A Machine Learning Approach as a Surrogate for a Finite Element Analysis: Status of Research and Application to One Dimensional Systems

Current maintenance intervals of mechanical systems are scheduled a priori based on the life of the system, resulting in expensive maintenance scheduling, and often undermining the safety of passengers. Going forward, the actual usage of a vehicle will be used to predict stresses in its structure, and therefore, to define a specific maintenance scheduling. Machine learning (ML) algorithms can be used to map a reduced set of data coming from real-time measurements of a structure into a detailed/high-fidelity finite element analysis (FEA) model of the same system. As a result, the FEA-based ML approach will directly estimate the stress distribution over the entire system during operations, thus improving the ability to define ad-hoc, safe, and efficient maintenance procedures. The paper initially presents a review of the current state-of-the-art of ML methods applied to finite elements. A surrogate finite element approach based on ML algorithms is also proposed to estimate the time-varying response of a one-dimensional beam. Several ML regression models, such as decision trees and artificial neural networks, have been developed, and their performance is compared for direct estimation of the stress distribution over a beam structure. The surrogate finite element models based on ML algorithms are able to estimate the response of the beam accurately, with artificial neural networks providing more accurate results.

[1]  Dean Abbott,et al.  Applied Predictive Analytics: Principles and Techniques for the Professional Data Analyst , 2014 .

[2]  Liang Wu,et al.  A Deep Learning Approach Replacing the Finite Difference Method for In Situ Stress Prediction , 2020, IEEE Access.

[3]  G. Karniadakis,et al.  Physics-informed neural networks for high-speed flows , 2020, Computer Methods in Applied Mechanics and Engineering.

[4]  M. Kubát An Introduction to Machine Learning , 2017, Springer International Publishing.

[5]  Paris Perdikaris,et al.  Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations , 2017, ArXiv.

[6]  Antonio J. Serrano,et al.  Machine Learning for Modeling the Biomechanical Behavior of Human Soft Tissue , 2016, 2016 IEEE 16th International Conference on Data Mining Workshops (ICDMW).

[7]  Genki Yagawa,et al.  Computational mechanics enhanced by deep learning , 2017 .

[8]  Wei Sun,et al.  A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis , 2018, Journal of The Royal Society Interface.

[9]  Maria Chierichetti,et al.  Surrogated finite element models using machine learning , 2021 .

[10]  Antonio J. Serrano,et al.  A framework for modelling the biomechanical behaviour of the human liver during breathing in real time using machine learning , 2017, Expert Syst. Appl..

[11]  Mohammad Ali Ahmadi,et al.  Prediction breakthrough time of water coning in the fractured reservoirs by implementing low parameter support vector machine approach , 2014 .

[12]  Maria Chierichetti,et al.  Moving sensors in structural dynamics , 2020, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[13]  German Capuano,et al.  Smart finite elements: A novel machine learning application , 2019, Computer Methods in Applied Mechanics and Engineering.

[14]  Steven A. Freeman,et al.  Use of Neural Networks to Identify Safety Prevention Priorities in Agro-Manufacturing Operations within Commercial Grain Elevators , 2019, Applied Sciences.

[15]  George E. Karniadakis,et al.  Hidden physics models: Machine learning of nonlinear partial differential equations , 2017, J. Comput. Phys..

[16]  Paris Perdikaris,et al.  Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..

[17]  Taiyong Li,et al.  A CEEMDAN and XGBOOST-Based Approach to Forecast Crude Oil Prices , 2019, Complex..

[18]  Olivier A. Bauchau,et al.  Comprehensive UH-60 loads model validation , 2010 .

[19]  Y. Kang,et al.  Estimation of sound absorption coefficient of layered fibrous material using artificial neural networks , 2020 .

[20]  Phaedon-Stelios Koutsourelakis,et al.  Stochastic upscaling in solid mechanics: An excercise in machine learning , 2007, J. Comput. Phys..

[21]  Yixin Chen,et al.  Optimal Action Extraction for Random Forests and Boosted Trees , 2015, KDD.

[22]  Shutao Wang,et al.  A new method of diesel fuel brands identification: SMOTE oversampling combined with XGBoost ensemble learning , 2020 .

[23]  W J Curnow,et al.  The efficacy of bicycle helmets against brain injury. , 2003, Accident; analysis and prevention.

[24]  Antonio J. Serrano,et al.  A finite element-based machine learning approach for modeling the mechanical behavior of the breast tissues under compression in real-time , 2017, Comput. Biol. Medicine.

[25]  Xiaoli Wang,et al.  Fault Diagnosis for Wind Turbines Based on ReliefF and eXtreme Gradient Boosting , 2020, Applied Sciences.

[27]  Kay Smarsly,et al.  Structural Health Monitoring based on Artificial Intelligence Techniques , 2007 .

[28]  Trenton Kirchdoerfer,et al.  Data-driven computational mechanics , 2015, 1510.04232.

[29]  Maria Chierichetti Load and Response Identification for a Nonlinear Flexible Structure Subject to Harmonic Loads , 2014 .

[30]  Chiara Grappasonni,et al.  A modal approach for dynamic response monitoring from experimental data , 2014 .

[31]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[32]  Jiwon Kim,et al.  Bridging finite element and machine learning modeling: stress prediction of arterial walls in atherosclerosis. , 2019, Journal of biomechanical engineering.

[33]  Zhenglin Tan,et al.  Nondestructive detection of sunset yellow in cream based on near-infrared spectroscopy and interval random forest. , 2020, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

[34]  M. Ruzzene,et al.  Prediction of UH-60A Blade Loads: Insight on Load Confluence Algorithm , 2014 .

[35]  Guowei Ma,et al.  XGBoost algorithm-based prediction of concrete electrical resistivity for structural health monitoring , 2020 .

[36]  David R. Anderson,et al.  Understanding AIC and BIC in Model Selection , 2004 .

[37]  Maria Chierichetti,et al.  An integrated approach for non-periodic dynamic response prediction of complex structures: Numerical and experimental analysis , 2016 .

[38]  Bjarne Grimstad,et al.  ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs , 2019, Comput. Chem. Eng..