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| A new type of non-probabilistic convex model for structural uncertainty analysis |
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Abstract The non-probabilistic convex model only requires the boundaries of structural uncertain parameters and is suitable for dealing with engineering problems with limited samples. However, the available convex models focus mainly on regular mathematical models, and thus may provide the excessive expansion of the uncertainty domain. In view of this, in this paper a new type of convex model, namely an interval and ellipsoidal intersection model, is proposed to bound the uncertainty domain, whereby the corresponding structural uncertainty propagation analysis method is investigated. Firstly, the interval and ellipsoidal intersection model is proposed to describe the uncertain domain, which can be constructed by taking the intersection of the interval model and the ellipsoidal model. Subsequently, the proposed model is applied to structural uncertainty propagation analysis, and two cases of the nonlinear response function are considered. For the weakly nonlinear response function, its linear approximation can be obtained by using the first-order Taylor series expansion, and then a semi-analytical method is developed to predict its structural response interval. For the strong nonlinear response function, its nonlinear approximation can be obtained by using the second-order Taylor series expansion, and then the Sequential Quadratic Programming (SQP) method is adopted to predict its structural response interval. Finally, the results from four numerical examples indicate that the proposed model generally offers a smaller volume of the uncertainty domain and a narrower structural response interval than the interval and ellipsoidal models; and the semi-analytical method has a higher efficiency than the Sequential Quadratic Programming (SQP) method and the Monte Carlo Simulation (MCS) method.
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Received: 09 September 2024
Published: 23 April 2025
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2025, Vol. 46 
