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The paper discusses service load measurements (weight of construction materials, small equipment and workers) conducted on 120 frame scaffoldings all over Poland in 2016-2018. Despite the fact that the scaffolding should ensure the safety of its users, most accidents on construction sites are caused by fall from height. Service loads are one of the elements affecting the safety of scaffolding use. On the basis of the studies, maximum load on one platform and maximum load on a vertical scaffolding module for one day were obtained. They were treated as the random variables of the maximum values. Histograms and probability density functions were determined for these variables. The selection of a probability distribution consisted in the selection of a probability density function by means of fitting curves to the study result histograms using the method of least squares. The analysis was performed for distribution Weibull and Gumbel probability density functions which are applied for maximum values of random variables. Parameters of these functions can be used for the purposes of the reliability analysis to calibrate partial safety factors in simulation of service load during the scaffolding failure risk assessment. Besides, the probability of not exceeding the standard loads provided for frame scaffoldings for 120 weeks was established on the aforementioned basis. The results of the presented research show that in Poland there is a high probability of exceeding the permissible service loads in one year and thus there is a high risk of scaffolding damage. [ABSTRACT FROM AUTHOR]

Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems' output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR). [ABSTRACT FROM AUTHOR]

This paper measures the cost of children using the random equivalence scale (RES). From the general population perspective, the deterministic microeconomic equivalence scales appear as continuous random variables. The stude derived the distribution of RES, assuming the lognormal distribution of income. The truncated distribution of RES can account for possible economies of scale in income or expenditure. The positional measures of the truncated distribution of RES may serve as single equivalence scales. A society's attitude towards inequality may help chose such scales. RES for Poland 2015 was estimated using microdata from the Household Budget Survey. Polish households exhibited a remarkable level of economies of scale in that year and the equivalence scales declined with expenditure. It was observed that the cost of bringing up a child is not constant; generally, it decreases with increasing household size. [ABSTRACT FROM AUTHOR]

The study presents a probabilistic stability analysis of a Baltic cliff in Jastrzębia Góra, Poland. Progressive slope erosion is a threat to adjacent buildings, so safety assessment of the slope is essential. The cliff shows a compound, multi-layered geological structure, which makes the analysis of its reliability a complex multivariate problem. A simple, straightforward computational procedure was proposed, incorporating the Response Surface Method (RSM) linked with the standard Monte Carlo (MC) simulation method and the Point Estimate Method (PEM). PEM samples make it possible to analyse the sensitivity of the cliff's stability to variation in subsoil parameters and to reduce the number of random variables of the problem. The proposed methods were tested in two cases: a high failure probability (undrained state) and a moderate failure probability (drained case). The so-called combined Response Surface Method (CRSM) proposed here may be successfully applied in geotechnical computations characterized by dispersion and uncertainty of soil data as well as a relatively high damage probability. [ABSTRACT FROM AUTHOR]

As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs-Beck test; (ii) checking for the random variable's independence using the Wald-Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable's stationarity using nonparametric tests, e.g., the Kruskal-Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher-Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson's χ2 test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov-Smirnov test, the Anderson-Darling test, the Liao-Shimokawa test, and Kuiper's test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz-Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz-Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP. [ABSTRACT FROM AUTHOR]