Abstract Line sampling is a method for efficient estimation of the failure (or rare event) probability. The method generates a set of samples on a hyperplane perpendicular to an important direction that points towards the failure domain, and estimates the probability of failure as a sample mean of one-dimensional probability integrals. The performance of the method strongly depends on the quality of the chosen important direction. Recently, an adaptive approach for adjusting the important direction during the simulation has been proposed, termed advanced line sampling (ALS). This contribution revisits the ALS method and shows that the ALS estimator can be viewed as a combination of estimators, each one corresponding to a direction in the adaptive sequence. We show that the combination implied by the original ALS is suboptimal and propose an alternative combination of estimators. The resulting method is termed combination line sampling (CLS). We demonstrate through three numerical examples that CLS outperforms the ALS estimator, in particular if the initially selected important direction is poor.

中文翻译：

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用于结构可靠性分析的组合线采样

摘要 线采样是一种有效估计故障（或罕见事件）概率的方法。该方法在垂直于指向失效域的重要方向的超平面上生成一组样本，并将失效概率估计为一维概率积分的样本均值。该方法的性能在很大程度上取决于所选重要方向的质量。最近，提出了一种在模拟过程中调整重要方向的自适应方法，称为高级线采样 (ALS)。这一贡献重新审视了 ALS 方法，并表明 ALS 估计量可以被视为估计量的组合，每个估计量对应于自适应序列中的一个方向。我们表明原始 ALS 隐含的组合是次优的，并提出了另一种估计量组合。由此产生的方法称为组合线采样 (CLS)。我们通过三个数值示例证明 CLS 优于 ALS 估计器，特别是如果最初选择的重要方向很差。