# Damage Diagnosis for Offshore Wind Turbine Foundations Based on the Fractal Dimension
## 1 Introduction
For example, in [15] a SHM approach verified on a full-scale foundation is presented. However, dynamic variability between different operational cases only allows the final results to indicate an overall stiffening of the structure but not to conclude whether damage is present or not. Regarding the third approach, the work by [PERSON] et al. [16] is noteworthy based on acceleration response data and calibrated computer models. However, this work is based in the usual operational modal analysis and holds the difficulties of this type of approach including the fact that only detection (but not classification of damage type) is acquired. In this work, facing the challenge posed by the previous references, different damage types are taken into account and its classification is achieved in an experimental down-scaled jacket WT foundation. It should be noted that the experimental testbed is a reduced model but well-founded for this proof-of-concept work as it is comparable to that employed in the following works: (i) [17], where damage detection is achieved via damage indicators; (ii) [18], where damage detection is obtained via statistical time series analysis; (iii) [19], based on principal component analysis and support vector machines; and (iv) [20], where a deep learning approach based on convolutional neural networks is employed. It is well known that machine learning requires a feature extraction preprocess. It is a challenge to find suitable features, sensitive to physical characteristics, that lead to the identification of the damage or fault [21]. In this work, the fractal dimension (FD) of the data time series is employed as the main feature. The FD has been used traditionally as a feature for medicine applications. For example, in [22] experiments on intensive care unit data sets show that the FD characterizes the time series better than the correlation dimension; in [23] FD is proven to be discriminant for the detection of epileptic seizures in intracranial electroencephalogram signals; and in [24] glaucomatous eye detection is proposed based on FD estimation. However, it was not until recently that FD has been explored as feature for structural damage detection. It is important to note the recent work by [PERSON] et al. [25], where FD for crack pattern recognition is studied. It is also important to note the work by [PERSON] et al. [26] where FD is shown to be effective to realize fault diagnosis of rolling element bearings and cope with the effects of variation in operating conditions. In this work, the FD feature is proposed for the vibration-response signals inspired by the physical insight that the different fractal structures of these signals should be capable to discriminate different types of damage in jacket-type offshore foundations. The paper is arranged as follows. First, the laboratory test bed and damage scenarios are briefly introduced in Section 2. Section 3 addresses the detailed statement of the developed damage diagnosis strategy that encompasses the following steps:  
1. data collection and manipulation;
2. fractal dimension feature extraction by means of the [PERSON]'s algorithm; and
3. normalization and classification tools. The experimental results are comprehensively stated in Section 4. Finally, conclusions are drawn in Section 5.