Multi-axial load spectrum extrapolation method for fatigue durability of special vehicles based on extreme value theory

[Display omitted] •A method for multi-axial load spectrum extrapolation based on extreme value theory is proposed for the first time.•The interaction between the internal damage of the structure with the external load spectrum is established for the equivalent synthesis of the multi-axial loading spectrum.•The Bayesian-based distribution parameter estimation method is developed to improve the deficiencies of maximum likelihood estimation methods and to avoid the issue of computational costs.•The grey relational analysis (GRA) is employed to determine the optimal threshold, which weakens the subjective factors and makes it easier for program implementation. A method for the multi-axial load spectrum extrapolation based on extreme value theory has been proposed herein, for the first time to the best of our knowledge. The relationship between the internal damage of the structure with the external multi-axial load spectrum is first established prior to extrapolation. The multi-axial load spectrum is then equivalently synthesized into a uni-axial load spectrum based on the interaction between the external forces and the internal stress state of the structure. The basic theory of the time-domain multi-axial load spectrum extrapolation method is developed, including (1) the multi-axial load spectrum extrapolation model establishment; (2) the optimal threshold determination based on grey relational analysis (GRA); (3) the fitting of the distribution function parameters based on the Bayesian parameter estimation method; and (4) the judgment of phase relationship between each channel of the multi-axial load spectrum. The rationality of the method proposed in this paper is verified through an application example. In the example, the multi-axial load spectrum measurement of a special vehicle is introduced, and the proposed multi-axial extrapolation method is applied. Finally, the validation of the multi-axial load spectrum extrapolation method – in terms of the characterized comparison and the durability simulation – is performed.