**Peer Reviewed**

**Source**

**Conference**

**Theme**

**Concept Tag**

- Artificial Intelligence (2)
- boundary (1)
- cell mapping (1)
- Copula (1)
- damage intensity (1)
- dependence (1)
- displacement (1)
- equation (1)
- fatigue damage (1)
- intensity (1)
- iteration (1)
- joint probability (1)
- loading environment (1)
- machine learning (2)
- mapping (1)
- matrix (1)
- modeling dependence (1)
- normal distribution (1)
- offshore projects planning and execution (2)
- Offshore Wind (1)
- Offshore Wind Turbine (1)
- offshore wind turbine site (1)
- platform design (2)
- probability (2)
- probability density function (1)
- renewable energy (2)
- reservoir simulation (2)
- significant wave height (1)
- State Space (1)
- subsea system (2)
- time step (1)
- transition (1)
- transition matrix (1)
- transition probability matrix (1)
- wave data (1)
- wave height (1)
- wind energy (2)
- wind speed (1)
- wind turbine (2)

**File Type**

ABSTRACT

Due to large variability of the offshore environment, the load analysis of an offshore wind turbine is a complex task. It is normally performed in the time domain, by running stochastic simulations. This is usually very time consuming due to the necessity of having long time series in order to obtain results with little bias, or to sample events with a low probability of happening. An alternative is to perform the analysis in the frequency domain. The drawback is that this method is only valid for linear systems, which makes it rather inaccurate for fatigue damage results. Also, there are well-known inaccuracies when estimating fatigue damage from a response spectrum. This paper investigates a novel approach based on probability evolution methods, which can obtain accurate results for linear, as well as non-linear systems. The method is not very well known, and a drawback is that it can be numerically challenging, especially for high-dimensional problems. The benefits of the method are that it evaluates all possible states of the wind turbine without generating a long signal in the time domain. We show how this can be used to efficiently evaluate fatigue damage.

INTRODUCTION

This paper presents a probability density evolution method in the time domain for a simplified wind turbine model with one mode. The cell mapping approach discretizes the two-dimensional phase space (Hsu, 1987). The method is evaluated using both deterministic and random loads and compared to time domain simulations. Different sizes in the discretization of the mesh and in the area of state space covered are investigated, to determine when the method converges towards the final solution. The algorithm has been programmed in Python with the Numba Just-In-Time compiler to help speed up the calculations. How to implement a simple stochastic load model by the cell-mapping method is discussed. The result is a joint response probability density that contains information about the extrema of the structure motion, and how often these occur. This allows for calculating Markov transition probabilities between minima and maxima from the response density, which then makes it possible to estimate fatigue damage. Determining the response probability density is done by many short time-domain integrations, instead of one or more long simulations. The main novelty introduced and demonstrated here is that as soon as one has calculated the cell mapping, one can easily obtain the peak transition matrix and use this to obtain fatigue damage estimates.

Artificial Intelligence, boundary, cell mapping, damage intensity, displacement, equation, fatigue damage, intensity, iteration, machine learning, mapping, matrix, offshore projects planning and execution, platform design, probability, renewable energy, reservoir simulation, State Space, subsea system, time step, transition, transition matrix, transition probability matrix, wind energy, wind turbine

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation (0.86)
- Management and Information > Information Management and Systems (0.67)
- Facilities Design, Construction and Operation > Offshore Facilities and Subsea Systems > Platform design (0.61)
- Facilities Design, Construction and Operation > Facilities and Construction Project Management > Offshore projects planning and execution (0.61)

Technology:

- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty (0.74)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (0.68)

ABSTRACT

Assessment of the structural integrity of an offshore wind turbine requires simulation of its structural response for many combinations of the wave and wind conditions that represent its lifetime loads. Modeling the dependence between the wind speed, wave height and wave period is very expensive because it requires a large amount of data. Assuming independence can lead to inaccurate estimation of the probability of failure. Some researchers assume that the wave height follows a standard distribution conditioned upon wind speed. We propose an alternative method that uses a copula to approximate the joint probability distribution of the wind speed, and the significant wave height. We believe that this approach is more complete because we obtain the joint distribution of the above quantities without making any assumption on their conditional distributions. To test the quality of the proposed approach, we use Monte Carlo simulation to generate sample values of the wind speed and wave heights, and validate the model with the available data.

Artificial Intelligence, Copula, dependence, joint probability, loading environment, machine learning, modeling dependence, normal distribution, offshore projects planning and execution, Offshore Wind, Offshore Wind Turbine, offshore wind turbine site, platform design, probability, probability density function, renewable energy, reservoir simulation, significant wave height, subsea system, wave data, wave height, wind energy, wind speed, wind turbine

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation (0.87)
- Management and Information > Information Management and Systems (0.69)
- Facilities Design, Construction and Operation > Offshore Facilities and Subsea Systems > Platform design (0.62)
- Facilities Design, Construction and Operation > Facilities and Construction Project Management > Offshore projects planning and execution (0.62)

Technology:

- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty (0.50)
- Information Technology > Artificial Intelligence > Machine Learning (0.47)

Thank you!