|
|
基于Lorenz-96模型的数据同化方法比较研究
|
Abstract:
目的：数据同化将观测数据和基于模型的方法有机结合，以实现更精准的预测和状态估计，在多个领域都发挥着积极的作用。近年来，数据同化在核工业领域的重要性不断上升。为了分析现有的同化算法在不同数据场景下的表现，本文对集成卡尔曼滤波(EnKF)、三维变分(3D-Var)和四维变分(4D-Var)数据同化方法进行了详细的对比分析。方法：为了验证上述同化方法在不同数据场景下的同化效果，本文利用Lorenz-96模型生成仿真数据，并添加不同误差水平的噪声，同时获取具有不同观测间隔的数据。利用不同的数据集对同化方法进行分析，通过统计分析时空均方根误差来评估同化效果。结果：实验结果表明：EnKF在不同观测噪声水平和观测间隔的数据下展现出卓越的同化效果，适用于实际复杂系统的数据同化。3D-Var由于仅在当前数据点进行同化，因此在同化速度上较为迅速；而4D-Var方法则对给定窗口内的数据进行同化，导致同化时间相对于3D-Var较长。
Introduction: Data assimilation seamlessly combines observational data with model-based methods to achieve more accurate predictions and state estimations, playing a positive role in multiple domains. In recent years, the significance of data assimilation in the nuclear industry has been steadily increasing. In order to assess the effectiveness of assimilation algorithms across various data scenarios, this paper conducts a comprehensive comparative analysis of data assimilation methods, including Ensemble Kalman Filter (EnKF), 3D-Var, and 4D-Var. Method: To validate the assimilation effectiveness of the methods above in various data scenarios, this study uses the Lorenz-96 model to generate simulated data. Different noise levels are added, and data with varying observation intervals are obtained. The assimilation methods are applied to different datasets, and the assimilation performance is evaluated through statistical analysis of the root mean square error in space and time. Result: The experimental results indicate that EnKF demonstrates excellent assimilation performance across different levels of observational noise and observation intervals, making it suitable for data assimilation in practical complex systems. Due to its assimilation being confined to the current data points, 3D-Var exhibits a faster assimilation speed. On the other hand, 4D-Var assimilates data within a given window, resulting in a relatively longer assimilation time than 3D-Var.
| [1] | 荣健, 刘展. 先进核能技术发展与展望[J]. 原子能科学技术, 2020, 54(9): 1638-1643. https://doi.org/10.7538/yzk.2020.youxian.0348 |
| [2] | 蒋祖跃. 秦山核电厂反应堆保护系统及其相关设备数字化改造规划和实施策略[J]. 原子能科学技术, 2010, 44(1): 65-69. https://doi.org/10.7538/yzk.2010.44.01.0065 |
| [3] | Lu, C., Lyu, J., Zhang, L., Gong, A., Fan, Y., Yan, J., et al. (2020) Nuclear Power Plants with Artificial Intelligence in Industry 4.0 Era: Top-Level Design and Current Applications—A Systemic Review. IEEE Access, 8, 194315-194332. https://doi.org/10.1109/access.2020.3032529 |
| [4] | Argaud, J.P., Bouriquet, B., Erhard, P., et al. (2010) Data Assimilation in Nuclear Power Plant Core. In: Progress in Industrial Mathematics at ECMI 2008, Springer, Berlin, 401-406. |
| [5] | Xue, M., Wang, D., Gao, J., Brewster, K. and Droegemeier, K.K. (2003) The Advanced Regional Prediction System (ARPS), Storm-Scale Numerical Weather Prediction and Data Assimilation. Meteorology and Atmospheric Physics, 82, 139-170. https://doi.org/10.1007/s00703-001-0595-6 |
| [6] | Rabier, F. (2005) Overview of Global Data Assimilation Developments in Numerical Weather‐Prediction Centres. Quarterly Journal of the Royal Meteorological Society, 131, 3215-3233. https://doi.org/10.1256/qj.05.129 |
| [7] | Roger, D. (1993) Atmospheric Data Analysis. Cambridge University Press, Cambridge. |
| [8] | Lewis, J.M., Lakshmivarahan, S. and Dhall, S. (2006). Dynamic Data Assimilation: A Least Squares Approach. Cambridge University Press, Cambridge. https://doi.org/10.1017/cbo9780511526480 |
| [9] | Carton, J.A. and Giese, B.S. (2008) A Reanalysis of Ocean Climate Using Simple Ocean Data Assimilation (Soda). Monthly Weather Review, 136, 2999-3017. https://doi.org/10.1175/2007mwr1978.1 |
| [10] | Houser, P.R., Shuttleworth, W.J., Famiglietti, J.S., Gupta, H.V., Syed, K.H. and Goodrich, D.C. (1998) Integration of Soil Moisture Remote Sensing and Hydrologic Modeling Using Data Assimilation. Water Resources Research, 34, 3405-3420. https://doi.org/10.1029/1998wr900001 |
| [11] | Salvatores, M., Palmiotti, G., Aliberti, G., Archier, P., De Saint Jean, C., Dupont, E., et al. (2014) Methods and Issues for the Combined Use of Integral Experiments and Covariance Data: Results of a NEA International Collaborative Study. Nuclear Data Sheets, 118, 38-71. https://doi.org/10.1016/j.nds.2014.04.005 |
| [12] | Usachev, L.N. and Bobkov Yu, G. (1972) Planning an Optimum Set of Microscopic Experiments and Evaluation to Obtain a Given Accuracy in Reactor Parameter Calculations. IAEA Nuclear Data Section. |
| [13] | Rowlands, J.L. and Macdougall, J.D. (1969) Use of Integral Measurements to Adjust Cross-Sections and Predict Reactor Properties. Medium: X 2016-05-11. https://doi.org/10.1680/tpofroad.44746.0022 |
| [14] | Saint-Jean, C., Archier, P., Habert, B., et al. (2010) Assessment of Existing Nuclear Data Adjustment Methodologies. A Report by the Working Party on International Evaluation Co-Operation of the NEA Nuclear Science Committee-Intermediate Report. |
| [15] | Guo, L., Wan, C. and Wu, H. (2022) Data Assimilation for the Burnup Distribution Applying the Three-Dimensional Variational and Artificial Neutral Network Algorithm. Annals of Nuclear Energy, 179, Article ID: 109419. https://doi.org/10.1016/j.anucene.2022.109419 |
| [16] | Garcia, H.E., Aumeier, S.E. and Al-Rashdan, A.Y. (2020) Integrated State Awareness through Secure Embedded Intelligence in Nuclear Systems: Opportunities and Implications. Nuclear Science and Engineering, 194, 249-269. https://doi.org/10.1080/00295639.2019.1698237 |
| [17] | Gong, H., Yu, Y., Li, Q. and Quan, C. (2020) An Inverse-Distance-Based Fitting Term for 3D-VAR Data Assimilation in Nuclear Core Simulation. Annals of Nuclear Energy, 141, Article ID: 107346. https://doi.org/10.1016/j.anucene.2020.107346 |
| [18] | Gong, H., Cheng, S., Chen, Z., Li, Q., Quilodrán-Casas, C., Xiao, D., et al. (2022) An Efficient Digital Twin Based on Machine Learning SVD Autoencoder and Generalised Latent Assimilation for Nuclear Reactor Physics. Annals of Nuclear Energy, 179, Article ID: 109431. https://doi.org/10.1016/j.anucene.2022.109431 |
| [19] | Nino Ruiz, E.D., Sandu, A. and Anderson, J. (2014) An Efficient Implementation of the Ensemble Kalman Filter Based on an Iterative Sherman-Morrison Formula. Statistics and Computing, 25, 561-577. https://doi.org/10.1007/s11222-014-9454-4 |
| [20] | Brajard, J., Carrassi, A., Bocquet, M. and Bertino, L. (2020) Combining Data Assimilation and Machine Learning to Emulate a Dynamical Model from Sparse and Noisy Observations: A Case Study with the Lorenz 96 Model. Journal of Computational Science, 44, Article ID: 101171. https://doi.org/10.1016/j.jocs.2020.101171 |
| [21] | Lorenc, A.C. (1986) Analysis Methods for Numerical Weather Prediction. Quarterly Journal of the Royal Meteorological Society, 112, 1177-1194. https://doi.org/10.1002/qj.49711247414 |
| [22] | Lorenc, A.C. (2003) The Potential of the Ensemble Kalman Filter for NWP—A Comparison with 4D‐Var. Quarterly Journal of the Royal Meteorological Society, 129, 3183-3203. https://doi.org/10.1256/qj.02.132 |
| [23] | ZHENG, D., LEUNG, J., LEE, B. and LAM, H. (2007) Data Assimilation in the Atmospheric Dispersion Model for Nuclear Accident Assessments. Atmospheric Environment, 41, 2438-2446. https://doi.org/10.1016/j.atmosenv.2006.05.076 |
| [24] | 唐秀欢, 李华, 包利红. 核事故实时释放量集合卡尔曼滤波反演算法研究[J]. 原子能科学技术, 2014, 48(增刊1): 415-420. https://doi.org/10.7538/yzk.2014.48.S0.0415 |
| [25] | An, P., Ma, Y., Xiao, P., Guo, F., Lu, W. and Chai, X. (2019) Development and Validation of Reactor Nuclear Design Code Corca-3D. Nuclear Engineering and Technology, 51, 1721-1728. https://doi.org/10.1016/j.net.2019.05.015 |
| [26] | Nino-Ruiz, E.D., Calabria-Sarmiento, J.C., Guzman-Reyes, L.G. and Henao, A. (2020) A Four Dimensional Variational Data Assimilation Framework for Wind Energy Potential Estimation. Atmosphere, 11, Article No. 167. https://doi.org/10.3390/atmos11020167 |
| [27] | Wikle, C.K. and Berliner, L.M. (2007) A Bayesian Tutorial for Data Assimilation. Physica D: Nonlinear Phenomena, 230, 1-16. https://doi.org/10.1016/j.physd.2006.09.017 |
| [28] | Descombes, G., Auligné, T., Vandenberghe, F., Barker, D.M. and Barré, J. (2015) Generalized Background Error Covariance Matrix Model (GEN_BE V2.0). Geoscientific Model Development, 8, 669-696. https://doi.org/10.5194/gmd-8-669-2015 |
| [29] | Ahmed, S.E., Pawar, S. and San, O. (2020) PyDA: A Hands-On Introduction to Dynamical Data Assimilation with Python. Fluids, 5, Article No. 225. https://doi.org/10.3390/fluids5040225 |
| [30] | Lorenz, E.N. and Emanuel, K.A. (1998) Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model. Journal of the Atmospheric Sciences, 55, 399-414. https://doi.org/10.1175/1520-0469(1998)055<0399:osfswo>2.0.co;2 |
| [31] | Huang, L., Leng, H., Li, X., Ren, K., Song, J. and Wang, D. (2021) A Data-Driven Method for Hybrid Data Assimilation with Multilayer Perceptron. Big Data Research, 23, Article ID: 100179. https://doi.org/10.1016/j.bdr.2020.100179 |
