Probabilistic Modeling and Risk Analysis

Emc² staff have studied different types of flaws (corrosion thinning, through-wall and surface cracks, mechanical damage, etc.), multiple site and multiple element damage of aging aircraft, and high temperature creep-fatigue assessment of engine components including turbine blades in life-extension studies for our clients. The piping and pipe component fracture efforts at Emc² have involved different flaw orientations (axial, circumferential, and helical for spiral-welded pipe), crack initiation and crack propagation evaluations including natural crack growth.

In 1984, under contract to NASA Lewis Research Center, developed the probabilistic load model for the space shuttle main engines. This model accounted for eleven different loading sources, including pressure, temperature, vibration, and acoustics. The result of that work provided a model to NASA that included the random nature of the engine loadings in an expert system code to calculate the effect of design changes and mission history profiles on the SSME loadings at critical engine components.

In 1989-94, the first probabilistic damage tolerant analyses and inspection evaluation of the Shuttle Training Aircraft (STA) under contract to NASA Johnson Space Center was performed. The STA is a modified Gulfstream II aircraft used to train astronauts to land the space shuttle. Because of the unique structural configuration and the nonstandard flight profiles used during training, significant uncertainty existed about the damage accumulation in the structure.
A team of researchers placed damage tolerant methods in a probabilistic mechanics framework to account for material property and loading variability. The team also designed an instrumentation plan, installed strain gages, and took load measurements from the aircraft. By combining the data on loads and material behavior in a probabilistic model the damage tolerant level was determined with confidence levels. The probability of detecting the damage during an inspection was investigated to allow NASA to schedule inspections more efficiently. In the case of the STA, inspection intervals were changed resulting in a savings of 9,700 labor hours while maintaining the aircraft above the NASA-defined fail safe level with 95% confidence.

NASA had planned to send an unmanned robotic system to Mars which would collect soil samples for return to Earth. Because the soil had to be treated as a biohazard NASA was required to demonstrate that the Earth Entry Vehicle (EEV), which was to be made of a carbon-carbon fiber composite, was able to re-enter the atmosphere and land, with any parachute system, and not fail with a probability less than 1 in 1,000,000. In this case failure was defined as the release of a 2 micron or larger particle. Because the failure criterion was explicitly stated in probabilistic terms staff from Emc² developed a probabilistic structural model combined with fast probability integrators to determine the probability of structural failure. Because the proposed material had yet to be manufactured the uncertainties in the material properties were too large to achieve the stated goal. However, the results could be used to determine where additional material property tests were need to reduce this uncertainty and thus focus future resource in the areas where the reduction of risk would be the greatest.

Emc² led the development of the probabilistic mechanics code to analyze the progression of damage due to fatigue, inter-granular stress corrosion cracking, and primary water stress corrosion cracking. Initially developed for the U.S. Nuclear Regulatory Commission (NRC), it was subsequently upgraded through an internationally sponsored program and released as PROLOCA (PRObabilistic Loss Of Coolant Accident) 3.0. This code the served as the basis for the joint government (NRC) and industry (Electric Power Research Institute) code xLPR (extremely Low Probability of Rupture) 1.0. Because of the code’s basis and importance it is being further developed by a second international program to produce PROLOCA 4.0. The primary advance for PROLOCA 4.0 is the new adaptive sampling methodology. This sampling technique allows the code to perform importance sampling as the calculations are being made. Sandia National Laboratories has evaluated this methodology and conclude that it can calculate probabilities on the order of 1 in 1,000,000 with 50,000 or fewer simulations