## 4 Damage Detection Using the Statistical Approach  
The aim of this paper is to detect bridge damage using statistical analysis of acceleration-based BWIM results. As the results of inferred GVWs are repeatable (consistent estimates of axle weights), there is a potential of the BWIM system to detect any change in bridge condition since acceleration is sensitive to damage. Damage is represented here as a global loss in bridge stiffness. Since the change in global stiffness affects the bridge accelerations of all types of bridges [44], the proposed method could be expanded to bridges made of different materials. The simulated bridge with various damage conditions and the half-car vehicle model are tested numerically, and the potential of the statistical approach for bridge health monitoring is assessed. A statistical approach is applied, comparing the mean inferred GVWs. Figure 7 illustrates a schematic diagram of the methodology for bridge damage detection using a statistical approach applied to the acceleration-based BWIM system data. It is seen in Figure 6a that the acceleration-based BWIM system underestimates the axle weights and is statistically biased. However, this inaccuracy is consistent, and therefore, it can be used as a baseline for detecting any change in the bridge condition. As the accelerations are sensitive to bridge damage, the statistical properties of the inferred GVWs change when the bridge is damaged. Global loss of stiffness is used as a proxy of damage. Loss of stiffness in a concrete bridge generally occurs due to change in concrete modulus of elasticity [27]. This change in bridge condition affects the bridge acceleration response, and hence affects the accuracy of the acceleration-based BWIM system. Figure 8 shows the effect of bridge damage on the mid-span acceleration response to a half-car vehicle using one class 'A' road profile. The velocity of the vehicles in Figure 8 is kept constant at 80 km/h. Figure 8: Effect of bridge damage in the mid-span bridge acceleration using the class ’A’ road profile. Figure 7: Schematic diagram of the methodology of bridge damage detection using the acceleration-based BWIM system. Due to damage, the acceleration-based BWIM system malfunctions as it uses the 'calculated' response (influence line) for the healthy bridge. The gross weights inferred by the BWIM system are presented in Figure 9 for 500 trucks using the half-car vehicle model. The relative axle weights, velocities, axle spacings and pre-existing bridge vibrations are chosen randomly for the trucks which are simulated on the bridge with a class 'A' profile with different percentage losses of stiffness. The percentage loss of stiffness ranges from 1% loss (low) to 10% loss (severe). It is acknowledged that 10% loss of stiffness is a significant change in bridge temperature; however, the higher loss percentages are shown to demonstrate the concept. As can be seen in Figure 9, the acceleration-based BWIM results demonstrate observable variation in the statistical properties when there is global loss of bridge stiffness. The variations of the means and standard deviations of the inferred GVWs with loss of stiffness are calculated. The relationship between the mean inferred GVWs and percentage loss of stiffness is found to be non-linear, but the standard deviation shows a significant and roughly linear increase with increase in the percentage stiffness loss (about 17.5% increase for 3% increase in stiffness loss and a coefficient of determination (R-squared) value of 99.6%) (see Figure 10a). The sensitivity of the standard deviation to loss of stiffness is considerably greater than first natural frequency, for example, as illustrated in Figure 10b. For each percentage loss of stiffness, 1 st bridge natural frequency is calculated using a fast Fourier transform of the bridge (forced) accelerations due to passing trucks. The vehicle axle weights and velocities are chosen randomly for each run. Figure 10b shows an almost linear negative slope with an R-squared value of 96.7%.