Study Of Structural Dynamic Reliability Based On Subset Simulation Method

Engineering structures will be subjected to various kinds of stochastic dynamic actionssuch as earthquakes, wind, waves and so on in the process of construction and use. And thedynamic reliability analysis methods need to be used to evaluate the safety of the structuralsystems under these stochastic dynamic actions. The dynamic reliability is the possibility ofthe structure to complete the predetermined functions within the given time, under thespecified conditions when they subjected to random dynamic load. Only to maintain thedynamic reliability at a certain level, the structure can satisfy many kinds of function thatdesign requirement needs in the service life. Therefore, the dynamic reliability analysismethod becomes a research hotspot in the field of civil engineering.Dynamic reliability analysis method is mainly divided into three kinds as the methodbased on process over-crossing theory or diffusion process theory and stochastic simulationmethod. The poisson process method and the Markov process method represent the methodbased on process over-crossing theory. FPK equation is theoretical basic of the method basedon diffusion process theory. The Monte Carlo method and its improved methods represent thestochastic simulation method. The method based on process over-crossing theory uses someassumptions that will bring a greater impact on the calculation accuracy of the structuraldynamic reliability. The method based on diffusion process theory can get the accuratenumerically theoretical solution but only suitable in the condition of response for thediffusion process or the structure for a very small number of degrees. The stochasticsimulation method needs nothing assumption so it has a good applicability. But this method’scomputational efficiency is often low, especially in the condition of small failure probabilityor large and complex structures its computation is often difficult to accept. This thesis isdevoted to explore a stochastic simulation method that has high computational efficiency andwhose computational accuracy is guaranteed.Subset simulation method is a new method to calculate the small failure probability. Thismethod can improve the computational efficiency effectively by reducing the samples. Itscalculation principle is deeply studied in this thesis. The small failure probability problemwill be transformed into the product of a series of larger conditional probabilities by usingthis method that introduces the fault events with inclusion relationship. Then much lesssamples are needed to computer these larger conditional probabilities and this is the key thatsubset simulation method can reduce sample numbers. The samples of these larger conditional probabilities are gotten by the Markov Chain Monte Carlo sampling method inmathematical statistics when the subset simulation method is used. At last the error analysisof subset simulation method has been carried out by this thesis. From the theoreticalderivation of the coefficient of variation, the effect of the conditional probabilities’ selectingand sampling numbers’ selecting on calculation error has been summarized then relevantrecommendations about the selecting can be given.Although the subset simulation method can effectively reduce the samples, it is still timeconsuming for the large and complex structures. The time-domain explicit stochasticsimulation method and the time-domain explicit iterative stochastic simulation method areour team’s latest research results for solving the linear and non-linear dynamic reliability oflarge and complex structures. The time-domain explicit expression, which applied to solvethe structural dynamic response in order to reduce the time of a single sample’s analysis, hasbeen derived. The calculation principle of subset simulation method has been introducedbases on these two methods. Therefore, two new methods which are called time-domainexplicit subset simulation method and time-domain explicit iterative subset simulationmethod have been explored to apply to the dynamic reliability of linear structure andnon-linear structure. The advantage of these two methods is that the time-domain explicitexpression has been applied to calculate the dynamic response in the conditionalprobabilities’ analysis, they can not only reduce the sampling numbers but also reduce thetime of a single sample’s analysis so the computational efficiency of dynamic reliability hasbeen further improved. The numerical examples indicate that the computational efficiency ofproposed methods is much higher in the case of small failure probability and multiple degreesof freedom.