A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures

• A hybrid identification method to deal with both measurement noise and model uncertainty.
• The measurement noise from the experiment is described by a set of random variables.
• The each uncertain parameter of a structure model is treated as an interval.
• A posterior probability density distribution strip enclosed by two bounding distributions.
• Successful applications in thermal property identification and load identification.

The hybrid inverse method based on Bayesian approach and interval analysis is presented for parameter identifications under uncertainty, which can deal with both measurement noise and model uncertainty. The measurement noise from an experiment may be described by a set of random variables, obeying a certain probability distribution. The each uncertain parameter of a structure model may be treated as an interval, and only the bounds of the uncertainty are needed. Because of the existence of the interval parameters, a posterior probability density distribution strip enclosed by two bounding distributions is then formed, rather than a single distribution that we usually obtain through the Bayesian identification for a deterministic structure. Using an interval analysis method, a structure response with small uncertainty levels can be approximated as a linear function of the interval parameters. A monotonicity analysis is adopted for marginal posterior distribution transformation, through which effects of the interval parameters on the posterior distribution strip can be well revealed. Based on the monotonicity analysis, finally, the mean estimates and confidence intervals of the unknown parameters are identified from the posterior distribution strip. Three numerical examples are investigated, and fine numerical results are obtained.