| Uncertainty caused by environmental effect or manufacturing error exists in practical mechanical engineering structures,the interaction among the parametric uncertainties may lead to the safety risk of structure or even failure.Therefore,more and more attention has been gradually paid to deal with the problem of uncertainty and analyze the reliability of structure.Probabilistic model is a commonly used method to measure parameter uncertainty.However,the analysis accuracy based on probabilistic model depends on a large number of the experiment data,which is frequently difficult to obtain because of the engineering constraints.The non-probabilistic convex model constructed through boundary information of structural parameters,is an effective approach to tackle the problem of uncertainty with limited sample data.The conventional non-probabilistic convex model utilizes a single convex set to measure the parametric uncertainties without considering about the distribution of the sample information.In addition,the structural design optimization based on non-probabilistic rarely combine reliability design with robust design or tolerance design.When the limited sample information has a multiple cluster or complex distribution,the Multi-Cluster Ellipsoidal Model(Multi-CEM)is used to effectively measure the parametric uncertainties in this paper,and then structural reliability analysis based on Multi-CEM is carried out.Considering about the robustness of structural reliability and tolerance design for structural dimensions,the corresponding multiple objective design optimization problems using the non-probabilistic convex model will be explored and researched respectively.The main research content of this paper as follows:(1)Structural reliability analysis using the multi-cluster ellipsoidal model is proposed in this dissertation.An expectation-maximization(EM)algorithm is adopted to perform Gaussian cluster analysis for the uncertainty samples with multi-cluster property.Then,an optimal Gaussian mixture model(GMM)can be generated for multi-cluster samples.To quantify each sample cluster,the critical elliptical contour feature of the GMM can be effectively employed to establish Multi-CEM,in which the distribution and clustering feature of uncertain samples are noticed.Meanwhile,the correlation of the uncertain variables can also be properly considered similar to the traditional ellipsoidal model.In reliability analysis,ellipsoidal models of Multi-CEM may appear various conditions.According to the additional samples generated in the overlap region,an approximate ellipsoidal model(AEM)can be established to approximate the overlap region of the case that there exists an intersection between two arbitrary components of Multi-CEM.Similar to the conventional ellipsoidal model,a ratio of the multidimensional volume between the reliability domain and the whole uncertainty domain is introduced to measure the reliability of structures.Combining the proposed Multi-CEM and Second Order Approximation Method(SOAM),the structural reliability can be efficiently and accurately computed.(2)Focusing on the issue that the robustness of the reliability of mechanical structures may be influenced by uncertainty factors,a multi-objective design optimization method for the robustness of structural reliability using non-probabilistic convex model is presented.Considering that correlative parameters and independent parameters may exist in practical structural parameters at the same time,ellipsoidal model can be used to effectively measure uncertainty of structural parameters with correlation.Interval model is introduced to describe the independent uncertain parameters,thus,the banded limit-state surface with a certain range of intervals is formed.In structural design optimization,attention is fixed on the worst limit state.First-order linear expansion is conducted for constrained performance functions around the design point,and then,sensitivity analysis is utilized to evaluate the robustness of structural reliability when the mean of uncertainty varies slightly.Considering the robustness of structural reliability,a multi-objective design optimization model using non-probabilistic convex model which is organically combined with conventional reliability-based design optimization is formulated.The micro multi-objective genetic algorithm and Sequential Optimization and Reliability Assessment(SORA)can be implemented to achieve multi-objective optimization results efficiently.(3)Considering the dimension tolerance design of structures,a multi-objective design optimization model using non-probabilistic convex model for optimizing the machining technological properties of mechanical structures is developed.Correlative parameters and independent parameters may exist in practical structural parameters at the same time.Thus,ellipsoidal model and interval model are introduced to conduct the structural design optimization under uncertainty.According to the intuitional and easily understandable mathematical form of ellipsoidal model and properties of ellipsoidal model that can reflect the correlation,a tolerance design index which can reflect the general level of tolerance can be constructed.And then,a multi-objective design optimization model can be formulated to balance structural reliability against manufacturing cost,in which optimization can be conducted for the basic size of design variables and its level of uncertainty at once.Interval model is introduced to measure the independent uncertain parameters,so that the worst limit state should be paid more attention to ensure the safety of structure.The micro multi-objective genetic algorithm can be implemented to achieve finding optimization and obtain the non-dominated solutions of the optimization model efficiently. |
