A phase field and deep-learning based approach for accurate prediction of structural residual useful life

Abstract In this work, we proposed a novel approach for the prediction of residual useful life (RUL) of structures through appropriately combining the phase field method and deep-learning. In this new approach, the phase field method is firstly utilized to obtain the structural responses of crack growth, which are further preserved as images. Then, the convolutional neural network (CNN) is constructed to establish a predictive model. The proposed approach is a hybrid model of both physical and data-driven techniques, which can build a bridge between traditional computational fracture mechanics and deep learning algorithms. Several numerical cases are studied to evaluate the prediction performance of the proposed approach. The analysis results demonstrate that the present approach is able to predict the RUL of the structures with high level of accuracy.

[1]  Fan Fei,et al.  A phase-field model of frictional shear fracture in geologic materials , 2020 .

[2]  N. Valizadeh,et al.  Extended isogeometric analysis for simulation of stationary and propagating cracks , 2012 .

[3]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[4]  S. Z. Feng,et al.  An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations , 2018 .

[5]  Timon Rabczuk,et al.  A phase-field modeling approach of fracture propagation in poroelastic media , 2018, Engineering Geology.

[6]  Rongjing Hong,et al.  HYGP-MSAM based model for slewing bearing residual useful life prediction , 2019, Measurement.

[7]  Zuozhou Pan,et al.  A two-stage method based on extreme learning machine for predicting the remaining useful life of rolling-element bearings , 2020 .

[8]  T. Q. Bui Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS , 2015 .

[9]  Guirong Liu,et al.  An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order , 2013 .

[10]  Chuanzeng Zhang,et al.  Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method , 2014 .

[11]  Zhenjun Ma,et al.  Data-driven algorithm for real-time fatigue life prediction of structures with stochastic parameters , 2020 .

[12]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[13]  Anthony Gravouil,et al.  2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture , 2017 .

[14]  Mark A Fleming,et al.  Fracture in tension–compression-asymmetry solids via phase field modeling , 2019 .

[15]  Wing Kam Liu,et al.  Phase field modeling of fracture in nonlinearly elastic solids via energy decomposition , 2019, Computer Methods in Applied Mechanics and Engineering.

[16]  Guirong Liu,et al.  Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth , 2012 .

[17]  X. Han,et al.  A novel multi-grid based reanalysis approach for efficient prediction of fatigue crack propagation , 2019, Computer Methods in Applied Mechanics and Engineering.

[18]  T. Rabczuk,et al.  T-spline based XIGA for fracture analysis of orthotropic media , 2015 .

[19]  Adam Glowacz,et al.  Fault diagnosis of electric impact drills using thermal imaging , 2021 .

[20]  B. Bourdin,et al.  Numerical experiments in revisited brittle fracture , 2000 .

[21]  David Nowell,et al.  Fatigue life prediction for Waspaloy under biaxial loading , 2018, Theoretical and Applied Fracture Mechanics.

[22]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[23]  Tinh Quoc Bui,et al.  Simulation of dynamic and static thermoelastic fracture problems by extended nodal gradient finite elements , 2017 .

[24]  Christian Miehe,et al.  Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations , 2010 .

[25]  Christian Miehe,et al.  A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits , 2010 .

[26]  Hassan Qjidaa,et al.  Image retrieval and classication using shifted Legendre invariant moments and Radial Basis Functions Neural Networks , 2019 .

[27]  Hehua Zhu,et al.  A mixed cover meshless method for elasticity and fracture problems , 2018, Theoretical and Applied Fracture Mechanics.

[28]  Stéphane Bordas,et al.  A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics , 2019, Acta Mechanica.

[29]  Xiang Li,et al.  Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning , 2019, Computer Methods in Applied Mechanics and Engineering.

[30]  Duc-Kien Thai,et al.  Gradient tree boosting machine learning on predicting the failure modes of the RC panels under impact loads , 2019, Engineering with Computers.

[31]  T. Belytschko,et al.  A three dimensional large deformation meshfree method for arbitrary evolving cracks , 2007 .

[32]  Bijay K. Mishra,et al.  The numerical simulation of fatigue crack growth using extended finite element method , 2012 .

[33]  Emilio Mart'inez-Paneda,et al.  Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme , 2019, Theoretical and Applied Fracture Mechanics.

[34]  Bijay K. Mishra,et al.  Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA , 2015 .

[35]  Enrico Zio,et al.  Combining Relevance Vector Machines and exponential regression for bearing residual life estimation , 2012 .

[36]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

[37]  Guizhong Xie,et al.  A novel triangular boundary crack front element for 3D crack problems based on 8-node serendipity element , 2019, Engineering Analysis with Boundary Elements.

[38]  Timon Rabczuk,et al.  Modeling and simulation of kinked cracks by virtual node XFEM , 2015 .

[39]  W. Zhou,et al.  Formulations of displacement discontinuity method for crack problems based on boundary element method , 2020 .

[40]  B. K. Mishra,et al.  A new multiscale phase field method to simulate failure in composites , 2018, Adv. Eng. Softw..

[41]  Timon Rabczuk,et al.  An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications , 2019, Computer Methods in Applied Mechanics and Engineering.

[42]  Timon Rabczuk,et al.  Transfer learning enhanced physics informed neural network for phase-field modeling of fracture , 2019, Theoretical and Applied Fracture Mechanics.

[43]  B. K. Mishra,et al.  A new multiscale XFEM for the elastic properties evaluation of heterogeneous materials , 2017 .

[44]  Minh Ngoc Nguyen,et al.  Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods , 2017, Theoretical and Applied Fracture Mechanics.

[45]  Qiao Wang,et al.  The phase-field model with an auto-calibrated degradation function based on general softening laws for cohesive fracture , 2020 .

[46]  B. K. Mishra,et al.  Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions , 2015 .

[47]  B. H. Nguyen,et al.  An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems , 2016 .

[48]  Soumen Bag,et al.  CNN-DMRI: A Convolutional Neural Network for Denoising of Magnetic Resonance Images , 2020, Pattern Recognit. Lett..

[49]  P. Kerfriden,et al.  Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth , 2017 .

[50]  Lei Chen,et al.  A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks , 2009 .

[51]  Pascal Vincent,et al.  Representation Learning: A Review and New Perspectives , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[52]  Jiawei Xiang,et al.  Improved deep convolution neural network (CNN) for the identification of defects in the centrifugal pump using acoustic images , 2020 .

[53]  Christian Miehe,et al.  Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids , 2015 .

[54]  Tinh Quoc Bui,et al.  Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement , 2018 .

[55]  Timon Rabczuk,et al.  Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation , 2019, Computer Methods in Applied Mechanics and Engineering.

[56]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[57]  Y. Feng,et al.  A phase-field model for mixed-mode fracture based on a unified tensile fracture criterion , 2020, Computer Methods in Applied Mechanics and Engineering.

[58]  Adam Glowacz,et al.  Novel Convolutional Neural Network (NCNN) for the Diagnosis of Bearing Defects in Rotary Machinery , 2021, IEEE Transactions on Instrumentation and Measurement.

[59]  Tinh Quoc Bui,et al.  On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis , 2016 .

[60]  B. K. Mishra,et al.  A simple, efficient and accurate Bézier extraction based T-spline XIGA for crack simulations , 2017 .