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P-CS不确定性量化模型与其性能数据驱动更新方法

P-CS UNCERTAINTY QUANTIFICATION MODEL AND ITS PERFORMANCE DATA-DRIVEN UPDATING METHOD

  • 摘要: 在实际工程中, 广泛存在大量的不确定性信息, 直接或间接影响着工程结构形式设计、结构性能评估与预测以及在役结构损伤识别等工作的开展与决策. 这些多源不确定性信息往往需要用多种不同的不确定性量化模型加以描述; 与此同时, 不确定性变量在使用过程中可能随时间变化且难以直接测量, 需要间接根据性能测试信息在使用工程中更新不确定性量化模型. 为兼顾上述两个问题, 本文基于等概率变换原则提出了一种P-CS (probability-convex set) 不确定性量化模型, 该模型将不确定性变量用概率随机变量与非概率凸集变量组合表征, 可统一表达概率模型、非概率模型以及非精确概率模型, 实现多源、多类型不确定性的统一量化. 本文进一步基于贝叶斯理论提出了一种针对该P-CS不确定性量化模型的性能数据驱动更新方法. 该更新方法根据性能测试数据信息更新P-CS不确定性量化模型参数取值的信度分布, 从而根据后验信度分布计算得出当前P-CS不确定性量化模型参数集合. 通过数值算例详述了P-CS不确定性量化模型的构建方法与其概率、非概率特性, 并验证了性能数据驱动更新P-CS模型方法的适用性.

     

    Abstract: Uncertainties in environmental loads and structural parameters are challenging phenomena which influence the structural design, the assessment and prediction of structural performance, and the damage identification of structures in service. These uncertainties may variously be objective or subjective from different sources, requiring appropriate mathematical modeling and quantification to obtain realistic analysis results of the behavior and reliability of engineering structures. In general, these uncertainties in different types and from multiple sources need to be described by different quantification models, involving probabilistic model, imprecise probabilistic model and non-probabilistic model. In addition, uncertainties may be time-varying during service time, and the direct measurements of uncertain variables are sometimes difficult to be carried out during the service of the structure. However, the performance test data, such as displacements, and stresses of structures, may be much more easily obtained when compared with the direct measurements. Facing the above issues, a novel uncertainty quantification model named P-CS (probability-convex set) model is proposed in this paper to enable uncertainties from multiple sources quantified in a uniform model. The P-CS model characterizes uncertainties as a combination of probabilistic random variables and a non-probabilistic convex set based on the principle of probability equivalence, which can make probabilistic model, imprecise probabilistic model and non-probabilistic model expressed under a uniform framework. On the basis of the P-CS model, a Bayesian updating method is proposed in this paper driven by performance test data. In this updating method, the allowable ranges of the parameters of P-CS model are divided into several subintervals respectively and then the credibility distribution of each parameter can be updated according to the performance test data, finally, parameters of P-CS model can be updated based on the posterior credibility distributions. Three numerical examples show the construction methods and the probabilistic and non-probabilistic properties of the P-CS model, and two mechanical examples are presented to validate the proposed Bayesian updating method.

     

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