With the rapid development of construction and operation scale of infrastructure such as bridges and tunnels, structural safety is becoming increasingly important. Structural health monitoring is a vital issue in structural safety, operation, and maintenance. Displacement monitoring is one of the most fundamental and routine tasks in structural health monitoring. Among various displacement measurement methods, the contact displacement measurement method is conceptually straightforward to implement. However, it requires specific environmental conditions for accurate measurements. The non-contact displacement measurement methods (e.g., level gauges and total stations) have widespread applications in engineering. However, they cannot satisfy the measurement requirement of long-span structures due to the large-scale range and high accuracy requirements. For deformation monitoring of long linear structures like bridges and tunnels, the displacement-relay series camera network method has been proven to be effective. With the increasing number of camera stations, the accumulated error can be caused due to uncertain factors such as feature extraction errors and model simplifications. It is a challenge to reduce the accumulated error of the camera network. Hence, this study aims to suppress the accumulated error effect, consequently enhancing the measurement accuracy of the camera network.

We first conduct the theoretical analysis to demonstrate the solution conditions for the displacement-relay series camera network method. Before the simulation study, the basic network configuration is defined. Then, the accumulated error effect of the camera network is investigated through numerical simulations. According to the simulation results, we propose a method based on error coefficients to reduce the accumulated error of the camera network. The error coefficient consists of the condition number of the measurement matrix and the station number of the network. Finally, we provide a direct characterization of network measurement errors to enable the investigation of cumulative effects resulting from displacement transmission errors in the camera network. The influence of benchmarks and survey marks' positions, and their numbers on the measurement accuracy of the displacement-relay camera network is thoroughly analyzed. Based on the analysis results, the camera network configuration is optimized, and an optimal distribution pattern for camera stations and mark points is advised. Finally, the feasibility of the proposed method is verified by field experiments.

We initially discuss the fundamental principle of displacement-relay series camera network and the necessity of benchmarks through the derivation of Eqs. (5)-(10), which also paves the way for extending the theoretical model to a complex camera network. In Section 3.1, the accumulated error effect of the camera network is investigated by integrating the theoretical foundation and formula derivation from Section 2. Subsequently, a detailed discussion of the error transmission effect and error suppression method is carried out through numerical simulations for the basic configuration of the series camera network. Next, the influence of network composition parameters on the transmission error is investigated (Figs. 5 and 6). The transmission errors for the distribution positions of all benchmarks and survey marks are studied (Figs. 7 and 10). A theoretical model that reflects the transmission error of the camera network is proposed by introducing the error coefficient as an evaluation index and leveraging the highly linear correlation between the measurement error and the error coefficient [Eq. (18)]. Finally, the proposed error reduction method is verified by the observation data obtained from a long-span cable-stayed bridge.

We focus on the mechanism and suppression methods of transmission error in the displacement-relay series camera networks. The results show that the displacement transmission link of dual-head cameras requires at least two benchmarks. There is a positive correlation among the number of camera stations, settlement amplitude, pitch angle variation, and network transmission error, while there is a negative correlation between the number of measurement marks and network transmission error. The proposed design method of camera network error suppression based on error coefficient can guide network configuration optimization. The measurement error of the camera network is highly correlated with the defined error coefficient, and the smaller error coefficient leads to a smaller measurement error. The camera stations should be placed at benchmarks to suppress accumulated errors. Replacing the mark points at the benchmarks with camera stations shows that the error suppression effect can reach over 60%, but the error suppression effect will weaken as the number of camera stations increases. The actual bridge verification results indicate that the measurement error is suppressed by 69.13%. The mark points are advised to be placed at camera stations to suppress accumulated errors. The simulation results show that this suppression method can optimize the transmission error of the basic configuration network from 2.88 to 1.01 mm. The actual bridge verification results show that the camera error is suppressed from 10.14 to 3.07 mm.