A Methodology of Design for Fatigue using an Accelerated Life Testing Approach with Saddlepoint Approximation 2019-01-0159
We present a new Accelerated Life Testing (ALT) methodology along with a design for fatigue approach, using Gaussian or non-Gaussian excitations. In both cases, the input uncertainty is propagated analytically to the output of the system. For the non-Gaussian case, a new random vibration method using Polynomial Chaos Expansion (PCE) is being deployed. The accuracy of fatigue life prediction at nominal loading conditions is affected by model uncertainty (system model and fatigue model error) and material uncertainty (such as the coefficients of the S-N curve). This uncertainty is reduced by performing tests at higher loading level. This reduces the test duration. The uncertain parameters are expressed through distributions with known mean and standard deviation. Based on the data obtained from experiments, we formulate an optimization problem to calculate the Maximum Likelihood Estimator (MLE) values of the uncertain model parameters. In our proposed ALT method, we lift all the assumptions on the type of life distribution or the stress-life relationship and we use Saddlepoint Approximation (SPA) method to calculate the respective PDFs. Then, we calculate the confidence intervals for the parameters using their local Fisher information matrix. The number of conducted experiments depends on the allowable variance of the predictions. After the uncertain parameters have been estimated, in the design for fatigue approach an RBDO process is developed to optimize the system’s characteristics (model parameters, fatigue and/or material properties) while subjected to probabilistic constraints. This optimization problem will determine optimal values of system parameters to achieve a fatigue reliability target. Our goal is to minimize the cost of testing while improving the accuracy of fatigue life prediction, and design structures which are both economic and reliable. The developed methods have wide practical applications in structural reliability, accelerated testing, design for lifecycle cost, preventive maintenance strategies, and fatigue reliability, among others. We will demonstrate all developments using a representative example.