The uncertainty in parameter estimation arises from structural systems’ input and output measured errors and from structural model errors. An experimental verification of the shuffled complex evolution metropolis algorithm (SCEM-UA) for identifying the optimal parameters of structural systems and estimating their uncertainty is presented. First, the estimation framework is theoretically developed. The SCEM-UA algorithm is employed to search through feasible parameters’ space and to infer the posterior distribution of the parameters automatically. The resulting posterior parameter distribution then provides the most likely estimation of parameter sets that produces the best model performance. The algorithm is subsequently validated through both numerical simulation and shaking table experiment for estimating the parameters of structural systems considering the uncertainty of available information. Finally, the proposed algorithm is extended to identify the uncertain physical parameters of a nonlinear structural system with a particle mass tuned damper (PTMD). The results demonstrate that the proposed algorithm can effectively estimate parameters with uncertainty for nonlinear structural systems, and it has a stronger anti-noise capability. Notably, the SCEM-UA method not only shows better global optimization capability compared with other heuristic optimization methods, but it also has the ability to simultaneously estimate the uncertainties associated with the posterior distributions of the structural parameters within a single optimization run.

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Due to the uncertainties originating from the underlying physical model, material properties and the measurement data in fatigue crack growth (FCG) processing, the prediction of fatigue crack growth lifetime is still challenging. The objective of this paper was to investigate a methodology for uncertainty quantification in FCG analysis and probabilistic remaining useful life prediction. A small-timescale growth model for the fracture mechanics-based analysis and predicting crack-growth lifetime is studied. A stochastic collocation method is used to alleviate the computational difficulties in the uncertainty quantification in the small-timescale model-based FCG analysis, which is derived from tensor products based on the solution of deterministic FCG problems on sparse grids of collocation point sets in random space. The proposed method is applied to the prediction of fatigue crack growth lifetime of Al7075-T6 alloy plates and verified by fatigue crack-growth experiments. The results show that the proposed method has the advantage of computational efficiency in uncertainty quantification of remaining life prediction of FCG.

This chapter introduces a novel swarm-intelligence-based algorithm named the comprehensive learning particle swarm optimization (CLPSO) to identify parameters of structural systems, which is formulated as a high-dimensional multi-modal numerical optimization problem. With the new strategy in this variant of particle swarm optimization (PSO), historical best information for all other particles is used to update a particle's velocity. This means that the particles have more exemplars to learn from and a larger potential space to fly, avoiding premature convergence. Simulation results for identifying the parameters of a five degree-of-freedom (DOF) structural system under conditions including limited output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness are presented to demonstrate improved estimation of these parameters by CLPSO when compared with those obtained from PSO. In addition, the efficiency and applicability of the proposed method are experimentally examined by a 12-story shear building shaking table model.