# A Deep Learning-Based Approach for the Identification of a Multi-Parameter BWBN Model
## 4 Results and Discussion  
### Results  
Based on the predicted parameters of the deep learning model, the predicted hysteretic loop can be obtained by substituting them into the BWBN model then comparing them with the hysteretic loops of the experimental data. There are 18 groups of data randomly extracted from the 3 failure modes of the database, with 6 failure modes for each failure mode. The selected samples are shown in Table 2. The comparison results are shown in Figure 5.  
It can be seen that the predicted hysteretic loop is basically consistent with the experimental hysteretic loop, which indicates that the deep learning prediction model has reached the expected setting. As shown in Figure 3, the current research method can easily and directly identify the parameters of the multi-parameter model without establishing a priori estimation or classifying the failure types. This proposed method is simple, thus, it solves the difficult problems encountered in the application of multi-parameter model. For further verifications of the correctness of the parameter identification method, the BWBN material constitutive model is embedded in OPENSEES software [71]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**BWBN Parameters** & \(\mathbf{\kappa}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) & \(\mathbf{n}\) & \(\delta_{\mathbf{v}}\) & \(\delta_{\mathbf{\eta}}\) & \(\xi_{\mathbf{s}}\) & \(p\) & \(q\) & \(\delta_{\mathbf{\psi}}\) & \(\lambda\) \\ \hline Hidden layer 1 & & & & & & \(11\) & & & & \\ Hidden layer 2 & & & & & \(17\) & & & & \\ Hidden layer 3 & & & & & \(15\) & & & & \\ Hidden layer 4 & & & & & \(17\) & & & & \\ Hidden layer 5 & & & & & \(11\) & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: The number of neurons of deep learning model. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Authors/Specimen** & **Failure** & **Span-to-Depth** & **Axial Load** & **Longitudinal** & **Transverse** \\  & **Mode** & **Ratio** & **Ratio** & **Reinforcement Ratio** & **Reinforcement Ratio** \\ \hline S1 & Atalay and Penzien, 1975, No. SS1 & & 5.50 & 0.20 & 0.02 & 0.02 \\ S2 & [PERSON] et al., 1988, NC-2 & & 3.00 & 0.21 & 0.02 & 0.02 \\ S3 & [PERSON] 1996, UC1C & & 2.00 & 0.35 & 0.02 & 0.00 \\ S4 & [PERSON] et al., 1999, C10-05S & & 3.00 & 0.05 & 0.02 & 0.01 \\ S5 & [PERSON] et al., 1988, No. 21 & & 2.18 & 0.11 & 0.04 & 0.63 \\ S6 & [PERSON], 2002, UCI2 & & 4.56 & 0.00 & 0.01 & 0.53 \\ \hline S7 & [PERSON], 1982, HPRC19-32 & & 1.5 & 0.35 & 0.0127 & 0.014 \\  & Wight and Sozen, 1973, No. 40.033 & & 2.87 & 0.114 & 0.0245 & 0.003 \\  & (West) & FS & 3.22 & 0.284 & 0.0194 & 0 \\ S9 & [PERSON] et al., 1998, Z CMH18 & & 2 & 0 & 0.032 & 0.51 \\ S10 & [PERSON] et al., 1985, No. 1 & & 2.58 & 0.00 & 0.01 & 0.26 \\ S11 & [PERSON], 2002, UCI5 & & 3.22 & 0.15 & 0.02 & 0.00 \\ \hline S12 & [PERSON] et al., 1998, SCMH18 & & 3.22 & 0.262 & 0.0303 & 0 \\ S14 & [PERSON] et al., 1985, No. 18 & & 1.5 & 0.1 & 0.032 & 0.51 \\ S15 & [PERSON], 1997, SZ & & 2 & 0.002 & 0.0136 & 0.13 \\ S16 & [PERSON] et al., 1987, No. 1 & & 1.09 & 0 & 0.0385 & 0.47 \\ S17 & [PERSON] et al., 1987, No. 8 & & 1.09 & 0.109 & 0.0385 & 1.34 \\ S18 & [PERSON] et al., 1988, No. 28 & & 1.64 & 0.166 & 0.0385 & 0.63 \\ \hline \end{tabular}
\end{table} 
Table 2: Test samples of RC Columns with different mode. Figure 5: _Cont_. Figure 5: Comparison of predicted hysteresis loop with experimental data. The parameters of the BWBN material constitutive are identified by the deep learning method. Finally, the assigned BWBN material constitutive model is added to the beam column joint element. The Eom's cast-in-situ cross joint experiment was selected as the experimental data [72]. Cyclic loading is carried out by the displacement loading method. The geometric dimensions and reinforcement of joints can be found in [72; 73]. Joint2d-1 joint is used as the joint numerical model, and the hysteretic material in the core area of the joint is simulated by the BWBN model.