Fig. 1 Scatterplot of the prior samples, along with their associated normalized weights w ̂ i s , obtained from the posterior consisting of a mixture of two Gaussian distributions More

Fig. 2 Acceptance rates for the SEMC sampler: target acceptance rate values α t r = { 0.100 , 0.283 , 0.440 , 0.800 , 0.900 , 1.000 } and starting step-size values u s = 1 = { 40 , 40 , 8 , 2 , 2 , 2 } More

Fig. 3 SDoF single-storey shear frame structure subjected to Coulomb friction More

Fig. 4 Schematic diagram of the SDoF single-storey shear frame structure subjected to Coulomb friction. Image adapted from Ref. [ 43 ]. More

Fig. 5 Spring-mass representation of the SDoF single-storey shear frame structure subjected to Coulomb friction More

Fig. 6 Shear frame structure: Plots of r and ϕ for the corresponding values of F μ ( t s ) for s = { 1 , … , 4 } More

Fig. 7 Shear frame structure: Nominal evolution models Γ 1 and Γ 2 More

Fig. 8 Shear frame structure: model identification results using SEMC and SMC—mean of the log-evidence ( log   [ P ( D 1 : s | M ) ] ), and its one-sigma bounds More

Fig. 9 Shear frame structure: acceptance rates result using SEMC and SMC—mean of the acceptance rates and its one-sigma bounds. Target acceptance rate: 0.283 (i.e., see Eq. (10) ). More

Fig. 10 Shear frame structure: parameter identification of F μ ( t s ) [ N ] using SEMC and SMC—mean of F μ ( t s ) , and its one-sigma bounds More

Fig. 11 Shear frame structure: posterior sample histogram profiles of the predicted values of F μ ( t s ) [ N ] using SEMC. The black dotted vertical line denotes the true value of F μ ( t s ) at a given s. More

Fig. 12 Shear frame structure: parameter identification of ω n ( rad / s ) ,   σ ϕ ( deg ) , and σ r using SEMC and SMC has given T 1 —their corresponding means, and one-sigma bounds. The reference values for the respective parameters are: { ω ... More

Fig. 13 Shear frame structure: parameter identification of ω n ( rad / s ) ,   σ ϕ (deg), and σ r using SEMC and SMC was given T 2 —their corresponding means, and one-sigma bounds. The reference values for the respective parameters are: { ω n , σ ... More

Fig. 1 Illustration of the optimal robust design points R ( z ∗ ) (orange) for the with noise contaminated upper- and lower‐bounds y ¯ and y ¯ for a specific design parameter z i , adapted from van Mierlo et al. [ 5 ] More

Fig. 2 Illustration of the predicted mean bound Δ y gp ( z ) = y ¯ gp ( z ) − y ¯ gp ( z ) and the minimum bound based on the confidence interval Δ δ ( z ) = δ ¯ μ + σ ( z ) − δ ¯ μ − σ ( z ) , adapted from van Mie... More

Fig. 3 Illustration of the learning function for a candidate point x * , showing the MI of the lower and upper bound; here the improvement of the lower bound is negative [ 5 ] More

Fig. 4 Illustration of the stopping criteria for a GP with noise; The illustration shows that the Δ δ for both the upper and lower bound three normal distributions are drawn N ( y ¯ , σ n ) , N ( y ¯ , σ gp ) , N ( y ¯ , σ total )... More

Fig. 5 Flowchart of the robustness under lack-of-knowledge method for noisy functions More