# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 1 Introduction
Multi-objective GAs allow the trade-off between competing criteria, such as sensitivity, redundancy, and robustness, to environmental noise, as seen in work by [15; 16]. These methods are especially relevant for structures with multiple load cases, where a limited number of sensors must still provide full spatial and modal coverage. More recently, data-driven and machine learning (ML) approaches have improved SHM systems, especially in contexts where analytical models are either unavailable or insufficient. ML models learn patterns from data, and this offers predictive capabilities in operational environments. [PERSON] and [PERSON] [17] highlight the growing use of ML models not only for load estimation but also as drivers of sensor placement. Different studies show that integrating sensor placement with the sensitivity of ML model can significantly improve prediction accuracy. [PERSON] [15] conducted a data-driven sensor placement method based on variable importance from ML models. Then, sensor locations are determined to be placed where the model is most sensitive. [PERSON] et al. [16] extended this concept by integrating FEM-based physical knowledge into Gaussian process regression models using physics-informed kernels, mean functions, and constraints. This physics-informed framework has enhanced model generalization and robustness under sparse or previously unobserved conditions. ML methods can be divided into artificial neural networks (ANNs), Support Vector Machines (SVMs), and Gaussian Process Models (GPMs). ANNs are quite similar to neural structures of the brain and are suitable for mapping complicated, nonlinear functions between sensor measurements and structural conditions. For instance, in [2] GA is applied to optimize sensor locations under varying environmental conditions, and optimal sensor locations are found that provide high damage detection performance (using ML models) as the temperature varies. Prior work [18] showed that ANNs can predict loads using only strain readings without information on force location. SVM is efficient for classification and regression with small datasets. Their kernel-based formulation enables them to generalize well, even in high-dimensional feature spaces. Additionally, GPMs are a Bayesian framework that output probabilistic prediction together with uncertainties. Such models are useful in SHM, with sparse or uncertain data [16; 19]. A recurrent Gaussian Process Regression-based approach utilized in the mode shape reconstruction from sensor locations, which were optimized based on structural dynamics data, was also shown in [19]. This represents a change in approach toward hybrid algorithms, which leverage physical insight and statistical learning. In recent years, machine learning methods have been successfully applied to operational load monitoring. In the previous work of the authors [18], an artificial neural network (ANN) was trained on numerically simulated strain data from a composite panel under various loading conditions, and this enabled load predictions only based on sensor inputs. In addition to this, the authors implemented an ANN on a low power FPGA platform [20], achieving real-time operational load monitoring with significant reductions in computation demand. These studies demonstrate that ANNs can effectively map strain measurements to load related structural conditions, such as stress or failure indicators, across a wide range of load cases. In both studies, neural networks were trained on data generated from finite element simulations. This paper continues that line of research by addressing a key limitation (suboptimal sensor placement) identified in those works. It is shown here that the performance of such machine-learning-based prediction models can be significantly improved when sensor positions and orientations are optimized. By optimizing sensor layout to maximize information capture across multiple load scenarios, the predictive accuracy and reliability of ANN-based load monitoring systems are enhanced.