# Seismic Ground Response Prediction Based on Multilayer Perceptron
## 3 Seismic Responses from MLP and Conventional Models
### Response Spectrum  
The response spectrum provides a convenient means to summarize the peak response of all possible linear single-degree-of-freedom systems to a particular component of ground motion. It is plotted with the peak value of a response quantity as a function of the natural vibration period of the system. It could be a practical approach to apply knowledge of structural dynamics to the design of structures and development of lateral force requirements in building codes [31]. The acceleration response spectra were generated from the acceleration time histories measured and estimated based on MLP and SHAKE2000. The results of 20 response spectra from 10 earthquake events are plotted and compared in Figures 7-12 to investigate the applicability of the MLP model for predicting the ground motion response. In the figures, a number on the left upper side in each graph represents the number of earthquake. EW and NS on the right upper side represent a directions of earthquake events measurement, east-west and north-south. Figure 8: Measured, predicted, and computed response spectra at FKSH18 for east-west and north-south directions. Figure 9: Measured, predicted, and computed response spectra at IBRH11 for east-west and north-south directions. Figure 11: Measured, predicted, and computed response spectra at IWTH21 for east–west and north–south directions. Figure 10: Measured, predicted, and computed response spectra at IBRH13 for east–west and north–south directions. For the site FKSH17 (Kayamata), the MLP model predicts both the magnitudes of response and the natural periods in which the response amplifies (peaks) very closely with the baseline (measured), with a few exceptions. For example, for the sixth earthquake event whose response spectrum exceeds 2g at most, the MLP model overestimates the response spectrum for the natural periods below 0.3 s. SHAKE2000 tends to overestimate overall the response spectra for all the earthquakes in the site. For the site FKSH18 (Miharu), the MLP model accurately traces the natural periods when the response spectra amplify, although it does not match the magnitudes of response as well as it did in FKSH17. Especially for the sixth earthquake event, it overestimates the motion throughout the natural periods. SHAKE2000 performs as well as the MLP model in this site. In some cases, such as the first and fourth earthquake events, SHAKE2000 predicts even better than the MLP model. It is difficult to say one model is better than the other for this site. For the site IBRH11 (Iwase), both the proposed MLP model and SHAKE2000 match the amplifications of response and the periods where the response amplifies close to the baseline. For the site IBRH13 (Takahagi), while the MLP model shows a similar performance to what it did for IBRH11, SHAKE2000 overestimates the ground response for most earthquakes. For the site IWTH21 (Yamada), the MLP model matches both the magnitudes of response and the natural periods in which the response amplifies closely to the measured response, except for the sixth and seventh earthquakes who have large response spectrum magnitudes. SHAKE2000 especially overestimated the ground response for the most ground responses in the site. For the site IWTH23 (Kamaishi), the MLP model basically matches baselines, with some exceptions--the sixth, seventh, and eighth earthquakes. SHAKE2000 overpredicts for all earthquakes. Consequently, the MLP model estimates the seismic motions on the surface based on the motions at the bedrock (or 100 m). It, however, tends to overpredict the response when the value of response spectrum at the surface reaches about 2 g. The response spectrum of 2 g is induced by earthquakes with huge magnitude, and earthquakes of this scale are not  
Figure 12: Measured, predicted, and computed response spectra at IWTH23 for east-west and north–south directions. common in the dataset used for the training of the MLP. As such, the MLP model presented in this study does not present good accuracy for strong earthquakes.