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Database-wide hazard modelling of the onset of DIII-D tearing modes with field features

Published online by Cambridge University Press:  17 October 2022

K.E.J. Olofsson*
Affiliation:
General Atomics, San Diego, CA, USA
C. Akçay
Affiliation:
General Atomics, San Diego, CA, USA
B.S. Sammuli
Affiliation:
General Atomics, San Diego, CA, USA
*
Email address for correspondence: olofsson@fusion.gat.com

Abstract

The rate of onset (hazard) of tearing modes is modelled probabilistically using statistical learning algorithms. Axisymmetric energy-density equilibrium fields are taken as raw high-dimensional input features which are reduced with principal component analysis. Signal processing of non-axisymmetric magnetics fluctuation array data provides the target information from which to learn. Model selection, visualization and calibration assessment procedures are detailed. The analysis is deployed at large scale across the DIII-D tokamak database. Standard model selection criteria suggest that the energy-density post-processed feature is a better choice for modelling the onset rate compared to the non-processed equilibrium reconstruction solution. Two example applications of the learned rate function are demonstrated: (i) proximity-to-onset discharge monitoring and (ii) database analysis showing an (expected) observational global trend that the general hazard increases as a plasma performance metric increases. An important connection between the hazard function and its use as a conditional probability generator is reviewed in the Appendix.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Bandyopadhyay, I., Barbarino, M., Bhattacharjee, A., Eidietis, N., Huber, A., Isayama, A., Kim, J., Konovalov, S., Lehnen, M., Nardon, E., et al. 2021 Summary of the IAEA technical meeting on plasma disruptions and their mitigation. Nucl. Fusion 61 (7), 077001.Google Scholar
Barr, J.L., Sammuli, B.S., Humphreys, D.A., Olofsson, K.E.J., Du, X., Rea, C., Wehner, W.P., Boyer, M.D., Eidietis, N.W., Granetz, R., et al. 2021 Development and experimental qualification of novel disruption prevention techniques on DIII-D. Nucl. Fusion 61 (12).CrossRefGoogle Scholar
Bishop, C.M., Connor, J.W., Hastie, R.J. & Cowley, S.C. 1991 On the difficulty of determining tearing mode stability. Plasma Phys. Control. Fusion 33 (4), 389.Google Scholar
Buttery, R.J., La Haye, R.J., Gohil, P., Jackson, G.L., Reimerdes, H., Strait, E.J. & the DIII-D Team 2008 The influence of rotation on the $\beta _N$ threshold for the 2/1 neoclassical tearing mode in DIII-D. Phys. Plasmas 15 (5).CrossRefGoogle Scholar
Candès, E.J., Li, X., Ma, Y. & Wright, J. 2011 Robust principal component analysis? J. ACM 58 (3).CrossRefGoogle Scholar
Caruana, R. & Niculescu-Mizil, A. 2006 An empirical comparison of supervised learning algorithms. In Proceedings of the 23rd International Conference on Machine Learning, pp. 161–168. ACM.CrossRefGoogle Scholar
Chen, T. & Guestrin, C. 2016 XGBoost: a scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 785–794. ACM.CrossRefGoogle Scholar
Fitzpatrick, R. 1993 Interaction of tearing modes with external structures in cylindrical geometry (plasma). Nucl. Fusion 33 (7), 10491084.CrossRefGoogle Scholar
Friedman, J.H. 2001 Greedy function approximation: a gradient boosting machine. Ann. Stat. 29 (5), 11891232.CrossRefGoogle Scholar
Gates, D.A. & Delgado-Aparicio, L. 2012 Origin of tokamak density limit scalings. Phys. Rev. Lett. 108, 165004.Google ScholarPubMed
Hastie, T., Tibshirani, R. & Friedman, J. 2009 The Elements of Statistical Learning, 2nd edn. Springer.CrossRefGoogle Scholar
Hole, M.J. & Appel, L.C. 2007 Fourier decomposition of magnetic perturbations in toroidal plasmas using singular value decomposition. Plasma Phys. Control. Fusion 49 (12), 19711988.CrossRefGoogle Scholar
La Haye, R., Chrystal, C., Strait, E., Callen, J., Hegna, C., Howell, E., Okabayashi, M. & Wilcox, R. 2022 Disruptive neoclassical tearing mode seeding in DIII-D with implications for ITER. Nucl. Fusion 62 (5), 056017.CrossRefGoogle Scholar
La Haye, R.J., Buttery, R.J., Guenter, S., Huysmans, G.T.A., Maraschek, M. & Wilson, H.R. 2000 Dimensionless scaling of the critical beta for onset of a neoclassical tearing mode. Phys. Plasmas 7, 3349.CrossRefGoogle Scholar
Lao, L.L., John, H.S., Stambaugh, R.D., Kellman, A.G. & Pfeiffer, W. 1985 Reconstruction of current profile parameters and plasma shapes in tokamaks. Nucl. Fusion 25 (11), 1611.CrossRefGoogle Scholar
Lawless, J.F. 2002 Statistical Models and Methods for Lifetime Data, 2nd edn. Wiley.CrossRefGoogle Scholar
Luxon, J.L. 2002 A design retrospective of the DIII-D tokamak. Nucl. Fusion 42, 614.CrossRefGoogle Scholar
MacKay, D. 2003 Information Theory, Inference, and Learning Algorithms. Cambridge University Press.Google Scholar
Moritz, P., Nishihara, R., Wang, S., Tumanov, A., Liaw, R., Liang, E., Elibol, M., Yang, Z., Paul, W., Jordan, M.I., et al. 2017 Ray: a distributed framework for emerging ai applications. https://doi.org/10.48550/arXiv.1712.05889CrossRefGoogle Scholar
Murphy, K. 2012 Machine Learning: A Probabilistic Perspective. MIT Press.Google Scholar
Olofsson, K.E.J., Hanson, J.M., Shiraki, D., Volpe, F.A., Humphreys, D.A., Haye, R.J.L., Lanctot, M.J., Strait, E.J., Welander, A.S., Kolemen, E., et al. 2014 Array magnetics modal analysis for the DIII-D tokamak based on localized time-series modelling. Plasma Phys. Control. Fusion 56 (9), 095012.CrossRefGoogle Scholar
Olofsson, K.E.J., Humphreys, D.A. & La Haye, R.J. 2018 Event hazard function learning and survival analysis for tearing mode onset characterization. Plasma Phys. Control. Fusion 60 (8), 084002.CrossRefGoogle Scholar
Olofsson, K.E.J., Sammuli, B.S. & Humphreys, D.A. 2019 Hazard function exploration of tokamak tearing mode stability boundaries. Fusion Engng Des. 146, 14761479.CrossRefGoogle Scholar
Pau, A., Fanni, A., Carcangju, S., Cannas, B., Sias, G., Murari, A., Rimini, F. & the JET Contributors 2019 A machine learning approach based on generative topographic mapping for disruption prevention and avoidance at JET. Nucl. Fusion 59 (10), 106017.CrossRefGoogle Scholar
Paz-Soldan, C. 2021 Plasma performance and operational space without ELMs in DIII-D. Plasma Phys. Control. Fusion 63 (8), 083001.CrossRefGoogle Scholar
Rasmussen, C.E. & Williams, C.K.I. 2006 Gaussian Processes for Machine Learning. MIT Press.Google Scholar
Rea, C., Montes, K.J., Pau, A., Granetz, R.S. & Sauter, O. 2020 Progress toward interpretable machine learning – based disruption predictors across tokamaks. Fusion Sci. Technol. 76 (2020), 912924.Google Scholar
Sammuli, B., Barr, J., Eidietis, N., Olofsson, K., Flanagan, S., Kostuk, M. & Humphreys, D. 2018 Toksearch: a search engine for fusion experimental data. Fusion Engng Des. 129, 1215.CrossRefGoogle Scholar
Strait, E.J. 2006 Magnetic diagnostic system of the DIII-D tokamak. Rev. Sci. Instrum. 77 (2), 023502.CrossRefGoogle Scholar
Strait, T., Munaretto, S. & Sweeney, R. 2019 Internal/external magnetic field decomposition: Application to disruption warning. In 61st Annual Meeting of the APS Division of Plasma Physics. American Physical Society.Google Scholar
Sweeney, R.M. & Strait, E.J. 2019 Decomposing magnetic field measurements into internally and externally sourced components in toroidal plasma devices. Phys. Plasmas 26 (1), 012509.CrossRefGoogle Scholar
Tinguely, R.A., Montes, K.J., Rea, C., Sweeney, R. & Granetz, R.S. 2019 An application of survival analysis to disruption prediction via random forests. Plasma Phys. Control. Fusion 61 (9), 095009.Google Scholar
Turco, F. & Luce, T. 2010 Impact of the current profile evolution on tearing stability of ITER demonstration discharges in DIII-D. Nucl. Fusion 50 (9), 095010.CrossRefGoogle Scholar
Turco, F., Luce, T., Solomon, W., Jackson, G., Navratil, G. & Hanson, J. 2018 The causes of the disruptive tearing instabilities of the ITER baseline scenario in DIII-D. Nucl. Fusion 58 (10), 106043.CrossRefGoogle Scholar
de Vries, P., Johnson, M.F., Alper, B., Buratti, P., Hender, T.C., Koslowski, H.R., Riccardo, V. & JET-EFDA Contributors 2011 Survey of disruption causes at JET. Nucl. Fusion 51 (5), 053018.CrossRefGoogle Scholar
Wesson, J. 2011 Tokamaks, 4th edn. Oxford University Press.Google Scholar