## 2 Materials and Methods
Two data sets were created to train and validate the metamodels--artificial neural network and Kriging. As stated above, the method for obtaining the structural response of the system was the simulation using the finite element method (FEM). Due to the fact that the problem incorporates large displacements (geometrical nonlinearities), the interaction between bodies (contact), and the elastic-plastic material constitutive models (physical nonlinearities), the solution was derived using the commercial software, Abaqus/Standard [22]. The method for obtaining the new shape for FEM analysis was developed by the authors and consisted of the Python routine, which modified the Abaqus input deck based on all of the 27 optimization input parameters. These parameters are the coefficients of the radial basis  
Figure 2: The distribution of the radial basis function centers—knots. functions with fixed center positions. Based on the calculated auxiliary field values and assumed threshold, each of the finite elements was judged as active or disabled (taking into account the removal of prior numerical analysis) and a new numerical model was created. In each FEM analysis, the pinned boundary conditions were used at both ends of the shock absorber. In the first step of the simulations, the assembly loads were applied (bracket clamping and suspension spring preload). The incremental compression bumper load was applied in the second step, up to the point at which the structure is losing stability. The considered example of the optimization consisted of 27 design parameters (variables), as shown in Figure 2 with RBF knots. The sampling plan in this case must be carefully chosen, in order to not force the design matrix to be quite excessive and to cover the design space in the most efficient manner. The main limitation is the total number of function calls (simulations) that can be used to create the sampling plan. Based on the available resources and the average calculation time, the maximum number of samples could not exceed 6750. Additionally, the sampling plan was divided into a 4:1 ratio; therefore, for each four training samples, one validation sample was kept separately for further surrogate quality assessment (validation). In this case, two plans were created:  
- 5400 samples for the training set and 1350 samples for the validation set. - 1350 samples for the training set and 340 samples for the validation set. In both cases, the design matrices were independent of each other, i.e., two sampling plans were created separately for training and validation data. With the first sets ready (5400 training and 1350 validation samples), an additional small set was created to investigate the effect of sample size on the quality of the metamodel. Therefore, a new sample plan with 340 samples was used for validation purposes, whereas the previous validation set of 1350 samples was used as a training set. In total, three sampling plans were used to create two sets of data for metamodeling purposes. There are numerous sampling plans available in the literature, among which full-factorial design of experiment (DOE), fractional-factorial DOE, Latin hypercube sampling (LHS), optimal Latin hypercube sampling (OLHS), orthogonal arrays, Sobol sequences, Box-Benhken sampling, or Monte Carlo methods are commonly incorporated in literature studies. The DOE approaches force the design matrix to grow exponentially, namely, full-factorial DOE for 27 factors on two levels requires 27, i.e., over 134 million analysis runs. In addition, only extreme values of the parameters are investigated; therefore, the actual nonlinear relations for parameters within their variation range can be lost. The schematic representation of different sampling plans for a small set of 2D data is shown in Figure 3. In the case of the factorial design, a uniform spread of design points is observed, even though the projection of the samples onto the axes is sparse.