Prediction of Tribological Properties of UHMWPE/SiC Polymer Composites Using Machine Learning Techniques
Abstract
:1. Introduction
2. Experimental Procedure
2.1. Methodology
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- Nine data points from the suggested study [16] were collected. To train the models, the SiC loading size, consolidation pressure, and holding time were used as features to determine the coefficient of friction (COF) and specific wear rate (SWR) of the resulting polymer composite combination.
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- Using the Mathematica language, two interpolation functions that best represented the correlation between the experimental independent and dependent variables were developed for the SWR and COF from the data points of [16], as shown in Equations (1) and (2), where the variables x, y, and z represent SiC loading, consolidation pressure, and holding time, respectively:
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- The interpolation functions were then used to generate a larger dataset consisting of 1499 data points within the bounds of the original nine points.
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- The five appropriate machine learning techniques selected were decision trees, random forests, k-nearest neighbors, support vector machine, and artificial neural network.
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- The dataset was partitioned into 2 components as 70% of the samples were used to train the models, while the remaining 30% were used as an unseen test set for models to predict values. Figure 1a and Figure 1b show the frequency of the training and the testing dataset for the COF and SWR, respectively.
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- Using Python, each technique was subjected to a grid search, or the repeated training of the algorithm on a set of data while varying the hyperparameters for each iteration, in order to find the optimal settings that produced the least error rates for each target variable (CoF and SWR). The data points were also rescaled depending on the method.
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- The model performances were then compared with each other through regression and error analyses. In order to observe the best performance, the primary metrics used for the comparison consisted of the following:
- (a)
- Root mean squared error (RMSE): a measure of how far off the predictions are from the true values of the test data points. A lower RMSE closer to 0 was indicative of a better performance. The distance measure is calculated as shown in Equation (1), where is the predicted value and x is the true value of each sample.
- (b)
- Mean absolute error (MAE): similar to the RMSE, the MAE is also used as a metric to observe the gap in errors between the predictions and true values of the samples. The value is calculated according to Equation (2), where is the predicted value and x is the true value of each sample.
- (c)
- Coefficient of determination (R2-score): also known as the R-squared value, it is a measure of the correlation between the dependent and independent variables. Ranging from 0 to 1.0 (or 0 to 100%), a higher value is indicative of a better regression fit. The coefficient of determination is calculated, as shown in Equation (3), where is the predicted value of the sample, is the mean of all sample points, and is the true value.
2.2. An Overview of Machine Learning
2.3. Machine Learning Techniques Implemented in the Current Study
3. Results and Analysis
3.1. Performance Analysis
3.1.1. Decision Tree
3.1.2. Random Forest
3.1.3. K-Nearest Neighbors
3.1.4. Support Vector Machine
3.1.5. Artificial Neural Network
4. Future Extension
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Trial No. | SiC Loading (wt%) | Consolidation Pressure (MPa) | Holding Time (min) | COF |
---|---|---|---|---|
1 | 1 | 10 | 10 | 0.172 |
2 | 1 | 16 | 15 | 0.173 |
3 | 1 | 22 | 20 | 0.181 |
4 | 4 | 10 | 15 | 0.177 |
5 | 4 | 16 | 20 | 0.186 |
6 | 4 | 22 | 10 | 0.189 |
7 | 7 | 10 | 20 | 0.184 |
8 | 7 | 16 | 10 | 0.185 |
9 | 7 | 22 | 15 | 0.187 |
Trial No. | SiC Loading (wt%) | Consolidation Pressure (MPa) | Holding Time (min) | SWR × 10−5 (mm3/Nm) |
---|---|---|---|---|
1 | 1 | 10 | 10 | 1.65 |
2 | 1 | 16 | 15 | 1.89 |
3 | 1 | 22 | 20 | 1.55 |
4 | 4 | 10 | 15 | 1.68 |
5 | 4 | 16 | 20 | 1.69 |
6 | 4 | 22 | 10 | 1.35 |
7 | 7 | 10 | 20 | 1.29 |
8 | 7 | 16 | 10 | 1.40 |
9 | 7 | 22 | 15 | 1.26 |
Model | Optimal Hyperparameters | RMSE (Test Set) | MAE (Test Set) | R2 Score (Test Set) | |||
---|---|---|---|---|---|---|---|
COF | SWR | COF | SWR | COF | SWR | ||
DT | Max. Depth: 50 | 0.00214 | 5.4 × 10−7 | 0.0014 | 3.7 × 10−7 | 0.9367 | 0.9579 |
RF | Min. Split: 3 | 0.00111 | 3.1 × 10−7 | 0.0007 | 2.1 × 10−7 | 0.9827 | 0.9861 |
Min. Leaf Samples: 1 | |||||||
Impurity Decrease Threshold: None | |||||||
SVM | Gamma: 0.25 | 0.000209 | 0.0002 | 0.0002 | 0.00016 | 0.9999 | 0.9998 |
Kernel: Radial Basis Function | |||||||
C Parameter: 100 | |||||||
Epsilon: 0.00001 | |||||||
KNN | No. of Neighbours: 8 | 0.016215 | 0.01511 | 0.0105 | 0.0105 | 0.98891 | 0.99098 |
Weights based on distance | |||||||
Distance Computation: Euclidean | |||||||
ANN | Epochs: 100 | 0.022596 | 0.03349 | 0.0184 | 0.02676 | 0.978471 | 0.95569 |
Optimizer: “Adam” | |||||||
Validation amount: 20% | |||||||
Learning Rate: 0.001 |
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Mohammed, A.J.; Mohammed, A.S.; Mohammed, A.S. Prediction of Tribological Properties of UHMWPE/SiC Polymer Composites Using Machine Learning Techniques. Polymers 2023, 15, 4057. https://doi.org/10.3390/polym15204057
Mohammed AJ, Mohammed AS, Mohammed AS. Prediction of Tribological Properties of UHMWPE/SiC Polymer Composites Using Machine Learning Techniques. Polymers. 2023; 15(20):4057. https://doi.org/10.3390/polym15204057
Chicago/Turabian StyleMohammed, Abdul Jawad, Anwaruddin Siddiqui Mohammed, and Abdul Samad Mohammed. 2023. "Prediction of Tribological Properties of UHMWPE/SiC Polymer Composites Using Machine Learning Techniques" Polymers 15, no. 20: 4057. https://doi.org/10.3390/polym15204057