Mechanical Reliability Analysis, Response Surface Method

As the first developed surrogate of implicit limit state equation, polynomial Response Surface Method (RSM) still plays an important role in reliability analysis in present. Although the developments of modern informatics and mathematics introduce some new methods, e.g. support vector machine and neural network, which show more advantage in reliability analysis of the implicit limit state, there exist many basic unsolved projects in these newly developing methods same as in the conventional polynomial RSM. Therefore this thesis devotes to the research of the conventional RSM, and the main contributions are listed as follows.(1) A new weighted linear RSM is presented. By constructing more reasonable weight, the most probable point (MPP) of the actual implicit limit state can be found quickly and robustly, and the efficiency of the RSM is improved consequently.(2) Through the combination of cumulative use of experimental points and weighted regression method, a weighted nonlinear RSM is presented. In contrast to the defect of linear RSM, where the non-linearity of the real limit state, cannot be taken into consideration, the weighted non-linearity RSM can account for the nonlinearity of the implicit limit state in some degree and result in improvement of the fitting precision. Cumulative use of experimental points and reducing the number of new experimental points in subsequent iteration also improve the efficiency of the weighted nonlinear RSM. Three possible forms of weight are compared and their applicable ranges are pointed out respectively. At the same time, a new index which can evaluate the dispersion degree of experimental points is presented, to help the selection of the reasonable weight in the weighted nonlinear RSM.(3) Based on the conventional RSM, an advanced RSM with high precision is presented. By use of the iterative strategy of linear fitting, the experimental points used in determining the response surface (RS) in the presented method are chosen closer to the actual limit state equation than that in the conventional RSM. On the other hand, by controlling the distance between the surrounding experimental points and the center experimental point, the experimental points can provide more information about the MPP of the actual limit state equation as the center experimental point converges to the actual MPP gradually. Therefore the actual limit state equation can be fitted very better by the improved experimental points, and the evaluation precision of the failure probability is increased. As this method is used in conjunction with the weighted RSM, it can improve the efficiency and precision further.(4) A new method for selecting experimental points is presented on the basis of interpolation. And a new RSM named as interpolation RSM is presented as well. In the presented method, the possibility of extrapolation, which exists in the conventional RSF, is avoided. Comparing to the conventional RSM, the computational cost and the computational complexity of the interpolation RSM are not increased, on the contrary, the fast convergence resulting from the closer experimental points to the real limit state equation improves the efficiency of the interpolation RSM.(5) Based on the unified fuzzy-random reliability model, an improved fuzz-random reliability model is proposed by taking a variable with fuzzy uncertainty and random uncertainty simultaneously into consideration. The form and the distribution parameters of equivalent probability density function are derived for the variable possessing the fuzzy uncertainty and the random uncertainty simultaneously.(6) The RSM of the random reliability is extended to the analysis of the fuzzy-random reliability, and the general RSM is presented. For the reliability analysis with fuzzy state, a piecewise RSM is presented to improve the precision of the fuzzy reliability estimation.