论文标题
贝叶斯倒置于各向异性液压相场骨折
Bayesian Inversion for Anisotropic Hydraulic Phase-Field Fracture
论文作者
论文摘要
在这项工作中，提出了针对液压相位横向各向同性和正交型各向异性骨折的贝叶斯反转框架。在其中，三个主要场是压力，位移和相位场，同时执行方向依赖性响应（通过类似惩罚的参数）。通过避免降解的各向异性能量的可压缩部分来引入新的裂纹驱动状态功能。对于贝叶斯倒置，我们采用延迟的排斥自适应大都市（DRAM）算法来识别参数。我们根据液压断裂观察（即最大压力）调整算法以估算参数。重点是由不同的变量引起的不确定性，包括弹性模量，Biot的系数，Biot的模量，动态流体粘度以及Griffith的能量释放速率，在各向同性液压裂缝的情况下，在各向异性环境中，我们在各向异性环境中确定了其他类似损坏的损坏。使用了几个数值示例来证实我们的算法发展。
In this work, a Bayesian inversion framework for hydraulic phase-field transversely isotropic and orthotropy anisotropic fracture is proposed. Therein, three primary fields are pressure, displacements, and phase-field while direction-dependent responses are enforced (via penalty-like parameters). A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. For the Bayesian inversion, we employ the delayed rejection adaptive Metropolis (DRAM) algorithm to identify the parameters. We adjust the algorithm to estimate parameters according to a hydraulic fracture observation, i.e., the maximum pressure. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot's coefficient, Biot's modulus, dynamic fluid viscosity, and Griffith's energy release rate in the case of the isotropic hydraulic fracture while in the anisotropic setting, we identify additional penalty-like parameters. Several numerical examples are employed to substantiate our algorithmic developments.
