First excursion probability sensitivity by means of domain decomposition method

This contribution introduces a novel framework for the first excursion probability sensitivity estimation, applicable to linear dynamic systems subject to a Gaussian excitation. The proposed methodology is based on Domain Decomposition method, and the sensitivity estimator is calculated as the partial derivative of the first excursion probability with respect to a design parameter, such as the geometrical dimensions of the system. The linearity of the system plays a key role in building an efficient estimator. Domain Decomposition Method exploits this feature by exploring the failure domain in a very convenient way due to its special structure, characterized by the union of a large number of elementary linear failure domains. This approach allows the sensitivity estimator to be derived as a byproduct of the first excursion probability estimator. The effectiveness of this technique is demonstrated through a numerical example involving a large-scale model.