Figure - available from: Mathematical Problems in Engineering
This content is subject to copyright. Terms and conditions apply.
Source publication
![An automobile frame structure [35].](publication/338968483/figure/fig4/AS:1084253903302657@1635517683050/An-automobile-frame-structure-35_Q320.jpg)
![An automobile frame structure [35].](publication/338968483/figure/fig5/AS:1084253903298562@1635517683106/An-automobile-frame-structure-35_Q320.jpg)
In practical engineering problems, the distribution parameters of random variables cannot be determined precisely due to limited experimental data. The hybrid uncertain model of interval and probability can deal with the problem, but it will produce extensive computation and it is difficult to meet the requirement of the complex engineering problem...
Citations
... In recent decades, various methods for analysing p-box uncertainties in theoretical and practical respects (Matthias et al. 2021) have been proposed, and these approaches are mainly classified as discrete methods, sampling methods, surrogate modelling methods and statistical moment methods. Discrete methods are mainly used for simple calculations between p-boxes, such as addition, subtraction, multiplication and division (Regan et al 2004;Xiao et al. 2020). By such methods, p-boxes are discretized into evidence structures, and Cartesian operations and interval analyses can be used to compute the output result. ...
Various epistemic uncertainties arise in practical engineering problems. In this paper, probability boxes (p-boxes) are used to unify multiple types of epistemic uncertainty, which include intervals, p-boxes and evidence variables. A collaborative interval quasi-Monte Carlo method (CIMCM) is presented to calculate the probability bounds of a model. The interval-based quasi-random sampling technique is applied to sample a range of intervals from unified input p-boxes. An interval that includes all random intervals is constructed. Rosen’s gradient projection method (RGPM) is utilized to solve the extreme output values of the numerical model based on the enveloping interval. A collaborative optimization method is presented to calculate the extreme values of the numerical model, the input variables of which are a range of intervals. The probability bounds of the model are finally computed by a statistical method. The presented method reduces the number of repeated search iterations for a range of optimization problems that include many overlapping domains. Two numerical examples and two engineering cases are investigated to demonstrate the effectiveness of the CIMCM.
... Liu et al. [12] constructed probability box model based on maximum entropy principle and provided a corresponding hybrid reliability analysis approach. By combining the traditional finite element method, Xiao et al. [13] proposed a vertex-based uncertainty propagation method to improve the performance of IMC based on the monotonicity and vertex analysis. Ghosh and Olewnik [14] improved the DLS by replacing the inner loop with sparse grid numerical integration and replacing the outer loop with optimization algorithms. ...
In the response analysis of uncertain structural models with limited information, probability-boxes can be effectively employed to address the aleatory and epistemic uncertainty together. This paper presents a copula-based uncertainty propagation method which can accurately perform uncertainty propagation analysis with correlated parametric probability-boxes. Firstly, the parameter estimation and Akaike information criterion analysis are utilized to select an optimal copula based on available samples, by which the joint cumulative distribution function is constructed for the correlated input variables. Then, using the obtained joint cumulative distribution function, the correlated parametric probability-boxes are transformed into independent normal variables, and an efficient method based on sparse grid numerical integration is proposed to calculate the bounds on statistical moments of a response function. Finally, numerical examples and an engineering application are provided to verify the effectiveness of the presented method.
