tempered Christoffel-加权多项式混沌扩展用于以韧性为导向的不确定性量化
Tempered Christoffel-Weighted Polynomial Chaos Expansion for Resilience-Oriented Uncertainty Quantification
AI总结：
本文提出 tempered Christoffel 加权多项式混沌扩展方法，通过优化回归加权方案提升不确定性量化中稳定性与尾部预测精度。
摘要：
准确且高效的不确定性量化对于在高影响低概率干扰下评估现代电力系统韧性至关重要。数据驱动的稀疏多项式混沌扩展（DDSPCE）提供了一种计算高效的替代框架，但可能因回归加权方案的影响而出现回归退化和分布尾部的准确性损失。本文通过引入 tempered Christoffel 加权最小二乘（T-CWLS）公式研究了回归加权方案对 DD-SPCE 替代方案的稳定性及尾部准确性的影响。温控指数被视为超参数，其影响通过与蒙特卡洛模拟相比的分布准确性进行检验。在配电系统负载削减案例研究中，所提出的方法将 95 百分位数偏差减少了 16%，5 百分位数偏差减少了 6%，并提高了回归稳定性指数超过 130%。结果表明，控制加权强度直接影响稳定性指数和尾部预测的准确性。
英文摘要：
Accurate and efficient uncertainty quantification is essential for resilience assessment of modern power systems under high impact and low probability disturbances. Data driven sparse polynomial chaos expansion (DDSPCE) provides a computationally efficient surrogate framework but may suffer from ill conditioned regression and loss of accuracy in the distribution tails that determine system risk. This paper studies the impact of regression weighting schemes on the stability and tail accuracy of DD-SPCE surrogates by introducing a tempered Christoffel weighted least squares (T-CWLS) formulation that balances numerical stability and tail fidelity. The tempering exponent is treated as a hyperparameter whose influence is examined with respect to distributional accuracy compared with Monte Carlo simulations. Case studies on distribution system load shedding show that the proposed method reduces 95th percentile deviation by 16%, 5th percentile deviation by 6%, and improves the regression stability index by over 130%. The results demonstrate that controlling the weighting intensity directly influences both stability index and the accuracy of tail prediction.
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