# Response Prediction for Linear and Nonlinear Structures Based on Data-Driven Deep Learning
## 5 Conclusions  
In this paper, the RNN and LSTM models were used to predict the responses of linear and nonlinear structures, respectively. Through the IDA for 60 original acceleration records, 582 new acceleration records were generated. The structural responses of linear and nonlinear structures under different seismic waves were analyzed by a numerical method. On this basis, label data were constructed to complete the training of the model. The trained models were used to predict the responses of linear and nonlinear structures. The main conclusions were obtained as follows:  
1. The RNN and LSTM models had good accuracy and generalization for predicting linear structural responses. Within the confidence interval [\(-10\%\), \(10\%\)], the confidence degrees of the prediction results by the RNN model for linear structural responses under the three clusters' seismic waves were 99.9%, 93.9%, and 97.1%, and those of the LSTM model were 99.5%, 92.4%, and 97.7%, respectively. Both the overall trend and details of the linear structure responses predicted by the two models were highly consistent with the true values. Both the RNN and LSTM models were capable of predicting the response of linear structures under different seismic waves. In addition, it was found that the non-stationary characteristics of seismic waves could reduce the prediction accuracy of the models. 2. The overall accuracy of the RNN in predicting nonlinear structural response was poor. Compared with the predicted results of linear structures, the prediction accuracy of the RNN model for nonlinear structure responses was significantly decreased. Within the confidence interval [\(-10\%\), \(10\%\)], the confidence degrees of the three clusters'  
Figure 15: Comparison of the numerical results and prediction results (LSTM model for nonlinear system, \(\left[\ddot{u}_{d},u_{b},\dot{u}_{6}\right]\)). (**a**) \(\ddot{u}_{d}\) under the action of the seismic wave in cluster 1. (**b**) \(u_{b}\) under the action of the seismic wave in cluster 1. (**c**) \(\dot{u}_{i6}\) under the action of the seismic wave in cluster 1. (**d**) \(\ddot{u}_{d}\) under the action of the seismic wave in cluster 2. (**e**) \(u_{b}\) under the action of the seismic wave in cluster 2. (**f**) \(\ddot{u}_{i6}\) under the action of the seismic wave in cluster 2. (**g**) \(\ddot{u}_{d}\) under the action of the seismic wave in cluster 3. (**h**) \(u_{b}\) under the action of the seismic wave in cluster 3. (**i**) \(\dot{u}_{i6}\) under the action of the seismic wave in cluster 3.  
responses predicted by the RNN model were just 90.6%, 82.3%, and 92.6%, respectively. The predicted results of the RNN model were consistent with the overall trend of the true value; however, the prediction effect for some details was extremely poor (especially in the reproduction of high-frequency characteristics and peak values). 3. The performance of the LSTM model was significantly better than that of the RNN model in predicting nonlinear structural responses. Within the confidence interval [\(-\)10%, 10%], the confidence degrees of the three clusters' responses predicted by the LSTM model were 90.2%, 86.7%, and 95.8%, respectively. Compared with the prediction result of linear structures, the prediction accuracy of the LSTM model for nonlinear structure responses was lower. The LSTM model could reproduce part of the response details of nonlinear structures. The trained LSTM and RNN models could be used to predict structural responses to earthquakes efficiently and quickly. However, data-driven deep learning has its own limitations. It is a black box model with poor interpretation. Every learning instance of ANNs is random, such as the random initialization of the weight and bias in every training cycle. How to ensure the stability of the model is worth receiving more attention. In addition, trained models are often used only for specific problems, which is very uneconomical.