## 3 Stochastic Load Conditions
### Traffic Conditions  
It is noteworthy that the traffic condition plays a significant role in evaluating the fatigue damage accumulation of the suspenders. A video containing 48 consecutive hours of traffic data on the suspension bridge was analyzed to obtain the essential traffic information, including the vehicle type, gross vehicle weight (GVW), lane occupancy, traffic density, etc. According to the traffic data, the vehicles could be categorized into seven types denoted as V1-V7, where V1 represents 2-axle mini-vans, V2 represents 2-axle sedan cars, and V3-V7 represent 2- to 7-axle trucks. The suspension bridge supports two-way four traffic lanes, and the hourly traffic volume (denoted as \(\eta\) for abbreviation) for the fast lane and the slow lane is illustrated in Figure 3a,b, respectively. Figure 3a,b show that the hourly traffic volume for both lanes is time-dependent and has the similar pattern; \(\eta\) is lower and relatively stable during 0:00-10:00 and 20:00-24:00, while \(\eta\) is much higher and stable during 10:00-20:00. To this end, by setting the threshold value as 200 vehicles per hour, the traffic conditions at the bridge site fall into two categories, as follows: (1) Free-flow with about 110 vehicles and 90 vehicles per hour for the fast lane and the slow lane, respectively; and (2) busy-flow with about 360 vehicles and 300 vehicles per hour for the fast lane and the slow lane, respectively. The probability of occurrence of free-flow condition and busy-flow condition is 0.583 (i.e., 14 h in one day) and 0.417 (i.e., 10 h in one day), respectively. Additionally, further analysis revealed that the vehicle occupancy ratios at each lane remained stable during the entire time, thus the vehicle occupancy ratios listed in Table 3 were employed for simulating both the free-flow traffic and busy-flow traffic conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & \(\mathbf{U}\) & **Range (m/s)** & **Probability of Occurrence (\%)** \\ \hline
1 & 0 (no wind) & \(<\)0.5 & 24.837 \\
2 & 2.0 m/s & 0.5–3 & 9.293 \\
3 & 4.5 m/s & 3–6 & 24.614 \\
4 & 7.5 m/s & 6–9 & 27.935 \\
5 & 10.5 m/s & 9–12 & 9.113 \\
6 & 13.5 m/s & 12–15 & 3.239 \\
7 & 16.5 m/s & 15–18 & 0.960 \\
8 & 20.0 m/s & \(>\)18 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Representative mean cross-wind and probability of occurrence. Figure 2: Wind rose diagrams: (**a**) Mean wind velocity (m/s); (**b**) probability of occurrence of wind direction. In addition to the traffic density and vehicle type, the vehicle gross vehicle weight (GVW) is also an important factor for traffic flow simulations. In the present study, the GVW of each vehicle type was first obtained and then fitted with commonly used distribution models. The suitability of the proposed distributions was examined by comparing their log-likelihood values and the distribution model with the maximum log-likelihood value was selected as a best fit [16]. It was found that the GVW of all the 7 types of vehicle followed the single-peak distribution and the optimal distribution model with the parameters for each type of vehicle is summarized in Table 4.  
With the vehicle information obtained through the analysis of the vehicle data, the traffic flow could be simulated based on the CA model. The simulation process mainly consists of three steps, which are briefly introduced herein:  
(1) Firstly, the number of vehicles for each vehicle type (V1-V7) was determined by multiplying the corresponding occupancy rate (in Table 3) with the effective daily traffic volume. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vehicle Type** & **Distribution Type** & **Mean Value (\(\mu\))** & **Standard Deviation (\(\sigma\))** \\ \hline V1 & Lognormal & 16.46 & 4.82 \\ V2 & Lognormal & 14.51 & 3.54 \\ V3 & Normal & 35.72 & 9.72 \\ V4 & Normal & 123.95 & 18.72 \\ V5 & Lognormal & 69.74 & 10.28 \\ V6 & Normal & 291.04 & 43.21 \\ V7 & Normal & 528.32 & 85.21 \\ \hline \hline \end{tabular}
\end{table}