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In the design, certification, and optimization of offshore wind turbines, extensive loads simulation is inevitable to develop reliable and cost-effective turbines. Description of the marine environment is based on a variety of techniques taking the stochastic nature of both, the wind and the water waves into account. The wind turbine is a highly dynamic system including effects of heavy rotating machinery and other significant nonlinearities leading to static, cyclic, transient, and stochastic loads. Due to the nature of the external loading, the system properties and the turbine design lifetime, offshore wind turbines are prone to fatigue-driven failure. For loads assessment, aero-hydro-servo-elastic tools are used including the coupled effects of the environment and the turbine to simulate the overall lifetime of the turbine in the harsh marine environment. These tools are constantly further developed and adapted to the needs of a fast-growing industry and newly arisi ng turbine concepts. Engineering approaches to allow for certification and reliable design are summarized in extensive guidelines and standards supporting engineers in daily design work

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Smooth concentmtion fields and balance equations for systems of mndom walkers are obtained by using the warsegmined space-time avemging method f m m [ t i ] and averages over the statistical ensemble. This yields a new cellular automaton numerical model for diffusion processes. The number of particles and the averaging space-time scale needed to appmximate the concentmtion, with a given precision, are obtained. Applications were made for systems with small concentrations and diffusion in mndom fields. Continuous modeling by space-time averages1 GAO, J.