A Bayesian collocation method for static analysis of structures with unknown-but-bounded uncertainties

This paper proposes a Bayesian collocation method (BCM) for static analysis of structures with unknown-but-bounded uncertainties (or interval uncertainties). Unlike the existing collocation methods which construct surrogate model using preselected samples at fixed points, the BCM chooses samples sequentially and adaptively. Based on Bayesian inference theorem, the BCM constructs a crude Gaussian process surrogate model of structural response with selected samples. Then two acquisition functions named upper expected improvement (El_UP) function and lower expected improvement (EL_LO) function are defined simultaneously to guide the selection of next samples. The samples will be collocated to the place where extrema of structural response are most likely to be found. The procedure will repeat until the convergence criterion is met. The extrema of the selected samples can be regarded as structural response bounds. Fewer samples are needed compared with existing collocation methods. Two numerical examples are used to demonstrate the accuracy and efficiency of the proposed method. The results are compared with those obtained by existing methods. The application of the method is performed by an engineering example. The results show the validity of the proposed method. (C) 2018 Elsevier B.V. All rights reserved.