Uncertainty Analysis Based On Probability And Fuzzy Theory And Research On Reliability-based Topology Optimization Algorithm

The purpose of structural reliability analysis is to determine the safety performance of the engineering system under the inevitable uncertain environment,such as load fluctuation,geometric variation,material manufacturing error,etc.Due to the universality and practicability,sampling method is widely used in the reliability analysis of mechanical systems.However,it requires generating huge number of samples to ensure the computational accuracy.In this paper,the improvements in the accuracy and efficiency of reliability computation are proposed in order to tackle this difficulty.Besides,for handling the aleatory uncertainties in engineering structures,a new hybrid reliability-based topology optimization method combining fuzzy and probabilistic models is proposed.The method can effectively address the epistemic and aleatory uncertainties with the high efficient and accurate.The achievements of this paper are summarized as follows:(1)An augmented weighted simulation method is proposed.The basic idea is introducing a series of intermediate events into weighted simulation method,in which a new optimization method is constructed to reasonably determine each intermediate event.In this way,the failure event is divided to a sequence of conditional events,and the failure probability is accordingly converted to the product of conditional probabilities.Furthermore,a space reduction strategy is proposed to increase the probability of the samples generated in each conditional event,which greatly improves the sampling efficiency.(2)A maximum volume sampling model is proposed.The basic idea is constructing an ellipsoid with the maximum volume in the safe domain,and a new maximum volume optimization method is proposed accordingly.Since only the samples located outside the enveloped domain are computed,the computational efficiency is greatly improved.Moreover,the uniform sampling strategy and Givens transformation are adopted to solve the optimization method efficiently.(3)A hybrid reliability-based topology optimization method for handling epistemic and aleatory uncertainties is proposed.First,a new triple-nested reliability-based topology optimization model based on fuzzy and probabilistic theory for describing the multi-source uncertainties is established.Then,an efficient single-loop optimization method is proposed to degrade the triple-nested optimization problem into a deterministic optimization problem using the Karush-Kuhn-Tucker optimality condition.Furthermore,the sensitivities of the hybrid reliability constraint with respect to the random probabilistic variables,fuzzy variables,and deterministic design variables are derived using the adjoint variable method.Finally,a cantilever beam example,an L-shape beam design and a 3D example are tested to verify the validity of the proposed single-loop method.