Estimation of Survival Function for Rayleigh Distribution by Ranking function:-

في هذا البحث تم تقدير دالة البقاء لتوزيع رالي من خلال تقدير معلمة هذا التوزيع باستخدام (طريقة متوسط المربعات الصغرى , طريقة الرتبية ) وتم استخدام دالة العضوية شبه المنحرف لتحويل هذا التوزيع الى التوزيع المضبب وتم تقدير دالة البقاء باستخدام بعض الدوال الرتبية وتم استخدام متوسط مربعات الخطأ لدوال البقاء لمعرفة من الافضل من البقية.In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast

Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique

Fuzzy reliability estimation for Frechet distribution by using simulation

The study has examined the estimation of Frechet distribution parameters with the shape parameter (α) and the scale parameter (β). Two estimation methods are used based on the maximum likelihood and Bayes methods. The life time data are fuzzy numbers. These estimations of parameters are employed to estimate the fuzzy reliability function of the distribution and to select the best estimate of the fuzzy reliability function by comparing the mean squares error (MSE) and the average absolute proportional error (MAPE). The results of simulation showed that the fuzziness is better than the real for all sample sizes and the fuzzy reliability at the estimates of the Bayes estimated is better than the maximum likelihood method. It gives the lowest average MSE and MAPE until to arrive at a minimum at sample size of n = 500

ENHANCEMENT AND COMPARISON OF ANT COLONY OPTIMIZATION FOR SOFTWARE RELIABILITY MODELS

In Common parlance, the traditional software reliability estimation methods often rely on assumptions like statistical distributions that are often dubious and unrealistic. The ability to predict the number of faults during development phase and a proper testing process helps in specifying timely release of software and efficient management of project resources. In the Present Study Enhancement and Comparison of Ant Colony Optimization Methods for Software Reliability Models are studied and the estimation accuracy was calculated. The Enhanced method shows significant advantages in finding the goodness of fit for software reliability model such as finite and infinite failure Poisson model and binomial models

Vertical wind profile characterization and identification of patterns based on a shape clustering algorithm

Wind power plants are becoming a generally accepted resource in the generation mix of many utilities. At the same time, the size and the power rating of individual wind turbines have increased considerably. Under these circumstances, the sector is increasingly demanding an accurate characterization of vertical wind speed profiles to estimate properly the incoming wind speed at the rotor swept area and, consequently, assess the potential for a wind power plant site. The present paper describes a shape-based clustering characterization and visualization of real vertical wind speed data. The proposed solution allows us to identify the most likely vertical wind speed patterns for a specific location based on real wind speed measurements. Moreover, this clustering approach also provides characterization and classification of such vertical wind profiles. This solution is highly suitable for a large amount of data collected by remote sensing equipment, where wind speed values at different heights within the rotor swept area are available for subsequent analysis. The methodology is based on z-normalization, shape-based distance metric solution and the Ward-hierarchical clustering method. Real vertical wind speed profile data corresponding to a Spanish wind power plant and collected by using a commercialWindcube equipment during several months are used to assess the proposed characterization and clustering process, involving more than 100000 wind speed data values. All analyses have been implemented using open-source R-software. From the results, at least four different vertical wind speed patterns are identified to characterize properly over 90% of the collected wind speed data along the day. Therefore, alternative analytical function criteria should be subsequently proposed for vertical wind speed characterization purposes.The authors are grateful for the financial support from the Spanish Ministry of the Economy and Competitiveness and the European Union —ENE2016-78214-C2-2-R—and the Spanish Education, Culture and Sport Ministry —FPU16/042

Applications and Modeling Techniques of Wind Turbine Power Curve for Wind Farms - A Review

In the wind energy industry, the power curve represents the relationship between the “wind speed” at the hub height and the corresponding “active power” to be generated. It is the most versatile condition indicator and of vital importance in several key applications, such as wind turbine selection, capacity factor estimation, wind energy assessment and forecasting, and condition monitoring, among others. Ensuring an effective implementation of the aforementioned applications mostly requires a modeling technique that best approximates the normal properties of an optimal wind turbines operation in a particular wind farm. This challenge has drawn the attention of wind farm operators and researchers towards the “state of the art” in wind energy technology. This paper provides an exhaustive and updated review on power curve based applications, the most common anomaly and fault types including their root-causes, along with data preprocessing and correction schemes (i.e., filtering, clustering, isolation, and others), and modeling techniques (i.e., parametric and non-parametric) which cover a wide range of algorithms. More than 100 references, for the most part selected from recently published journal articles, were carefully compiled to properly assess the past, present, and future research directions in this active domain

Failure Prognosis of Wind Turbine Components

Wind energy is playing an increasingly significant role in the World\u27s energy supply mix. In North America, many utility-scale wind turbines are approaching, or are beyond the half-way point of their originally anticipated lifespan. Accurate estimation of the times to failure of major turbine components can provide wind farm owners insight into how to optimize the life and value of their farm assets. This dissertation deals with fault detection and failure prognosis of critical wind turbine sub-assemblies, including generators, blades, and bearings based on data-driven approaches. The main aim of the data-driven methods is to utilize measurement data from the system and forecast the Remaining Useful Life (RUL) of faulty components accurately and efficiently. The main contributions of this dissertation are in the application of ALTA lifetime analysis to help illustrate a possible relationship between varying loads and generators reliability, a wavelet-based Probability Density Function (PDF) to effectively detecting incipient wind turbine blade failure, an adaptive Bayesian algorithm for modeling the uncertainty inherent in the bearings RUL prediction horizon, and a Hidden Markov Model (HMM) for characterizing the bearing damage progression based on varying operating states to mimic a real condition in which wind turbines operate and to recognize that the damage progression is a function of the stress applied to each component using data from historical failures across three different Canadian wind farms