Discussions on non-probabilistic convex modelling for uncertain problems

Abstract

Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To overcome the complexity and diversity of the formulations of current convex models, in this paper, a unified framework for construction of the non-probabilistic convex models is proposed. By introducing the correlation analysis technique, the mathematical expression of a convex model can be conveniently formulated once the correlation matrix of the uncertain parameters is created. More importantly, from the theoretic analysis level, an evaluation criterion for convex modelling methods is proposed, which can be regarded as a test standard for validity verification of subsequent newly proposed convex modelling methods. And from the practical application level, two model assessment indexes are proposed, by which the adaptabilities of different convex models to a specific uncertain problem with given experimental samples can be estimated. Four numerical examples are investigated to demonstrate the effectiveness of the present study.

Reliability-based Design Optimization of Structures with Disturbed Design Variables and Dependent Uncertainties

“…The key step of solving equation ( 2) is to resolve the dependent uncertainties. MP model was proposed to deal with the coexist of dependent and independent uncertain variables, and MP-II model was considered to be the best one [19]. Therefore, in this section, MP-II model in [19] is used to construct the uncertainty domain in engineering structural design, and in this way, the correlation between uncertain variables can be handled.…”

“…MP model was proposed to deal with the coexist of dependent and independent uncertain variables, and MP-II model was considered to be the best one [19]. Therefore, in this section, MP-II model in [19] is used to construct the uncertainty domain in engineering structural design, and in this way, the correlation between uncertain variables can be handled. The idea of MP-II model is to use a multi-dimensional parallelogram to enclose all the sample values of uncertain variables.…”

Interval uncertainty analysis of a confined aquifer

“…The use of deterministic, large-well method calculations similarly do not rule out the effects of changes in hydrogeological conditions. Starting from the uncertain boundary, and combining with the non-probability set theory convex model method 19 – 21 , the equation for calculating the water inflow with upper and lower limits can be derived. From the initial deterministic, simple large-well method, to the consideration of uncertain parameter variation fused with the large-well method, the uncertain factors in the calculation can be expressed in the form of interval change, and integrated into the calculation 22 .…”

Non-Probabilistic Time-Varying Reliability-Based Analysis of Corroded Pipelines Considering the Interaction of Multiple Uncertainty Variables

“…The interval model and the ellipsoid model are the most widely used in the field of non-probabilistic reliability. The interval model can only deal with independent variables, while the ellipsoid model can deal with problems involving dependent variables [18,19]. Thus, the modeling method of the ellipsoid convex set model is applied to practical engineering involved interaction research [20].…”