Damage Equivalent Load Synthesis and Stochastic Extrapolation for Fatigue Life Validation

Present verification of the fatigue life margins on wind turbine structures utilizes damage equivalent load (DEL) computations over limited time duration. In this article, a procedure to determine long term fatigue damage and remaining life is presented as a combination of stochastic extrapolation of the 10-minute DEL to determine its probability of exceedance and through computationally fast synthesis of DELs using level-crossings of a Gaussian process. Both the synthesis of DELs and long-term stochastic extrapolation are validated using measured loads from a wind farm. The extrapolation for the blade root flap and tower base fore-aft damage equivalent moment is presented using a three-parameter Weibull distribution, whereby the long term damage equivalent load levels are forecast for both simulated and measured values. The damage equivalent load magnitude at a selected target probability of exceedance provides an indicator of the integrity of the structure for the next year. The extrapolated damage equivalent load over a year is validated using measured multi-year damage equivalent loads from a turbine in the Lillgrund wind farm, which is subject to wakes. The simulation of damage equivalent loads using the method of level crossings of a Gaussian process is shown to be able to reconstruct the damage equivalent load for both blade root and tower base moments. The prediction of the tower base fore-aft DEL is demonstrated to be feasible when using the Vanmarcke correction for very-narrow band processes. The combined method of fast damage equivalent load computations and stochastic extrapolation to the next year, allows a quick and accurate forecasting of structural integrity of operational wind turbines.

On spectral asymptotic of quasi-exactly solvable quartic potential

Motivated by the earlier results of Masoero and De Benedetti (Nonlinearity 23:2501, 2010) and Shapiro et al. (Commun Math Phys 311(2):277–300, 2012), we discuss below the asymptotic of the solvable part of the spectrum for the quasi-exactly solvable quartic oscillator. In particular, we formulate a conjecture on the coincidence of the asymptotic shape of the level crossings of the latter oscillator with the asymptotic shape of zeros of the Yablonskii–Vorob’ev polynomials. Further we present a numerical study of the spectral monodromy for the oscillator in question.

Model for Risk Calculation and Reliability Comparison of Level Crossings

There is not a single country in the world that is so rich that it can remove all level crossings or provide their denivelation in order to absolutely avoid the possibility of accidents at the intersections of railways and road traffic. In the Republic of Serbia alone, the largest number of accidents occur at passive crossings, which make up three-quarters of the total number of crossings. Therefore, it is necessary to constantly find solutions to the problem of priorities when choosing level crossings where it is necessary to raise the level of security, primarily by analyzing the risk and reliability at all level crossings. This paper presents a model that enables this. The calculation of the maximal risk of a level crossing is achieved under the conditions of generating the maximum entropy in the virtual operating mode. The basis of the model is a heterogeneous queuing system. Maximum entropy is based on the mandatory application of an exponential distribution. The system is Markovian and is solved by a standard analytical concept. The basic input parameters for the calculation of the maximal risk are the geometric characteristics of the level crossing and the intensities and structure of the flows of road and railway vehicles. The real risk is based on statistical records of accidents and flow intensities. The exact reliability of the level crossing is calculated from the ratio of real and maximal risk, which enables their further comparison in order to raise the level of safety, and that is the basic idea of this paper.