## 2 Strain Gauge Location Optimization Based on a Minimum Correlation Criterion
### The Proposed Improved Correlation Method Based on a Minimum Correlation Criterion
Step 2: Build the training dataset and test dataset  
The training dataset should be as comprehensive as possible in response to the operational load characteristics of the aircraft wing structure. For a real aircraft, as many monitoring points as possible should be used to obtain the strain vector under a variety of combined loading conditions, but this requires a lot of costs, so the finite element model can be constructed through virtual loading measurement to obtain the strain vector matrix. The strain values of \(m\) original monitoring points under \(n\) combined loading conditions are evaluated, as illustrated in Table 1. A strain vector with \(n\) elements is obtained at each original monitoring location; some data are selected as the training dataset in \(n\) loading conditions, while some data are utilized as the testing set, and the sample number of the training dataset is much larger than that of the testing dataset. Step 3: Initial selection of original monitoring points for the first stage  
The strain values of each strain gauge are computed for various loading conditions via the FEM, and the strain monitoring point with the largest strain can be selected as the initial monitoring point. Then, the Pearson correlation coefficient of different monitoring points is calculated with the normalized column vector in Table 1, and the (redundant) monitoring points with a high correlation coefficient are removed, which is also considered the minimum distance constraint. \[d_{ij}=\sqrt{\left(x_{i}-x_{j}\right)^{2}+\left(y_{i}-y_{j}\right)^{2}+\left( z_{i}-z_{j}\right)^{2}}\geq\varepsilon, \tag{3}\]  
where \(\left(x_{i},y_{i},z_{i}\right)\) indicates the coordinates of the \(i\)-th strain gauge location and \(\varepsilon\) is the threshold with a positive value. Step 4: Determine the optimal monitoring locations in the second stage  
It is assumed that after the initial screening in the first stage, there are still \(p\) monitoring points; all of the \(p\) monitoring points will be taken as the first monitoring point successively, and the other monitoring points are sorted in turn. It should be noted that it is preferred that the monitoring point with the largest strain value is adopted as the first monitoring point to boost the efficiency. The improved correlation coefficient value between the remaining \(p\)-\(1\) strain monitoring locations and the first strain monitoring point is evaluated. The second monitoring point is the monitoring point with the minimum absolute value of the improved \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Load Conditions**} & \multicolumn{2}{c}{**Strain Value of**} & \multicolumn{2}{c}{**Strain Value of**} & \multicolumn{2}{c}{**Strain Value of**} \\  & **Monitoring Point 1** & **Monitoring Point 2** & & **Monitoring Point \(m\)** \\ \hline
1 & 580 & 720 &... & 317 \\ \hline
2 & 423 & 302 &... & 965 \\ \hline... &... &... &... &... \\ \hline \(n\) & 121 & 217 &... & 198 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Strain values of monitoring points under different load conditions (unit: \(\mu\varepsilon\)). correlation coefficient. Then, the improved correlation coefficient between the remaining \(p\)-2 strain monitoring locations and the first two strain monitoring points is computed. The strain monitoring point corresponding to the least improved correlation coefficient is the third monitoring point. In turn, the \(p\) monitoring points are screened and sorted. Based on the results of the above order, monitoring points 1, 2, 3,..., \(p\) are individually selected. The operational loads of the test set are predicted using multivariate linear regression to determine whether the \(p\)-monitoring point sequence meets the requirement of the load prediction accuracy. If the prediction accuracy does not satisfy the requirement, we must increase the monitoring points until the load prediction accuracy is satisfied. It should be noted that this proposed correlation method requires numerous strain monitoring points for the initial selections.