Inverse Directional Simulation: an environmental contour method providing an exact return period

Nikolay Dimitrov

doi:10.1088/1742-6596/1618/6/062048

Nikolay Dimitrov

Open Access

https://doi.org/10.1088/1742-6596/1618/6/062048

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Abstract

This study presents an improved approach for drawing environmental contours, derived from the inverse First Order Reliability Method (iFORM). It is shown that the approach used in the iFORM method is not accurate as it only takes into account a fraction of the probability space behind the contour line-which means that the iFORM method provides inherently non-conservative environmental contours. iDS, an alternative solution based on the chi-square distribution is suggested, and its adequacy is demonstrated with a Monte Carlo simulation. An expression is derived for computing sector-constrained environmental contours where the exceedance probability is contained within specific range of interest for one or more variables. The newly suggested environmental contour methods are applied on measured wind and turbulence time series and compared with the iFORM method.

Highlights

Environmental contours [1] are widely used in the wind, offshore and marine industries as means for characterizing the joint statistical distribution for extreme combinations of stochastic environmental conditions such as wind speed, turbulence, wave heights and periods, and gust magnitudes [2][3][4][5]
It is shown that the approach used in the inverse First Order Reliability Method (iFORM) method is not accurate as it only takes into account a fraction of the probability space behind the contour line – which means that the iFORM method provides inherently non-conservative environmental contours. Inverse Directional Simulation (iDS), an alternative solution based on the chi-square distribution is suggested, and its adequacy is demonstrated with a Monte Carlo simulation
In iFORM, the i.i.d. space is based on the standard normal distribution, and the environmental contours are drawn as circles with radius computed through the use of multivariate normal distribution probability. iFORM is the basis for the definition of the Extreme Turbulence Model (ETM) load case defined by the IEC61400-1, ed.3 design standard [8], meaning that it has an impact on wind turbine design

Summary

Introduction

Environmental contours [1] are widely used in the wind, offshore and marine industries as means for characterizing the joint statistical distribution for extreme combinations of stochastic environmental conditions such as wind speed, turbulence, wave heights and periods, and gust magnitudes [2][3][4][5]. In this case about 1100 samples are outside the contour, showing that the iFORM underestimates the exceedance probability by about an order of magnitude This has implications for, among other, wind turbine design as the environmental contours are used for multiple purposes – one example is the extreme turbulence model (ETM) which is the basis of design load case DLC1.3 in the IEC61400-1 standard [8], and which represents the 50-year return period combination of wind and turbulence as computed by iFORM. It is suggested that the linear limit state approximation is replaced by a hypersphere in standard normal space, and that this is an exact solution for the return period This approach is inspired by the Directional Simulation method used in structural reliability problems [11],[12], and will be referred to as inverse Directional Simulation (iDS). Figure 4. 1-year return period contours for mean wind speed and turbulence at the Høvsore site, Denmark

Discussion

Conclusions