## 1 Introduction  
To ensure that wind turbine blades fulfill the design requirements, they are subjected to load-carrying capacity experimental tests under extreme loading and fatigue resistance tests. Additionally, it is common practice to perform tests to derive the blades' basic dynamic properties, such as natural frequencies and damping ratios. These are essential for the dynamic behavior and structural integrity of the entire wind turbine [1]. In this context, modal analysis is an engineering and technological tool that contributes to carry out these tests. It is also a constant topic of research and development towards new techniques and computational algorithms that lead to identifying the parameters that describe the dynamic behavior of modern engineering structures and mechanical systems [2, 3]. The resulting modal models, as a product of the identification process, are used in vibration absorbers design, vibration control schemes, mechanical design, and structural health monitoring (SHM), among other important applications. Nowadays, numerous modal parameter identification algorithms, in time or frequency domain, have been reported in the literature and research articles [4, 5, 6], although most of these techniques are essentially designed to be performed in a post-processing context due to their asymptotic and recursive nature, those methodologies are unsuitable to be applied to adaptive or real-time vibrations absorption schemes like those proposed in [7; 8]. For online applications suitable to be applied in structural health monitoring and adaptive vibration control schemes, it is highly desirable to perform the parameter identification in real time, preferably online and in the nominal operation conditions of the system. Since 1996, as reported in [9], several online modal parameter identification schemes have been developed using neural networks and artificial intelligence (AI). It is also important to consider that classical mathematical models for dynamic and vibrating systems are linear assumptions of their dynamic behavior such that it is possible to use basic and well known approaches like least squares and auto-regressive models [3; 10; 11; 12; 13; 14]. However, the use of modern materials in structural engineering, high displacements, geometrical restrictions, and complex behavior are now becoming common in modern mechanical structures, resulting in inherent non-linear phenomena (e.g., stiffness, damping, and excitation), and as a result, despite of the numerous advantages of the linearity assumption on mechanical systems, there are cases where the linear methods are no longer effective or even valid, as reported in [15; 16; 17]. In this work, we use a set of mathematical tools: Operational calculus, algebraic identification, and Hilbert transformation, to determine in time domain and online, the principal modal parameters of a wind turbine blade given one single output measurements of its free vibrations response. As a complement of our analysis, we apply the Hilbert transformation to the FRF of the system to have an indicator for the presence of non-linearities; we use the properties of this linear transformation as reported in [18] considering the interesting updates and applications reported in [17]. Then, we apply an algebraic approach to transform a complex calculus problem into an algebraic equation [19; 20; 21] in terms of the parameters to be identified. The main contributions of the present work are summarized as follows:  
* An algebraic technique for online and time-domain estimation of natural frequencies and damping ratios is evaluated in an experimental case study. * The evaluated estimation approach is performed in time-domain and on-line, where a small interval of time is required for the technique to provide accurate results. * Compared to other modal parameters identification methods, a significant reduction of the amount of time and data required for the estimation process is the main highlight. * Only measurements of single output signals are required.