# Prediction of Dynamic Responses of Flow-Induced Vibration Using Deep Learning
## 3 Deep Learning Model for Dynamic Response Prediction of FIVs  
### FIV Tested Data for Learning  
Experiments were performed with the learning data using the second-generation Vck system developed by MRELab. Figure 6 shows the single-cylinder converter mounted in the LTFSW channel. The Reynolds number in the range of 30,000 \(<\) Re \(<\) 120,000 and the flow velocity in the range of 0.395 m/s \(<\) U \(<\) 1.315 m/s were the tested data conditions used in this study. When the mass ratio (m* = m\({}_{\text{osc}}\)/m\({}_{\text{d}}\)) was 1.343, the spring constant (K) was 400, 600, 755, 1000, and 1200 N/m, and the harness damping ratio (\(\zeta_{\text{harness}}\)) for each spring constant was 0.04, 0.08, 0.12, 0.16, 0.2, and 0.24. Table 1 and Figure 7 show the results for the dynamic responses of a single rigid circular cylinder mounted with PTC [11; 12; 14]. In addition, the specifications of the single cylinder oscillator model, along with the tested conditions, are summarized in Table 2.  
Figure 6: Schematic of the LTFSW channel and single cylinder converter [12]. Through testing under the above conditions, the parameters to train the tested data of the single-cylinder amplitude and natural frequency of the system for the deep learning model were first extracted. A total of six parameters were extracted, as follows: spring constant K, harness damping ratio of the system \(\zeta_{\text{harness}}\), number of rotations of the induction generator to circulate the water in the LTFSW channel \(f_{\text{motor}}\), natural frequency of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Particular** & & & & \\ \hline \hline \(K\) (N/m) & 400 & 600 & 755 & 1000 & 1200 \\ Temperature (\({}^{\circ}\)C) & & & 20.5 & & \\ \(\mu\) (N-s/m\({}^{2}\)) & & & \(1.004\times 10^{-3}\) & & \\ \(\
u\) (m\({}^{2}\)/s) & & & \(9.940\times 10^{-7}\) & & \\ \(\rho\) (kg/m\({}^{3}\)) & & & 999.72965 & & \\ D (m) & & & 0.0889 & & \\ L (m) & & & 0.89535 & & \\ mdisplacement (kg) & & & 5.425 & & \\ moscillation (kg) & & & 7.285775 & & \\ madded (kg) & & & 5.425 & & \\ \(\zeta_{\text{structure}}\) & & & 0.02 & & \\ f\({}_{\text{n,water}}\) & 0.893 & 1.093 & 1.227 & 1.412 & 1.546 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Particulars of single-cylinder oscillator model. Figure 7: Configuration of passive turbulence control (PTC) on the cylinder [11]. the cylinder in water, \(\rm f_{n,water}\), reduced velocity U*, and finally the Reynolds number Re. Correlation analysis was then performed to identify the effects of the extracted parameters on the dependent variables, amplitude (A/D), and frequency (\(\rm f_{cyl}\)) of the cylinder. The correlation coefficient was calculated using the Pearson method in this study, which is a parametric correlation coefficient, as shown in Table 3.  
Equation (1) shows the expression used to calculate the correlation coefficient of the Pearson method. \[ \begin{split}\text{Pearson Coefficient(r)}=\frac{n\sum X_{i}Y_{i} -\sum X_{i}\sum Y_{i}}{\sqrt{n\sum X_{i}^{2}-(\sum X_{i})^{2}}\sqrt{n\sum Y_{i} ^{2}-(\sum Y_{i})^{2}}}\\ \text{where }\text{X}=\text{Independent variable}\\ \text{Y}=\text{Dependent variables}\\ \text{n}=\text{Number of specimens}\end{split}  \tag{1}\]  
The four input values of the deep learning model selected through correlation analysis were: K, \(\rm\zeta_{\rm harness}\), U*, and Re. The variables U* and Re were selected, which have large positive linear relationships with the amplitude of the cylinder. The variable K was added as it had a relatively large correlation, and there were no other variables that correlated with the frequency compared to the amplitude of the cylinder. Finally, by adding \(\rm\zeta_{\rm harness}\) with a negative correlation coefficient to the amplitude and frequency of the cylinder, the four selected input parameters are obtained. For the output parameters, the amplitude ratio A/D of the cylinder in FIVs and the cylinder frequency, \(\rm f_{cyl}\), at the nodes of the output layer, respectively, were predicted.