## Appendix B  
Important topics pertaining to the use of the LHS technique in bridge design with correlated parameters and the validation of the suggested CAE ANN approach are covered here. _On the small databases and applied LHS technique_  
The lack of data (small databases) is a problem in many engineering disciplines, especially in those where observed phenomena are complex and related experiments are very costly because of the size of the specimens. However, small databases did not restrict researchers in these fields in the past to model phenomena with statistical approaches,where multi-dimensional functional relationships were assumed. Models were not always the best, but the main problem did not lie in number of parameters but rather in the complex relationships between them (see, for example, the determination of ultimate drift for RC columns, provided by [PERSON] [38], and later by Eurocode 8 [39], compared to the better CAE ANN model [30]). It turns out that the properly designed CAE ANN model always yields better results than existing statistical models. Moreover, predicted results accompanied by proposed measures (local standard deviation and/or percentiles, density of data, etc.) provide additional information on the quality of the prediction. Other CAE ANN models from the field of metallic materials also confirm that conclusion--that the application of CAE ANN models in real production confirms all the expected results (i.e., improvement in yield in steel production [40], influence of the human factor in the quality of production [41], etc.). In the application of LHS, it was assumed that 26 samples represent strong base cases. Note that bridge design demands many iterations from many participants (engineers, architects, investors, regulators) before coming to a final design. Therefore, in LHS implementation, additional samples were generated around each original sample, taking into account LHS principles. By doing this, the main correlations between samples were preserved (the mean of each basic sample is still the same), while additional samples simply enabled better generalization between the data points in multi-dimensional problem space. Moreover, by taking into account epistemic and aleatory uncertainties, the proposed CAE ANN model became more robust by \"smoothing\" the predicted solutions, which basically represents the mean values of the output parameters under consideration. Predicted percentiles (which are calculated locally), on the other hand, enable design engineers to obtain an estimation of the variability of actual prediction (see Equation 8). The authors believe, based on previous experience with similar problems, that such an application of the LHS method is reasonable and justified. _On the validation of the proposed CAE ANN approach_  
We are searching for a smoothness parameter that controls the \"smoothness\" of the solution during the \"learning\" phase of CAE ANN. In essence, the \"leave-one-out\" technique is used in an iterative process to establish this parameter. This implies that one sample is predicted using the other samples, and the process is repeated for every sample in the database, excluding the one that is being considered. In this manner, even with small datasets, proper validation can be obtained. Note that the practical applicability of conventional ANN models is usually limited. We found that the smoothness parameter corresponding to the smallest error (which represents the sum of the squares of the differences between the predicted and actual values of the output data) yields results that are often unusual and do not correspond to or confirm the engineering perception of the phenomenon. At the expense of a small increase in the smoothness parameter (and thus an increase in the error by a maximum of a few %) we obtained significantly more robust and \"smooth\" solutions to the problem. Such solutions in cases for which analytical results exist as solutions to differential equations are very similar to the solutions of CAE ANN models.