# Seismic Ground Response Prediction Based on Multilayer Perceptron
## 3 Seismic Responses from MLP and Conventional Models
### Prediction Errors  
The discrepancy between the response spectra of the models and the baseline of each ground motion was quantified as an error, as presented in Equation (3), for each site.  
\[\text{Error}=Sa_{measured}-Sa_{predicted} \tag{3}\]  
where \(Sa_{measured}\) is the spectral acceleration of the measurement, and \(Sa_{predicted}\) is the spectral acceleration of the prediction from the MLP or SHAKE2000 model. An average of 20 errors in each station (average error) was calculated with Equation (4):  
\[\text{Average Error}=\frac{1}{n}\sqrt{\sum_{i=1}^{n}(\text{Error}_{i})^{2}} \tag{4}\]  
where \(n\) is the number of ground motions in each station.  
The errors and the average errors of MLP and SHAKE2000 predictions for the six sites are plotted in Figures 13 and 14. In the figures, the thin lines represent errors for 20 individual earthquake measurements, and the thick lines the average of errors for 20 earthquake measurements. For the site FKSH17, the errors are higher for the natural periods between 0.1 and 0.3 s than for other periods. The errors from SHAKE2000 are much higher than those from MLP for this site. For the site FKSH18, both models produced higher errors for the natural periods from 0.1 to 0.5 s. Errors from a large earthquake event caused the most of the average errors (for this site, the sixth earthquake). (for this site, the sixth earthquake). For the sites in Ibarakiken, IBRH11 and IBRH13, both models generated low errors throughout the natural period except for the sixth earthquake. For the site IWTH21, the average errors of the MLP model are low over all the periods as it matches the baseline closely. The average errors of SHAKE2000 seem higher, as it overestimated the response of the ground. For the site IWTH23, the MLP model has larger average errors than SHAKE2000 especially for the periods from 0.06 to 0.1 s. SHAKE2000 outperformed the MLP model in this site.  
Even though the results varied a little from site to site, overall, the MLP model produced smaller errors than SHAKE2000. Figure 15 presents and summarizes the total errors of predictions for all sites by MLP and SHAKE2000. The thin lines represent the average errors of the earthquake predictions for each site by Equation (4); the thick lines global errorsof all six sites (all the thin lines) by Equation (5).  
\[\text{Global Error}=\frac{1}{n}\sqrt{\sum_{i=1}^{n}(\text{Average Error}_{i})^{2}} \tag{5}\]  
where \(n\) is the number of the sites. The thick blue colored lines are for MLP and the thick red for SHAKE2000.  
Figure 13: Errors in the ground motions by the MLP model.  
Figure 14: Errors in the ground motions by SHAKE2000.  
As shown in Figure 15, the total average errors of the MLP model particularly stand out for the periods from 0.06 to 0.1 s and from 0.3 to 0.5 s. The high average errors for the period between 0.06 and 0.1 s are due to the errors of the site IWTH23, and the errors for the period between 0.3 and 0.5 s are due to those of IBRH11. The average errors of SHAKE2000 are emphasized in the period between 0.1 and 0.3 s by the earthquake measurements from Fukushima (FKSH17, FKSH18) and Iwateken (IWTH21, IWTH23).  
Throughout the periods, the MLP model outperformed SHAKE2000 in predicting the seismic response on the surface based on the ground motion in the bedrock.