# Combined Use of Modal Analysis and Machine Learning for Materials Classification

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Modal Analysis

^{−010}<<< 0.95 which is assuring that the mesh is suitable and of a high quality for further calculations. Modal analysis was performed with the same plate, changing the material each time, for collecting the results in order to find general relations or trends that govern the behavior of these materials using ML. In addition, mode shapes were obtained that elucidate the displacement under the resonance frequency. The first three mode shapes of copper plate are illustrated in Figure 2. The resonance frequencies were extracted and later read by Python (Python Software Foundation, Wilmington, DE, USA) (accessed on 2 July 2021) in order to process the data.

#### Kirchhoff Thin Plate Model

#### 2.3. Data Processing

#### 2.3.1. Deep Learning Approach

#### 2.3.2. Machine Learning Approach

#### 2.3.3. Model Evaluation

#### 2.3.4. Data Processing and Analysis

## 3. Results and Discussions

#### 3.1. Isotropic Materials

#### 3.2. Orthotropic Materials

## 4. Conclusions

- The study demonstrated the ability to classify engineering materials, including isotropic and orthotropic materials, by applying ML algorithms on the modal analysis results. The proposed ML approaches could reach an accuracy of 100% when interrelations were created between the inputs to the ML algorithms (combined linear regression approach in this study).
- The Keras model was not suitable for this study as it showed 50% accuracy when compared to the ML approaches. The study validates the classification applicability based on the resonance frequency information, which may broaden the horizon of further applications such as a device that can classify the materials based on their modal analysis.
- The study showed a novel method of using the extracted data from modal analysis to accurately classify and identify the engineering materials as well as validate the efficiency of using induced interrelations between the mode number and its corresponding resonance frequency to increase the accuracy of the proposed machine learning methods.
- The study validated the classification applicability based on the resonance frequency information, which may broaden the horizon of further applications such as a device that can classify the materials based on their modal analysis. A further study could include other modal analysis parameters, such as damping ratios using experimental data as it will be by default assumed to be zero in ANSYS.
- Potential future studies can study other DL approaches and the deployment of neural networks that could achieve promising classification studies. Further extensions and relations can be established for detailed material properties identification through deploying the concept of ML and DL into the field of mechanical engineering, which would further confirm the modern concept of science integration.
- The results of this study can boost non-destructive materials characterizations and analysis methods in general, not just the explored modal analysis example, as ML and DL deal mainly with data regardless of the acquiring method.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The studied plate with dimensions of 250 mm in length, 125 mm in width and 5 mm in thickness, using ANSYS.

**Figure 2.**(

**a**–

**c**) Overview of different mode shapes obtained of the copper plate after the processing of data.

**Figure 3.**The explanation of the Kirchhoff-Love plate model. Where 1 is the plate thickness, u is the plate displacement amplitude, w is the difference between centers of deformed and non-deformed plate, δw/δx is the strain due to the applied force on the element and dx is an infinitesimal element in the x-axis.

**Figure 6.**Isotropic test set accuracy results for 2D and 3D input to the ML model using different ML approaches.

**Figure 13.**Overall summary and procedure of using ML and DL in engineering materials classification.

Mode Number | Frequency for the Studied Materials [Hz] | |||
---|---|---|---|---|

Stainless Steel | Magnesium | Epoxy Carbon Woven (230 GPa) Wet | Epoxy E-Glass UD | |

1 | 66.376 | 67.086 | 82.419 | 61.665 |

2 | 280.78 | 278.47 | 169.44 | 161.35 |

3 | 412.82 | 416.48 | 511.09 | 383.84 |

Accuracy | Logistic Regression | Decision Tree | K-Nearest Neighbors | Linear Discriminant | Naive Bayes | Support Vector Machine |
---|---|---|---|---|---|---|

Training set | 0.55 | 1.00 | 0.51 | 0.56 | 0.51 | 1.00 |

Test set | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 |

**Table 3.**Accuracy values for different machine learning algorithms with the combined linear regression approach applied on the isotropic materials’ results.

Accuracy | Logistic Regression | Decision Tree | K-Nearest Neighbors | Linear Discriminant | Naive Bayes | Support Vector Machine |
---|---|---|---|---|---|---|

Training set | 1.00 | 1.00 | 1.00 | 0.56 | 1.00 | 1.00 |

Test set | 0.88 | 1.00 | 1.00 | 0.50 | 1.00 | 0.50 |

**Table 4.**Accuracy values for different machine learning algorithms with the combined linear regression approach applied on orthotropic materials’ results.

Accuracy | Logistic Regression | Decision Tree | K-Nearest Neighbors | Linear Discriminant | Naive Bayes | Support Vector Machine |
---|---|---|---|---|---|---|

Training set | 0.88 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 |

Test set | 0.68 | 1.00 | 1.00 | 1.00 | 1.00 | 0.50 |

**Table 5.**Accuracy values for different machine learning algorithms applied on the 3D test datasets for isotropic and orthotropic materials.

Accuracy | Logistic Regression | Decision Tree | K-Nearest Neighbors | Linear Discriminant | Naive Bayes | Support Vector Machine |
---|---|---|---|---|---|---|

Isotropic | 0.88 | 1.00 | 1.00 | 0.50 | 1.00 | 0.50 |

Orthotropic | 0.68 | 1.00 | 1.00 | 1.00 | 1.00 | 0.50 |

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**MDPI and ACS Style**

Abdelkader, M.; Noman, M.T.; Amor, N.; Petru, M.; Mahmood, A. Combined Use of Modal Analysis and Machine Learning for Materials Classification. *Materials* **2021**, *14*, 4270.
https://doi.org/10.3390/ma14154270

**AMA Style**

Abdelkader M, Noman MT, Amor N, Petru M, Mahmood A. Combined Use of Modal Analysis and Machine Learning for Materials Classification. *Materials*. 2021; 14(15):4270.
https://doi.org/10.3390/ma14154270

**Chicago/Turabian Style**

Abdelkader, Mohamed, Muhammad Tayyab Noman, Nesrine Amor, Michal Petru, and Aamir Mahmood. 2021. "Combined Use of Modal Analysis and Machine Learning for Materials Classification" *Materials* 14, no. 15: 4270.
https://doi.org/10.3390/ma14154270