# VoI-Based Optimization of Structural Assessment for Spatially Degrading RC Structures
## 5 Sensitivity of the Vol to Initial Assumptions
### Prior Distribution of the Corrosion Parameters  
The diffusion coefficient can be difficult to estimate when one is not sure about the properties of the concrete in the existing structure and when no monitoring data are available. Furthermore, the diffusion coefficient varies in time, and hence the prior estimate at a certain time instant might differ from the actual value. When changing the mean of the diffusion coefficient from 64.5 to 258 mm\({}^{2}\)/year, the VoI can vary with an amount of \(\xi\)34,000, as illustrated in Table 5. While the monitoring strategy with the highest VoI remains the same, the difference in VoI between two techniques is not always of the same order of magnitude. Hence, when taking into account the uncertainty on the estimates of the prior and posterior costs (see Section 6), the optimal strategy might change. When the Coefficient of Variation (COV) of the diffusion coefficient is varied, the influence of the VoI is also given in Table 5. Here, the influence of the VoI is of the order of magnitude of \(\xi\)35,000, which is 18% of the total bridge value for a variation in COV of the diffusion coefficient from 0.05 to 0.2. Moreover, the influence differs depending on the monitoring technique considered. The VoI remains the largest when mode shapes are available (strategy 1), but for the lowest COV the difference with the static strains (strategy 3) is limited. Furthermore, when comparing the strain mode shapes (strategy 2) with the static strains, another technique might be chosen depending on the assumed COV for the diffusion coefficient.  
For the corrosion rate, different parameters are available in literature for different exposure classes. Some of these models are given in Table 6. When there is doubt on which model to use, the impact on the VoI can be large, ranging from a large positive to a large negative VoI, as can be seen in Table 5. Moreover, the optimal monitoring strategy might change, with large differences in VoI between the different strategies.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Vol Strategy 1** & **Vol Strategy 2** & **Vol Strategy 3** \\ \hline \(\mu_{D}\) & & & \\ \hline
64.5 & 4524 & 3483 & \(-\)3309 \\
129 & 46,538 & 37,620 & 36,306 \\
258 & 33,276 & 32,789 & 28,497 \\ \hline \(\mathbf{COV}_{D}\) & & & \\ \hline
0.05 & 37,391 & 31,551 & 36,853 \\
0.1 & 46,538 & 37,620 & 36,306 \\
0.2 & 69,726 & 66,850 & 63,571 \\ \hline \(V_{corr}\) & & & \\ \hline Model 1 & 98 & 36,049 & 70,780 \\ Model 2 & 4633 & 5173 & 1427 \\ Model 3 & \(-\)25,940 & \(-\)38,187 & \(-\)15,587 \\ Model 4 & 81,156 & 65,126 & 53,845 \\ \hline \(\mu_{Cs}\) & & & \\ \hline
0.05 & \(-\)3821 & \(-\)4265 & \(-\)8793 \\
0.1 & 46,538 & 37,620 & 36,306 \\
0.2 & 35,813 & 35,472 & 31,155 \\ \hline \(\mathbf{COV}_{Cs}\) & & & \\ \hline
0.05 & 43,967 & 34,010 & 40,857 \\
0.1 & 46,538 & 37,620 & 36,306 \\
0.2 & 31,631 & 39,037 & 30,337 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Vol for different monitoring strategies as a function of the parameters of the distributions of the corrosion variables (for the strategies, reference is made to Table 2).  
The surface chloride concentration is also a difficult parameter to estimate. The initial value is once taken half and once double the value originally considered, and it is found that the influence on the VoI is very large and can range from a negative VoI to a large positive VoI, as can be seen in Table 5. Moreover, depending on the value of mean of the chloride concentration at the surface of the concrete (\(\mu_{Gs}\)), the difference in VoI between two techniques might change. When changing the COV of the surface chloride concentration, the influence on the VoI is also illustrated in Table 5. Again, the optimal monitoring strategy might change depending on the prior assumptions.