# Adaptive Probabilistic Optimization Approach for Vibration-Based Structural Health Monitoring
## 1 Introduction  
Over the last few decades, there have been rapid advances in the use of damage diagnostics and damage detection for structural health monitoring (SHM) [1]. These advances have emerged hand-in-hand with the development of sensor technologies and data processing capabilities. The use of damage detection is crucial for the analysis and maintenance of large and complex structural installations with a relatively long lifespan. In the literature, several SHM methods have been developed for damage identification using strain modes, ultrasonic waves, electromechanical impedance, frequency response functions, and modal properties such as natural frequencies and mode shapes [2; 3; 4; 5; 6; 7]. However, most of the techniques presented in the literature have used deterministic models which often exclude elements of uncertainty and variability that are inherent in environmental conditions and measurements. The use of the frequency response function (FRF) for damage detection and structural health monitoring has been widespread [8; 9; 10]. Recently, the use of FRF has been augmented by using artificial neural networks (ANN) and genetic algorithms (GA) for damage detection [11; 12; 13]. It has been specifically observed that ANN could be used for the detection of nonlinear damage with a high level of accuracy [11]; however, most of the techniques that use ANN require a large amount of training data. Some recent studies have also used machine learning algorithms to detect damage under varying operational and environmental conditions [14]. It is observed that the training data should cover the full range of operational and environmental variability for the successful use of machine learning for damage detection, while developing a capability to identify a dynamic response that is triggered by damage [14]. While FRF has been found to be very useful for damagediagnostics, it is widely acknowledged that signal processing and analysis are critical in structural health monitoring due to the issues associated with sensor noise, measurement inaccuracies, etc. [15]. Furthermore, a large amount of training data is required to capture operational and environmental variability for machine learning algorithms. Model properties of structures in conjunction with the wavelet transform and optimization methods have also been used by many researchers for damage detection [16]. Wavelet-based methods are frequently used due to their ability to detect local discontinuities or singularities due to small cracks and the associated properties [17; 18]. The use of wavelets in the literature includes the use of a global damage sensitivity trait by using the Haar wavelet [19] or the use of a diagnostic technique to identify the magnitude and location of a crack in beams by using skewness and kurtosis of mode shapes [20]. Another algorithm in the literature makes use of Symlets to detect mixed-mode cracks in large warren truss structures by utilizing natural modes [17]; however, the use of coarse sampling in large structures makes it challenging to use such an algorithm to accurately detect the extent and location of damage. In general, it can be stated that mode shape-based methods are highly sensitive to sampling and quality of sensor measurements [18], but the availability of full-field methods such as 3D digital image correlation (3D-DIC) and Continuous-scan laser Doppler vibrometry (CSLDV) have made it possible to measure a large number of velocities and displacements with relatively high accuracy [21; 22]. To investigate the sensitivity of overall damage detection to local and global damage, many optimization-based methods have been used in the literature with the aim of minimizing sensor measurements. To demonstrate the robustness and capabilities of these techniques, large and complex structural applications have been tested by using numerical and experimental examples [23; 24; 25; 26].