Reliability measure approach considering mixture uncertainties under insufficient input data

Abstract

目的 可靠性优化需要精确度量含不确定性变量的系统可靠性。然而, 工程实践中往往不能获取充足的样本数据计算 可靠性指标, 因此本文针对不完备数据下的系统可靠性度量开展研究。 创新点 1. 提出了随机变量、稀疏变量以及区间变量混合不确定性下的可靠性度量方法; 2. 本方法可以推广到p-box 和 证据理论变量等不确定性变量。 方法 1. 建立不完备数据下的失效概率函数; 2. 基于中间辅助变量实现失效概率的一致性计算; 3. 针对数据不完备前 提下失效概率自身也是不确定性变量的问题, 对失效概率指标进行敏感度分析; 4. 将提出的失效概率计算方法 推广到p-box 变量、多模态分布变量以及证据理论变量; 5. 采用经典函数案例验证方法的有效性, 并将方法应 用于锻压机的可靠性分析。 结论 1. 不完备数据下的系统可靠性存在较大的不确定性; 2. 通过中间辅助变量可以精确分析混合不确定性下系统的 失效概率, 确定失效概率的随机分布特性; 3. 提出的方法可以用较少的计算时间获得准确的可靠性结果; 4.本 文方法可以扩展到更多不确定性类型的可靠性分析, 辅助混合不确定性优化设计。 Reliability analysis and reliability-based optimization design require accurate measurement of failure probability under input uncertainties. A unified probabilistic reliability measure approach is proposed to calculate the probability of failure and sensitivity indices considering a mixture of uncertainties under insufficient input data. The input uncertainty variables are classified into statistical variables, sparse variables, and interval variables. The conservativeness level of the failure probability is calculated through uncertainty propagation analysis of distribution parameters of sparse variables and auxiliary parameters of interval variables. The design sensitivity of the conservativeness level of the failure probability at design points is derived using a semi-analysis and sampling-based method. The proposed unified reliability measure method is extended to consider p -box variables, multi-domain variables, and evidence theory variables. Numerical and engineering examples demonstrate the effectiveness of the proposed method, which can obtain an accurate confidence level of reliability index and sensitivity indices with lower function evaluation number.