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This paper aims to evaluate the reliability analysis for steel beam which represented by the probability of Failure and reliability index. Monte Carlo Simulation Method (MCSM) and First Order Reliability Method (FORM) will be used to achieve this issue. These methods need two samples for each behavior that want to study; the first sample for resistance (carrying capacity R), and second for load effect (Q) which are parameters for a limit state function. Monte Carlo method has been adopted to generate these samples dependent on the randomness and uncertainties in variables. The variables that consider are beam cross-section dimensions, material property, beam length, yield stress, and applied loads. Matlab software has been adopted to generate these pseudo-random variables dependent on its statistical characteristics such as coefficient of variance and probability density function that gathered from a review of literatures.

This work presents the modeling of the electrical response of monocrystalline photovoltaic module by using five parameters model based on manufacture data-sheet of a solar module that measured in stander test conditions (STC) at radiation 1000W/m² and cell temperature 25 . The model takes into account the series and parallel (shunt) resistance of the module. This paper considers the details of Matlab modeling of the solar module by a developed Simulink model using the basic equations, the first approach was to estimate the parameters: photocurrent Iph, saturation current Is, shunt resistance Rsh, series resistance Rs, ideality factor A at stander test condition (STC) by an iteration process. To implement the iteration process, a numerical approach based on the Newton Raphson method has been implemented and programmed in Matlab. The second mathematical model used in Matlab/Simulink using equations for each parameter to determine the parameters at all operating conditions. The Matlab program gives the information about the behavior of the practical PV module, under different atmospheric conditions. The model accuracy was also analyzed through finding out the compatibility between the practical and the theoretical aspects at different solar radiation intensity 500, 750 and 1000 W/m2 by extracting the error ratios. The results show that there is difference between theoretical (modeled) and experimental, the best validation (less error) between five parameters model and experimental maximum power results at radiation 500, 750, 1000 W/m2 and STC was 5.5%, 19%, 18% and 12.3% in January respectively, due to the decreases in ambient temperature and thus decreases in the temperature of solar module in January led to increase in maximum output power and producing best validation between model and experimental in this month.

In this paper, several combination algorithms between Partial Update LMS (PU LMS) methods and previously proposed algorithm (New Variable Length LMS (NVLLMS)) have been developed. Then, the new sets of proposed algorithms were applied to an Acoustic Echo Cancellation system (AEC) in order to decrease the filter coefficients, decrease the convergence time, and enhance its performance in terms of Mean Square Error (MSE) and Echo Return Loss Enhancement (ERLE). These proposed algorithms will use the Echo Return Loss Enhancement (ERLE) to control the operation of filter's coefficient length variation. In addition, the time-varying step size is used.The total number of coefficients required was reduced by about 18% , 10% , 6%, and 16% using Periodic, Sequential, Stochastic, and M-max PU NVLLMS algorithms respectively, compared to that used by a full update method which is very important, especially in the application of mobile communication since the power consumption must be considered. In addition, the average ERLE and average Mean Square Error (MSE) for M-max PU NVLLMS are better than other proposed algorithms.