Fong Jeffrey T, Heckert N Alan, Filliben James J, Marcal Pedro V, Freiman Stephen W
National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
J Res Natl Inst Stand Technol. 2021 Dec 7;126:126036. doi: 10.6028/jres.126.036. eCollection 2021.
Three types of uncertainties exist in the estimation of the minimum fracture strength of a full-scale component or structure size. The first, to be called the "model selection uncertainty," is in selecting a statistical distribution that best fits the laboratory test data. The second, to be called the "laboratory-scale strength uncertainty," is in estimating model parameters of a specific distribution from which the minimum failure strength of a material at a certain confidence level is estimated using the laboratory test data. To extrapolate the laboratory-scale strength prediction to that of a full-scale component, a third uncertainty exists that can be called the "full-scale strength uncertainty." In this paper, we develop a three-step approach to estimating the minimum strength of a full-scale component using two metrics: One metric is based on six goodness-of-fit and parameter-estimation-method criteria, and the second metric is based on the uncertainty quantification of the so-called A-basis design allowable (99 % coverage at 95 % level of confidence) of the full-scale component. The three steps of our approach are: (1) Find the "best" model for the sample data from a list of five candidates, namely, normal, two-parameter Weibull, three-parameter Weibull, two-parameter lognormal, and three-parameter lognormal. (2) For each model, estimate (2a) the parameters of that model with uncertainty using the sample data, and (2b) the minimum strength at the laboratory scale at 95 % level of confidence. (3) Introduce the concept of "coverage" and estimate the fullscale allowable minimum strength of the component at 95 % level of confidence for two types of coverages commonly used in the aerospace industry, namely, 99 % (A-basis for critical parts) and 90 % (B-basis for less critical parts). This uncertainty-based approach is novel in all three steps: In step-1 we use a composite goodness-of-fit metric to rank and select the "best" distribution, in step-2 we introduce uncertainty quantification in estimating the parameters of each distribution, and in step-3 we introduce the concept of an uncertainty metric based on the estimates of the upper and lower tolerance limits of the so-called A-basis design allowable minimum strength. To illustrate the applicability of this uncertainty-based approach to a diverse group of data, we present results of our analysis for six sets of laboratory failure strength data from four engineering materials. A discussion of the significance and limitations of this approach and some concluding remarks are included.
在估算全尺寸部件或结构尺寸的最小断裂强度时存在三种不确定性。第一种，称为“模型选择不确定性”，在于选择最适合实验室测试数据的统计分布。第二种，称为“实验室规模强度不确定性”，在于根据实验室测试数据估算特定分布的模型参数，据此估算材料在一定置信水平下的最小失效强度。为了将实验室规模的强度预测外推到全尺寸部件的强度预测，存在第三种不确定性，可称为“全尺寸强度不确定性”。在本文中，我们开发了一种三步法，使用两个指标来估算全尺寸部件的最小强度：一个指标基于六个拟合优度和参数估计方法标准，另一个指标基于全尺寸部件所谓A基准设计许用值（95%置信水平下99%的覆盖率）的不确定性量化。我们方法的三个步骤如下：(1) 从五个候选分布，即正态分布、双参数威布尔分布、三参数威布尔分布、双参数对数正态分布和三参数对数正态分布中，为样本数据找到“最佳”模型。(2) 对于每个模型，估算(2a) 使用样本数据带有不确定性的该模型参数，以及(2b) 在95%置信水平下实验室规模的最小强度。(3) 引入“覆盖率”的概念，并针对航空航天工业中常用的两种覆盖率，即99%（关键部件的A基准）和90%（不太关键部件的B基准），估算部件在95%置信水平下的全尺寸许用最小强度。这种基于不确定性的方法在所有三个步骤中都是新颖的：在步骤1中，我们使用综合拟合优度指标对“最佳”分布进行排名和选择；在步骤2中，我们在估算每个分布的参数时引入不确定性量化；在步骤3中，我们基于所谓A基准设计许用最小强度的上下公差极限估计引入不确定性指标的概念。为了说明这种基于不确定性的方法对不同数据集的适用性，我们展示了对来自四种工程材料的六组实验室失效强度数据的分析结果。本文还包括对该方法的意义和局限性的讨论以及一些结论性评论。
