## 3 Experimental Results
### Experimental Results
#### 3.2.1 Experiment 1: Quantitative Analysis and Comparison on Random Loads  
In this experiment, random loads are applied on the GARTEUR model, and the proposed approach is quantitatively evaluated. For the case of symmetrically distributed sensors, the data in [25] is adopted, in which the signals for random excitation is Gaussian white noise. Similar Gaussian white noise random excitations are also applied for the asymmetrically distributed sensors. The Siemens LMS Test.lab [44] is used for random signal generation.  
To validate the effectiveness of the proposed method, quantitative comparative analyses are conducted between regularization based methods and data-driven methods for load identification. Two regularization-based load identification methods are selected, namely the TSVD regularization and Tikhonov regularization-based method. For the data-driven method, two approaches in the time domain, namely the TDNN-based approach [24], one-dimensional CNN with attention mechanism (1D-att-CNN)-based approach [25], and one approach in the wavelet domain, the wavelet-LSTM [30], are compared.  
In the comparative experiments, the regularization parameters for TSVD and Tikhonov methods were obtained using the GCV method [45]. For the TDNN method [24], a three-layer shallow network was employed with the input being the time-domain vibration signal within a time window. The 1D-att-CNN method [25] used the described network structure with the input being the time-domain vibration signal within a time window, and the network structure consisted of two layers of stacked attention-based one-dimensional convolutional layers and one fully connected layer. For the wavelet-LSTM method [30], the network input was the 8 th-order Meyer wavelet decomposition within a time window, consistent with the input of the proposed method. The network was designed with two layers of LSTM and one fully connected layer, with 128 neurons in the LSTM layer. To ensure fairness in the comparison, the time window for the original input of the neural network-based methods, including the proposed method, is set to 256. The learning rate and number of training epochs are set to be the same for all data-driven approaches. Table 3 provides quantitative comparison results of load identification for the proposed algorithm and the other comparative methods.  
From Table 3, it can be observed that, compared to the regularization-based methods, the four data-driven methods yield better identification results. For the case of symmetrical sensor distribution, the proposed method outperforms the other three data-driven load identification methods in terms of both the RMSE and CC metrics. For the asymmetrical ones, the proposed method is the second best in terms of RMSE metric and the best in termsof the CC metric. The comparisons between the performances of different sensor distributions shows that the regularization-based method would be sensitive to the sensor positions, while the propose method would give a relative stable identification result, with the CC metric near 0.97 for both sensor distributions. Figure 5 gives the the detailed comparisons for different approaches with respect to the ground truth loads with symmetrical sensor distribution. The comparisons show the identified random loads with respect to the ground truth values for time stamp 12.2 s to 13.2 s. From Figure 5, it can be seen that the three data-driven-based methods (Figure 5b-d) would outperform the regularization-based method (Figure 5a). Figure 5b shows that the wavelet-LSTM [30] approach would output more oscillating identification results. The time domain method [25] and the proposed method would output good identification results. However, the proposed method outperforms the time domain method [25] in terms of RMSE and CC.