Research On The Reliability And Sensitivity Analysis Of Structural Systems Under Consideration Of Fuzzy Uncertainty

Traditional structural reliability and sensitivity analysis is based on the theory of the probability.The probability density function of the geometric composition,material performance and external load of the structure of aeronautics and astronautics aircraft is estimated by enormous sample data.Because of the cost limit in practical engineering,the probability density function is difficult to estimate accurately.Since the limitations exsited in the random reliability method and sensitivity analysis with lacked statistical data,the research of the paper mainly contains the time-dependent reliability theory,safety life model analysis under the required failure possibility constraint for structure,the efficiency algorithm to solving the safety life based on Kriging meta-model and global sensitivity analysis method for multivariate output based on the fuzzy Hausdorff distance.Main contents and innovations are summarized as follows:?1?For measuring the safety degree of the structure under the fuzzy uncertainty in the given time interval,the time-dependent failure possibility?TDFP?is proposed based on the possibility theory of the safety measure.Since the structural failure is defined as the performance function of the structure which is less than zero,the TDFP is defined as the possibility of the performance function which is less than zero under the fuzzy uncertainty in the given time interval,and it is measured by the supremum of the membership of the performance function locating in the failure domain in the given time interval.When the membership level of the performance function is larger than the TDFP,the structure always locates in the safe domain in the given time interval,thus the defined TDFP is reasonable to measure the time-dependent safety degree under the fuzzy uncertainty.For evaluating the proposed TDFP,the double-loop nested optimization method is established firstly,but the computational cost of the double-loop nested optimization method is too huge to solve the problems in practical engineering.Thus,a single-loop optimization method which transforms the estimation of the TDFP to the time-independent failure possibility by the extreme value is established to save the computational cost.?2?For ensuring safety service of structure under fuzzy uncertainty,an efficient approach for safety life analysis under the safety requirement is proposed.Considering the widely used failure possibility of structure involving fuzzy uncertainty as the safety measure index,the safety life under the required failure possibility constraint is defined as the upper boundary of the service time interval,over which the actual time-dependent failure possibility?TDFP?is less than the target failure possibility.As the upper boundary of the service time interval is less than the safety life,the actual TDFP of the structure is also less than the target failure possibility to ensure the safe operation of the structure.Furthermore,the direct dichotomy method and the equivalent constraint method?ECM?are established to solve the safety life.Since solving the safety life under the required failure possibility constraint is the inverse process of solving TDFP over the specified service time interval,moreover the TDFP is a non-decreasing function of the upper boundary of the service time interval,the safety life under the required failure possibility constraint can be searched by the direct dichotomy method.But the direct dichotomy method needs to calculate the TDFP at all searching points of the safety life iterately,thus the computational cost is very large.In order to decrease the computational cost of solving the safety life,the corresponding ECM is established.The key of ECM is that the constraint of the actual TDFP is equivalently transformed to that of the lower boundary of the minimum of the output response,through which the computational cost of solving the safety life is greatly reduced.The equivalence between the constraint of the actual TDFP and that of the lower boundary of the minimum of the response function is strictly proved by the reduction to absurdity.The solutions of the safety life based on the ECM are also established.?3?For reducing the cost of computation of safety life of structural system involving the fuzzy uncertainty in the complicated engineering,the function relationship between the lower bound of extreme response of the structural system at ?_ft^*-cut?target failure possibility?and the time variable t is approximated by the adaptive Kriging meta-model,which transform the solution of the safety life under the required failure possibility to the solution of zero point of the meta-model.The above meta-model method requires the optimization of the lower bound of the extreme response,in order to further improve the computation efficiency of safety life,the adaptive Kriging meta-model of the dynamic response which is used to approximate with time-dependent performance function is proposed.The Kriging meta-model of the function relationship between the lower bound of extreme response and the time variable t and the dynamic response is constructed by adopting reasonable learning function and the stopping criterion.Compared with the direct dichotomy method combined with ECM,the computational cost of safety life is greatly reduced by two meta-models.?4?For measuring the effects of the model fuzzy inputs on the performance of the model outputs,the global sensitivity index?GSI?based on fuzzy vector Hausdorff distance is proposed.In the proposed GSI,the Hausdorff distance between the conditional model outputs while the fuzzy input is fixed and the unconditional model outputs is used to measure the difference due to the fixed fuzzy input and the global sensitivity index evaluating the effects of the fuzzy input on the model outputs is established by the weighted average of the difference while the fuzzy input screening its value region.Furthermore,the proposed GSI is extended to the condition that the distribution parameters of random inputs have fuzzy uncertainty,and measures the effects of fuzzy distribution parameters on the statistical characters of random model output.Finally,the efficient solution strategy to evaluate the effects of the fuzzy distribution parameters on the mean of the model outputs is established,by combing the unscented transformation with the kriging meta-model.