Sensitivity Analysis For The Structural System With The Fuzzy Uncertainty

In engineering practice,there are various uncertainties in the properties of material,geometry of systems and applied loads.Investigating the effects of these uncertainties on the output performance of the structural systems is of great significance for predicting the structural behavior,developing reasonable risk evaluation and reliability model.At present,the research on random uncertainty has been more complete,while the research about fuzzy uncertainty needs to be further studied.This paper,therefore,develops the theory of global sensitivity analysis for structural systems with the fuzzy uncertainty,which can provide useful information for the engineering design and optimization.The detailed contents and innovations are listed below:1)For structural systems with random uncertainty of input variables and fuzzy uncertainty of its distribution parameters,the propagation of uncertainties from the fuzzy distribution parameters to the statistical characters of output is investigated.According to this,the fuzzy effect index,which is used to measure the contribution of distribution parameters on statistical characters of output,is constructed based on the area difference between the membership functions.In consideration of time demanding calculation by using traditional Monte Carlo method,the Extended Monte Carlo method and Rejection Sampling method are proposed to calculate efficiently.2)In order to evaluate the effect of fuzzy distribution parameters on the statistical characters of output better,the fuzzy distance index is proposed as a global sensitivity measure.On the basis of the definition of the distance between interval numbers,the distance between fuzzy numbers is defined and proved,and then the fuzzy distance index is brought forward according to the distance difference between the membership functions.For reducing the computational cost,the UT-based Kriging surrogate method and UT-based space partition method are proposed,which solve computation efficiency problem well when traversing fuzzy membership level and deterioration of accuracy problem due to large parameter dispersion or highly nonlinear function.3)Considering the inevitable nested loops and multiple optimization process in the fuzzy computation,the possibility-probability transformation is used to solve the sensitivity analysis problem efficiently.According to the principles of constant amount of uncertainty and a reasonable appropriate scale,uncertainty invariance transformation method is put forward,which realizes the inverse transformation between fuzzy membership function and random density function.And then the consistency of the importance rankings before and after transformation is verified via a large number of different types of examples.This shows that the use of uncertainty invariance transformation method can effectively reduce the computational cost and obtain accurate importance ranking for sensitivity analysis with fuzzy uncertainty.4)In consideration of the facts,such as only insufficient information is allowed,inputs and model change with spatial and time and so on,the sensitivity analysis of dynamic model with mixed inputs is studied.Treating the uncertain static inputs as independent random variables,the dynamic inputs as Gaussian processes,the moment independent index is brought forward to measure the influence of the static and dynamic inputs on model output.Here,the infectious diseases problem is applied to perform the value of this sensitivity measure in real life.