结构的时变可靠度分析方法及优化设计研究

发布时间：2018-09-02 06:09

【摘要】：在外部荷载、服役环境和材料内部因素的作用下,工程结构或结构构件的强度、承载能力、可靠度随着时间发展逐渐降低,对其安全有效服役产生影响。为了保证结构服役期间的安全性,对结构进行时变可靠度分析及优化设计十分重要。结构的时变可靠度分析具有以下特点:1)外部载荷作用或性能退化规律往往用随机过程进行描述;2)极限状态方程一般具有隐式功能函数的特点;3)工程结构的可靠度问题一般涉及的是小失效概率问题;4)常用的可靠度分析方法存在计算量大、效率不高等缺点。因此只有建立完善的时变可靠度分析模型,开发高效的时变可靠度算法,才能有效地解决复杂结构时变可靠度分析及优化设计问题,满足实际工程设计的需求。针对以上问题,本文的主要研究内容和取得的成果如下:(1)考虑结构可靠性分析中普遍存在的隐式极限状态方程和小失效概率特征,提出了计算小失效概率的AK-SS方法。即,用基于少量样本点的Kriging代理模型近似真实极限状态方程,并通过主动学习方法逐步更新该模型,同时将此代理模型与子集模拟方法(subset simulation,SS)相融合,显著改善小失效概率的计算精度和效率。将AK-SS方法用于地下隧道衬砌结构的可靠度分析,得到合理结果,表明该方法对于处理工程实际结构中小失效概率问题十分有效。(2)考虑结构单调退化过程中的时间作用和冲击作用,提出了基于混合随机过程的时变可靠度分析模型。采用Gamma随机过程模拟时间作用引起的退化、Poisson随机过程描述随机冲击作用,提出更为全面的复合退化模型;将贝叶斯推理方法与时变可靠度模型相结合,利用样本信息更新模型中的不确定参数,减小了退化模型中的不确定性。该时变可靠度分析模型为工程实际结构中含有检测数据、模型不确定性的时变可靠度分析问题提供了有效方法。(3)针对结构功能函数非单调变化的情况,结合极值方法和AK-SS方法,提出了混合EGO-AK-SS时变可靠度计算方法。该方法采用混合EGO(Mixed Efficient Global Optimization)算法建立时变功能函数的Kriging极值响应面,结合AK-SS算法,逐步改善极值响应面的精度,同时计算失效概率。该方法集中了混合EGO计算效率高、AK-SS方法处理隐式小失效概率的优势,应用于简单机械结构,提高了计算效率,适合求解实际结构的时变可靠度。(4)针对含有时变概率约束的可靠度优化设计问题,提出了混合EGO-SORA时变可靠度优化设计方法。利用(3)中的混合EGO方法将时变概率约束转化为时不变形式,建立约束函数的Kriging极值响应面。采用SORA(sequential optimization and reliability assessment)方法,将可靠度优化设计转换为序列确定性优化设计及可靠度逆分析,利用当前的最可能失效点更新约束函数的Kriging极值响应面。该方法具有混合EGO方法处理时变可靠度的高精度及SORA求解可靠度优化设计的高效率的特点,应用于简单机械结构,提高了计算效率,可用于处理工程实际中的时变可靠度优化设计问题。
[Abstract]:Under the action of external load, service environment and internal factors of materials, the strength, bearing capacity and reliability of engineering structures or structural members gradually decrease with the development of time, which will affect their safe and effective service. The time-varying reliability analysis of structures has the following characteristics: 1) the external load action or the performance degradation law is often described by stochastic process; 2) the limit state equation (LSE) generally has the characteristics of implicit function; 3) the reliability problem of engineering structures generally involves the problem of small failure probability; 4) the reliability analysis method commonly used has calculation. Therefore, only by establishing a perfect time-varying reliability analysis model and developing an efficient time-varying reliability algorithm can the time-varying reliability analysis and optimization design of complex structures be effectively solved to meet the needs of practical engineering design. The following are: (1) Considering the implicit limit state equation and small failure probability, an AK-SS method for calculating the small failure probability is proposed. That is, the Kriging proxy model based on a small number of sample points is used to approximate the real limit state equation, and the model is updated step by step by active learning method. The AK-SS method is applied to the reliability analysis of underground tunnel lining structure, and the results show that the method is very effective in dealing with the problem of small and medium failure probability in engineering practice. (2) Considering the monotonic degradation of structure. A time-varying reliability analysis model based on mixed stochastic process is proposed. Gamma stochastic process is used to simulate the degradation caused by time effect, Poisson stochastic process is used to describe the stochastic impact effect, and a more comprehensive composite degradation model is proposed. The time-varying reliability analysis model provides an effective method for the time-varying reliability analysis of engineering structures with test data and model uncertainties. (3) In view of the non-monotonic variation of structural function, the time-varying reliability analysis model is combined. A hybrid EGO-AK-SS time-varying reliability calculation method is proposed based on the extremum method and AK-SS method. The Kriging extremum response surface of time-varying function is established by using the hybrid EGO (Mixed Efficient Global Optimization) algorithm, and the precision of the extremum response surface is improved step by step with the AK-SS algorithm, and the failure probability is calculated simultaneously. Considering the advantages of EGO calculation efficiency and AK-SS method in dealing with implicit small failure probability, this method is applied to simple mechanical structures, which improves the calculation efficiency and is suitable for solving time-varying reliability of practical structures. (4) A hybrid EGO-SORA time-varying reliability optimization design method is proposed for reliability optimization problems with time-varying probability constraints. Hybrid EGO method transforms time-varying probability constraints into time-invariant forms and establishes Kriging extremum response surface of constraint functions. SORA (sequential optimization and reliability assessment) method is used to transform reliability optimization design into sequential deterministic optimization design and inverse reliability analysis, and update the reduction with the current most likely failure point. Kriging extremum response surface of bundle function. This method has the characteristics of high accuracy in dealing with time-varying reliability by hybrid EGO method and high efficiency in solving reliability optimization design by SORA. It is applied to simple mechanical structures and improves calculation efficiency. It can be used to deal with time-varying reliability optimization design problems in engineering practice.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB114.3

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