Rotating machinery prognostics: State of the art, challenges and opportunities

The gamma process is a natural model for degradation processes in which deterioration is supposed to take place gradually over time in a sequence of tiny increments. When units or individuals are observed over time it is often apparent that they degrade at different rates, even though no differences in treatment or environment are present. Thus, in applying gamma-process models to such data, it is necessary to allow for such unexplained differences. In the present paper this is accomplished by constructing a tractable gamma-process model incorporating a random effect. The model is fitted to some data on crack growth and corresponding goodness-of-fit tests are carried out. Prediction calculations for failure times defined in terms of degradation level passages are developed and illustrated.

Covariates and random effects in a gamma process model with application to degradation and failure.

Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty

Stochastic prognostics for rolling element bearings

Uncertainty quantification and model validation of fatigue crack growth prediction

: A statistical investigation of the fatigue crack propagation process was conducted. Sixty-eight replicate constant amplitude crack propagation tests were conducted on 2024-T3 aluminum alloy. The following distributions were considered: two-parameter normal distribution, three-parameter log-normal distribution, three-parameter Weibull distribution, two-parameter gamma distribution, three-parameter gamma distribution, the generalized three- parameter gamma distribution, and the generalized four-parameter gamma distribution. From the experimental data, the distribution of N as a function of crack length was best represented by the three-parameter log-normal distribution. Six growth rate calculation methods were investigated and the method which introduced the least amount of error into the growth rate data was found to be a modified secant method. Based on the distribution of da/dN, which varied moderately as a function of crack length, replicate a vs. N data were predicted. This predicted data reproduced the mean behavior but not the variant behavior of the actual a vs. N data.

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The Statistical Nature of Fatigue Crack Propagation

This investigation incorporates the development and control of microstructure and properties into a computer aided design/computer aided manufacturing (CAD/CAM) environment for materials design. An integrated computer model has been developed which predicts the microstructure and properties based on the material processing and the material composition. The material processing includes the extrusion parameters and the aging conditions employed during heat treatment. The material being utilized as a demonstration medium is a special precipitation hardenable aluminum-lithium-zirconium (Al-Li-Zr) alloy which has been direct-chill (D.C.) cast and direct extruded. A model has been developed based on a series of quantitative transmission electron microscopy (TEM) investigations to predict microstructure from the composition and material processing. This model, referred to as the microstructural model, provides the basis for the overall CAD/CAM model for materials design. Also included is an analysis of the microstructural mechanisms that contribute to the strengthening of precipitation hardened alloys that contain shearable precipitates. A number of existing models regarding particle shearing and looping mechanisms in precipitation hardened systems were evaluated regarding their suitability in describing the Al-Li aging and strengthening behavior. These analytical models are incorporated with the microstructural model to make theoretical predictions for the critical resolved shear strength.

B. M. Hillberry

Papers

The Statistical Nature of Fatigue Crack Propagation

Integration of Microstructural Development and Properties Design Into the CAD/CAM Environment