Abstract
To avoid the shortages and limitations of probabilistic and non-probabilistic reliability model for structural reliability analysis in the case of limited samples for basic variables, a new imprecise probability model is proposed. Confidence interval with a given confidence is calculated on the basis of small samples by gray theory, which is not depending on the distribution pattern of variable. Then basic probability assignments and focal elements are constructed and approximation methods of structural reliability based on belief and plausibility functions are proposed in the situation that structure limit state function is monotonic and non-monotonic, respectively. The numerical examples show that the new reliability model utilizes all the information included in small samples and considers both aleatory and epistemic uncertainties in them, thus it can rationally measure the safety of the structure and the measurement can be more and more accurate with the increasing of sample size.
Highlights
In reliability assessment of a structure, some factors, such as the complexity of internal mechanism, the limitation of people’s knowledge and errors in manufacturing, will produce a variety of uncertainties
Fuzzy reliability model is having the aid of statistical method to obtain membership function, which is similar with probabilistic reliability model
The Basic Probability Assignments (BPAs) are constructed and structural reliability is calculated by evidence reasoning
Summary
In reliability assessment of a structure, some factors, such as the complexity of internal mechanism, the limitation of people’s knowledge and errors in manufacturing, will produce a variety of uncertainties. The motivation of this study is constructing a new imprecise probabilistic reliability model to evaluate structure reliability with insufficient experimental data using evidence theory and gray theory, in which gray theory is used to estimate the confidence interval of experimental data. The Basic Probability Assignments (BPAs) are constructed and structural reliability is calculated by evidence reasoning.
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