# VoI-Based Optimization of Structural Assessment for Spatially Degrading RC Structures
## 4 Case Study: A Simply Supported RC Girder Bridge
### Optimization of the Time of Monitoring  
To determine its optimal value, the time of monitoring is increased in steps of five years between the time at which the prior reliability index starts to decrease and the prior time of repair. Hence, the first times of monitoring considered are 15, 20, 25, 30, 35, 40, and 45 years since the time of construction. The minimum posterior costs for measuring strain mode shapes (strategy 2) are found at 35, 40, and 45 years. Hence, the range [34 years, 46 years] years is also considered, with step sizes of 1 year. The lower and upper boundaries of the interval are taken one year apart from the previously identified optimal times of monitoring to verify whether there is no increase in Vol just before or after these times. The results are visualized in Figure 6 for two cases. The first case assumes repair model 7 (see further) and a reliability threshold of \(\beta_{repair}=3\). The monitoring strategy is strategy 2 with strain mode shapes measured at 10 elements (case 1). The second case gives the Vol as a function of time for repair model 1 (see further) with reliability threshold \(\beta_{repair}=3\) and monitoring strategy 2 with strain mode shapes measured at 50 elements (case 2).  
Figure 5: Optimal sensor placement considering the first four modes and no correlation between the sensor locations. The two vertical lines support the explanation on how to read the figure.  
Figure 6: Influence of the time of monitoring on the Vol for the considered case study.  
In the next step, for monitoring at 35 years or monitoring at 44 years and case 1 (since for these times of inspection the largest Vol was found for case 1), the number of sensors is increased. These results are given in Figure 7 (label 'Strategy 2'). Here, it can be seen that under these specific assumptions, applying a larger number of sensors is not worth the extra cost. Moreover, the behavior is almost the same for the two times of monitoring. Only when sensors are placed at locations chosen such that sensor locations are present at all elements in which the structure is discretized and hence all elements of the random fields, a noticeable difference in Vol is found between the two times of monitoring.  
For strategy 1, where mode shapes are available as monitoring data, 20, 35, and 50 sensor locations are considered. These values are chosen based on practical considerations, where for dynamic monitoring of a bridge of this size, generally 20-50 accelerometers are used. The influence of the number of sensors on the Vol is visualized in Figure 7 (labeled 'Strategy 1'). Here, the largest Vol is found for the lowest number of sensors at 44 years, but the influence of the number of sensors on the Vol is very small. The Vol is also larger than for strategy 2, when monitoring is performed at 44 years but smaller for monitoring at 35 years.  
Finally, in strategy 3, static strain data is considered, respectively, at 20, 35, and 50 locations. Here, the number of sensors is also based on advice from experts. The results are given in Figure 7 (labeled 'Strategy 3'). Under the current assumptions, for monitoring at 44 years, the influence of the number of sensors on the Vol is limited, and the Vol is lower than for the strategy 1. For monitoring at 44 years, a larger Vol is found for the lowest number of sensors, and the Vol is larger than for the strategy 1.