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# "Application of Gaussian process regression for structural analysis" presented at CERI2018 by Rui Teixeira

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The current paper discusses the applicability of Gaussian process regressions, also known as Kriging models, in the context of structural and reliability analysis. Due to their flexibility these models appear in the field of structural analysis in many forms. Applications to approximate limit state functions, replace the computational expensive codes that solves the dynamic of complex systems, or replicate stochastic fields can be identified. Due to this fact, a discussion on the different parameters that depend on the implementation procedure chose to use these model is presented in the current paper. Design of experiments, polynomial approximation, correlation function, hyperparameters convergence and estimation function are the main global variables analysed. When implementing a Gaussian regression or Kriging model, the user is faced with the choice of these before any further progress. The discussion presented complements previous works on the implementation of such models in the sense that it focus on the structural analysis application and on how these parameters influence the accuracy. It is shown that depending on the approximation, significant advantage can be taken from understanding these major variables. Different examples are presented to support the understanding of the problem and the main conclusions on the applicability of the Gaussian regression models as surrogates for structural analysis are drawn.

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### "Application of Gaussian process regression for structural analysis" presented at CERI2018 by Rui Teixeira

1. 1. Workshop CERI, UCD, Dublin Wednesday 29th August 2018
2. 2. Rui Teixeira, Alan O’Connor and Maria Nogal Application of Gaussian process regression for structural analysis
3. 3. Introduction • CERI paper “Application of Gaussian process regression for structural analysis” discussed the importance of the model’s variables. • Gaussian process regression models, or Kriging models, have seen an increase in its application to structural problems. 𝐺 𝑥 = 𝑓 𝜷; 𝑥 + 𝑍 𝑥 Polynomial Component :𝑓 𝜷; 𝑥 = 𝛽1 𝑓1 𝑥 + ⋯ + 𝛽 𝑝 𝑓𝑝 𝑥 𝑍 𝑥 is Gaussian process with mean 0 and covariance 𝑪. 𝑥𝑖, 𝑥𝑗 = 𝜎2 𝑅 𝑥𝑖, 𝑥𝑗; 𝜽 , 𝑖, 𝑗 = 1 … 𝑘 Depends on 3 parameters: 𝜎2 , 𝜽 and 𝜷. Example of application to Offshore Wind Turbine (OWT):
4. 4. SN OWT Fatigue Surrogate 𝐷 𝑇 = ෍ 𝑖=1 𝑆 𝑛 ሻ𝑛 𝐸(𝑆𝑖 ሻ𝑛 𝑆𝑁(𝑆𝑖 IEC61400 and DNV guidelines. Run multiple time domain simulations at Θ operational states and count stresses and cycles using counting algorithm (e.g. rainflow counting) Plus SN curve and: Expensive!
5. 5. LHS DoE Approximation • Common approach in literature works. • Not consistent.
6. 6. Learning criteria • Kriging enables notion of improvement. • Relation to the physical problem of fatigue. • Learning criteria.
7. 7. Comparison with standard methodology • Robust even when only the corner of the space were given. • Convergence to the 1 year prediction.
8. 8. Comparison with standard methodology Compare with the traditional binning of data. Reduction of computational time up to 80% without compromising accuracy. Reduction never inferior to 50% for all the cases studied. • SN slopes of 3, 5 and double 3 and 5.
9. 9. Conclusions • Gaussian process regression models are: • Flexible. • Cost efficient surrogates of complex models. • Enclose uncertainty. • Provide a notion of improvement if needed. • May enclose a noise component. Possible definition of a full-field interpolator of statistical distributions. • DoE most important. But other variables can be used to improve convergence. In particular hyperparameters.
10. 10. The TRUSS ITN project (http://trussitn.eu) has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453 Thanks for your attention