Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of t...Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs.PCEs for models with independent inputs have been extensively explored in the literature.Recently,different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications.Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs.However,the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions,respectively.In this paper,we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions.The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output.The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency.Four numerical examples are implemented to validate the proposed algorithm.The source code is made publicly available for reproducibility.展开更多
Prolonged power outages debilitate the economy and threaten public health. Existing research is generally limitedin its scope to a single event, an outage cause, or a region. Here, we provide one of the most comprehen...Prolonged power outages debilitate the economy and threaten public health. Existing research is generally limitedin its scope to a single event, an outage cause, or a region. Here, we provide one of the most comprehensiveanalyses of large-scale power outages in the U.S. from 2002 to 2019. This analysis is based on the outage datacollected under U.S. federal mandates that concern large blackouts, typically of transmission systems and excludemuch more common but smaller blackouts, typically, of distribution systems. We categorized the data into fouroutage causes and computed reliability metrics, which are commonly used for distribution-level small outagesonly but useful for analyzing large blackouts. Our spatiotemporal analysis reveals six of the most resilient U.S.states since 2010, improvement of power resilience against natural hazards in the south and northeast regions,and a disproportionately large number of human attacks for its population in the Western Electricity CoordinatingCouncil region. Our regression analysis identifies several statistically significant predictors and hypotheses forU.S. resilience to large blackouts. Furthermore, we propose a novel framework for analyzing outage data usingdifferential weighting and influential points to better understand power resilience. We share curated data andcode as Supplementary Materials.展开更多
基金This work was supported in part by the U.S.National Science Foundation(NSF grants CMMI-1824681,DMS-1952781,and BCS-2121616).
文摘Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs.PCEs for models with independent inputs have been extensively explored in the literature.Recently,different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications.Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs.However,the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions,respectively.In this paper,we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions.The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output.The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency.Four numerical examples are implemented to validate the proposed algorithm.The source code is made publicly available for reproducibility.
基金the National Science Foundation(NSF grant CMMI-1824681)。
文摘Prolonged power outages debilitate the economy and threaten public health. Existing research is generally limitedin its scope to a single event, an outage cause, or a region. Here, we provide one of the most comprehensiveanalyses of large-scale power outages in the U.S. from 2002 to 2019. This analysis is based on the outage datacollected under U.S. federal mandates that concern large blackouts, typically of transmission systems and excludemuch more common but smaller blackouts, typically, of distribution systems. We categorized the data into fouroutage causes and computed reliability metrics, which are commonly used for distribution-level small outagesonly but useful for analyzing large blackouts. Our spatiotemporal analysis reveals six of the most resilient U.S.states since 2010, improvement of power resilience against natural hazards in the south and northeast regions,and a disproportionately large number of human attacks for its population in the Western Electricity CoordinatingCouncil region. Our regression analysis identifies several statistically significant predictors and hypotheses forU.S. resilience to large blackouts. Furthermore, we propose a novel framework for analyzing outage data usingdifferential weighting and influential points to better understand power resilience. We share curated data andcode as Supplementary Materials.
