60 J. Zeng et al. Numerical Simulations This study employs numerical simulations to collect vehicle vertical acceleration signals as vehicles traverse bridges under various conditions. The data collection focuses on both the baseline and damaged states of bridges, with the dynamic interaction between vehicles and bridges simulated using an iterative decoupled Vehicle-Bridge Interaction (VBI) model. In the baseline case, vertical vibration signals were recorded as twelve distinct vehicles, modeled using a one-axle moving spring-mass system, traversed the bridges. These vehicles varied in mass, spring constant, and speed, with combinations of three masses, two spring constants, and two speeds to represent different vehicle types. Each vehicle made 20 passes over each bridge, generating a total of 240 signals per bridge. The bridges used in these simulations shared identical properties except for their lengths. Bridges Bridge-1-SS through Bridge-10-SS were single-span bridges, while bridges Bridge-11-TS through Bridge-20-TS were two-span bridges with an additional support located at mid-span. A validation case, identical to the baseline, was included to ensure consistency and reliability in the monitoring process. The validation state served as a baseline comparison against future damaged scenarios, ensuring that the monitoring system can differentiate between normal and damaged conditions accurately. To simulate structural damage, a reduction in stiffness was introduced. Specifically, a 30% stiffness reduction was applied to the mid-span region of the bridges, affecting 1/4 of the total bridge length. This damage was designed to reflect realistic structural deterioration and assess the method’s ability to detect such changes. As in the baseline and validation cases, each vehicle crossed the damaged bridges 20 times, generating 240 signals for each damaged bridge. The study focuses on two representative bridges: Bridge-4-SS (Single-Span) and Bridge-17-TS (Two-Span), chosen to assess the method’s performance across different structural types. . During all simulations, the vertical acceleration signals of the vehicles were collected. To mimic real-world conditions, 10% artificial noise was added to these signals. To enhance the clarity of the signals, a Gaussian low-pass filter was applied to suppress high-frequency noise while preserving the key signal components related to the bridge’s structural response. Analysis This section presents the analysis of the structural health monitoring process using the signal-level approach, focusing on direct comparisons of the vehicle acceleration signals collected from multiple bridges. The goal of this method is to identify structural damage by analyzing changes in the correlation coefficients between the signals from different bridges over time. Signal-Level comparison and correlation coefficient calculation The analysis begins with preprocessing the vehicle acceleration signals. The original time-domain signals collected from vehicles crossing the bridges are transformed into the frequency domain and resampled to focus on the 0-20 Hz range[6]. This frequency range is chosen because it encompasses the typical fundamental frequencies of bridges. In our study, the highest first-mode frequency among all the bridges is 5.7 Hz, and the highest second-mode frequency is 8.5 Hz. Both of these frequencies occur on the shortest two-span bridge, ensuring that no critical information is lost by focusing on the 0-20 Hz range. Following the preprocessing, the Correlation Coefficient (CC) Matrix is constructed. For a system of mbridges, indexed by i =1, 2, . . . ,m, the Correlation Coefficient Matrix CC[i,j] is computed to quantify the correlation between the vehicle acceleration signals of Bridge i andBridge j. CC[i,j] = 1 P ×Q PX p=1 QX q=1 R(Si p,S j q) (1) In this equation, Si p represents the resampled frequency-domain signal from the p-th run on Bridge i, andSj q denotes the resampled frequency-domain signal from the q-th run on Bridge j. The terms P and Qrefer to the total numbers of vehicle runs on Bridges i andj, respectively. The functionR(Si p,Sj q denotes the Pearson correlation coefficient between the signals Si p andSj q. The vehicles entering each bridge are entirely random, meaning that no specific sequence or order of vehicles is assumed across the bridges. This randomness is important to consider in the correlation analysis, as it reflects realistic traffic conditions and ensures that the method can handle different vehicle combinations over time.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==