# Vibration Control with Reinforcement Learning Based on Multi-Reward Lightweight Networks
## 4 Experimental Results and Discussion
### Optimal Reward Function Combination  
To explore the most suitable combination of reward functions, we synthesized the original reward function, variance, root mean square, and mean from [26], as detailed in Table 2. Under the conditions of employing both DRSN methods in the Actor and Critic networks, along with the application of prioritized experience replay, we experimented with various combinations of reward functions and drew conclusions. When used individually, the original reward function performed the poorest compared to variance, root mean square, and mean. Among the combined functions, as highlighted in red, the combination with the root mean square exhibited the most favorable effects. However, the data highlighted in blue indicated that the original reward function might have a detrimental impact on the combination, often leading to decreased performance. Therefore, we recommend using the  
Figure 9: The control signal, Fourier transform signal, action signal, and reward value obtained through experimentation. The first row (**a-d**) exhibits the time-domain signals from four sensors, where the x-axis denotes time steps (300 time points were captured in the experiment, scaled to the range [0.0, 0.3] by dividing by 1000), while the y-axis represents the original signal in red and the controlled signal in blue. Clearly, through effective algorithmic control, the blue signals gradually shift towards zero. The second row (**e-h**) displays the frequency-domain signals obtained by performing Fourier transforms on the data from the first row for each sensor. It is noticeable that the red non-controlled signals primarily concentrate within the range of [0–100] Hz, with fewer signals in other frequency domains. However, the controlled blue signals exhibit a significant reduction in the frequency domain. The third row (**i-l**) illustrates the control signals emitted by the controller. The x-axis corresponds to the same time steps as in the first row, while the y-axis represents control signal values within the range of [\(-\)1.0, 1.0], due to the final network layer of the controller utilizing the tanh activation function. The final row (m) represents the reward values, where the x-axis indicates the episode, and the y-axis depicts the reward value for each episode.  
combination of root mean square and mean values, which performs better in most cases, resulting in the maximum reduction of up to 20.240 dB.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**V, MSV, RMS, OM** & **Reduction (dB)** \\ \hline V & 15.988 \\ MSV & 16.032 \\ RMS & 16.284 \\ OM & 13.722 \\ V, MSV & 3.496 \\ V, RMS & 16.094 \\ V, OM & 12.062 \\ MSV, RMS & 20.240 \\ MSV, OM & 3.518 \\ \hline \hline \end{tabular}
\end{table}
Table 2: In the cases of TD3 and DRSN, with combinations of multiple reward functions, we denote the variance, mean square value, root mean square, and original method as V, MSV, RMS, and OM, respectively. In the same experimental setting, the OM reward function exhibits negative effects, while the root mean square generates positive impacts.  
Figure 10: In this figure, (**a**) depicts the network with DRSN and TD3 framework without prioritized experience replay, while (**b**) shows the network with DRSN and TD3 framework with prioritized experience replay; (**c**) represents training without prioritized experience replay for 1000 episodes, and (**d**) illustrates training with prioritized experience replay for 1000 episodes.