# Genetic Multi-Objective Optimization of Sensor Placement for SHM of Composite Structures
## 1 Introduction  
Structural health monitoring (SHM) became a paradigm in the operation of numerous structures and transport means, especially in civil and mechanical engineering, due to the ability to continuously evaluate structural conditions based on measured response and building prognostic models based on this. Currently, SHM is incorporated into the latest design and operation concepts, such as condition-based maintenance (CBM), the philosophy used in aviation, where maintenance is scheduled according to the current condition of the structure only [1, 2]. SHM is also an integral part of the newest solutions in civil engineering, such as building information modelling (BIM) [3, 4] and the concept of digital twins [5], where it plays a crucial role in the acquisition and management, being the main source of data for the evaluation of structural condition. Regardless of the advancement of the mentioned concepts and approaches based on them, there are still unsolved problems influencing their performance. One of these problems is an appropriate sensor placement that determines the effectiveness of the condition evaluation of a tested structure. It is especially important in the case of SHM systems based on modal analysis, one of the oldest and most widely used approaches in both civil and mechanical engineering [6]. Recent studies of the authors [7, 8] demonstrated the need for the application of an advanced machine-learning approach for this task to find a balance between the performance and cost of an SHM system. There are a plenty of different optimal-sensor-placement (OSP) strategies for SHM. A systematic review on different approaches can be found in [9, 10, 11]. From these optimization strategies, one group is of sequential-based sensor placement strategies where subsequent steps are based on sequentially eliminated sensor locations that contribute less to the objectivefunctions [10; 12] or otherwise by adding sensor locations that enhance the value of the evaluation function [10; 13]. Another group are simple or metaheuristic optimization strategies such as greedy algorithms [14], and bioinspired e.g., evolutionary, ant colony, particle swarm, or physically inspired e.g., simulated annealing algorithms [10]. Among the above meta heuristics, evolutionary methods have become evident [10]. These algorithms can be easily customized to the needs of the optimization problem because the objective function can be independently constructed without the need for reconfiguration of the optimization routine, similarly to other heuristic approaches. The objective functions can be built based on classical objectives, e.g., Fisher information matrix (FIT), mutual information (MI), etc., [10] as well as based on outcomes of the SHM system [9] which allows for building different optimization strategies. Increasingly often, different cost functions are taken in order define objective of SHM with an OSP problem. This requires defining of the multiterm weighted objective function or the necessity to build an appropriate aggregation operator [7]. Because in OSP various evaluation functions can be considered and for the SHM systems the performance and costs are counterparts [9], the multi-objective optimization strategies have been recognized as useful strategies. In [15], a decision-making multi-objective optimization based on a particle-swarm algorithm was used. The authors have used a minimum dependency based on Modal Assurance Criteria (MAC), minimum of redundancy based on similarity measure, and the maximization of signal-quality strength as a multi-objective. The obtained Pareto front solution was filtered using the decision-making membership action to select a subset of obtained solutions. Another study, shown in [16], was based on multi-objective genetic optimization with the application of two objectives using modal shapes. One of the objective was used to compare the modes of the structure amongst themselves, and the other was used to compare the modes of the same structure in two different configurations.