Sensitivity analysis and calibration of phenomenological models for seismic analyses

Phenomenological models used in seismic structural analyses are often based on parameters without explicit physical meaning, which must be calibrated by fitting experimental responses. Parameter calibration, as an inverse problem, may suffer from ill-posedness, and thus the results are always to be critically examined before accepting them. In this paper, a comprehensive methodology, comprising repeated optimisation runs, local and global sensitivity analysis and simplified uncertainty analysis is described with the aim of providing some guidelines to assess the calibration results. As exemplary case study, the calibration of a phenomenological model for steel members by means of a series of experimental tests is presented. The experimental response of nominally identical beams tested under monotonic, cyclic and pseudo-dynamic loading were used in the pro-cedure. The main findings of the work indicate that the optimisation process based on Genetic Algorithms is able to find optimal solutions in terms of fidelity to the experimental tests: However, being the problem ill-posed, the same level of fitting may be attained by solutions characterised by different model parameters. Local and global sensitivity analyses may help assess the identifiability of the parameters, while a-posteriori uncertainty analysis provides an estimation of the uncertainty in the prediction. It is shown that increasing the number of calibration tests may reduce the ill-conditioning of the problem, and thus a multi-objective approach is strongly re-commended. Finally, a novel procedure recently developed based on tolerance-based Pareto dominance is shown to give similar results to those provided by computationally expensive sensitivity analyses at the computational cost of a single calibration analysis.