Small Sample Reliability Analysis Methods And Applied Research

The small-sample reliability analyses often occur in engineering. On the basis of the availably internal and oversea researches, it is studied intensively in this thesis. The main contributions of the thesis are as follow:(1) A logarithm criterion is presented for the enumeration of the significant fatigue failure modes, which reduces the possibility of missing important fatigue failure modes. Based on the enumeration of the significant fatigue failure modes of structure system and one-sided tolerance factor, an algorithm for predicting fatigue life of complex structure system is presented.(2) Bootstrap method is firstly employed to evaluate low confidence limit of population percentile under small number of test-sample. Large number of simulation is implemented to verify the advantage of the method. A semiparameter Bootstrap method is investigated to determine low confidence limit for the reliability as well.(3) Based on the weighted least square method and Bootstrap technique, a new method is presented to estimate the three parameter P-S-N curves of fatigue life. This method considers the fact that that the variances of fatigue life logarithms are different at different stress levels, and provides the best linear unbiased estimators for the P-S-N curvers.(4) Since small size fatigue tests provide limited information for the fatigue life, conventional P-S-N curves may be inclined to be non-conservative. Currently, the confidence-survivability-stress-life (usually denoted as C-P-S-N) curves are popularly suggested to improve the believability of fatigue test estimation. A new method on the basis of Bootstrap technique is developed to determine the C-P-S-N curves under limited fatigue tests in the thesis.(5) Support vector machine (SVM) and support vector regression (SVR) are introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the First Order ReliabilityMethod (FORM) and the Monte Carlo Simulation (MCS).(6) For estimating failure probability of nonlinear implicit limit state function, support vector machine and support vector regression are presented in conjunction with weighted linear response surface method. Integrating the WLRSM with the SVM/SVR effectively, the better surrogate of the implicit nonlinear limit state function can be constructed by the SVM/SVR around the design point, and the precision of the failure probability is improved for the implicit nonlinear limit state function.(7) A support vector machine response surface method is presented to alleviate the computational effort. The SVR is employed to establish the surrogate of the implicit performance function;however, the rigid polynomial is employed in the classical Respone Surface Method. SVR model is then connected to FORM to calculate reliability index and form an iterative process.