Probabilistic damage tolerance analysis using adaptive multiple importance sampling

icaf2023 Tracking Number 11

The continued operational safety (COS) of commercial and military fleets relies highly on Probabilistic Damage Tolerance Analysis (PDTA) tools to effectively assess and manage the risk of structural failure. PDTA enables risk assessment and management by calculating single-flight-probability-of-failure (SFPOF). The SFPOF of an aircraft component is challenging to compute due to its small probability, typically 10-7 or less. Traditionally, it is calculated with limitations on the number of random variables and assumptions on fracture mechanics that may affect the confidence in the SFPOF estimate. Furthermore, these limitations and assumptions inhibit the use of the latest developments in fracture mechanics modeling, structural health monitoring, material modeling, and manufacturing due to the absence of efficient probabilistic methods to successfully calculate the fleet risk. Under Federal Aviation Administration (FAA) sponsorship, our team has been developing a risk assessment computer code, SMART|DT, for aircraft structures that can account for the variability of important parameters such as material properties, usage, inspection probability of detection, and build quality. This presentation will focus on an Adaptive Multiple Importance Sampling (AMIS) method that provides 5 to 6 orders of magnitude improvement in computational efficiency for performing comprehensive PDTA. The most fundamental aspect of AMIS is that it will detect the important values for each variable that contribute the most to the SFPOF. In addition, since the probability-of-failure is needed at multiple flight hours (say every 500 hours) to assessing risk, a mixture density is developed across all times requested by the user that is a weighted mixture of densities. The AMIS method presented here, allows one to consider more realistic fracture mechanics models and a larger number of random variables than has been previously possible. It enables one to use this methodology not only for the COS of aircraft fleets; but also for applications such as digital twin modeling, virtual testing, and other new applications. Two real-case scenario examples are presented to demonstrate the accuracy and efficiency of the AMIS method using a comprehensive set of random variables. The examples demonstrate how AMIS can be applied to fleet management of aircraft fleets.