# Decision Support Models for Operations and Maintenance for Offshore Wind Farms: A Review
## 2 Operation and Maintenance: Influential Factors
### Weather and External Factors  
[PERSON] et al. [56] present a Markovian wave height model that uses tri-diagonal transition matrices. This model can be used in any Monte Carlo simulation for offshore simulations. [PERSON] and [PERSON] [57] present a study on the persistence of different marine environmental parameters based on [PERSON] theory. They assume that the process governing the distribution of the persistence of marine environmental conditions can be regarded as a stationary first order Markov process. The transition matrix for this Markov process can be established from recorded weather data. They use a discrete time Markov chain and compare the transition matrix of the original Markov process with a simplified two-by-two matrix with transition probabilities from below and above a certain threshold. According to their investigations, six to eight different states in the Markov model are sufficient to adequately model the marine environmental parameters. Finally, they also show that the Markov model has a better performance than the Kuwashima-Hogben model [58] in terms of persistence distribution. [PERSON] and [PERSON] [59] present a continuous-space discrete time Markov model of higher order to model significant wave height peak period and wind speed. The Markov model can be used to generate new sequences of the time series. [PERSON] [60] investigated the uncertainty of wind speed forecasts and found that the statistical distribution of the prediction errors (deviation between predicted and measured wind speed) is Gaussian. [PERSON] et al. [11] use autoregressive (AR) models to model both the wave height and wind speed. For the wind speed an AR model of order 2 is used and for the wave heights an AR model of order 20 is used. To use these AR models some transformations of the data must be conducted. For the wind speed, a fit of the monthly mean and diurnal variations must be removed. For the significant wave height, a fit of the monthly means is removed, and a Box-Cox transformation is applied. [PERSON] et al. [30] use a hidden Markov model (HMM) to calculate the waiting time for each failure. This HMM calculates the waiting time based on meteorological site characteristics, seasonality is respected, the HMM is robust to model uncertainty and the variability in the meteorological site conditions is preserved. [PERSON] et al. [12] on the other hand use a discrete time Markov chain model to generate time series of the wave height. The wind speed is generated according to a correlation matrix. [PERSON] et al. [14] use a multivariate autoregressive time series to model correlated wind speeds and wave heights. [PERSON] and [PERSON] [61] calculate the maintenance delays due to sea state with a closed form probabilistic model. In their model, they consider access restrictions and a Weibull distribution for the weather, fitted to represent the conditions of a given site. [PERSON] et al. [62] present a multivariate Markov model to generate sea state time series. The sea state is a combination of wind speed, wind direction, wave height, wave direction and wave period. They present two ways of capturing the seasonal variation within the sea state. The first method is to use monthly models assuming piece-wise stationarity. The second model uses a data transformation to deal with the seasonal variation. In their simulation model, [PERSON] and [PERSON] [PERSON] and [PERSON] (1986) use a Markov chain process to simulate weather time series. They assume a perfect weather forecast for the duration of the next shift. The met ocean module from [PERSON] and [PERSON] (2007) uses re-sampling of wind and wave data and provides wind shear model parameters as well as operational limits for each equipment type in addition to the time series for wind speed and significant wave height. [PERSON] et al. [PERSON] _et al._ (2007) use significant wave height and wind speed at hub height in hourly resolution as input to their model. The only uncertainty is therefore the variation within the given data.