A probabilistic method is presented for modelbased prognosis of crack growth under variable amplitude loading. Experiment is conducted to simulate a throughthickness crack growth of a panel that undergoes near constant as well as large variable amplitude loading during the cycles. Visual inspection is taken periodically to measure the crack length. In the experiment, several uncertainties are encountered due to the material and geometric variances, infrequent inspection and measurement noises. Bayesian approach is employed to account for this, which is to estimate the crack growth model parameters conditional on the provided measurements, and to predict the future growth in the probabilistic way. For numerical implementation, Particle Filter method is used to characterize the distribution in the form of random samples. The advantages of the method are: it favorably predicts the crack retardation and acceleration under the variable amplitude loading, and it captures the individual difference of each crack growth due to the variability even with the identical specimen and conditions. Several specimens are tested to demonstrate this. Two models with one being the classical Paris and the other the Huang model are employed to examine the importance of choosing proper physics model in the prognosis. Keywords-prognostics and health management (PHM); model-based prognositcs; bayesian inference; particle filter; variable amplitude loading; crack growth

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In this study, crack growth in a center-cracked plate is predicted under mode I variable amplitude loading, and the result is validated by experiment. Huang's model is employed to describe crack growth with acceleration and retardation due to the variable loading effect. Experiment is conducted with Al6016-T6 plate, in which the load is applied, and crack length is measured periodically. Particle Filter algorithm, which is based on the Bayesian approach, is used to estimate model parameters from the experimental data, and predict the crack growth of the future in the probabilistic way. The prediction is validated by the runto-failure results, from which it is observed that the method predicts well the unique behavior of crack retardation and the more data are used, the closer prediction we get to the actual run-to-failure data.

Bayesian formulation is presented to address the parameters estimation under uncertainty in the crack growth prediction subjected to variable amplitude loading. Huang's model is employed to describe the retardation and acceleration of the crack growth during the loadings. Model parameters are estimated in probabilistic way and updated conditional on the measured data by Bayesian inference. Markov Chain Monte Carlo (MCMC) method is employed for efficient sampling of the parameter distributions. As the model under variable amplitude loading is more complex, the conventional MCMC often fails to converge to the equilibrium distribution due to the increased number of parameters and correlations. An improved MCMC is introduced to overcome this failure, in which marginal PDF is employed as a proposal density function. A center- cracked panel under a mode I loading is considered for the feasibility study. Parameters are estimated based on the data from specimen tests. Prediction is carried out afterwards under variable amplitude loading for the same specimen, and validated by the ground truth data.

A Planetary gear can transmit high torque ratio stably and, therefore, the gear is widely used in industrial applications, i.e., wind turbines, automobiles, helicopters. Unexpected failure of the planetary gear results in substantial economic loss and human casualties. Extensive efforts have been made to develop the fault diagnostic techniques of gears; however, the techniques are mostly concerned about spur gears. This is mainly because understanding of complex dynamic behaviors of a planetary gear is lacking, such as multiple gear contacts, non-stationary axis of rotation, etc. This study thus proposes model-based fault diagnostics for a planetary gear that is based upon its dynamic analysis. Instead of vibration signals, this study uses transmission error (TE) signals for fault diagnostics of the planetary gear because TE signals (a) are directly related to the dynamic behaviors of gear mesh stiffness and (b) increase as damages on a gear mesh reduce the gear mesh stiffness. A lumped parameter model was used for modeling dynamic behaviors of the planetary gear. For more precise modeling, mesh phase difference–between sun, ring, and planet gear– and contact ratio were taken into account in the lumped parameter model. After acquiring transmission error signals from the model, order analysis and data processing were executed to generate health related data for the planetary gear. Consequently, it is concluded that the use of transmission error signals helps gain understanding of complex dynamic behaviors of the planetary gear and diagnose its potential faults.