Bayesian kriging regression for the accuracy improvement of beam modeled T-junctions of buses and coaches structures with a methodology based on FEM behavioral analysis

Detailed Study on the Behavior of Improved Beam T-Junctions Modeling for the Characterization of Tubular Structures, Based on Artificial Neural Networks Trained with Finite Element Models

“…It is noted that there are significant differences in the precision of some spring directions, especially for T2 joint configuration, where UX, UY, RX, and RZ show an average error of approximately one third with respect to the rest of directions. In any case, the worst-case average error keeps below 7% regardless spring directions and junction configurations (6.7% for RY in T2), which already supposes a significant error improvement with respect to the original deviation in beam type structural models, which can reach up to 90% according to [19].…”

“…Using the same data from [19] the experimental design for the neural network analysis had a five dimensional input and six dimensional output, where the input values represented the dimensions of the analyzed T-junction profiles (E1, E2, E3, g1, and g2) and the output values represented the calculated stiffness values for the alternative T-junction model having 3 axial spring (k ux , k uy , k uz ) and 3 rotational springs (k rx , k ry , k rz ) at the junction level as presented in Figure 3.…”

“…This T-junction introduces a total of six elastic elements at the joint level, three of them behaving as linear springs (represented by the letter k) and noted with the sub index ux, uy, and uz corresponding to (u) displacement and (x, y, z) the axial directions and another three corresponding to (r) rotations along the (x, y, z) axial directions. This approach was also used by [19], in which multiple simulations utilizing the most common profiles found in buses and coaches upper structures were performed, followed by a statistical analysis in order to obtain regression models for the calculation of the stiffness values for the alternative T-junctions, based on the profile dimensions (E1, E2, E3, g1, and g2). They utilized a Bayesian Kriging regression model that provided satisfactory results, however, the regression equations obtained were notably complicated having, in some cases, more than 33 terms per equation, making them impractical for everyday use in the wide industry.…”

“…Taking into consideration the benefits of the implementation of neural networks for finite element analysis, the authors considered of great interest the development of a methodology for the estimation of the stiffness values utilizing ANN as an alternative to the utilization of Bayesian Kriging regressions similar to those utilized in [19], that provided satisfactory results although not realistic from the practical point of view due to the complexity of the obtained equations. In fact, ANNs have been used as a valid alternative to such Kriging networks in various articles for the creation of metamodels [25,26] providing very satisfactory results.…”

A Quantitative Validation Method of Kriging Metamodel for Injection Mechanism Based on Bayesian Statistical Inference

“…Choi et al [27] addressed the epistemic uncertainty in a structural reliability analysis using the Bayesian kriging approach, which treats the probability as a random variable and establishes the probability density function (PDF) of the limit state function with favorable accuracy. Romero et al [28] applied a kriging interpolator that includes Monte Carlo computation of Bayesian inference and sensitivity analysis to predict the values of the elastic elements that correspond to an alternative beam T-junction model for optimizing the behaviors of the upper structures of buses and coaches. Belligoli et al [29] employed a Bayesian calibration of a computational fluid dynamics (CFD) model and the kriging metamodel of a real process to quantify the epistemic uncertainty of ultrasonic flow meter measurements in non-ideal flow conditions.…”