THERMAL SCIENCE
International Scientific Journal
CORRELATION ANALYSIS BASED ON NEURAL NETWORK COPULA FUNCTION
ABSTRACT
The joint-distribution function between variables plays an important role in reliability analysis. A method is proposed for constructing the function using a neural network, which is used to construct a copula model under arbitrarily measured data, including the input and output values of the neural network using an empirical cumulative distribution. Three traditional copula function models are constructed based on the Kendall rank-correlation coefficients. Based on the Euclidean distance method, the neural network copula and three copula function models are compared.
KEYWORDS
PAPER SUBMITTED: 2021-12-15
PAPER REVISED: 2022-06-10
PAPER ACCEPTED: 2022-06-13
PUBLISHED ONLINE: 2023-06-11
THERMAL SCIENCE YEAR
2023, VOLUME
27, ISSUE
Issue 3, PAGES [2081 - 2089]
- Phoon, K. K., Kulhawy, F. H., Characterisation of Model Uncertainties for Laterally Loaded Rigid Drilled shafts, Geotechnique, 55 (2005), 1, pp. 45-54
- Goda, K., Statistical Modeling of Joint Probability Distribution Using Copula: Application to Peak and Permanent Displacement Seismic Demands, Structural Safety, 32 (2010), 2, pp. 112-123
- Leira, B. J., Probabilistic Assessment of Weld Fatigue Damage for a Non-Linear Combination of Correlated Stress Components, Probabilistic Engineering Mechanics, 26 (2011), 3, pp. 492-500
- Nelsen, R. B., An Introduction to Copulas, Springer, New York, USA, 2006
- Sklar, A., Functions de Repartition an Dimensions Etleurs Max'ges, Publications de l'Institut de Statistique de l'Universit6 de Paris, 8 (1959), pp. 229-231
- Kjersti, A., et al., Pair-Copula Constructions of Multiple Dependence, Insurance Mathematics & Economics, 44 (2009), 2, pp. 182-198
- Subimal, G., Modelling Bivariate Rainfall Distribution and Generating Bivariate Correlated Rainfall Data in Neighbouring Meteorological Subdivisions Using Copula, Hydrological Processes, 24 (2010), 24, pp. 3558-3567
- Tang, X. S., et al., Bivariate Distribution Models Using Copulas for Reliability Analysis, Proceedings of the Institution of Mechanical Engineers, 227 (2013), 5, pp. 499-512
- Liu, J. W., et al., Research and Development on Deep Learning (in Chinese), Application Research of Computers 31 (2014), 7, pp. 1921-1930
- Li, H. B., et al., Structural Reliability Calculation Method Based on the Dual Neural Network and Direct Integration Method, Neural Computing & Applications, 29 (2018), 7, pp. 425-433
- Fan, R., et al., Survey of Research on Statistical Correlation Analysis (in Chinese), Mathematical Modeling and Its Applications, 3 (2014), 1, pp. 1-12
- Daliakopoulos, I. N., et al., Groundwater Level Forecasting Using Artificial Neural Networks, Journal of Hydrology, 309 (2005), 1, pp. 229-240
- Yu, W., et al., Tensorizing GAN with High-Order Pooling for Alzheimer's Disease Assessment, IEEE Transactions on Neural Networks and Learning Systems, 33 (2021), 9, pp. 4945-4959
- You, S., et al., Fine Perceptive Gans for Brain MR Image Super-Resolution in Wavelet Domain, IEEE Transactions on Neural Networks and Learning Systems, On-line first, doi.org/10.1109/TNNLS.2022.3153088, 2022
- Hu, S., et al., Bidirectional Mapping Generative Adversarial Networks for Brain MR to PET Synthesis, IEEE Transactions on Medical Imaging, 41 (3021), 1, pp. 145-157
- Yu, W., et al., Morphological Feature Visualization of Alzheimer's Disease via Multidirectional Perception GAN, IEEE Transactions on Neural Networks and Learning Systems, On-line first, doi.org/10.1109/TNNLS.2021.3118369, 2021