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.

1. Workshop
CERI, UCD, Dublin
Wednesday 29th August 2018

2. Rui Teixeira, Alan O’Connor and Maria Nogal
Application of Gaussian
process regression for
structural analysis

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. 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. LHS DoE Approximation
• Common approach in literature works.
• Not consistent.

6. Learning criteria
• Kriging enables notion of
improvement.
• Relation to the physical
problem of fatigue.
• Learning criteria.

7. Comparison with standard methodology
• Robust even
when only the
corner of the
space were
given.
• Convergence to
the 1 year
prediction.

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. 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. 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