# Behaviour Investigation of SMA-Equipped Bar Hysteretic Dampers Using Machine Learning Techniques
## 6 Conclusions  
A novel bar hysteretic dampers equipped with shape memory alloy (SMA) bars, named SMA-BHDs, as an added damper to isolation systems, was studied in this paper. In order to predict the cyclic behaviour of these dampers, 630 numerical models including different geometrical and mechanical properties were constructed in SeismoStruct software. The obtained hysteretic curves from numerical models were idealised by bilinear curves to achieve pre- and post-yield parameters such as the first yield point displacement (\(D_{y}\)), elastic stiffness (\(K_{e}\)), and post-yield stiffness ration (\(\alpha\)). The analyses show that the existing analytical equation for determining \(D_{y}\) is not consistent with obtained results from hysteretic curves and needs modification. Moreover, there is no analytical equation for estimating _the_\(\alpha\) parameter. Therefore, two machine learning approaches, named artificial neural network (ANN) and group method of data handling integrated by a neural network (GMDH-NN), were utilised to estimate the \(D_{y}\) modification factor (\(\beta\)) and propose an equation for \(\alpha\) parameter for the first time. An overview of the results of this paper is presented as follows:  
1. As expected, by substituting SMA bars instead of steel bar in bar hysteretic dampers, no residual displacement could be seen in hysteretic curves, which shows the excellent performance of SMA-BHDs as added dampers to isolation systems. 2. Considering the ANN models with one hidden layer and varying neuron numbers between 3 to 25, the neural networks with 10 and 6 hidden neurons were selected as the optimised network structure for \(\beta\) and \(\alpha\) parameters, respectively. The ANN (\(\beta\)) model has the R values of 0.9972, 0.9958, and 0.9916 in training, testing, and validation data sets and considerably small MSE values of 0.00012 and 0.00047, and MAPE values of 2.60% and 3.31%, in training and testing data sets, respectively. On the other hand, ANN (\(\alpha\)) model has the R values of 0.9986, 0.9966, and 0.9972 in training, testing, and validation data sets and MSE values of 0.00007 and 0.00008, and MAPE values of 2.34% and 2.43%, in training and testing data sets, respectively. 3. In the GMDH-NN models, similarly to ANN models, around 25% of all databases (97 data from 389 data) were randomly set aside for the test stage and considered unseen data. The results show that the proposed ANN models with higher R\({}^{2}\) and lower error values in both the training and testing stages outperform the proposed GMDH-NN models. However, compared with the ANN model, GMDH-NN models present more user-friendly and easy-to-interpret closed-form equations. 4. The sensitivity analysis of the input parameters in the developed ANN and GMDH-NN models for estimating both \(\beta\) and \(\alpha\) parameters showed that the calculated SMA bars length (\(L\)) variable with higher R and RMSE values is the most influential input variable. Furthermore, the number of SMA bars (\(N\)) with lower impact values on the R and RMSE has the least effect. Conceptualisation, H.J., D.R.E. and M.K. ; methodology, D.R.E., H.J. and M.K. ; software, S.A.N.J., H.J. and D.R.E. ; validation, D.R.E., H.J. and A.K. ; formal analysis, D.R.E., H.J., V.F. and A.K. ; investigation, H.H., M.K., S.A.N.J. and V.F. ; resources, H.J., D.R.E., A.K. and N.F. ; data curation, D.R.E. and H.J. ; writing--original draft preparation, H.J., A.K., H.H. and S.A.N.J. ; writing--review and editing, H.J., D.R.E., V.F., N.F. and M.K. ; visualisation, H.J., D.R.E., H.H. and N.F. ;supervision, H.J., D.R.E. and M.K. ; project administration, H.J., D.R.E. and M.K. ; funding acquisition, V.F. and M.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Institutional Review Board Statement**: Not applicable. **Informed Consent Statement**: Not applicable. **Data Availability Statement**: The data presented in this study are available on request from the corresponding author.