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• Avoid processing signals with non-causal filtering; this can introduce post-disruption effects into pre-disruption data
• Pre-processed signals in database to avoid excessive smoothing and interpolation
• Analyzed 7/40 dimensionless or machine-independent parameters from database using a machine learning algorithm
• Difference in timescales on DIII-D and C-Mod evident when comparing design points and time evolution of parameters
• Poorer predictive capability on Alcator C-Mod compared to DIII-D may be due to faster disruption-relevant timescales
• At present data acquisition rate, difficult to predict disrupts• Compare performance of other ML algorithms and study
dependence on new features as the database is updated
Disruption Warning Database Development and Exploratory
Machine Learning Studies on Alcator C-ModK. Montes, C. Rea, R. Granetz
Plasma Science and Fusion Center, Massachusetts Institute of Technology
Introduction
Conclusions and Future Work
References
Disruption Warning Database• SQL database of > 40 parameters from 1821 shots (~160k time
slices) from 2015 C-Mod campaign• Only time slices in Ip flattop included; composed of non-disruptive
discharges and discharges that disrupted during the flattop• Ignored intentional massive gas injection (MGI) disruptions
• Each database record consists of all parameter values at one time slice, recorded every 20 ms; for each disruption, take additional time slices every 1 ms during the 20 ms period before disruption
C-Mod and DIII-D Comparison• Given input parameters Ԧ𝑥 and historical knowledge of disrupted shots
𝑌, how can we find patterns to distinguish disruptions in our database?
• Random forest for classification using 3 different labeling schemes
AXUV diode channel (no smoothing)
𝑃𝑟𝑎𝑑 with non-causal smoothing (not ok near disruptions) from blackened bolometer
Non-causal filtering example: 𝑃𝑟𝑎𝑑calculation on C-Mod taken from AXUV diode to avoid non-causal filter
Total # of Shots 1821
Non-Disruptive Flattop Shots 1160
Disruptions in Flattop 206
Intentional MGI Disruptions 17
𝐼𝑃 Flattop
Shot # 1150501010
[1] C. Rea et al. APS (Oct. 2017)[2] O. Sauter and Y. Martin Nuclear Fusion 40 (2000) 955[3] C. M. Greenfield et al. Plasma Physics and Controlled Fusion 46 (2004) 12B[4] G.M. Wallace et al. IAEA Conference (2012)[5] J. Vega et al. Fusion Engineering and Design 88 (2013)[6] E. Alpaydin, “Introduction to Machine Learning”, 2nd Edition, MIT Press[7] L. Breiman, “Random Forests”, Machine Learning, 45(1), 5-32, 2001
Major Radius
Minor Radius
Toroidal Field
Plasma Current
Confinement Time [2]
Current Relaxation Time [3,4]
DIII-D 1.67 m 67 cm ~2 T 3.0 MA ≈ 0.1 𝑠 ~ 1 𝑠
C-Mod 68 cm 22 cm 3-8 T 0.4-2 MA ≈ 0.04 𝑠 ~ 0.2 𝑠
• Common cause of C-Mod disruptions is radiative collapse from high-Z first wall molybdenum (1-2 ms timescale)
• In contrast, DIII-D has low-Z carbon wall; most disruptions due to MHD instabilities
Supervised Learning for Classification
Binary Phase Classification:• ‘stable’ = non-disrupted or > 40
ms from disruption• ‘disruptive’ = < 40 ms from
disruption
Classification Accuracy:• Disruptive: 48.5 % • Stable: 99.3 %• Overall: 97.3 %
Binary Classification:• ‘non-disrupted’ = sample from
shot with no disruption• ‘disrupted’ = sample from
disrupted shot
Classification Accuracy:• Disrupted: 52.6 % • Non-Disrupted: 97.0 %• Overall: 91.2 %
• Predicting and mitigating disruptions in tokamaks is critical to the mission of sustaining a fusion plasma
• To understand what causes disruptions, we want to answer:• Which parameters are correlated with the approach of a
disruption? What are their threshold levels?• Are the thresholds reached with significant warning time?• Are there combinations of parameters that are useful?• Are the same parameters useful on different tokamaks?
• Goal: Develop a disruption warning algorithm that works in near real-time, embedded in the plasma control system
Yes No
Yes No
𝑥1 > −0.55
𝑥2 > 0.3
branchesR1
R3R2
Minimize impurity measure to determine splitting value at each node:
leaves
decision node
1 Plasma Current Error Fraction ip_error_frac
2 Internal Inductance li
3 Greenwald Fraction n/nG
4 q95 (Safety Factor at r = 0.95a) q95
5 Poloidal Beta Ratio betap
6 Loop Voltage Vloop
7 Radiated Power Fraction prad_frac
Multi-Class Classification:• ‘non-disrupted’ = sample from
shot with no disruption• ‘far from disr’ = sample from
disrupted shot > 40 ms from disruption
• ‘close to disr’ = sample from disrupted shot < 40 ms from disruption
Classification Accuracy:• Non-Disrupted: 97.4 % • Far from Disr: 37.3 %• Close to Disr: 53.3 %
Overall Accuracy: 90.1 %
• Large overlap of internal inductance distributions compared to DIII-D for time slices grouped via the multi-class classification case;
Supervised Learning
Learn 𝑌 = 𝑓(𝑥)
Unsupervised Learning
Search 𝑋 = Ԧ𝑥 for structure & patterns
ClusteringDiscover groupings in parameter space
Machine Learning Algorithms
AssociationDiscover rules that
relate data
Classification𝑌 = discrete (class)
Regression𝑌 = continuous
(likelihood or time)
Linear regression, neural networks, random forest, etc.
Random forest, logistic regression, support vector machines, etc.
K-means clustering, self-organizing maps, Gaussian mixture models, etc.
Apriori algorithm, equivalence class transformation, etc.
40
par
amet
ers
Ip (MA)
ne (m-3)
q95
[1] C. Rea et al. APS (Oct. 2017)
Shot # 1150806029
C-Mod li distribution mean
Power Spike Before C-Mod Disruption