## 3 Numerical Studies
For all parameters, the line plots converge to a stationary distribution after approximately 300 iterations. The evolution of the generated samples is illustrated in Figure 4a-c, confirming the rapid convergence of parameters \(k_{1}\), \(k_{5}\), and \(\zeta_{1}\) for the three scenarios. Although not presented in this paper, similar results are obtained for the other parameters. Figure 5a-c presents the marginal posterior probability distributions of the estimation parameters \(k_{1}\), \(k_{5}\), and \(\zeta_{1}\), respectively, for the three scenarios using 6000 samples generated after convergence. Similar results were obtained for the other parameters. Note that the histograms for all parameters shows a normal distribution centered around the realistic parameter value, which means the posterior mean approximates the realistic parameter value. All parameters in Figure 5a-c do not correspond to the respective prior uniform distributions. The prior uniform distributions give equal probability to the entire parameter range, which represent the ignorance about the truth of the hypothesis before we have analyzed the current data. The posterior pdf is then dominated by the likelihood function, and the choice of the prior becomes largely irrelevant. The SCEM-UA method considers tuning the prior probability distribution of parameters towards achieving an appropriate posterior probability distribution, during each evolution. This highlights the ability of the SCEM-UA method to search good model parameter sets without any prior knowledge of the system parameters. The summarizing statistics of the posterior parameter distributions are presented in Table 3 for each scenario. Figure 4: Generated samples for the three estimation parameters (\(k_{1},k_{5}\), \(\zeta_{1}\)): (**a**) Case 1: 0% noise + Full Outputs; (**b**) Case 2: 10% noise + Full Outputs; (**c**) Case 3: 10% noise + Partial Outputs. Figure 5: Marginal posterior probability distributions of the three estimation parameters (\(k_{1}\), \(k_{5}\), \(\zeta_{1}\)): (**a**) Case 1: 0% noise + Full Outputs; (**b**) Case 2: 10% noise + Full Outputs; (**c**) Case 3: 10% noise + Partial Outputs. Naturally, estimates of the parameters obtained using the partial measurements are less precise. A marked decrease in accuracy can also be observed when the measurement error is increased. In partial measurements and noise polluted scenarios, Table 3 shows relative errors to be a little higher, ranging from 0.24 to 2.63%, indicating a considerable measurement uncertainty (insufficient observations with errors). The damping parameters are poorly estimated, as it has small influence on the overall response generally. Hence, estimates for a damping coefficient based on measured time-domain responses may contain large uncertainties depending on the noise content in the observed data. The identified parameter set cannot be a single reliable value set due to uncertainties that persist during measurement, and therefore, should be represented with a posterior probability distribution. Secondly, to compare the SCEM-UA methodology performance with other global optimization algorithms, such as GA, PSO, BB-BC, and SCE-UA, parameter identification for a 10-DOF structural system, used by [PERSON] et al. [5] as a benchmark model for structural parameter estimation, is presented and structure properties are given in Table 4. In this example, **M**, **C**, and **K** are unknown. White Gaussian noise with the RMS of the force scaled to 1000 N is chosen as input force loading at the 5 th floor. Acceleration measurement data at floors 1, 2, 4, 6, 8, and 10 are available in the unknown mass case. Parameter estimation of the model with 10% noise scenario is investigated for the sake of comparison. The SCEM-UA algorithm was implemented with q = 30 complexes including 20 points in each complex. The estimation parameter sets are tabulated in Table 4. The prior uniform information is assumed.