Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method

For the system with the fuzzy failure state, the effects of the input random variables and the fuzzy failure state on the fuzzy probability of failure for the structural system are studied, and the moment-independence global sensitivity analysis（GSA） model is proposed to quantitatively measure these effects. According to the fuzzy random theory, the fuzzy failure state is transformed into an equivalent new random variable for the system, and the complementary function of the membership function of the fuzzy failure state is defined as the cumulative distribution function（CDF） of the new random variable. After introducing the new random variable, the equivalent performance function of the original problem is built. The difference between the unconditional fuzzy probability of failure and conditional fuzzy probability of failure is defined as the moment-independent GSA index. In order to solve the proposed GSA index efficiently, the Kriging-based algorithm is developed to estimate the defined moment-independence GSA index. Two engineering examples are employed to verify the feasibility and rationality of the presented GSA model, and the advantages of the developed Kriging method are also illustrated.

Non-probabilistic Hydraulic Turbine Blade Vibration Reliability Research Based on Fuzzy Failure Criterion

In hydraulic turbine engineering,turbine blade vibration reliability assessment is of great significance. Based on the interval mathematical theory, the variables existing in hydraulic turbine blade are described as interval variables. Considering the fuzzy failure criterion of turbine blade distancing from resonance and vibration fatigue stress,fuzzy possibilistic reliability is expressed and analyzed qualitatively taking normal bathtub function as the membership function of blade resonance failure and deflection major type function as the membership function of the intensity failure. As a result,hydraulic turbine blade vibration reliability is analyzed based on the fuzziness of variables and failure criterion. A safer working environment is provided under possibility context by comparing with the qualitative conclusions in the past literature.

FUZZY FAILURE ANALYSIS OF COAL PILLARS FOR SUBSIDENCE CONTROL

Randomness and fuzziness involved in rock failure analysis are discussed in the present paper.Fuzzy stochastic process is introduced to simulate pillar/strata deformation process.Study shows that the evolution from damage to failure of the rock materials under complex stress environments conforms to diffusion process.Coal pillar strength is analyzed using fuzzy failure analysis in two coal mines.

A FUZZY MODEL FOR THE FAILURE OF COMPOSITE STRUCTURES

In this paper, the fuzzy theory is used to describe the uncertainty in failure definition of composite structures. The concept of structural failure level (SFL) is suggested and a method of evaluation is presented.

Fuzzy Random Reliability Analysis of Blocky Rock-Mass in Slopes

Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of them is ignored. In this paper, a fuzzy probability approach and a fuzzy JC method are presented for the reliability analysis. The two methods have been applied to stability analysis of a certain slope of permanent ship lock in the Three-Gorges Project. The results obtained from these two methods are basically the same. However, compared with the fuzzy probability means, the fuzzy JC method can reflect the real situation better because it uses a fuzzy-based analysis applied to not only limit state equation but also mechanical parameters.

Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.

Moment Method Based on Fuzzy Reliability Sensitivity Analysis for a Degradable Structural System

For a degradable structural system with fuzzy failure region, a moment method based on fuzzy reliability sensitivity algorithm is presented. According to the value assignment of performance function, the integral region for calculating the fuzzy failure probability is first split into a series of subregions in which the membership function values of the performance function within the fuzzy failure region can be approximated by a set of constants. The fuzzy failure probability is then transformed into a sum of products of the random failure probabilities and the approximate constants of the membership function in the subregions. Furthermore, the fuzzy reliability sensitivity analysis is transformed into a series of random reliability sensitivity analysis, and the random reliability sensitivity can be obtained by the constructed moment method. The primary advantages of the presented method include higher efficiency for implicit performance function with low and medium dimensionality and wide applicability to multiple failure modes and nonnormal basic random variables. The limitation is that the required computation effort grows exponentially with the increase of dimensionality of the basic random vari- able; hence, it is not suitable for high dimensionality problem. Compared with the available methods, the presented one is pretty competitive in the case that the dimensionality is lower than 10. The presented examples are used to verify the advantages and indicate the limitations.