Uncertainty analysis of a structural–acoustic problem using imprecise probabilities based on p-box representations

• P-box representation is used to treat the uncertainty of structural–acoustic system.
• A first-order matrix decomposition perturbation method (FMDPM) for interval analysis is proposed.
• An efficient interval Monte Carlo method based on FMDPM is derived.
• The practical engineering application of the proposed method is investigated.

Imprecise probabilities can capture epistemic uncertainty, which reflects limited available knowledge so that a precise probabilistic model cannot be established. In this paper, the parameters of a structural–acoustic problem are represented with the aid of p-boxes to capture epistemic uncertainty in the model. To perform the necessary analysis of the structural–acoustic problem with p-boxes, a first-order matrix decomposition perturbation method (FMDPM) for interval analysis is proposed, and an efficient interval Monte Carlo method based on FMDPM is derived. In the implementation of the efficient interval Monte Carlo method based on FMDPM, constant matrices are obtained, first, through an uncertain parameter extraction on the basis of the matrix decomposition technique. Then, these constant matrices are employed to perform multiple interval analyses by using the first-order perturbation method. A numerical example is provided to illustrate the feasibility and effectiveness of the presented approach.