| Reliability and fatigue life estimation are important in acquisition, maintenance and operation of engineering products. Time-dependent reliability has become an important area of research in recent years, in order to design products which perform their desired function throughout their lifecycle. Without considering the reliability degradation through time, munexpected failures may occur and lifecycle cost may increase due to potential warranty costs, repairs and loss of market share. In this research, we introduce three new methods for calculating the uncertainty in the output of dynamic, linear and non-linear vibratory systems excited by Gaussian and non-Gaussian input random processes. After the calculation of output uncertainty, we estimate the time-dependent reliability as well as the probability distribution of fatigue life.;The first method we introduced, performs reliability analysis of linear vibratory systems with random parameters, excited by stationary or non stationary Gaussian random processes. We space-fill the input parameter space and for each design point, we calculate the corresponding time-dependent conditional probability of failure, using random vibration principles and an integral equation involving up-crossing and joint up-crossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities. Using this metamodel we can estimate the conditional probabilities for any set of input parameters. Finally, the total probability theorem is applied to calculate the overall time-dependent probability of failure.;The second methodology calculates the statistics of the output process of a linear vibratory system excited by non-Gaussian random processes, condisering the effects of skewness and kurtosis. The non-Gaussian processes are characterized using their first four statistical moments and a correlation structure. For the output processes, the moments and autocorrelation can be calculated analytically. A stochastic metamodel is developed for the output, to generate new trajectories without solving the system. Finally, fatigue analysis is performed and the PDF of fatigue life is calculated.;The third methodology is similar with the second, but is applicable to nonlinear vibratory systems excited by non-Gaussian random processes. The four moments and autocorrelation of output processes, are calculated using time integration of the system differential equations of motion. The time-dependent probability of failure is calculated, using a stochastic metamodel developed for the output process.;All new methodologies are demonstrated with representative examples. |
