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

Abstract

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.

Keywords: artificial neural networks; beam analysis; finite element; gradient boosting regression trees; machine learning; random forest trees; structural monitoring.

Figure 1

Concept of the approach. On the left, the numerical predictions before the application of the machine learning (ML) approach are not representative of the behavior of the system. After the ML algorithm is applied, the numerical prediction is a good representation of the actual system.

Figure 2

Schematic of ML training approach. Quantities $p_1\left(t\right),p_2\left(t\right),\dots ,p_m\left(t\right)$ are evaluated in the finite element model, and the ML model is trained using these quantities as inputs.

Figure 3

Numerical model of the beam and spatial load distribution for training the ML algorithms.

Figure 4

Frequency analysis for load distribution for case 1.

Figure 5

The structure of artificial neural networks (ANNs) [38].

Figure 6

ANN MAE in predicting the acceleration variable ‘Acc’ased on epoch number. Orange line: Actual values; blue-line: Averaged values.

Figure 7

RMSE for 10-fold cross-validation of the random forest (RF) model.

Figure 8

RMSE for 10-fold cross-validation of the XGBoost model.

Figure 9

MAE for 10-fold cross-validation of the RF model.

Figure 10

MAE for 10-fold cross-validation of the XGBoost model.

Figure 11

Deformed shape at t = 3.7498 s.

Figure 12

Snapshot of time history at x = 0.2057 m.

Figure 13

Zoom of time history at x = 0.2057 m.