Abstract Calculation of derivatives on discrete measurement data with unequal intervals is often required in geotechnical engineering, such as interpretation of stiffness reduction curve of soil from pressuremeter test data, pile lateral responses from inclinometer data. Such a task is however tricky and challenging, because a small error or noise in the measurements may amplify and lead to huge fluctuations in the derivatives obtained. The amplification becomes increasingly significant as the order of derivative increases. It is therefore of great importance to evaluate reliability of the derivatives obtained and quantify the uncertainty associated with the derivative calculation. A Bayesian compressive sampling-based method is proposed in this paper to address this problem. It not only provides high-order derivatives on discrete measurement data, even at un-sampled locations, but also quantifies the uncertainty associated with the derivatives obtained and offers an index to evaluate reliability of the derivatives obtained. The proposed approach is illustrated using both real-life pressuremeter data and numerical example of pile lateral responses. A comparison is also made between the proposed method and several existing methods in geotechnical literature. It shows that the proposed method performs better than existing methods and it is applicable to problems with both elastic and plastic soil responses.

中文翻译：

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使用贝叶斯压缩采样对具有不等测量间隔的离散数据进行微分并量化微分中的不确定性

摘要 岩土工程中经常需要对不等间隔的离散测量数据进行导数计算，例如根据压力计测试数据解释土壤刚度降低曲线，根据测斜仪数据解释桩侧向响应。然而，这样的任务是棘手和具有挑战性的，因为测量中的小误差或噪声可能会放大并导致获得的导数的巨大波动。随着导数阶数的增加，放大变得越来越重要。因此，评估获得的导数的可靠性并量化与导数计算相关的不确定性非常重要。本文提出了一种基于贝叶斯压缩采样的方法来解决这个问题。它不仅提供离散测量数据的高阶导数，即使在未采样的位置，也可以量化与获得的导数相关的不确定性，并提供一个指标来评估所获得的导数的可靠性。使用真实压力计数据和桩横向响应的数值示例说明了所提出的方法。还对所提出的方法与岩土工程文献中的几种现有方法进行了比较。结果表明，所提出的方法比现有方法性能更好，并且适用于弹性和塑性土响应的问题。使用真实压力计数据和桩横向响应的数值示例说明了所提出的方法。还对所提出的方法与岩土工程文献中的几种现有方法进行了比较。结果表明，所提出的方法比现有方法性能更好，并且适用于弹性和塑性土响应的问题。使用真实压力计数据和桩横向响应的数值示例说明了所提出的方法。还对所提出的方法与岩土工程文献中的几种现有方法进行了比较。结果表明，所提出的方法比现有方法性能更好，并且适用于弹性和塑性土响应的问题。