Structural Reliability Research Based On Dimensionality Reduction Algorithm

A structure may be affected by some uncertain factors in practical engineering,such as the material properties,the geometry,the strength,the loads and so on.It is very important to deal with the uncertain variables reasonably for the structural reliability analysis.In traditional reliability analysis,the uncertain variables can be described by probabilistic model.However,the uncertain variables need a great amount of samples to identify the distribution type they comply with and to define their corresponding probabilistic density functions.And a little error may lead to the pseudo results.Non probabilistic model does not need that so many samples as the probabilistic model and a simple uncertain model can be built to analyze the structure effectively.For complicated structures in practical,there are usually multiple failure modes with mixed uncertain variables,which need structural system reliability model to solve.Mean while,different kinds of variables may have different effects and have different sensitivities.In this dissertation,based on the dimensionality reduction algorithm,the probabilistic structural reliability analysis model and the model with subjective and objective mixed uncertain variables and its simplified model were constructed.Moreover,the structural system reliability analysis model,combining the Taylor expansion method with probabilistic network evaluation technique,was constructed.Meanwhile,the structural reliability sensitivity analysis model corresponding to the simplified model was built.To some extent,the present computing method of the structural reliability analysis was enlarged.This dissertation has following work:1.Structural probabilistic reliability analysis model based on dimensionality reduction algorithm was proposed.For the situation that the structural performance functions maybe implicit or may have high-dimensional nonlinear properties in the complicated structures,combining the dimensionality reduction algorithm with the Edgeworth series method,a new structural reliability model was proposed.Numerical examples testified the advantages of the method,which did not need to solve the performance functions' derivatives and did not need to search the(Most Probable Failure Point,MPP),but with a high precision for the structural analysis.2.Subjective and objective mixed reliability analysis model based on dimensionality reduction algorithm was proposed.In practical structures,the uncertain parameters may have both the subjective and the objective uncertain properties,which can be described,respectively,by the random variables,the interval variables and the fuzzy variables,corresponding to different reliability analysis model.This model not only can be used in random-fuzzy-interval structural reliability analysis,but also can be used in random-interval or random-fuzzy ones.The situation of concluding both the subjective and the objective variables is considered,overcoming the single traditional probabilistic model or the single non probabilistic model's limits.And the expansion of the interval operations is avoided.A new direction is supplied for the present subjective and objective mixed reliability analysis.3.Under the base of studying the random-interval variables,based on the dimensionality reduction algorithm and the probabilistic network evaluation technique,a structural system reliability analysis model was proposed,corresponding to the random-interval structural reliability analysis model.Combining the dimensionality reduction algorithm and the Taylor expansion,variables transformation,Gauss-Hermite integral method and the Edgeworth series,the failure probability intervals of every failure modes are computed.The correlation is considered,deducing the correlation coefficient formula.Using Taylor expansion to the correlation coefficient formula,the interval expressions are obtained.The interval of the reliability index of every failure mode is computed by the probabilistic network evaluation technique.The numerical examples verified the model's correctness and feasibility.4.A structural reliability sensitivity analysis model with subjective and objective mixed variables involved was proposed.Using the random-interval structural reliability model,considering the relations between the statistical moments and the reliability index of the structural performance function,obeying the function differentiation rule,after the dimensionality reduction,the sensitivity interval formulae of the original moment of the single dimension function,the original and central moments of the structural performance function,respect to the basic random variables,were deduced.And moreover,the sensitivity of the failure probability interval respect to the basic random variables was also deduced.This model supplies a new way to compute the sensitivity of the structural reliability with random-interval variables.