An efficient numerical method to solve inverse fuzzy-uncertain viscoelastic problems of identification

When there exists fuzzy uncertainty in experimentally determined information, viscoelastic constitutive parameters to be identified are treated as fuzzy variables, and a two-stage strategy cooperating with particle swarm method is presented to identify membership functions of fuzzy parameters. At each stage, inverse fuzzy problem is formulated as a series of alpha-level strategy-based inverse interval problems, which are described by optimization problems and are solved utilizing particle swarm method. Forward interval analysis required in inverse interval analysis is conducted by solving two optimization problems via modified coordinate search algorithm. To alleviate heavy computational burden, dimension-adaptive sparse grid (DSG) surrogate is embedded in optimization process. The surrogate is constructed on a solid platform of high fidelity deterministic solutions, which is provided by scaled boundary finite element method and temporally piecewise adaptive algorithm. Eventually, membership functions of fuzzy parameters can be obtained by fuzzy decomposition theorem with interval bounds acquired at each of alpha-sublevels. Parallelization is realized for construction of DSG surrogate and implementation of particle swarm method for a further computation reduction. Numerical examples are provided to illustrate effectiveness of proposed approach, where regional inhomogeneity and impact of measurement points selection on identification results are explored.