Machine learning assisted stochastic-XFEM for stochastic crack propagation and reliability analysis

Abstract We present a novel stochastic extended finite element (S-XFEM) method for solving fracture mechanics problems under uncertainty. The proposed S-XFEM couples XFEM and a novel multi-output Gaussian process based machine learning algorithm, referred to as the hybrid polynomial correlated function expansion (H-PCFE). With this approach, the underlying stochastic fracture mechanics problem is decoupled into multiple classical fracture mechanics problems. Since solution of a classical fracture mechanics problem is computationally expensive, we utilize the H-PCFE model as a surrogate to emulate the behavior of the system. Training samples required for training the H-PCFE model are generated by using the XFEM. Because of the intrinsic capability of XFEM in providing a mesh insensitive solution, the proposed approach can provide reasonable result from a coarse mesh. On the other hand, H-PCFE is capable of providing highly accurate solution from very few training samples. Overall, the proposed S-XFEM is highly efficient in solving stochastic fracture mechanics problems. The proposed approach is used for solving three stochastic fracture mechanics problems. Different case studies involving reliability analysis and stochastic fracture propagation have been reported. The procedure yields highly accurate results for all problems, indicating its possible applications to other large scale systems.