In order to accurately estimate the fatigue life a floating structure, it is necessary to have a large set of discrete environmental conditions. If the damage to a structure largely stems from wave-induced forces, then the creation of a set of environmental conditions or ‘bins’ is trivial. However, when considering a floating platform supporting a wind turbine, it is necessary to consider not only the wave conditions, but also the wind conditions (and perhaps current, if possible). Thus, it is common to have greater than 5 dimensions in the timeseries (e.g., significant wave height, wave period, wave direction, wind speed, wind direction, etc). The creation of bins in two dimensions is quite easily solved by creating an arbitrary grid and taking the mean of all the observations which fall in a specific cell. In higher dimensions, a p-dimensional cell is not easily visualized and so the resulting set of bins cannot easily be graphically represented. In this paper, an iterative algorithm is developed to convert N observations, each with p-dimensions, into a set with M discrete bins, where M << N.
The algorithm presented borrows heavily from the maximum dissimilarity algorithm used in a wide array of fields. The benefit of using this algorithm is that there is no ‘bias’ introduced by an initial grid from the user. That is, given a desired final number of clusters and a certain distance tolerance, a unique set of cluster exists for a given data set. Inherently, the algorithm selects a diverse array of observations, usually including extreme events or outliers, which may have undue impact on the fatigue life of a structure. Although the algorithm is computationally expensive O(N2M), reductions in computational cost are possible. Most importantly, the algorithm can be written in such a way that memory constraints are not an issue even for N = O(105).
The clustering algorithm is described in both graphical and logical terms. A case study is presented, using publicly available data from the Netherlands Enterprise Agency. The data is visualized in two dimensions with the final number of bins equaling approximately 50, 100, 200, 500, 1000, and 2000 bins. These bins are compared with a previous algorithm from these authors. Various measures are presented to assess the fidelity of a set of bins with respect to the initial observations. Each set of bins are analyzed and it is clear the MDA-based algorithm outperforms the previous algorithm.