## 5 Reliability Analysis  
One of the relevant analyses of structures is also the assessment of the reliability of structures. In this paper, we deal with static and probabilistic analysis of the base plate. The probabilistic analysis, in this case, was calculated using FEM in the ANSYS program, where the RSM method (response surface method) was used as an optimization method, which, unlike the Monte Carlo method, requires fewer simulations. In our case, we had 500 iterations set. The individual input parameters to the probabilistic analysis vary according to the Gaussian distribution. In this case, one output parameter was set, which changed depending on two or four input parameters. The two input parameters entered were soil elastic modulus _E_s1_ and _E_s2_. Quantities were characterized by probability density (PDF), distribution function (CDF), and a histogram. Both types and distributions of individual input and output parameters are given in Table 1, and shown in Figure 7. It can be seen from Figure 7 that the moduli of elasticity of the soils _E_s1_ and _E_s2_ have a Gaussian distribution. \begin{table}
\begin{tabular}{c c c c} \hline
**Input Variable** & **Deterministic** & **Distribution** & **Variable Range** \\ \hline _E_s1_ (GM) & 70,000 & GAU & \(0.04\times 70\),000 \\ _E_s2_ (SC) & 10,000 & GAU & \(0.05\times 10\),000 \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristics of input variables for probability analysis. Figure 5: (a) Deformation (m) of the surface of the elastic half-space; (b) Contact stress (kPa) under the base plate. Figure 6: (a) Specific bending moment m\({}_{x}\) (kNm/m); (b) Specific bending moment m\({}_{y}\) (kNm/m). The distribution is characterized by probability density (PDF), distribution function (CDF), and described by the histogram in Figure 7. According to the CDF (cumulative distribution function, Figure 8 on the right) we can determine the probability of the corresponding parameter \(W\_MAX\) (maximum deformation value). The probability, that the maximum deflection is greater than 43 mm, indicates that the design is unreliable at \(8.48\times 10^{-2}\). The evaluation of the probability sensitivity is based on the evaluation of the mutual relations between all random input parameters and any output parameter. According to the user's specification, Spearman's degree, correlation coefficient, or Pearson linear correlation coefficient can be used. To plot the sensitivity of a given particular random output parameter, the random input variables are divided into two groups, i.e., those that are significant (important) and those that are insignificant (not important) for that output parameter. Plotting the sensitivity graphs of a given output parameter will contain only significant random input parameters (Figure 9). Figure 8: (a) Histogram of the output parameter \(W\_MAX\); (b) CDF function of the output parameter \(W\_MAX\). Figure 7: (a) Probability density (PDF) and distribution function (CDF) divisions of input variable \(E\_s1\); (b) PDF and CDF divisions of input variable \(E\_s2\). The four input parameters entered were soil elastic moduli _E_s1_ and _E_s2_ and Poisson soil numbers _mi_s1_ and mi_s2. Quantities were characterized by probability density (PDF), distribution function (CDF) and a histogram. The division of _E_s1_ and _E_s2_ was according to Figure 7, _mi_s1_ and _mi_s2_ are shown in Figure 10.  
Types and distributions of individual input parameters are given in Table 2 and the output parameters are shown in Figures 7 and 10. In Figure 10 we can see that the Poisson constants of the soils have a Gaussian distribution. The probability of the corresponding output parameter _W_MAX_ can also be determined according to the CDF (cumulative distribution function, Figure (b)b). In this case, if four input parameters are entered into the calculation, the design probability is \(7.83\times 10^{-2}\) unreliable, for the output parameter the maximum deflection is greater than 43 mm.