Commercial wind turbines modeling using single and composite cumulative probability density functions

81 8-354-2674 Abstract - Simple models for the patterns as well as their cumulative gain probability and probability density functions of the JPUNASA Deep Space Network (DSN) antennas are developed. These a~ needed for the study and evaluation of interference from unwanted sources such as the emerging terrestrial system, High Density Fixed Service (HDFS), with the Ka-band receiving antenna systems in Goldstone Station of the JPLNASA Deep Space Network. Several different models for the high gain ground antennas of the JPUNASA Deep Space Network @SN) are considered. The model definitions are then used to evaluate cumulative probability functions and probability density functions for the gain values at a receiving antenna randomly located anywhere in the far field of the model antenna. Both two-dimensional models which simulate the pattern in a plane cut through the boresight of the antenna and the range of the angle from boresight to *180 degrees and three- dimensional ones in which the pattem is given anywhere in the half-space above the ground, with the range of angle from zero at boresight to 90 degrees are considered. In both cases, regular as well as smooth interpolated models have been developed. The gain value as seen by a receiver at a random location and exposed to the radiation from a transmitting antenna with a given gain profile, can be thought of as a uniformly distributed random variable. Formulas are derived and various plots are presented for the gain models and their associated cumulative probability functions and probability density functions.

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field.

ABSTRACTThe left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.

Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

In this paper, the probabilistic behavior of plain concrete beams subjected to flexure is studied using a continuous mesoscale model. The model is two-dimensional where aggregate and mortar are treated as separate constituents having their own characteristic properties. The aggregate is represented as ellipses and generated under prescribed grading curves. Ellipses are randomly placed so it requires probabilistic analysis for model using the Monte Carlo simulation with 20 realizations to represent geometry uncertainty. The nonlinear behavior is simulated with an isotropic damage model for the mortar, while the aggregate is assumed to be elastic. The isotropic damage model softening behavior is defined in terms of fracture mechanics parameters. This damage model is compared with the fixed crack model in macroscale study before using it in the mesoscale model. Then, it is used in the mesoscale model to simulate flexure test and compared to experimental data and shows a good agreement. The probabilistic behavior of the model response is presented through the standard deviation, moment parameters and cumulative probability density functions in different loading stages. It shows variation of the probabilistic characteristics between pre-peak and post-peak behaviour of load-CMOD curves.

This paper presents the measured results of a switching DC excitation control system on a self-excited wind induction generator (WIG) under sudden connection of a static load. An intelligent power-system recorder/monitor is employed to measure three-phase voltages and currents at the terminals of the WIG and the load for 5 minutes. A laboratory 300 W wound-rotor induction machine driven by a blushless DC motor is utilized to simulate the studied WIG system. Since the generated harmonic currents are randomly varied, total harmonic distortion of current (THD <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> ) using cumulative probability density function is employed to determine the penetration of harmonic distortion due to the addition of witching DC excitation system. The results show that the harmonic currents generated by the studied WIG may be severely amplified to a higher level by the excitation capacitors connected at its stator terminals.

River response to rapid Holocene environmental change: evidence and explanation in British catchments

The majority of color histogram equalization methods do not yield uniform histogram in gray scale. After converting a color histogram equalized image into gray scale, the contrast of the converted image is worse than that of an 1-D gray scale histogram equalized image. We propose a novel 3-D color histogram equalization method that produces uniform distribution in gray scale histogram by defining a new cumulative probability density function in 3-D color space. Test results with natural and synthetic images are presented to compare and analyze various color histogram equalization algorithms based upon 3-D color histograms. We also present theoretical analysis for nonideal performance of existing methods.

On the properties of the coefficient of determination in regression models with infinite variance variables

By using the direct approach to the analysis of the serial-search spread-spectrum code acquisition, the author presents the approximate analysis of the cumulative probability density function (CDF) of the acquisition time. This approach is based on the binomial approximation to the distribution of the partial acquisition times, instead of the Gaussian one used previously. The binomial approximation gives very accurate results but, more importantly, it shows that the analysis of the arbitrary detection/verification scheme can be reduced to the much simpler analysis of the equivalent single-dwell system, whose parameters depend only on the mean test times and not on their distribution. Based on the exact results, simple closed-form approximations are derived for the CDF in the case of the straight-line serial search with uniform a priori distribution, which might be useful in practice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

Engineers, economists, hydrologists, social scientists, and behavioural scientists often deal with data belonging to the unit interval. One of the most common approaches for modeling purposes is the use of unit distributions, beginning with the classical power distribution. A simple way to improve its applicability is proposed by the transmuted scheme. We propose an alternative in this article by slightly modifying this scheme with a logarithmic weighted function, thus creating the log-weighted power distribution. It can also be thought of as a variant of the log-Lindley distribution, and some other derived unit distributions. We investigate its statistical and functional capabilities, and discuss how it distinguishes between power and transmuted power distributions. Among the functions derived from the log-weighted distribution are the cumulative distribution, probability density, hazard rate, and quantile functions. When appropriate, a shape analysis of them is performed to increase the exibility of the proposed modelling. Various properties are investigated, including stochastic ordering (first order), generalized logarithmic moments, incomplete moments, Rényi entropy, order statistics, reliability measures, and a list of new distributions derived from the main one are offered. Subsequently, the estimation of the model parameters is discussed through the maximum likelihood procedure. Then, the proposed distribution is tested on a few data sets to show in what concrete statistical scenarios it may outperform the transmuted power distribution.

As wind energy adoption is growing, ensuring the efficient operation and maintenance of wind turbines becomes essential for maximizing energy production and minimizing costs and downtime. Many AI applications in wind energy, such as in condition monitoring and power forecasting, may benefit from using operational data not only from individual wind turbines but from multiple turbines and multiple wind farms. Collaborative distributed AI which preserves data privacy holds a strong potential for these applications. Federated learning has emerged as a privacy-preserving distributed machine learning approach in this context. We explore federated learning in wind turbine condition monitoring, specifically for fault detection using normal behaviour models. We investigate various federated learning strategies, including collaboration across different wind farms and turbine models, as well as collaboration restricted to the same wind farm and turbine model. Our case study results indicate that federated learning across multiple wind turbines consistently outperforms models trained on a single turbine, especially when training data is scarce. Moreover, the amount of historical data necessary to train an effective model can be significantly reduced by employing a collaborative federated learning strategy. Finally, our findings show that extending the collaboration to multiple wind farms may result in inferior performance compared to restricting learning within a farm, specifically when faced with statistical heterogeneity and imbalanced datasets.

Wind turbines are operating under very complex and uncontrolled environmental conditions, including atmospheric turbulence, atmospheric boundary layer effects, directional and spatial variations in wind shear, etc. Over the past decades, the size of a commercial wind turbine has increased considerably. All the complex and uncontrolled conditions mentioned above result in uncertainties of aerodynamic loads calculation on very large wind turbine blades and thus better numerical codes are needed for predicting the loads in the design phase. With the aim to eliminate these uncontrolled effects and improve the aerodynamic models, in last decades, several important experimental campaigns of different wind turbine models have been performed in large wind tunnels. The objective of such experiments (e.g. using the NREL wind turbine and the MEXICO rotor) is to provide high quality measurement data which can be used to validate numerical models and improve different fidelity numerical codes, particularly for predicting wind turbine aerodynamic loads.

In this paper, the performance of a mixed Terahertz/free-space optical (THz/FSO) wireless transmission system is studied, where the joint effects of channel fading and pointing errors are considered for both THz and FSO links. Employing the semi-blind amplify-and-forward protocol, we derive the cumulative distribution function and probability density function of the end-to-end signal-to-noise ratio. By applying the derived statistics, exact expressions for the outage probability (OP), average bit error rate (BER), and average channel capacity are obtained. In order to attain useful physical insights, asymptotic OP and average BER expressions are also presented. Based on them, the diversity gain is determined, which is shown to depend on channel fading and pointing errors of both links. In addition, by taking into account the hardware impairments, the OP of the non-ideal hardware system is derived. Moreover, the analysis is extended to multi-antenna scenarios and the asymptotic OP is obtained. Finally, illustrative numerical results are plotted and it can be observed that the path loss, channel fading, pointing errors and hardware impairments lead to a considerable degradation in system performance.