# Automation of Experimental Modal Analysis Using Bayesian Optimization
## 1 Introduction  
The vibrational characteristics of structures represent one of the key design targets in mechanical, aerospace, and civil engineering, as well as in many other domains. Typically, the dynamic behavior is described by a linear model which relates time-varying input forces on the structure of interest to its (also time-varying) displacements [1]. Most often, modal models which are based on the so-called modal parameters eigenfrequencies, mode shapes, and modal damping are used due to their intuitive physical interpretability [2]. In this context, one also speaks of poles containing the combined information of eigenfrequency and modal damping. Building up and evaluating these models is, depending on the chosen approach, either called computational or experimental modal analysis (EMA). Even though simulations have improved in recent years, real-world experiments are still needed in cases in which high accuracy is essential, or in order to calibrate the computational analyses, as, for example, demonstrated by [PERSON] and [PERSON] [3]. EMA is typically performed under laboratory conditions [4], which may not be sufficient for capturing the vibrational characteristics of a generally nonlinear system using the linear modal model. In contrast, operational modal analysis (OMA) is performed under operational conditions, an approach which is typically more accurate but comes with additional challenges such as only partial or missing input force measurements [4]. Given a set of data, a variety of methods exists for estimating the modal parameters of a system. In case the modes are identified one at a time rather than all at once, they are called single-degree-of-freedom methods [5]. Popular examples include the peak-picking, the circle-fit, and the line-fit methods [5], as well as the two-stage least squares identification presented by [PERSON] [6]. When dealing with closely spaced modes, so-called multi-degree-of-freedom (MDOF) methods, which consider multiple modes simultaneously, typically perform better [5]. This can, for example, be done by solving a nonlinear optimization problem [5, 6], the global rational fraction polynomial method [5], theleast squares rational function (LSRF) method [7], global singular value decomposition (SVD) [5], the least squares complex exponential (LSCE) method [8], the least squares complex frequency-domain (LSCF) method or its polyreference version, the so called \"PolyMAX\" method [9], or various stochastic subspace identification (SSI) methods [10]. Depending on whether they operate on time series or frequency information, these algorithms can either be clustered as time-domain (e.g., SSI or the LSCE method) or frequency-domain (e.g., the circle-fit method, global SVD, or the LSCF method) approaches. The algorithms themselves are beyond the scope of this paper. However, all approaches have in common that the model order must be set, which directly relates to the question of how many modes are to be identified. Although strategies exist for determining a suitable model order based on the measured data, it is more common to first considerably overestimate the number of modes and identify modal parameters for several model orders and, second, to select an appropriate number of modes based on the combined information [4; 5]. This approach helps to reduce biases in the identified modes [4]. However, when proceeding in this way, many spurious or mathematical modes occur which must be separated from the true, physical modes. The central element of this strategy is the so-called stabilization diagram, which displays the identified modes in a model order over frequency plot [4]. In the past, selecting appropriate modes from the stabilization diagram has required a high level of user interaction and expert knowledge [11; 12]. To simplify the process, [PERSON] et al. [13] first made use of several methods to eliminate spurious modes applicable to state spaced models and, second, introduced a set of rules to mimic the selection of modes by the user.