The prediction of structural properties of Ni-Ti shape memory alloy by the supervised machine learning methods Oleh Yasniy 1, Nadiia Lutsyk 1, Vladyslav Demchyk 1, Halyna Osukhivska 1 Olha Malyshevska 2 1 Ternopil Ivan Puluj National Technical University, Ruska str. 56, Ternopil, 46008, Ukraine 2 Ivano-Frankivsk National Medical University, Galytska Str. 2, Ivano-Frankivsk, 76018, Ukraine Abstract Shape memory alloys (SMAs) possess unique properties, namely, they retain their original form after loading while being, for instance, heated. The structural properties of pseudoelastic NiTi SMA, such as the dependencies of stress and strain range upon the number of loading cycles, were studied by employing the methods of supervised machine learning (ML). The obtained results are quite accurate, which can be seen from the calculated mean average error (MSE) and root mean squared error (RMSE). In general, ML methods can be utilized to solve such kinds of tasks very efficiently. Keywords 1 machine learning, neural network, random forest, NiTi shape memory alloy, stress and strain ranges 1. Introduction Shape memory alloys (SMAs) ‘memorise’ or retain their initial shape when under the action of thermomechanical or magnetic fields [1]. SMAs have gained vast attention recently in a wide range of applications, that are based on their peculiar properties, namely, in products [2], structural elements [3], automotive [4], aerospace [5, 6], mini actuators and micro-electromechanical systems (MEMS) [7, 8], etc. Therefore, due to their ubiquitous widespread, it is highly important to study their structural properties, namely, the dependencies of stress and strain upon the number of loading cycles. A number of related computer modelling and simulations was performed in the studies [9-11]. Since the testing procedures are often quite costly and time-consuming, it is advisable to use the methods of artificial intelligence (AI), specifically, machine learning (ML) approaches. The number of tasks was solved efficiently by ML methods in the papers [12-14]. Thus, the aim of this paper was to predict the dependencies of stress and strain ranges upon number of loading cycles for NiTi SMA utilizing the supervised ML methods. 2. Methods The dependencies of stress range and strain on the number of loading cycles for the four specimens, that were taken from study [15] were predicted by methods of machine learning in the programming platform Orange 3.34.0 [16]. This software allows to build visually the flowcharts and obtain the results in the form of models, numerical data and plots. Proceedings ITTAP’2023: 3rd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22–24, 2023, Ternopil, Ukraine, Opole, Poland EMAIL: oleh.yasniy@gmail.com (A. 1); lutsyk.nadiia@gmail.com (A. 2); demchykv@tntu.edu.ua (A. 3); osukhivska@tntu.edu.ua (A. 4); o16r02@gmail.com (A. 5) ORCID: 0000-0002-9820-9093 (A. 1); 0000-0002-0361-6471 (A. 2); 0000-0002-7663-9332 (A. 3); 0000-0003-0132-1378 (A. 4); 0000-0003- 0180-2112 (A. 5) ©️ 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) CEUR ceur-ws.org Workshop ISSN 1613-0073 Proceedings In general, for each of four specimens, two model were built. On the input of each model there were given the dependencies of the respective physical quantity on the number of loading cycles. The number of loading cycles was treated as an independent variable, and the physical quantity was chosen as a dependent variable. To increase the accuracy of modelling results, the dataset was augmented. The data augmentation was performed by interpolating the original experimental data by 1-Dimensional Akima spline. Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is changing fast [17]. Figure 1: Model flowchart, which was built in the programming environment Orange For each specimen, the dataset was split into two unequal parts. The training dataset contained 66% of the total dataset. The regression dependencies were built by methods of random forests, neural networks, gradient boosting, support vector machines (SVM), AdaBoost, and k-nearest neigbors methods. Each of the obtained models was checked additionally by k-fold cross-validation method 10 times. Fig. 1 shows the flowchart of one model, built in the programming environment Orange. 3. Results and discussion There was performed the estimation of structural properties of specimens, made of NiTi SMAs. In general, there were tested 4 specimens. The number of specimen, as well as the sample size for stress and strain range versus the number of loading cycles are presented in Table 1. Table 1. Specimen number and sample sizes for stress and strain ranges versus the number of loading cycles. Table 1 Specimen number and sample sizes for stress and strain ranges versus the number of loading cycles Sample size specimen # Δε(N) Δσ(N) 10 1004 1004 13 771 771 16 1059 2049 17 942 942 Table 2 presents the results in the form of various prediction errors, such as root mean square error (RMSE) and mean average error (MAE), as well as correlation coefficient R2 for Δε and Δσ, assessed for specimen #10. Table 2 Prediction errors and correlation coefficient for Δε and Δσ, built for specimen # 10 using various supervised ML methods Specimen # 10 Δε Δσ 2 Model RMSE MAE R RMSE MAE R2 Ada Boost 0.014 0.008 1.000 0.776 0.196 0.999 Gradient Boosting 0.019 0.013 1.000 0.802 0.268 0.999 kNN 0.019 0.006 1.000 0.636 0.133 1.000 Neural Network 0.153 0.109 0.987 1.586 1.061 0.997 Random Forest 0.017 0.008 1.000 0.581 0.163 1.000 SVM 0.298 0.244 0.950 14.667 13.527 0.744 The lowest errors for specimen # 10 were shown by Ada Boost and kNN for Δε, and random forest and kNN for Δσ. Fig. 2 (a, b, c, d) displays the plots of predicted versus true values of the respective physical quantities, built by the afore-mentioned ML methods. a) Δε Ada Boost b) Δε kNN c) Δσ Random Forest d) Δσ kNN Figure 2: The predicted versus true values of physical quantities. a) built for Δε by means of Ada boost method; b) built for Δε by means of kNN method; c) built for Δσ using Random Forest method; d) built for Δσ using kNN method As it can seen from Fig. 2, the calculated points are very close to the bisector of the first coordinate angle, that confirms the high prediction accuracy. The modelling was also performed for the specimen #13. Table 3 contains the prediction errors and correlation coefficient for Δε and Δσ, estimated for specimen # 13 using various ML methods. Table 3 Prediction errors and correlation coefficient for Δε and Δσ, built for specimen # 13 using various supervised ML methods Specimen # 13 Δε Δσ 2 Model RMSE MAE R RMSE MAE R2 Ada Boost 0.071 0.008 0.981 0.607 0.176 1.000 Gradient Boosting 0.071 0.010 0.981 0.619 0.225 1.000 kNN 0.078 0.007 0.977 0.557 0.112 1.000 Neural Network 0.235 0.176 0.796 1.165 0.718 0.998 Random Forest 0.074 0.008 0.980 0.544 0.155 1.000 SVM 0.144 0.080 0.923 13.615 12.797 0.770 For this particular specimen, the lowest errors were obtained by employing Ada Boost and kNN for Δε, and random forest and kNN for Δσ. The plots of predicted versus true values of the respective physical quantities, built by the afore- mentioned ML methods for specimen # 13 can be seen on Fig 3 (a, b, c, d). a) Δε Ada Boost b) Δε kNN c) Δσ Random Forest d) Δσ kNN Figure 3: The predicted versus true values of physical quantities for specimen # 13 a) built for Δε by means of Ada boost method; b) built for Δε by means of kNN method; c) built for Δσ using Random Forest method; d) built for Δσ using kNN method Table 4 contains the forecast errors and correlation coefficient for Δε and Δσ, built for specimen # 16 using several supervised ML methods. Table 4 Prediction errors and correlation coefficient for Δε and Δσ, built for specimen # 16 using various supervised ML methods Specimen # 16 Δε Δσ 2 Model RMSE MAE R RMSE MAE R2 Ada Boost 0.016 0.001 0.971 0.150 0.040 1.000 Gradient Boosting 0.016 0.002 0.971 0.174 0.078 1.000 kNN 0.016 0.001 0.971 0.099 0.023 1.000 Neural Network 0.041 0.025 0.815 0.439 0.257 0.999 Random Forest 0.018 0.002 0.964 0.115 0.033 1.000 SVM 0.077 0.067 0.343 12.133 11.186 0.426 For the specimen # 16, the lowest errors were obtained by employing Ada Boost and kNN for Δε, and random forest and kNN for Δσ. Table 5 presents the errors and correlation coefficient for Δε and Δσ, obtained for specimen # 17 by means of different ML methods. Table 5 Prediction errors and correlation coefficient for Δε and Δσ, built for specimen # 17 using various supervised ML methods. Specimen # 17 Δε Δσ Model RMSE MAE R2 RMSE MAE R2 Ada Boost 0.061 0.005 0.961 5.550 0.467 0.866 Gradient Boosting 0.061 0.006 0.961 5.542 0.498 0.867 kNN 0.052 0.004 0.971 4.419 0.316 0.915 Neural Network 0.186 0.085 0.630 5.660 1.115 0.861 Random Forest 0.058 0.005 0.964 3.896 0.339 0.934 SVM 0.152 0.092 0.751 10.815 8.849 0.492 For the specimen #17, the lowest errors were obtained by Random Forest and kNN for Δε and Δσ. 4. Conclusions There were predicted the structural properties of pseudoelastic NiTi SMA, namely, the dependencies of stress and strain range upon the number of loading cycles, by employing the methods of supervised learning methods. The predicted versus true values of those two physical quantities were built. They are very close to the bisector of the first coordinate angle, which confirms high prediction accuracy. The best results in terms of RMSE and MSE were shown by Ada Boost and kNN for Δε, and by Random forest and kNN for Δσ. 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