Surrogate models for the blade element momentum aerodynamic model using non-intrusive Polynomial Chaos Expansions

In typical industrial practice based on IEC standards, wind turbine simulations are computed in the time domain for each mean wind speed bin using a few number of unsteady wind seeds. Software such as FAST, BLADED or HAWC2 can be used to capture the unsteadiness and uncertainties of the wind in the simulations. The statistics of these aeroelastic simulations output are extracted and used to calculate fatigue and extreme loads on the wind turbine components. The minimum requirement of having six seeds does not guarantee an accurate estimation of the overall statistics. One solution might be running more seeds; however, this will increase the computation cost. Moreover, to move beyond Blade Element Momentum (BEM) based tools toward vortex/potential flow formulations, a reduction in the computational cost associated with the unsteady flow and uncertainty handling is required. This study illustrates the unsteady wind aerodynamic statistics' stationary character based on the standard turbulence models. This character is shown based on the output of NREL 5MW simulations. Afterwards, we propose a non-intrusive Polynomial Chaos Expansion approach to build a surrogate model of the loads' statistics, NREL 5MW rotor thrust and torque, at each time step, to estimate the extreme statistics more accurately and efficiently.

Limit Properties of the Largest Entries of High-Dimensional Sample Covariance and Correlation Matrices

In this paper, we consider the limit properties of the largest entries of sample covariance matrices and the sample correlation matrices. In order to make the statistics based on the largest entries of the sample covariance matrices and the sample correlation matrices more applicable in high-dimensional tests, the identically distributed assumption of population is removed. Under some moment’s assumption of the underlying distribution, we obtain that the almost surely limit and asymptotical distribution of the extreme statistics as both the dimension p and sample size n tend to infinity.

Extreme Ground Snow Loads in Europe from 1951 to 2100

Lightweight roofs are extremely sensitive to extreme snow loads, as confirmed by recently occurring failures all over Europe. Obviously, the problem is further emphasized in warmer climatic areas, where low design values are generally foreseen for snow loads. Like other climatic actions, representative values of snow loads provided in structural codes are usually derived by means of suitable elaborations of extreme statistics, assuming climate stationarity over time. As climate change impacts are becoming more and more evident over time, that hypothesis is becoming controversial, so that suitable adaptation strategies aiming to define climate resilient design loads need to be implemented. In the paper, past and future trends of ground snow load in Europe are assessed for the period 1950–2100, starting from high-resolution climate simulations, recently issued by the CORDEX program. Maps of representative values of snow loads adopted for structural design, associated with an annual probability of exceedance p = 2%, are elaborated for Europe. Referring to the historical period, the obtained maps are critically compared with the current European maps based on observations. Factors of change maps, referred to subsequent time windows are presented considering RCP4.5 and RCP8.5 emission trajectories, corresponding to medium and maximum greenhouse gas concentration scenarios. Factors of change are thus evaluated considering suitably selected weather stations in Switzerland and Germany, for which high quality point measurements, sufficiently extended over time are available. Focusing on the investigated weather stations, the study demonstrates that climate models can appropriately reproduce historical trends and that a decrease of characteristic values of the snow loads is expected over time. However, it must be remarked that, if on one hand the mean value of the annual maxima tends to reduce, on the other hand, its standard deviation tends to increase, locally leading to an increase of the extreme values, which should be duly considered in the evaluation of structural reliability over time.

Crossover of Failure Time Distributions in a Model of Time-Dependent Fracture

An important question in the theory of fracture is what kind of lifetime distributions may exist for materials under load. Here, this is studied in the context of a one-dimensional fracture model with local load sharing under a constant external load, “creep.” Simulations of the system with Weibull distributed initial lifetimes for the elements show that the limiting distribution follows from extreme statistics and takes the Gumbel form eventually, with longer and longer crossovers in the system size from a Weibull-like distribution, depending on the initial Weibull exponent.

Methodology for multi-criteria assessment of working conditions as an object of qualimetry

The article considers several modern scientific papers substantiating the need for assessing workplace safety and focusing on methods applied for the quantitative assessment of working conditions. The analysis found unsolved problems in qualimetry, which could lead to the development of new practical and generally applicable methods to effectively assess working conditions. The analysis proved the relevance of the topic and helped to determine the aim of the article, i.e., the development of a methodology for the quantitative assessment of working conditions in industries, considering harmful production factors. An exponential distribution, which belongs to the theory of extreme statistics, was proposed for the transition of heterogeneous single indicators of harmful factors into a dimensionless scale. Affine transformations were used to combine dissimilar scales, making it possible to divide segments on dissimilar scales into equal proportions. The article proposes a step-by-step method for determining a complex indicator of working conditions in industries. The proposed methodology allows management decisions that minimise the deviation in actual values of harmful factors from the optimal ones. The developed technique was tested at one specific metallurgical production site.

Superspreading of airborne pathogens in a heterogeneous world

Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We find that diseases that have a short duration of high infectiousness can give extreme statistics such as 20% infecting more than 80%, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation efforts applied to our model. We find that the effect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity.

Determination of Energy and Electric Capacity of On-Board Supercapaci-tor Regenerative Energy Storage

Purpose. Development of a method for determining the main functional parameters of on-board supercapacitor recuperative energy storage based on the asymptotic theory of extreme statistics by Gumbel, taking into account stochastic nature of changes in recuperated voltage and current. Methodology. To achieve this purpose, methods, devices and computer systems for temporary registration of recuperated voltages and currents on operating electric locomotives, methods of the theory of random processes and methods of probabilistic and statistical processing of registrograms of voltages and currents were used. Findings. A computational and experimental method for estimating recuperative energy has been proposed and practically applied. A probabilistic method has been developed for determining the energy and electric capacity of on-board supercapacitor recuperative energy storage units. Numerical probabilistic and statistical calculations of the energy and electric capacity of on-board storage for the VL8 and VL11M6 electric locomotives during their operation in the sections of Prydniprovska railway have been carried out. It was found that the energy and electric capacity of on-board storage devices are distributed according to an exponential law with a clear prevalence of their minimum values and in compliance with direct proportionality between them. Originality. For the first time, an autonomous phase of recuperative braking mode of an electric rolling stock has been developed, which makes it possible to significantly reduce the mass and dimension of a supercapacitor storage. The asymptotic theory of extreme statistics by Gumbel was adapted to the method for calculating energy and electric capacity of an on-board storage device, which made it possible to take into account the influence of stochastic nature of changes in the recuperated voltage and current. The probabilistic influence regularities of the change nature in the recuperation energy on the capacity of on-board storage in the phase of recuperative braking have been established. Further development was obtained by a computational-experimental method for assessing the recuperative energy, based on monitoring and using the time dependences of voltage and current obtained in real modes of recuperative braking. For the first time in electric traction systems, it was proposed to carry out the transition from the recuperative braking mode to the recuperative regeneration mode. Practical value. The developed method and technique based on it make it possible to evaluate functional parameters of on-board storage device of all types of electric rolling stock, considering stochastic nature of recuperated voltages and currents. Numerical-graphic dependences of the energy intensity and capacity of the on-board storage are recommended for predicting and evaluating these parameters for various modes of recuperative braking. Since the task of designing an on-board storage unit (in terms of mass and dimensions) is ambiguous, therefore, in each specific case of the type of electric locomotive and recuperation modes, it must be solved individually, taking into account the probability of the corresponding capacitance values.

Two decades of distributed global radiation time series across a mountainous semiarid area (Sierra Nevada, Spain)

The main drawback of the reconstruction of high-resolution distributed global radiation (Rg) time series in mountainous semiarid environments is the common lack of station-based solar radiation registers. This work presents 19 years (2000–2018) of high-spatial-resolution (30 m) daily, monthly, and annual global radiation maps derived using the GIS-based model proposed by Aguilar et al. (2010) in a mountainous area in southern Europe: Sierra Nevada (SN) mountain range (Spain). The model was driven by in situ daily global radiation measurements, from 16 weather stations with historical records in the area; a 30 m digital elevation model; and 240 cloud-free Landsat images. The applicability of the modeling scheme was validated against daily global radiation records at the weather stations. Mean RMSE values of 2.63 MJ m−2 d−1 and best estimations on clear-sky days were obtained. Daily Rg at weather stations revealed greater variations in the maximum values but no clear trends with altitude in any of the statistics. However, at the monthly and annual scales, there is an increase in the high extreme statistics with the altitude of the weather station, especially above 1500 m a.s.l. Monthly Rg maps showed significant spatial differences of up to 200 MJ m−2 per month that clearly followed the terrain configuration. July and December were clearly the months with the highest and lowest values of Rg received, and the highest scatter in the monthly Rg values was found in the spring and fall months. The monthly Rg distribution was highly variable along the study period (2000–2018). Such variability, especially in the wet season (October–May), determined the interannual differences of up to 800 MJ m−2 yr−1 in the incoming global radiation in SN. The time series of the surface global radiation datasets here provided can be used to analyze interannual and seasonal variation characteristics of the global radiation received in SN with high spatial detail (30 m). They can also be used as cross-validation reference data for other global radiation distributed datasets generated in SN with different spatiotemporal interpolation techniques. Daily, monthly, and annual datasets in this study are available at https://doi.org/10.1594/PANGAEA.921012 (Aguilar et al., 2021).

Support Vector Machines Model of the Nonlinear Hydrodynamics of Fixed Cylinders

Data-driven modeling is considered as a prospective approach for many conventional physical problems including ocean applications. Among various machine learning techniques, support vector machine stands out as one of the most widely used algorithms to establish models connecting pertinent features to physical quantities of interest. This paper takes the experimental data for a fixed cylinder in shallow water as the baseline data set and explores the modeling of nonlinear wave loads by the support vector machine (SVM) regression method. Different feature and target selections are studied in this paper to establish the nonlinear mapping relations from ambient wave elevations and kinematics to nonlinear wave loads. The performance of the SVM regression model is discussed and compared with nonlinear potential flow theory focusing on the overall statistics (standard deviation and kurtosis), which is critical for fatigue and extreme statistics analysis.