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. machine learning, neural network, random forest, NiTi shape memory alloy, stress and strain 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. Proceedings ITTAP'2023: 3rd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22-24, 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); 0000-0003Proceedings
ranges
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.
2020 Copyright for this paper by its authors. CEUR
ceur-ws.org
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].
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.
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. 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.
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.
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 aforementioned ML methods for specimen # 13 can be seen on Fig 3 (a, b, c, d).
Table 4 contains the forecast errors and correlation coefficient for Δε and Δσ, built for specimen # 16 using several supervised ML methods.
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.
For the specimen #17, the lowest errors were obtained by Random Forest and kNN for Δε and Δσ.
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. It can be further concluded, that the methods of supervised ML can efficiently predict the afore-mentioned dependencies, and are the promising method to solve such kinds of tasks. 5. References [6] D. J. Hartl and D. C. Lagoudas, Aerospace applications of shape memory alloys,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 221, no. 4, Apr. (2007): 535–552, doi: 10.1243/09544100jaero211. [7] L. Sun et al., Stimulus-responsive shape memory materials: A review, Materials in Engineering, vol. 33, Jan. (2012): 577–640, doi: 10.1016/j.matdes.2011.04.065. [8] M. Kohl. Shape Memory Microactuators (Microtechnology and MEMS). 1 ed. Heidelberg:
Springer-Verlag Berlin, (2010). [9] Petryk, M.R., Khimich, A., Petryk, M.M., Fraissard, J. Experimental and computer simulation studies of dehydration on microporous adsorbent of natural gas used as motor fuel, 2019. Fuel239, pp. 1324-1330. [10] Okipnyi, I.B., Maruschak, P.O., Zakiev, V.I. et al. Fracture Mechanism Analysis of the HeatResistant Steel 15Kh2MFA(II) After Laser Shock-Wave Processing. J Fail. Anal. and Preven. 14, 668–674 (2014). https://doi.org/10.1007/s11668-014-9869-4. [11] Hutsaylyuk, V., Lytvynenko, I., Maruschak, P., Schnell, G., Seitz, H. A new method for modeling the cyclic structure of the surface microrelief of titanium alloy ti6al4v after processing with femtosecond pulses Materials, 2020, 13(21), pp. 1-8, 4983. [12] Alyamani, A., & Yasniy, O. Classification of EEG signal by methods of machine learning. Applied
Computer Science, 16(
No 4, (2018):7–12, doi: 10.33108/visnyk_tntu2018.04. [16] Bioinformatics Laboratory, University of Ljubljana, “Data mining.”
URL:https://orangedatamining.com/ [17] Akima, H. A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures.
Journal of the ACM, Association for Computing Machinery, 17(