Integration of reliability and sensitivity assessment with data assimilation for improved decision support

工程结构和系统的管理需要在其预期使用寿命内对其性能进行充分的预测。对于大多数应用来说，存在有效的数值模型来进行这种预测，但这些模型的参数通常是不确定的或随机的。当对这些系统的可靠性感兴趣时，这一点尤其重要，因为罕见事件最受不确定性的影响。由于不确定性来自不同的来源，人们已经认识到，作为一个单一的数字提供可靠性的估计并不总是足够的，特别是如果基础计算是基于模糊的信息。在许多情况下，分离不同不确定性来源对最终预测的影响是可取的。这种对不确定性的多态处理导致了基础结构可靠性分析中的计算挑战，这将在本项目中得到解决。该项目的目标是开发一个整体框架，以自适应地估计结构可靠性及其对不同信息下设计参数变化的敏感性。这项工作是基于最近提出的使用顺序重要性抽样的可靠性分析方法，以及罕见事件贝叶斯分析的新方法。后者在许多（如果不是大多数的话）工程应用中是感兴趣的，其中数据同化（例如通过监测和收集现场数据）是减少不确定性和提高可靠性的有效方法。该框架应与不确定量的低维表示和潜在复杂工程模型的自适应代理模型相结合，以提高估算的计算效率。考虑到多态不确定性，该框架将能够研究表示工程决策支持的可靠性和敏感性的有效方法，这将是该项目第二阶段的重点。

The management of engineering structures and systems requires adequate predictions of their performance throughout their intended service life. For most applications, effective numerical models for such predictions exist, but the parameters of these models are commonly uncertain or random. This is particularly relevant when the interest is in the reliability of these systems, because rare events are most affected by uncertainty. Because the uncertainty arises from different sources, it has been recognized that it is not always sufficient to provide an estimate of reliability as a single number, in particular if the underlying calculation is based on vague information. In many instances, it can be desirable to separate the influence of different sources of uncertainty on the final prediction. Such a polymorphic treatment of uncertainties leads to computational challenges in the underlying structural reliability analysis, which will be addressed in this project. The goal of this project is to develop an integral framework to adaptively estimate the structural reliability and its sensitivity to changes in design parameters under varying information. This work is based on a recently proposed method for reliability analysis using Sequential Importance Sampling, as well as new approach for Bayesian analysis of rare events. The latter is of interest in many - if not most - engineering applications, where data assimilation (e.g. by monitoring and collection of field data) is an effective way of reducing uncertainty and increasing reliability. The framework shall be combined with lower-dimensional representations of uncertain quantities and adaptive proxy models of the potentially complex engineering model for enhancing the computational efficiency of the estimation. The framework will enable the investigation of effective ways for representing reliability and sensitivities for engineering decision support in view of polymorphic uncertainties, which will be the focus of the second phase of the project.