# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 4 Results
#### Obtained Results for Different Numbers of Sensors  
In the strain-based optimization with a single sensor, the best objective function obtained was 0.27, and this was achieved at a coordinate (168, 77, 74) mm with an orientation angle of \(88^{\circ}\). The optimal placement and orientation are illustrated in Figure 14, and the convergence performance across the tests is shown in Figure 15.  
Figure 13: Contour plots of temperature distribution maps for load cases 1 to 7, shown in subfigures (**a**–**g**), respectively. In temperature distribution-based optimization, the best objective function achieved using two sensors is 0.17. The optimal sensor placements are (162, 74, 74) with the optimal angle of 50\({}^{\circ}\) and (296, 43, 74) with the optimal angle of 111\({}^{\circ}\) shown in Figure 20. Furthermore, Figure 21 shows how evolutionary algorithms converge for two sensor placements in the temperature distribution case. Figure 19: The objective function in each iteration of evolutionary algorithm for independent tests of two sensors for strain-based optimization. Figure 17: The objective function in each iteration of evolutionary algorithm for independent tests of a single sensor for temperature distribution-based optimization. Based on the findings of this work, the optimizations using three sensors provided the best objective functions. For the strain-based optimization, the best objective function value was 0.12. The optimal coordinates and corresponding orientation angles for each sensor are (173, 80, 74) mm at 87\({}^{\circ}\), (59, 50, 74) mm at 81\({}^{\circ}\), and (274, 96, 74) mm at 110\({}^{\circ}\). The optimal coordinates and orientation of the sensors used in this optimization are shown in Figure 22, and the behavior of the genetic algorithm convergence for the three strain-based sensors are shown in Figure 23.  
Figure 21: The objective function in each iteration of evolutionary algorithm for independent test for temperature distribution-based optimization. Figure 20: The optimal placement and orientation of two sensors in temperature-based optimization. In the temperature-based optimization using three sensors, the objective function attained is 0.12. To find this result, the algorithm determined the optimal placements at (168, 77, 74) mm, (57, 55, 74) mm, and (296, 44, 74) mm, with respective angles of 65\({}^{\circ}\), 93\({}^{\circ}\), and 104\({}^{\circ}\). These optimal coordinates and angles are illustrated in Figure 24, and the test chart for this case is shown in Figure 25.  
Figure 23: The objective function in each iteration of evolutionary algorithm for independent test for three sensors for strain-based optimization. Figure 13:0 The optimal placement and orientation of three sensors in temperature-based optimization. Figure 13:1 The objective function in each iteration of evolutionary algorithm for independent test for three sensors for temperature distribution-based optimization. The results clearly demonstrate the effectiveness of increasing the number of optimally placed sensors in improving monitoring accuracy for both strain and temperature fields. For both types of optimizations, the objective function decreased as the number of sensors increased. The decrease in objective function shows improved coverage and detection capability. This illustrates that multiple optimally placed and oriented sensors can better capture the maxima across different load cases. But it is important to note that the number of sensors must be less than the number of load cases because if there are more sensors, this leads the sensors to capture similar or overlapping data [7,34]. In strain-based optimizations, the result obtained based on a single sensor placement is acceptable. But the two- and three-sensor configurations improved the result more, and this highlights the benefits of spatial diversity and directional complementarity.