# Optimization of Sensor Placement for Modal Testing Using Machine Learning
###### Abstract  
Modal testing is a common step in aerostructure design, serving to validate the predicted natural frequencies and mode shapes obtained through computational methods. The strategic placement of sensors during testing is crucial for accurately measuring the intended natural frequencies. However, conventional methodologies for sensor placement are often time-consuming and involve iterative processes. This study explores the potential of machine learning techniques to enhance sensor selection methodologies. Three machine learning-based approaches are introduced and assessed, and their efficiencies are compared with established techniques. The evaluation of these methodologies is conducted using a numerical model of a beam to simulate real-world scenarios. The results offer insights into the efficacy of machine learning in optimizing sensor placement, presenting an innovative perspective on enhancing the efficiency and precision of modal testing procedures in aerostructure design. modal testing; sensor placement; machine learning; finite element method; beam analysis; multifrequency response +
Footnote †: journal: Medical  
post-processed, with the exact methodology being dependent on the excitation signal. These data may then be analyzed using a frequency response function in order to derive the natural frequencies and mode shapes of the structure under assessment. Placing the sensors on the structure must be done with care, as their placement can substantially influence the results of a modal test. Large numbers of sensors increase the cost of testing because of the equipment and labor required to set up the test. As modal testing is principally concerned with structural dynamics, an ideal sensor selection would result in the lowest number of sensors that allows each sensor's contribution to the analysis to be greatest [7]. The goal of optimizing sensor placement is to determine the most information about the structure's behavior while minimizing the required number of sensors [7]. In early modal testing, sensor placement relied on engineering judgment and institutional knowledge derived from the fundamentals of vibration [8]. Although this may still be used in certain situations, such as with a well-understood structure or for simple geometries, novel structures present difficulties for this approach. Additionally, tight timelines due to budget constraints or limited access to testing facilities reduce the time available to refine sensor placement during testing [3]. As such, determining an efficient methodology for sensor placement has real implications for increasing efficiency. As a result, several methodologies have been developed to assist engineers in determining appropriate sensor placement for modal testing and structural health monitoring. In general, methods for optimal sensor placement can be divided into two broad categories: model-based methods and data-driven methods. Model-based methods define the placement of sensors based on information derived from a numerical model, such as a finite element model or a multi-body model. Specifically in modal testing, existing model-based methods used for sensor placement include the Effective Independence Method (EIM) and the Iterative Residual Kinetic Energy approach (IRKE) [9]. Other techniques, such as those using information entropy, have also been developed [4]. A brief overview of these techniques is provided in Section 2. Data-driven sensor placement strategies have also been proposed to extract the oscillatory characteristic directly from experimental measurements without requiring the need of a numerical model [10; 11; 12; 13]. [PERSON] at el. [10] proposed a sensor placement approach that relies on a repetition of in situ trial measurements on bridges with different sensor positioning in order to avoid the need to rely on finite element data. The measured in situ data are used to train a Recurrent Gaussian Process Regression until a sufficient number of sensors is identified.