# Damage Diagnosis for Offshore Wind Turbine Foundations Based on the Fractal Dimension
## 1 Introduction  
Structural health monitoring's (SHM) main purpose is to diagnose in time damage that affects the integrity of a structure and determine whether repair or reinforcement actions are required to avoid or delay its degradation. Generally, SHM strategies consist of the following steps:  
1. the strategic placement of sensors in the overall structure;
2. data collection and communication; and
3. analysis of the measured data. It is important to note that, in a wide variety of applications, guided waves, which is a nondestructive approach, is the usual standard. This approach relies on exciting the structure with low frequency ultrasonic waves and then sensing the reflected response waves. Thus, the method relies heavily on the fact that the input excitation is known and also that other perturbations can be filtered or neglected. On the one hand, in civil infrastructures, such as bridges, it is feasible to assume that external perturbations can be neglected or filtered with respect to the induced excitation, see [1, 2]. On the other hand, in other applications, as in aerospace, the structure can only be diagnosed with this approach when it is not in service. This strategy is used, for example, in [3] where a multiarea scanning ultrasonic system is built in a hangar to rapidly scan the airplane overall structure. This type of _not in service_ diagnose (the airplane can be diagnosed during no-flight conditions, when it is in the hangar) or neglecting the external perturbations (as in SHM for standard civil structures as bridgesor buildings) cannot be straightforwardly extrapolated to the main research area of the present work: wind turbines. Online and in-service SHM for wind turbines (WTs) are extremely important. WTs are extremely large structures subject to remarkable external unknown excitations such as wind and waves in the offshore case. Thus, SHM strategies for WTs must be able to cope with unknown significant external excitations hindering the use of the standard exciting-and-sensing approach [4]. To face this challenge, in this work, a vibration-response-only SHM strategy is stated to monitor online and during service a WT offshore fixed foundation by using only the excitation caused by the external and unknown perturbations. Offshore wind power will expand dramatically in the next two decades, multiplying by 15 by 2040 to a minimum of 345 gigawatts (GW) of installed capacity, according to the Offshore Wind Outlook 2019 report of the International Energy Agency [5]. However, this achievement will only be possible through cost-competitiveness of offshore wind, which depends entirely on SHM capacity to switch preventive maintenance to predictive one [6]. Thus, SHM for offshore assets is imperative to guarantee its exploitability. Hence, in this work, a SHM methodology for offshore fixed foundations is proposed. Nowadays, the SHM systems for WTs are mostly deployed to blades [7] and tower [8] but research of SHM for offshore support structures is still scarce [9]. The state of the art in this very specific area has three main research lines:  
1. model-based, using, for example, the finite element method as in [10; 11; 12];
2. data-based using solely experimental and/or real data; and
3. a hybrid approach that makes use of real and/or experimental data and numerical models. Regarding the first option, the work of [PERSON] et al. is noteworthy [13] where crack detection of monopile offshore foundations is accomplished based on numerical simulations of fatigue cracks. Regarding the second option, a comprehensive review is given in [14] about SHM of offshore WTs through the statistical pattern recognition paradigm. In this review, it is shown that the usual strategy, regarding offshore WT damage detection, is to identify changes in the modal properties. However, this strategy requires detailed attention to take into account the operational and environmental impact, and usually only damage detection (but not classification) is accomplished.