# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 1 Introduction  
In SHM (Structural Health Monitoring), measurements are taken continuously in order to monitor the conditions of the structures [1]. The measurement data can help to track changes in material properties, geometry, boundary conditions, and system connectivity, and can be gathered from the sensors [1]. Therefore, the placements and orientations of sensors determine the effectiveness of the SHM system. Despite significant improvements in SHM, problems with sensor placements still exist because of the complexity of structural responses under different loading conditions [2]. Nowadays, integration of FEM and experimental strain results have improved strain measurement precisions for real-time SHM. These advancements are helpful to make advanced cyber-physical systems in SHM, which improve the ability to monitor and respond to structural issues effectively [3, 4]. A lot of research has been conducted regarding optimal sensor placements. The Effective Independence (EFI) method and Fisher Information Matrix (FIM) [5] have been used widely. These methods were developed to improve modal identifiability, especially for large and complex structures. Over time, iterative strategies, like the one proposed byBagirgan et al. [6], have emerged. In the approach the mobile sensors are used adaptively to refine sensor placement based on updated structural models. [PERSON] et al. [7] summarized approaches emphasizing adaptability, robustness, and sensitivity to operational variability. [PERSON] et al. [8] carried out a hybrid optimal sensor placement strategy that combines QR factorization, sequential sensor placement, and a generalized genetic algorithm to determine both the number and positions of sensors. The method uses modal assurance criterion to evaluate sensor layout performance. In addition, [PERSON] et al. [9] conducted a unified sensor placement framework that integrates modal strain energy, effective independence, and a modified modal assurance criterion. Their approach uses modal reduction to reduce complexity and explores multiple placement methods individually and in combination, offering adaptable sensor layouts validated through numerical tests on a simply supported truss. Furthermore, [PERSON] et al. [10] introduced a stiffness separation method that partitions large-scale steel truss structures into smaller substructures, dramatically reducing the computational effort required to invert high dimensional stiffness matrices without sacrificing accuracy. They refined the formulation to ensure force-displacement compatibility and demonstrated on space-truss models that isolate subregions, shrink matrix sizes, and speed up damage identification. Furthermore, [PERSON] et al. [11] applied a partial-model-based variant of this approach to a full-scale long span steel truss bridge. Their method uses local stiffness models rather than a full global model to detect and quantify member damage. By comparing Nelder-Mead and quasi-Newton optimizations, they confirm that using partial models not only simplifies modeling complexity by over 90% but also enables efficient, accurate detection of damage in service bridges. FIM selects the optimal placements of sensors in order to maximize information acquisition [12]. [PERSON] and [PERSON] [12] extended the classical FIM-based method by iteratively adjusting sensor locations between high and low information areas until FIM determinant or trace stabilization, ensuring that each selected sensor location contributed meaningfully to parameter observability. The evolution of sensor placement has been accelerated by multi-objective optimization algorithms. For example, [PERSON] et al. [13] used multi-objective optimization that combined FIM and mode-shape interpolation to improve sensitivity to structural changes and enhance accuracy of modal shape reconstruction. Genetic algorithms (GAs) in particular have proven effective for navigating the high-dimensional, non-convex landscape of sensor placement [14].