36 Inferring Structural Variability Using Modal Analysis in a Bayesian Framework 373 36.6 General Remarks In this paper, a Bayesian approach was used for the geometrical uncertainty quantification in a controlled experiment of a metallic frame. Since there is uncertainty related to the position of vertical beams of the frame, the available FE model had to be re-meshed and evaluated several times. This called for the use of metamodels in order to make the computational cost of the analysis affordable. Two metamodels were employed and benchmarked: (a) RBNN and (b) GPE The accuracy of the surrogate models was compared using different sample sizes of Sobol sampling designs. The RMSE of predicted and validation data was used as basis for comparison. The following remarks related to the metamodels can be stated: • Both metamodels presented acceptable accuracy in representing the synthetic data for the six modal frequencies of the frame. • The larger the sample size used for the training process, the more accurate the metamodel becomes. • The GPE presented higher computational cost in both training and validation phases. This is attributed to well-known computational bottlenecks in both the training and validation phases. • The RBNN presented the lowest spent computational cost, since the correlation length parameter did not need to be optimised and due the fact that in the validation phase, no correlation matrix are needed to be evaluated at the new tested data. Despite the calculated RMSE showed very close to the GPE, the RBNN needs a statistical framework in order to allow uncertainty quantification of the estimated values. • The TMCMC model updating presented good accuracy in determining the geometrical parameter uncertainties based on the nine measured experimental mode frequencies. References 1. Ching J, Chen YC (2007) Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J Eng Mech 33(7):816–832 2. Khodaparast HH, Mottershead JE, Badcock KJ (2011) Interval model updating with irreducible uncertainty using Kringing predictor. Mech Syst Sign Process 25:1204–1226 3. Billings SA, Wei H-L, Balikhin MA (2007) Generalized multiscale radial basis function networks. Neural Networks 20:1081–1094 4. Lin G-F, Chen L-H (2004) A spatial interpolation method based on radial basis function networks incorporating a semivariogram model. J Hydrol 288:288–298 5. O’Hagan A (2006) Bayesian analysis of computer code outputs: a tutorial, reliability. Eng Syst Safe 91:1290–1300 6. Haykin S (1999) Neural networks: a Comprehensive Foundation, 2nd Edition, Prentice-Hall, 842p 7. Sobol IM (1967) Distribution of points in a cube and approximate evaluation of integrals. Comput Maths Math Phys 7:86–112
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