In this paper, for the first time using of Bayesian Regularized artificial neural network (BRANN) model, which is a novel method of among soft computing (SC) methods (such as fuzzy logic, genetic programming, neural network) to predict the rotational capacity of wide-flange steel beams. Steel is one of the most commonly used materials in construction industries, mainly in steel structures. There are many researches and studies on the behavior of a structural member of steel structure such as beams under different types of loading. The accurate estimation of rotation capacity (plastic rotation capacity) is of significant importance issue for plastic and seismic analysis and design of steel structures especially for high rise building (nonlinear behavior). Similarly, the moment redistribution in a steel structure also depends on the rotation capacity of the section. So the determination and accurate prediction of rotation capacity of steel structures members such as wide flange beams become an important task. Using different methods such as finite element, regression and statistical methods in previous studies has been used in recent years. Therefore, in order to estimate the more accurate value of the rotational capacity of wide flange beams, artificial neural networks are used with the Bayesian learning process. The Bayesian Regularized network assigns a probabilistic nature to the network weights, allowing the network to automatically and optimally penalize excessively complex models. The proposed technique (BRANN) reduces the potential for overfitting and overtraining, improving the prediction quality and generalization of the network. The proposed model (BRANN) is based on experimental data that collected from previous studies. After a comprehensive review of existing literature, 77 data of wide flange beam were selected which had experienced to determined rotation capacity. For this purpose, Half-length of flange, height of web, thickness of flange, thickness of web, length of beam, yield strength of flange and yield strength of web were consider as input parameters (six inputs) while rotation capacity is treated as target of the Bayesian Regularized artificial neural network model. The Bayesian Regularized artificial neural network is modeled in MATLAB software and applied to predict the rotation capacity. The results of this model were compared with experimental results and other models and equations that presented in the past (including Genetic programming (GP), Li equation and Kemp Equation. An analysis is carried out to check the performance of the proposed BRANN model based on the common criteria such as Mean Absolute Percentage Error (MAPE). The optimal and best model should have the lowest values of MAPE, this parameter is 20. 32% for BRANN, 23. 49% for a Genetic Programming model that proposed by Cevik, 47/20% for Li’ s Equation and 56. 98% for Kemp’ s equations. The results of Bayesian Regularized artificial neural network approach indicate a good agreement between the predicted and measured data. Furthermore, the Bayesian Regularized artificial neural network model shows the most optimized results compared to all the previous model and equations. The result indicated that the Bayesian Regularized artificial neural network could be used as a powerful tool for engineers and researcher to solve this kind of problems.

The paper addresses a problem of tracking multiple number of frequencies using Regularized Autoregressive (RAR) approximation. The RAR procedure allows to decrease approximation bias, comparing to other AR-based frequency detection methods, while still providing competitive variance of sample estimates. We show that the RAR estimates of multiple periodicities are consistent in probability and illustrate dynamics of RAR in respect to sample size and signal-to-noise ration by simulations.

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.

Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the Regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.

Variable selection in Poisson regression with high dimensional data has been widely used in recent years. we proposed in this paper using a penalty function that depends on a function named a penalty. An Atan estimator was compared with  Lasso and adaptive lasso. A simulation and application show that an Atan estimator has the advantage in the estimation of coefficient and variables selection.