# Automation of Experimental Modal Analysis Using Bayesian Optimization
## 1 Introduction
The rules depend on several parameters, for which default values were set. They found that the proposed approach performs well on in-flight flutter data for an aircraft. A short review on such mode separation rules, which, in the end, emulate the actions and decisions of an experienced user, was provided by [PERSON] and [PERSON] [14]. The latter further mentioned in-flight data analysis and structural health monitoring as possible applications. Their work was extended by [PERSON] et al. [1], who also referred to [PERSON] et al. [13] by developing a rule-based automatic modal parameter selection approach. Peer group comparisons between modal analysis novices and experts on two comprehensive data sets proved that the approach leads to skill-independent results and an overall productivity gain of 50%. A different approach was followed by [PERSON] and [PERSON] [11], who compared several Fuzzy c-means clustering techniques with and without an additional genetic algorithm (GA) for the initialization of finding pole candidates. It was found that the Gustafson-Kessel algorithm with initial values from a GA resulted in the best clusters of poles. Some clusters were immediately discarded based on their contribution ratio, their compactness measures, and corresponding thresholds. For each remaining cluster, the pole closest to its center was chosen as the final result, which was positively evaluated by comparing it to the poles found by experts. All of the works presented still rely on user-defined thresholds and are thus not fully automated [12]. This drawback was overcome by [PERSON] et al. [12], who, in addition to a very comprehensive literature review, proposed a three-stage approach for fully automated modal parameter estimation. First, all modes were classified as either spurious or potentially stable by eleven soft and three hard validation criteria. Second, the remaining poles were hierarchically clustered to find similar modes and, finally, the mode with a modal damping closest to the median damping of the corresponding cluster was selected. The approach was successfully tested on several data sets. However, the results were only benchmarked against modal parameters retrieved by a manual analysis. A comparison of the modal model with the original data set was not performed. A very similar strategy was followed by [PERSON] et al. [15]. However, the latter allowed larger damping values, used different features representing the soft validation criteria, and selected the final poles by averaging all pole candidates per cluster. Additionally, they examined the influence of the maximum model order and found that their approach was less sensitive to it than that by [PERSON] et al. [12]. The method was applied to an OMA data set and successfully compared to EMA and finite element analysis results. [PERSON] et al. [16] proposed slight adaptations to the approach of [PERSON] et al. [15] and proved their effectiveness in an ablation study for a helicopter blade data set. Additionally, the eigenfrequency identification was validated on a simulated data set. Again, no validation against the original data set was conducted in [PERSON] et al. [15] and [PERSON] et al. [16]. It can be concluded that a consensus has been formed in the state-of-the-art regarding the basic approach of automatically extracting modal parameters [12; 15; 16]. However, it was not evaluated how well the identified modal model replicates the original data set using, for example, the frequency response assurance criterion (FRAC), nor was this the focus of the modal parameter extraction. Furthermore, the parameters which required user input in earlier approaches [11; 13; 14; 1] were replaced by metrics performed on the input data set [12; 15; 16], which is believed to unnecessarily restrict the solution space for the final modal parameters. The present paper presents an alternative approach, in which Bayesian optimization is used to find the optimal values of any required hyperparameters.