# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 1 Introduction
This paper builds upon the earlier findings by integrating sensor optimization into the model development process, thereby strengthening the overall robustness of machine learning applications in structural health monitoring. The practical applicability is where OLM is implemented: airplanes, bridges, pipelines, wind turbines, and underground vehicles for the mining industry [21; 22; 23]. Previous work by the authors [24] proposed optimizing single sensor placement for a single load case to maximize measurements in 2D structures. Maximizing sensor measurements allows for more accurate load monitoring and can enable the use of lower resolution data acquisition hardware. This study extends that concept to include multiple sensors, multiple load cases, different measured quantities, and 3D structures. The novelty of the proposed method is that a new idea for objective function was formulated. By minimizing this function, optimal positions and orientations of any number of sensors can be found for multiple load case scenarios. The assumption is that the number of sensors is relatively small compared to the number of possible load cases of the structure. The proposed method was verified on optimization of sensor placement and orientation in an example composite structure under different loading conditions. The optimization was performed assuming two different physical quantities that are measured, strain and temperature. Strain measurements can be implemented in structural monitoring systems (e.g., to find force value and location or maximal stress value in the structure), and temperature measurements can be implemented in a thermal load monitoring system (e.g., to find the highest temperature in the structure, thermal expansion, or thermal stress where heterogenous temperature distribution occurs). Sensor placement optimization is carried out to minimize the difference between measured and actual physical field values in composite structures. A genetic algorithm is used to iteratively select the optimum sensor configuration from candidate locations that can provide the best objective function. In this study, numerical models of composite structure with 1, 2, and 3 sensors (and multiple load cases) are considered. To validate this work, predictions from optimally placed sensors were compared to those from randomly placed sensors through a feedforward ANN. Simulated measurements from both random and optimized configurations were used as inputs to ANN. Then, it was trained to predict structural load parameters, such as maximum temperature, applied force, and equivalent von Mises stress. The same ANN structure was applied to all the load cases, with no information about load location. Each configuration was subjected to 500 independent training trials. The prediction accuracy was measured using root mean square error (RMSE). For all the cases, optimized sensor placement produced significantly reduced errors and more consistent performance, confirming that sensor placement optimization plays a crucial role in load prediction model effectiveness. The structure of this paper is as follows: Section 2 gives a description of the optimization problem and explains the objective function and design variables. It also outlines the sensor modeling approach, constraints, and how sensor readings are simulated for strain and temperature cases. Section 3 gives a description of the numerical implementation, including optimization setup and the finite element model. Section 4 shows the sensor placement optimization for several sensor setups with an objective function evaluation. This section also consists of validation, where optimized sensor configurations are compared to random ones. Conclusions and discussions on the implications of the work to structural health monitoring applications are given in Section 5.