open access

https://hdl.handle.net/2115/100479

Output probability density function estimation based on the weighted kernel density estimation method under variable distribution parameters

英語

importance sampling

2026-07-01

Proceedings of the 10th International Symposium on Reliability Engineering and Risk Management (ISRERM 2026)

The probability density function (PDF) of structural output plays an important role in statistical characteristic analysis of structural performance. Studies have proposed effective algorithms for solving the output PDF under fixed distribution parameters (DP) of random input variables. However, when obtaining the output PDF for arbitrary DP realizations, these methods require repeated calculations. To avoid the enormous computational cost required by numerical simulations for obtaining the structural output PDF under arbitrary DP realizations, this paper proposes a weighted kernel density estimation (KDE) method based on a single set of samples in augmented space. First, the weights of augmented samples required for estimating the output PDF under given DP realization are derived based on the principle of probability conservation. Second, to address the tail estimation errors of KDE, an adaptive truncation strategy is further introduced. By setting the truncation point of the output PDF and obtaining corresponding important samples, the proposed weighted KDE can be applied to obtain the truncated output PDF, which is then assembled to the complete output PDF using the conditional probability formula. The adaptive strategy iteratively determines a series of truncation points that progressively leads the tail of the PDF, enabling more accurate estimation of the PDF tail. Examples demonstrate that the proposed method, requiring single simulation run, significantly outperforms traditional KDE methods in efficiency while ensuring accuracy.

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