Unified uncertainty analysis under probabilistic, evidence, fuzzy and interval uncertainties

Lü

Numerical Meth Engineering

2022

For addressing the low efficiency of structural reliability analysis under the random‐interval mixed uncertainties (RIMU), this paper establishes the line sampling method (LS) under the RIMU. The proposed LS divides the reliability analysis under RIMU into two stages. The Markov chain simulation is used to efficiently search the design point under RIMU in the first stage, then the upper and lower bounds of failure probability are estimated by LS in the second stage. To improve the computational efficiency of the proposed LS under RIMU, the Kriging model is employed to reduce the model evaluation numbers in the two stages. For efficiently searching the design point, the Kriging model is constructed and adaptively updated in the first stage to accurately recognize the Markov chain candidate state, and then it is sequentially updated by the improved U learning function in the second stage to accurately estimate the failure probability bounds. The proposed LS under RIMU with Kriging model can not only reduce the model evaluation numbers but also decrease the candidate sample pool size for constructing the Kriging model in two stages. The presented examples demonstrate the superior computational efficiency and accuracy of the proposed method by comparison with some existing methods.

Section: Example 3: a Frame Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient method for estimating failure probability bounds under random‐interval mixed uncertainties by combining line sampling with adaptive Kriging

Lü

Numerical Meth Engineering

2022

“…However, the uncertain parameters with insufficient information tend to be generalized, so the method is not universal. Long et al (2019) proposed a unified framework for uncertainty analysis under probability, evidence, fuzzy and interval uncertainties, by which the quantities with sufficient data, sparse data and subjective information can be simultaneously considered. More uncertain distributions will aggravate the complexity and difficulty of analysis, and some parameters between different distributions cannot be clearly defined.…”

Section: Introductionmentioning

confidence: 99%

Based-restraining interval extension improved truncation algorithm for response analysis of uncertain mechanical systems

Liu

et al. 2021

Purpose This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function. Design/methodology/approach To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed. Findings The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results. Originality/value Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

Numerical Meth Engineering

“…[10][11][12][13][14][15] In engineering practice, random and epistemic uncertainties often exist simultaneously. 16 This article focuses on hybrid RBDO under random and epistemic uncertainties, where random and epistemic uncertainties are, respectively, described by probability theory and interval model. In hybrid RBDO under random and interval uncertainties (HRBDO-RI), the reliability of constraints is often estimated by hybrid reliability analysis methods.…”

Section: Introductionmentioning

confidence: 99%

A new hybrid reliability‐based design optimization method under random and interval uncertainties

Zhang

Gao

Xiao

2020

Summary This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI.