,t obs t obs t P( t obs t Real-time Data Fusion for Nuclear Fusion /5

9 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( initial estimate particles true value Real-time Data Fusion for Nuclear Fusion /5

10 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( measured, t= Real-time Data Fusion for Nuclear Fusion /5

11 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( resampled, t= Real-time Data Fusion for Nuclear Fusion /5

12 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( evolved, t= Real-time Data Fusion for Nuclear Fusion /5

13 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( measured, t= Real-time Data Fusion for Nuclear Fusion /5

14 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( resampled, t= Real-time Data Fusion for Nuclear Fusion /5

15 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( evolved, t= Real-time Data Fusion for Nuclear Fusion /5

16 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( measured, t= Real-time Data Fusion for Nuclear Fusion /5

17 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( resampled, t= Real-time Data Fusion for Nuclear Fusion /5

18 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( evolved, t= Real-time Data Fusion for Nuclear Fusion /5

19 ydata fusion in theory We can also include our prior knowledge of the system dynamics Kalman Filter optimal for linear systems with Gaussian noise developed in the 6s flew on the Apollo missions Etended Kalman Filter local linearisation of non-linear systems with Gaussian noise Particle Filter fully non-linear system and noise e.g. linear model ( = +.5 with bimodal measurement (aliasing, mirroring or modulo π P( t obs t obs t obs t obs t,t P( measured, t= Real-time Data Fusion for Nuclear Fusion /5

20 yeisting applications of data fusion in tokamaks Lots of potential because one parameter can be measured in different ways different parameters are linked by common geometry Offline Integrated Data Analysis [Fischer, this conference] Minerva [Svensson 8 PPCF, von Nessi PoP] L/H-mode identification [e.g. Giannone PPCF] Z eff [Verdoolaege IEEE] Real-time [Fischer F Sci Tech, ] RAPTOR [Felici, this conference] disruption prediction [several contributors, this conference] MHD mode number tracking [e.g. Galperti PPCF, Alves 3 PPCF] Real-time Data Fusion for Nuclear Fusion 5/5

21 yntm Stabilisation NTMs decrease confinement and can cause disruptions stabilise or prevent NTMs with localised heating and current drive ECCD Real-time Data Fusion for Nuclear Fusion 6/5

22 yntm Stabilisation NTMs decrease confinement and can cause disruptions stabilise or prevent NTMs with localised heating and current drive ECCD requires accurate targetting: accuracy < w island in AUG, accuracy < cm in ITER, accuracy < 3 cm [Sauter PPCF, La Haye 8 NF] more power required if ECCD deposition is less accurate growth rate dw/dt [ms ]. w marg ECCD off ECCD on w sat. 6 w [cm] NTM w island Real-time Data Fusion for Nuclear Fusion 6/5

23 yntm Stabilisation NTMs decrease confinement and can cause disruptions stabilise or prevent NTMs with localised heating and current drive ECCD requires accurate targetting: accuracy < w island in AUG, accuracy < cm in ITER, accuracy < 3 cm [Sauter PPCF, La Haye 8 NF] more power required if ECCD deposition is less accurate in terms of mirror angle <.. ITER mirrors specified to ±.5 requires accurate localisation growth rate dw/dt [ms ]. w marg ECCD off ECCD on w sat. 6 w [cm] NTM w island Real-time Data Fusion for Nuclear Fusion 6/5

24 yntm Localisation - Method : Equilibrium NTMs only occur at flu surfaces with rational q location of q surfaces can be obtained from equilibrium equilibrium is a pre-requisite for EC ray-tracing calculations + always available, even before NTM appears difficult to diagnose to q profile large uncertainty of flu surface location Real-time Data Fusion for Nuclear Fusion 7/5

25 ASDEX Upgrade yntm Localisation - Method : Te Fluctuations NTM detected as B by Mirnov coils and T e by ECE inversion radius can be associated with an ECE channel (change of correlation phase by π [Reich et al. F Sci Tech. ] ECE channel location is known at the midplane + + low uncertainty in ECE channel identification uncertainty improves for big NTMs some false positives midplane location must be transposed to deposition location reintroduces uncertainty only useful once island eists Real-time Data Fusion for Nuclear Fusion ECRH ECE 8/5

26 yntm Localisation - Method 3: Amplitude ASDEX Upgrade decreases when EC is well aligned + no spatial resolution limitation ρq=.5.6 ρeccd.5 ρtarget. 6 NTM width [au] NTM amplitude is B island width ρ [no units] #967 ep sim time [s] B is a noisy measurement search for min B is non-linear difficult for control amplitude changes can be due to adding or removing NBI power only useful if EC approimately on target only useful once island eists [Humphreys et al. PoP. 6] Real-time Data Fusion for Nuclear Fusion 9/5

27 Equilibrium σ =. ysensor Functions P(NTM pos ρ pol.6.8 T e Fluctuations σ =. weighted by the NTM amplitude Ḃ P(NTM pos ρ pol Amplitude σ =. negative if amplitude increases weighted by + dβ dt one peak for each gyrotron which is within. ρ pol of the q-surface P(NTM pos.. ρ pol.6.8 Real-time Data Fusion for Nuclear Fusion /5

28 ydata Fusion for NTM Localisation use a grid-based filter - like a particle filter without resampling avoids sample impoverishment since NTM can occur anywhere, anytime more computation since more grid points needed for same resolution maintain likelihood estimate for each sensor separately, then add Real-time Data Fusion for Nuclear Fusion /5

29 ydata Fusion for NTM Localisation use a grid-based filter - like a particle filter without resampling avoids sample impoverishment since NTM can occur anywhere, anytime more computation since more grid points needed for same resolution maintain likelihood estimate for each sensor separately, then add instead of normalising every time-step, use a forgetting factor τ forget (mag = τ forget (ECE =. s τ forget (ampl =.7 s time [s] time [s] Real-time Data Fusion for Nuclear Fusion /5

30 ydata Fusion for NTM Localisation use a grid-based filter - like a particle filter without resampling avoids sample impoverishment since NTM can occur anywhere, anytime more computation since more grid points needed for same resolution maintain likelihood estimate for each sensor separately, then add instead of normalising every time-step, use a forgetting factor τ forget (mag = τ forget (ECE =. s τ forget (ampl =.7 s compensate the cumulative effects of a long τ forget with weights w(mag = w(ece = w(ampl = time [s] time [s] Real-time Data Fusion for Nuclear Fusion /5

31 yapply Fused Data to Feedback #357 - test archived data ρ pol.8.6 mag estimate data fus estimate w [cm] ρ ρ NTM pol pol ECE estimate data fus estimate data fus estimate EC 6 time [s] 5 5 Real-time Data Fusion for Nuclear Fusion /5

32 yapply Fused Data to Feedback tracks mag estimate before NTM appears #357 - test archived data ρ pol.8.6 mag estimate data fus estimate w [cm] ρ ρ NTM pol pol ECE estimate data fus estimate data fus estimate EC 6 time [s] 5 5 Real-time Data Fusion for Nuclear Fusion /5

33 yapply Fused Data to Feedback tracks mag estimate before NTM appears tracks ECE estimate when island is large and EC off #357 - test archived data ρ pol ρ pol ECE estimate data fus estimate mag estimate data fus estimate w [cm] ρ NTM pol data fus estimate EC 6 time [s] 5 5 Real-time Data Fusion for Nuclear Fusion /5

34 yapply Fused Data to Feedback tracks mag estimate before NTM appears tracks ECE estimate when island is large and EC off ampl changes show if NTM is at the EC deposition location - or not! #357 - test archived data ρ pol ρ pol ECE estimate data fus estimate mag estimate data fus estimate w [cm] ρ NTM pol data fus estimate EC 6 time [s] 5 5 Real-time Data Fusion for Nuclear Fusion /5

35 yapply Fused Data to Feedback tracks mag estimate before NTM appears tracks ECE estimate when island is large and EC off ampl changes show if NTM is at the EC deposition location - or not! result is better than any of the diagnostics by themselves #357 - test archived data ρ pol ρ pol ρ pol w NTM [cm] ECE estimate data fus estimate mag estimate data fus estimate data fus estimate EC 6 time [s] 5 5 Real-time Data Fusion for Nuclear Fusion /5

36 yapply Fused Data to Feedback tracks mag estimate before NTM appears tracks ECE estimate when island is large and EC off ampl changes show if NTM is at the EC deposition location - or not! result is better than any of the diagnostics by themselves in FB, sweep target around ma likelihood, down to 9% ρ pol ρ pol ρ pol w NTM [cm] #357 - FB simulation NTM mag estimate data fus estimate NTM ECE estimate data fus estimate NTM data fus estimate target EC.5 3 time [s] Real-time Data Fusion for Nuclear Fusion /5

37 yapply Fused Data to Feedback tracks mag estimate before NTM appears tracks ECE estimate when island is large and EC off ampl changes show if NTM is at the EC deposition location - or not! result is better than any of the diagnostics by themselves in FB, sweep target around ma likelihood, down to 9% real-time C ++ version ready to run ρ pol ρ pol ρ pol w NTM [cm] #357 - FB simulation NTM mag estimate data fus estimate NTM ECE estimate data fus estimate NTM data fus estimate target EC.5 3 time [s] Real-time Data Fusion for Nuclear Fusion /5

38 #365 s Equilibria: EQI( Diagnostics: ECE Radiometer ECE Radiometer (-6 yalternative Concepts for Position Control magnetic diagnostics susceptible to drift in long pulse eperiments radiation damage in reactors need alternatives for DEMO the more options the better [Santos NF ] Reflectometry measures n e profiles and can estimate gaps ECE can estimate the separatri position where T e ev take care with shine-through Soft X-Ray can estimate position of ma radiation as proy for z centre Trad [ev] 3 R aus.6.8. R [m] [SXR images courtesy of M. Weiland, to be published] Real-time Data Fusion for Nuclear Fusion 3/5

39 ydata Fusion for Position Control P(R P(R P(R P(R P(R AUG mag refl total ECE model R [m] Real-time Data Fusion for Nuclear Fusion /5

40 ydata Fusion for Position Control P(R P(R P(R P(R P(R AUG mag refl total ECE model R [m] Real-time Data Fusion for Nuclear Fusion /5

41 ydata Fusion for Position Control P(R AUG mag P(R DEMO mag (slow P(R refl P(R refl P(R ECE P(R ECE P(R model P(R model P(R total P(R total R [m] R [m] Real-time Data Fusion for Nuclear Fusion /5

42 yconclusions Data fusion in nuclear fusion mature methods eist potential to eploit these techniques in fusion eperiments - more than we have so far will be vital for diagnostics in a reactor Two eamples shown NTM localisation combining equilibrium, ECE and amplitude performs well in FB simulations ready to test in eperiment plasma position estimation concept involving many diagnostics Real-time Data Fusion for Nuclear Fusion 5/5