Uncertainty Characterization Methods for Sparsely Sampled Quantity: A Tradeoff Analysis Considering Propagation

• Published in: AIAA journal 2020-07, Vol.58 (7), p.3129-3138
• Main Authors: Yang, Qiang, Han, Guokai, Xie, Weihua, Meng, Songhe, Jin, Hua
• Format: Article
• Language: English
• Subjects: Composite materials; Constitutive models; Extreme values; Mathematical models; Methods; Propagation; Reliability; Uncertainty
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/1.J058449

The reliable characterization of uncertainties is critical for system evaluations and safety designs. However, insufficient samples are frequently encountered especially in composite materials. Four characterization methods for sparsely sampled quantities (SSQs) were discussed in the current study, including extreme value (EV) interval, tolerance interval (TI), optimized kernel density estimation (KDE), and the Dempster–Shafer (D-S) theory. Two different problems, a Sandia challenge function and a constitutive model for C/SiC composites, are considered for method evaluations. Performances of different methods are evaluated regarding reliabilities and errors in the output quantity derived with the uncertainty propagation. A manufactured solution method is employed. Results show that the TI, KDE, and D-S methods converge to the true distribution with increasing samples, whereas the EV method tends to expand the uncertainties. Under small samples (≤18), the TI method exhibits the highest reliability, and the KDE method exhibits the smallest error. Under extremely small samples (≤3) the D-S method offers a balance between reliability and error. The TI method can apply well in the constitutive model for the characterization of material uncertainties, where failure is of high consequence and conservatism is emphasized. The obtained results are general and can be employed in the future material characterization with experimental data.