# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 6 Conclusions  
This study considered optimization of sensor placements for strain and temperature field monitoring using genetic algorithms. The methodology was applied to configurations of one, two, and three sensors, for both strain-based and temperature-based monitoring. In all the configurations, increasing the number of optimally placed sensors improved monitoring accuracy, as indicated by the progressive reduction in objective function values from 0.27 to 0.12 for strain-based, and from 0.23 to 0.12 for temperature-based monitoring. The best sensor positions not only provided enhanced spatial coverage but also considered the detection direction sensitivity of the sensors. This shows the importance of both position and orientation in maximizing structural health monitoring effectiveness. The genetic algorithms converged towards an optimal solution within a practical number of iterations. The presented framework constitutes a scalable, data-driven, and computationally efficient approach to improve sensor-based load monitoring. The limitation is that this method does not optimize the number of sensors. The optimization method was further validated by evaluating its influence on the precision of load predictions from artificial neural networks. Prediction models trained with sensor data from optimally placed and oriented sensors showed a substantial improvement over models using randomly placed sensors. For 500 training trials, the RMSE in prediction of temperature, applied force, and von Mises stress were consistently and significantly reduced when optimal configurations of the sensors were used. In all the cases, the average error and variability were dropped, even by an order of magnitude, which confirmed that \begin{table}
\begin{tabular}{c c c} \hline \hline
**Title 1** & **Random** & **Optimal** \\ \hline Minimal value & 0.0054 & 0.0042 \\ Maximal value & 0.8523 & 0.2814 \\ Average & 0.0667 & 0.0261 \\ Standard deviation & 0.1285 & 0.0216 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical comparison of prediction accuracy of 500 training trials of stress prediction model based on sensor measurements with sensors in random and optimal positions and orientations; all values in MPa. Figure 29: Histogram of maximal equivalent von Mises stress prediction accuracy of 500 training trials for (**a**) random sensor positions and orientations each try and (**b**) optimal sensor positions and orientations. the optimization method significantly improves prediction precision across different load conditions without requiring knowledge of the load location. The developed methods and algorithms, as well as the obtained results are considered by the authors as a starting point for future research, including the following directions: (a) experimental verification of load predictions based on optimal sensor network for multiple load cases; (b) introducing multi-objective optimization of the sensor placement for maximization of the prediction accuracy and minimization of the number of sensors; (c) defining and solving an optimization problem that allows us to find minimal number of temperature and strain sensors and their optimal mutual positions in thermomechanical coupled problems. Conceptualization, W.K. and W.M. ; methodology, W.K., W.M. and I.T.J. ; FE modeling, W.M. and I.T.J. ; optimization software, W.K. and I.T.J. ; numerical validation, W.M. ; formal analysis, W.K. and W.M. ; investigation, W.K., W.M. and I.T.J. ; resources, W.K., W.M. and I.T.J. ; data curation, W.K., W.M. and I.T.J. ; writing--original draft preparation, I.T.J. ; writing--review and editing, W.K. and W.M. ; visualization, W.M. and I.T.J. ; supervision, W.K. and W.M. ; project administration, W.K. and W.M. ; funding acquisition, W.K., W.M. and I.T.J. All authors have read and agreed to the published version of the manuscript. This research was partially funded by 'The Excellence Initiative--Research University' program at the Silesian University of Technology, 2025 (grant number: 10/040/SDU/10-21-02; recipient: W.M.).