## 5 Application of Train Axle Loads Identification Method  
### Pre-Processing of Strain Measurement Data  
The strain time history curves from 20 measurement points located at the quarter and mid-span sections of the simply supported composite beam bridge were continuously recorded by the data acquisition instrument for each passing train. The strain measurement data were found to contain high-frequency environmental noise (Figures 7a,b and 8a,b). To mitigate this noise, a Butterworth low-pass filter was employed. The Butterworth filter is characterized by a smooth frequency response in the passband and a gradual attenuation in the stopband. In MATLAB software (Version 2012a), the passband cutoff frequency of the Butterworth low-pass filter was set to 2.2/1000 (normalized at 1000 Hz), while the stopband cutoff frequency was set to 4.4/1000 (normalized at 1000 Hz). The passband and stopband attenuations were configured as 0.1 and 2.2, respectively. Additionally, since strain data from measurement points on the quarter and mid-span sections were collected using two separate data acquisition devices, inconsistencies in total duration and amount of time history data arose. To synchronize these data-sets, zero-point filling was applied before and after the strain time series. Following these pre-processing steps, the strain time history curves for the quarter and mid-span measurement points of the simply supported composite beam bridge are presented in Figures 7c,d, and 8c,d. The typical strain time history curve of the quarter-span strain measurement points on the simply supported composite beam bridge is depicted in Figure 7. At these points, both ends of the strain time history curve exhibit steady fluctuations before and after the passage  
Figure 7: Strain time history of measurement points on the quarter-span section of the simply supported composite beam bridge: **(a)** initial strain under the forward train; **(b)** initial strain under the reverse train; **(c)** pre-processed strain under the forward train; **(d)** pre-processed strain under the reverse train. of a train. During the train's traversal across the bridge, the strain time history curve shows seven local peaks, with the middle five peaks being more pronounced and the outermost two slightly smaller. Some measurement points may exhibit less pronounced peaks on both sides. Regarding peak strain, during the passage of a forward train (Figure 7a,c), the maximum measured strain in the strain time history curve occurs at measurement point Q4-2 on the bottom flange of the far-right I-beam, reaching approximately 85 \(\mu\varepsilon\). The strain peaks decrease as the measurement points approach the opposite side. Conversely, when a train moves in reverse (Figure 7b), the highest peak strain is observed at measurement point Q2-3 on the bottom flange of the second I-beam, with a magnitude of about 60 \(\mu\varepsilon\). Similarly, the strain peaks decrease as the measurement points approach the positive side. Additionally, strain values on the upper flange of the I-beam generally exhibit smaller peak strains and experience compressive stress. The typical strain time history curve of measurement points at the mid-span of the simply supported composite beam bridge is depicted in Figure 8. At these mid-span measurement points, both ends of the strain time history curve exhibit steady fluctuations before and after the train passes over the bridge. In contrast to the quarter-span measurement points, the strain time history curve during the passage of a forward train shows only 5 local peaks. Conversely, during the passage of a reverse train, the peaks and valleys of the strain time history curve at mid-span measurement points are less pronounced. Regarding peak strain, during the passage of a forward train (Figure 8a,c), the maximum measured strain in the strain time history curve occurs at measurement point M4-2 on the bottom flange of the far-right I-beam, reaching approximately 97 \(\mu\varepsilon\).