# Benchmarking for Strain Evaluation in CFRP Laminates Using Computer Vision: Machine Learning versus Deep Learning

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## Abstract

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## 1. Introduction

## 2. Conceptual Distinction of Traditional Machine Learning and Deep Learning

- Supervised learning a training dataset that includes an output with labeled answers or target values for the input data. The dataset consists of pairs of input–output data and are used in the training to build the ML model. Afterwards, the target variable or the class will be predicted based on this ML model in different types of problems, such as regression or classification.
- Unsupervised learning is supposed to predict the output without any existing specification or supervision. Thus, in this technique, the correct answer is not given to the system. The system detects the patterns and structural information that share common properties.
- Reinforcement learning instead of providing a training set, the system describes the algorithm with three components: a goal, a list of allowed actions, and the environmental constraints. With these specifications, the ML model experiences the process of achieving goals based on trial and error. The ML model objective is to choose actions that maximize the expected reward and learn the best policy. The notable progress in computer hardware technologies and explosive increment in available data had required slightly more advanced algorithms in ML, such as deep learning, which outperforms its predecessors [19]. The terms machine learning and deep learning have a historical and methodological hierarchical relationship, which is presented in Figure 2 [16].

## 3. Dataset

#### 3.1. Image Settings

#### 3.2. Digital Deformation and Noise

#### 3.3. Training, Validation, and Testing

## 4. Methodology

#### 4.1. Architecture

#### 4.2. Machine Learning with Regression Methods for Computer Vision

#### 4.2.1. Filtering

#### 4.2.2. Edge Detection

#### 4.2.3. Machine Learning Algorithms

#### 4.3. Deep Learning with Regression for Computer Vision

## 5. Analysis of Results

#### 5.1. Machine Learning

#### 5.2. Deep Learning

#### 5.3. Benchmarking

## 6. Conclusions

- The architecture based on deep learning clearly provides the most feasible and accurate solutions, with high confidence measurements of the strain evolution during the pre-stress application;
- The deep learning algorithms proved to be robust to noise on the images, unlike the machine learning solutions tested, where the noise affects the quality of the results obtained;
- The architecture based on the ResNet34 deep learning algorithm achieved better performance, reaching the lowest root mean square error (RMSE) of 0.057‰ for strain prediction;
- In addition, ResNet34 also reached the highest explained variance, 0.9996, close to the perfect value of 1, and the highest covariance of 7.12 × 10
^{−6}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFRP | Carbon-Fiber-Reinforced Polymer |

RMSE | Root Mean Square Error |

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**Figure 1.**Application of Carbon-Fiber-Reinforced Polymer (CFRP) laminates: (

**a**) pre-stress application on the laminates; (

**b**) final application of the laminates (images provided by S&P, Clever Reinforcement Iberica—Materiais de Construçao, Lda.).

**Figure 9.**Polynomial Regression and Decision Tree Regression results. (

**a**) Polynomial Regression predictions. (

**b**) Polynomial Regression predictions by quantile variations. (

**c**) Decision Tree Regression predictions. (

**d**) Decision Tree Regression predictions by quantile variations.

**Figure 10.**Fully connected neural network (FCNN) and Random Forest results. (

**a**) Random Forest Regression predictions. (

**b**) Random Forest Regression predictions by quantile variations. (

**c**) FCNN with regression predictions. (

**d**) FCNN with regression predictions by quantile variations.

**Figure 11.**Support Vector Regression (SVR) results. (

**a**) Support Vector Regression predictions. (

**b**) Support Vector Regression predictions by quantile variations.

**Figure 12.**ResNet and GoogLeNet results. (

**a**) GoogLeNet with regression predictions. (

**b**) GoogLeNet with regression predictions by quantile variations. (

**c**) ResNet with regression predictions. (

**d**) ResNet with regression predictions by quantile variations.

**Figure 13.**ResNet with regression vs. machine learning predictions. (

**a**) ResNet with regression vs. FCNN with regression predictions. (

**b**) ResNet with regression vs. Polynomial Regression predictions. (

**c**) ResNet with regression vs. Random Forest Regression predictions. (

**d**) ResNet with regression vs. Support Vector Regression predictions. (

**e**) ResNet with regression vs. Decision Tree Regression predictions.

**Figure 14.**ResNet with regression RMSE vs. the rest. (

**a**) ResNet with regression RMSE vs. Random Forest Regression RMSE. (

**b**) ResNet with regression RMSE vs. FCNN with regression RMSE. (

**c**) ResNet with regression RMSE vs. Polynomial Regression RMSE. (

**d**) ResNet with Regression RMSE vs. Support Vector Regression RMSE. (

**e**) ResNet with regression RMSE vs. Decision Tree Regression RMSE. (

**f**) Resnet with regression RMSE vs. GoogLeNet with regression RMSE.

Algorithm | Number of Layers | Number of Epoch | Learning Rate | Batch Size |
---|---|---|---|---|

GoogLeNet | 22 | 200 | 0.001 | 1 |

ResNet | 34 | 500 | 0.001 | 32 |

Algorithm | Mean Squared Error (‰) | RMS Error (‰) | Explained Variance | Covariance ($\times {10}^{-6}$) | R^{2} |
---|---|---|---|---|---|

Polynomial Regression | 0.3498 | 0.5914 | 0.9493 | 6.5199 | 0.9494 |

Decision Tree Regression | 0.2609 | 0.5108 | 0.9620 | 6.6470 | 0.9622 |

Random Forest Regression | 0.2560 | 0.5060 | 0.9631 | 6.6327 | 0.9629 |

Support Vector Regression | 0.5925 | 0.7698 | 0.9141 | 6.2753 | 0.9142 |

Fully Connected Neural Network | 0.4050 | 0.6364 | 0.9411 | 6.7609 | 0.9392 |

GoogLeNet + Regression | 0.1852 | 0.4303 | 0.9989 | 7.0399 | 0.9990 |

ResNet + Regression | 0.0032 | 0.0570 | 0.9996 | 7.1225 | 0.9996 |

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**MDPI and ACS Style**

Valença, J.; Mukhandi, H.; Araújo, A.G.; Couceiro, M.S.; Júlio, E.
Benchmarking for Strain Evaluation in CFRP Laminates Using Computer Vision: Machine Learning versus Deep Learning. *Materials* **2022**, *15*, 6310.
https://doi.org/10.3390/ma15186310

**AMA Style**

Valença J, Mukhandi H, Araújo AG, Couceiro MS, Júlio E.
Benchmarking for Strain Evaluation in CFRP Laminates Using Computer Vision: Machine Learning versus Deep Learning. *Materials*. 2022; 15(18):6310.
https://doi.org/10.3390/ma15186310

**Chicago/Turabian Style**

Valença, Jónatas, Habibu Mukhandi, André G. Araújo, Micael S. Couceiro, and Eduardo Júlio.
2022. "Benchmarking for Strain Evaluation in CFRP Laminates Using Computer Vision: Machine Learning versus Deep Learning" *Materials* 15, no. 18: 6310.
https://doi.org/10.3390/ma15186310