  In many fields of science and engineering, models with different fidelities
are available. Physical experiments or detailed simulations that accurately
capture the behavior of the system are regarded as high-fidelity models with
low model uncertainty, however, they are expensive to run. On the other hand,
simplified physical experiments or numerical models are seen as low-fidelity
models that are cheaper to evaluate. Although low-fidelity models are often not
suitable for direct use in reliability analysis due to their low accuracy, they
can offer information about the trend of the high-fidelity model thus providing
the opportunity to explore the design space at a low cost. This study presents
a new approach called adaptive multi-fidelity Gaussian process for reliability
analysis (AMGPRA). Contrary to selecting training points and information
sources in two separate stages as done in state-of-the-art mfEGRA method, the
proposed approach finds the optimal training point and information source
simultaneously using the novel collective learning function (CLF). CLF is able
to assess the global impact of a candidate training point from an information
source and it accommodates any learning function that satisfies a certain
profile. In this context, CLF provides a new direction for quantifying the
impact of new training points and can be easily extended with new learning
functions to adapt to different reliability problems. The performance of the
proposed method is demonstrated by three mathematical examples and one
engineering problem concerning the wind reliability of transmission towers. It
is shown that the proposed method achieves similar or higher accuracy with
reduced computational costs compared to state-of-the-art single and
multi-fidelity methods. A key application of AMGPRA is high-fidelity fragility
modeling using complex and costly physics-based computational models.
