## 3 Experimental Results
### Experimental Results
#### 3.2.2 Experiment 2: Quantitative Analysis and Comparison on Sinusoidal Loads  
To further verify the identification performances on different types of dynamic loads, in this experiment, the proposed approach is quantitatively evaluated on the different sinusoidal loads using the above two metrics. Quantitative comparisons between the performances proposed approach and those of the performances of other approaches are also provided. For the sinusoidal loads, two loads are evaluated on the symmetrically distributed sensors and the asymmetrical ones, respectively. In particular, \(F_{sin1}=5\sin(20\pi t)\) and \(F_{sin2}=5\sin(30\pi t)\) are applied to the symmetrical distribution, while \(F_{sin3}=4\sin(20\pi t)\) and \(F_{sin4}=4\sin(30\pi t)\) are applied to the asymmetrical one. Table 4 gives the quantitative evaluation on different sinusoidal loads when accelerometer sensors are symmetrically and asymmetrically distributed. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Sensor Distribution** & **Load** & **RMSE** & **CC** \\ \hline Symmetric & \(5\sin(20\pi t)\) & 0.5830 & 0.9999 \\ Symmetric & \(5\sin(30\pi t)\) & 0.3361 & 1.0000 \\ Asymmetric & \(4\sin(20\pi t)\) & 0.3572 & 0.9999 \\ Asymmetric & \(4\sin(30\pi t)\) & 0.4451 & 0.9999 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Load identification performances evaluations on sinusoidal loads. In the experiments, different sensor distributions and sinusoidal signals with different frequency are considered. In each experiment, identification results with very high CC are obtained. Figure 5: The detailed comparisons of the identified random loads with respect to the ground truth values with different approaches. In this comparison, the symmetrical sensor distribution is utilized. 1 regularization method (**a**), 1 wavelet based data–driven method (**b**) and 1 time domain data–driven method (**c**) are compared with the proposed approach. (**a**) Comparisons of the estimated loads using Tikhonov method with respect to the ground truth values. (**b**) Comparisons of the estimated loads using wavelet–LSTM method with respect to the ground truth values. (**c**) Comparisons of the estimated loads using 1D-att-CNN method with respect to the ground truth values. (**d**) Comparisons of the estimated loads using the proposed method with respect to the ground truth values. From Table 4, it can be seen that in both cases of symmetrically and asymmetrically distributed sensors, sinusoidal loads of different frequencies can be well identified, with all CC metrics of almost 1. To further evaluate the proposed method, we choose 1 regularization based method, namely the TSVD regularization method, and 1 data-driven method, the attention based 1D-CNN [25] for quantitative comparisons. Table 5 gives the comparison results. It can be seen that the two data-driven method would outperform the regularization based method. The 1D-CNN [25] method obtains a better RMSE metric that the proposed method; however, the CC metric for both 1D-CNN [25] and our method are almost 1. Figure 6 gives the identified loads from 0 s to 5 s for \(F_{sin1}\) (symmetrically distributed sensors) from different approaches, respectively. It can be seen that the 1D-CNN [25] method and the proposed method output similar identification results. Figure 6: The detailed comparisons of the identified sinusoidal loads with respect to the ground truth values with different approaches. In this comparison, the symmetrical sensor distribution is utilized. The load is \(F_{sin1}=5 sin(20\pi t)\). One regularization-based method and one data-driven method are compared. It can be seen that the proposed method would output similar identification results to those of the 1D CNN based method [25]. (**a**) Comparisons of the estimated sinusoidal loads using TSVD regularization method with respect to the ground truth values. (**b**) Comparisons of the estimated sinusoidal loads using 1D-att-CNN method with respect to the ground truth values.