11:20   Session 17: Probabilistic modelling and risk analysis  Chair: Michael Gorelik 11:20 20 mins Probabilistic damage tolerance analysis using adaptive multiple importance sampling Juan Ocampo, Nathan Crosby, Harry Millwater, Michael Reyer, Sohrob Mottaghi, Marv Nuss, Christopher Hurst, Beth Gamble Abstract: 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. 11:40 20 mins Probabilistic lifing of a second oversize hole modification Guillaume Renaud, Éric Dionne, Min Liao Abstract: Enlarging a hole to its second oversize is a common airframe maintenance operation. Early in the life of the Royal Canadian Air Force (RCAF) CF-188, this structural modification was seen as a confidence cut, leading to a full life reset at the enlarged hole. However, after some accumulated usage, airframe cracks may become too large to be completely removed by the cut, yet too small to be reliably detected by typical Non-Destructive Inspection (NDI) methods. As such, guidelines have been established to assume that, after a certain level of expended airframe fatigue life, a residual crack would exist at all holes that underwent a second oversize modification. However, as the CF-188 fleet approaches retirement, it appears that this conservative guideline results in likely unnecessary costly inspections for several Life Limiting Items (LLI). The National Research Council of Canada (NRC) has been tasked by the RCAF to evaluate and further develop a practical probabilistic analysis methodology proposed by the CF-188 maintenance, repair and overhaul contractor, L3Harris, to better evaluate the risk associated with second oversized holes. This probabilistic lifing method establishes a post-modification safe life by combining the probability of cracks exceeding the cut size at the modification incorporation time with the probability of crack detection associated with the selected NDI method. This updated safe life, corresponding to an acceptable cumulative probability of failure, is intended to be applied fleet-wide and was shown by NRC to be conservative for the analysis of an investigated location, LLI 855. Enhancement to the proposed method were assessed and proposed by NRC. These enhancements assume the worst case of probability of detection, include modifications to apply the method tail-by-tail, and modify the method to make it compatible with the current CF-188 risk assessment methodology. Although it needs to be tested on additional LLIs, the proposed probabilistic methodology has already been shown to be useful to reduce maintenance costs by saving a late inspection for the investigated LLI, while maintaining the risk level acceptable. 12:00 20 mins Practical application of structural risk assessment with SMART|DT Viola Ferrari, Min Liao, Michea Ferrari, Michel Guillaume Abstract: Structural risk assessments are highly relevant to assure the structural integrity over the whole life-cycle of an aircraft. The Aircraft Structural Integrity Program (ASIP) of the US Air Force introduces design guidance based on deterministic crack growth prediction for safety critical components. Today, with the increase of computational power, probabilistic methods instead of deterministic analysis can be deployed. Probabilistic Risk Assessment (PRA) offers the benefit of taking uncertainty into account and leads to less conservative estimates while meeting safety requirements. Research organizations such as the National Research Council Canada (NRC) or the Defense Science and Technology Organization in Australia (DSTO) are already assessing safety critical elements with PRA. RUAG AG is interested in the application of this method for current and future military aviation systems. Based on the research performed by these organizations, the application of PRA is assessed. The probabilistic calculations are performed with the software tool SMART|DT. Structural engineering and fatigue data is needed for such an assessment, which includes equivalent crack growth data, pre-crack size distributions (EPS), loading distributions and probability of detection (POD). The possibilities of the tool are assessed with four case studies with different data sets (amount of data, quality of data, etc.). Based on the case studies, existing methods are explored and implemented for the input data in order to perform calculations with the software SMART|DT acquisition. For better understanding PRAs and their application for the system, evaluations are performed including comparisons between various spectra, different material data and the influence of different distributions for the probability of failure. With the applied methodologies and the use of SMART|DT tool, the case studies show very conservative results compared to current crack finding during fleet inspections. The application of the tool must be assessed on a case-by-case basis depending on the available input data. The paper shows a possible application of PRAs using the available data with limited effort in the data gathering process and includes simple ways for the data preparation and application in SMART|DT based on known PRA methodologies.

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