基于吉布斯采样与压缩感知的二维非平稳CPT数据快速插值方法

静力触探试验(Cone Penetration Test,CPT)常被用于确定地下土体分层情况及层内土体的力学参数等。由于工期、工程投入、技术等条件限制,沿水平方向的CPT钻孔数目通常非常有限,有必要利用空间插值或随机模拟来估计未采样位置的CPT试验数据。提出一种有效的蒙特卡洛方法,可直接根据有限的CPT试验钻孔数据估计未采样位置的CPT数据,该方法将二维贝叶斯压缩感知框架与吉布斯采样相结合,并引入克罗内克积以提高其计算效率,然后用一系列数值及实际工程案例验证了所提方法的可靠性。结果表明:该插值方法合理,不仅能如实反映数据本身的非平稳特点,且采用序列更新技术后可显著降低时间成本,具有更强的适应能力。此外,插值结果的准确性、可靠性与已有CPT钻孔的距离成反比、与已有钻孔的数目成正比,反映出方法本身数据驱动的特点。

Efficient interpolation method for 2D non-stationary CPT data using Gibbs sampling and compressive sampling

Cone penetration test (CPT) is commonly used to determine the stratification of underground soil and the mechanical parameters of soils in stratification. Due to time, resources and/or technical constraints, the number of CPT soundings along with a horizontal direction is generally limited. In such cases, spatial interpolation or stochastic simulation methods is a necessary choice to estimate CPT data at un-sampled locations. This paper proposes an efficient method for simulating CPT data at un-sampled locations directly from a limited number of CPT records. The approach couples the framework of 2D Bayesian compressive sensing with Gibbs sampling, where Kronecker product is introduced for facilitating its simulation efficiency. Both numerical simulations and case histories are used to illustrate the presented method.Results show that the proposed method is reasonable, which can not only reflect the non-stationary characteristics of the data, but also significantly reduce the time cost and have reasonable adaptability after using the sequential updating technique. In addition, the accuracy and reliability of interpolation are negatively and positively proportional to the distance from existing CPT soundings and the number of existing CPT soundings, which demonstrates the data-driven nature of the proposed method.