Nonparametric Risk Assessment of Gas Turbine Engines

Abstract

The accuracy associated with risk assessment of gas turbine engine components is highly dependent on the statistical models used to represent the fundamental random variables. Although parametric models are commonly used to represent the random variables, they are often a poor fit near the tails of the distributions. Also, they may not address some of the general relationships among multiple random variables (e.g., multimodality, skewed discontinuities, among others). In this paper, a nonparametric approach is used to model the probability densities associated with rainflow stress pair data for actual military aircraft engine usages. The data are represented using univariate and multivariate Epanechnikov kernels where the window width is adaptively adjusted to address the number of data points in all regions of the distributions. A brief summary of the nonparametric adaptive kernel density estimator is presented including details regarding a specific algorithm. Algorithm performance is illustrated for standard parametric probability density functions and for rainflow stress pairs associated with military aircraft engine usage histories. The results can be applied to fracture risk prediction of gas turbine engine components subjected to complex usages.

Probabilistic Mission Identification of Aircraft Engine Usage Using Nonparametric Density Estimation Techniques

“…As shown in Fig. 2, the probability density at a given location can be estimated as the sum of the contributions of the kernels associated with each data point [3]:…”

“…This statistical characterization of mission usage would also be valuable for forecasting the impact of anticipated changes in the mission mix for both legacy aircraft and new aircraft. To facilitate such forecasting an approach has been developed that formulates the probability density functions (PDFs) for each mission using a non-parametric estimation procedure [3]. This non-parametric approach is more flexible than traditional parametric approaches (e.g.…”

“…The method, called Probabilistic Mission Identification (PMI), predicts the most likely mission type based on volume integration of the region common to both the flight history and the standard mission. A nonparametric adaptive kernel method [3][4][5] is used to address the modeling challenges commonly associated with rainflow stress densities.…”