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• Design a SIR N model for capturing spatiotemporal characteristics of spreading risks. • Reveal the relation between spreading risk and the network topology of human movement. • Construct a resilient strategy to control and contain the spreading risk of contagious diseases. Spreading risks of contagious diseases have threatened human lives and disrupted the global economy. Protecting humanity from contagious diseases, such as coronavirus, is a critical task of our time. Unlike other types of risks, the spreading of contagious diseases could be enhanced by human movements. As human movements are inherently dynamic and heterogenous, it brings challenges in analyzing the spreading on a large scale. Here, we combine network theory and epidemiology models to construct a SIR N model for capturing spatiotemporal characteristics of spreading risks. With mean-field theory and Lyapunov theorem, our model reveals the relation between spreading risk and the network topology of human movement. The model allows us to construct a resilient strategy to control and contain the risk. The approach is tested retrospectively with coronavirus cases in China and the United States. Our results adequately interpret the historical trends and justify the resilience of nations' strategies. The model demonstrates a pattern of resilience in dynamic networks, which could shed light on handling contagious risks. [ABSTRACT FROM AUTHOR]

Highlights • A general failure-pursuing sampling framework is proposed for efficient reliability analysis. • The framework always pursues the local region sensitive to the prediction accuracy from a global perspective. • Various active learning functions can be adopted to locally exploit the sensitive Voronoi cell. • A model-free response-distance learning function is developed to avoid relying on the characteristics of different surrogates. Abstract Design of experiment and active learning strategy are vital for the surrogate-based reliability analysis. However, the existing sampling and modeling methods usually ignore some useful information that can guide the choice of training samples, or heavily rely on the characteristics of surrogates. These lead to the inefficiency of sampling strategies or limit the application respectively. Therefore, this work proposes a failure-pursuing sampling framework, which is able to adopt various surrogate models or active learning strategies. In each iteration, it organically and sequentially takes into account the joint probability density function of random variables, the individual information at candidate points and the improvement of the accuracy of predicted failure probability. To measure the probability of the improvement, a global predicted failure probability error is proposed based on the real-time reliability analysis result. Furthermore, Voronoi diagram is applied to partition the sampling region into some local cells for keeping the uniformity of the training samples. Besides, a model-free response-distance function is developed and combined with the framework to avoid relying on the characteristics of surrogates, such as the statistical information provided by Kriging. Finally, four examples are investigated to demonstrate the applicability, stability and generality of the proposed method. [ABSTRACT FROM AUTHOR]

• Unmodeled dynamics recovery of a hidden degradation model. • Improving the accuracy of model-based failure prognostics. • Integrating data-driven model with physics-based degradation model. • Practical application to failure prognostics of miter gates. Understanding the degradation of the quoin block is vital for failure prognostics in miter gates. Due to the complicated degradation mechanism, degradation models based on simplifications and assumptions cannot accurately describe the damage evolution. It is observed that small errors in a simplified degradation model can lead to a large discrepancy in the remaining useful life estimation attributed to error accumulation over time. Aiming to address this issue in failure prognostics, this paper presents a dynamic model correction framework for a simplified degradation model using strain measurements. In the proposed framework, a polynomial chaos expansion (PCE) model is employed to compensate the missing physics in a simplified stochastic degradation model. A maximum likelihood estimation method is developed to estimate the uncertain parameters of the simplified physics-based degradation model along with the unknown PCE model parameters using strain measurements as the observables. The updated damage degradation model is then applied to failure prognostics of a miter gate. Results of a case study show that the proposed approach can effectively improve the accuracy of failure prognostics in miter gates. [ABSTRACT FROM AUTHOR]

• The time-dependent wrong-classification probability is developed. • Global and local Kriging modeling methods are used for limit state approximation. • False classification rate is proposed to measure the global accuracy. • Estimation error of failure probability is derived to measure the local accuracy. Time-dependent reliability-based design optimization is an effective tool to guarantee a high reliability of the product during the full life cycle. However, the necessarily repeated probabilistic constraint evaluations bring big computational burden when this tool is applied to the complex engineering systems. To reduce the computational cost, this work employs Kriging model to approximate the limit states of time-consuming probabilistic constraints, and proposes the global and local Kriging modeling methods respectively based on the wrong-classification probability. The global one aims to reduce the wrong-classification probability in the vicinity of the whole limit states, while the local one focuses on the limits states that are potentially visited by the optimum. Based on the wrong-classification probability, two indices, i.e. false classification rate and estimation error of failure probability, are derived to measure the global and local accuracies of limit states respectively. For the global or local Kriging modeling, the approximated Kriging constraint maximizing the false classification rate or the estimation error of failure probability will be updated by the point with the maximum wrong-classification probability. Results of four case studies demonstrate the efficacy of the proposed methods. [ABSTRACT FROM AUTHOR]

• Estimation error-guided adaptive Kriging modeling method is proposed. • The probability of wrong state classification is defined and derived. • The maximum real-time estimation error is derived for series and parallel system. • Both the probability and estimation error assist the refinement of Kriging. In order to approximate the multiple limit state functions for different failure events, the active learning Kriging model proposed for component reliability analysis has been extended to system reliability analysis. Meanwhile, many efficient sampling strategies have been applied to reduce the high computational burden. However, these strategies meet a challenge in wasting some training points and terminating the training process inappropriately, since they do not directly relate to the estimation error of system failure probability. To address the challenge, this work proposes an estimation error-guided adaptive Kriging method. As Kriging prediction may be inaccurate before being well trained, the predicted system failure probability may deviate from the true result. To quantify this estimation error, the true number of failure points is approximated by adding the number of predicted failure points and the number of wrongly classified points. Since it is impossible to learn the exact number of wrongly classified points, its confidence interval is derived based on the probability of making wrong state classification. Subsequently, the refinement of Kriging is achieved by using the probability to identify new points and using the estimation error to determine the termination, which has been demonstrated by three different cases. [ABSTRACT FROM AUTHOR]

• Develop a rapid Subdomain Uncertainty-guided Sampling (SUS) framework. • Derive the analytic expression for the standard deviation of feasibility function. • Propose a novel Optimized Feasibility Metric (OFM) for active learning. • Define Proportion of Misclassified Samples (PMS) as the stopping criterion. • Integrate OFM and PMS into SUS for time-variant reliability analysis. Active learning strategy combined with single-loop Kriging method has attracted much attention for Time-dependent Reliability Analysis (TRA). Large sample pool across all time instants is required to comprehensively cover the failure surface. Identifying training samples with most existing methods requires assessing the response of the entire sample pool, leading to high time costs. Similarly, to assist in identifying critical sampling regions, evaluating failure probability with a large sample pool in each iteration is also time-consuming. Additionally, higher-order uncertainty information is typically ignored, impairing the sampling efficiency. To address these issues, a Subdomain Uncertainty-guided Kriging (SUK) Method is proposed. Stochastic processes are first equivalently converted to random variables. By simultaneously sampling random variables and time parameter, an equivalent sample pool with significantly reduced size is generated for adaptive sampling. With a concise subdomain uncertainty assessment function, critical sampling region, i.e. sensitive subdomain, is distinguished efficiently. By comprehensively considering both the expectation and standard deviation of feasibility function, a novel Optimized Feasibility Metric (OFM) is then proposed for active learning. The proportion of misclassified samples is analytically deduced as stopping criterion. Finally, comparison results on four examples demonstrate the good performances of the proposed subdomain uncertainty-guided Kriging method. [ABSTRACT FROM AUTHOR]

• A single-loop Kriging couples subset simulation is proposed for time-variant analysis. • Deriving the most probable extreme response metric for failure probability estimation. • Improving maximum error-guided adaptive sampling strategy for updating Kriging. • Adapting the stopping criterion thresholds to different intermediate failure events. Time-dependent reliability analysis (TRA) plays an important role in improving the validity and practicability of product reliability evaluation over an interested life interval. Conventional TRA for high-reliability product, however, requires tackling two main challenges: (1) the inaccurate analysis of small failure probability problem and (2) the computationally expensive time-variant performance function. In this paper, a single-loop Kriging coupled with subset simulation (SLK-co-SS) method is proposed to address these challenges. By introducing time-dependent intermediate failure events, the estimation of small failure probability is first converted into a product of larger condition probabilities, which can be estimated by a proposed most probable extreme value method based on the trained Kriging model. We then develop an improved maximum error-guided adaptive sampling strategy to sequentially train and update the Kriging model in every intermediate failure event. To make more training samples located at the high potential region of time-dependent limit state surface, the error-tolerance threshold of updating stopping criterion varies with the intermediate failure events. The comparison results on four examples demonstrate the good capability and applicability of proposed SLK-co-SS method. [ABSTRACT FROM AUTHOR]