This paper investigates the application of discrete probability distribution (DPD) methods [1, 2] to probabilistic assessments of structural integrity in aging systems. Two domains are examined: aging aircraft structures and natural gas pipelines. These applications differ markedly in nondestructive evaluation (NDE) methods, which vary significantly in cost and capability to detect small cracks.In aging aircraft analysis, damage tolerance approaches—standard in most aircraft structural integrity programs—typically assume the presence of an initial flaw (often modeled as a through-wall crack for conservative crack growth projections). This assumption enables evaluation of remaining life and inspection intervals to prevent unstable propagation. In contrast, for aging natural gas pipelines, failure is generally defined at the onset of a through-wall crack (leading to leakage or rupture), necessitating distinct models for crack initiation, growth, and instability, as well as tailored inspection strategies (e.g., in-line tools).The paper focuses on explaining the theoretical foundations of the DPD method and its application to refine the joint probability density function (joint PDF) of relevant random variables. This improved joint PDF serves as input to a machine learning program for enhanced uncertainty quantification, risk prediction, or surrogate modeling in probabilistic fracture mechanics contexts. Results to date indicate that the parameters governing DPD accuracy and the time to first crack instability are separable from other factors (e.g., material properties, loading spectra). This separability simplifies sensitivity analyses and computational requirements. Furthermore, a dynamic (time-dependent) analysis is essential, as these parameters evolve with the age of the structure due to cumulative fatigue, environmental effects, or changing inspection performance.
[1] S. Kaplan, "On The Method of Discrete Probability Distributions in Risk and Reliability Calculations - Application to Seismic Risk Assessment," Risk Analysis, vol. 1, no. 3, pp. 189–196, 1981.
[2] R. E. Kurth and D. C. Cox, "Discrete Probability Distributions for Probabilistic Fracture Mechanics," Risk Analysis, vol. 5, no. 3, pp. 235–240, 1985.