Nonlinear problems are more challenging and almost complex to be solved. A recently developed Homotopy Perturbation Method (HPM) is introduced. This method is used to represent the system as a less complicated (almost linear) model. To verify the effectiveness, HPM based model is compared with the original nonlinear dynamic in both open and closed loop PI controller. The simulation results reveal the ability of the proposed method.

The objective of this study is to develop a material-nonlinear-analysis algorithm based on the Transfer Matrix Method (TMM). This newly developed algorithm can be used to perform nonlinear analyses of continuous beam systems. The nonlinear transfer matrix is derived from the general frame stiffness matrix, and the Gauss-Lobatto integration scheme is employed for numerical integration. In the TMM, the system equation has a constant number of system unknowns, regardless of the total degree-off-freedom number in the structure and the system response (either linear or nonlinear). As a result, TMM can be used efficiently, both for linear and nonlinear structural analyses. In this study, a secant nonlinear algorithm, required in nonlinear TMM, is employed, due to its good compromise between the convergence rate and numerical stability. To verify the accuracy and efficiency of the developed TMM, four numerical examples are selected and analyzed. The analysis results are compared with those obtained by the highly accurate flexibility-based frame model, in terms of global and local responses.

Face recognition from digital images is used for surveillance and authentication in cities, organizations, and personal devices. Internet of Things (IoT)-powered face recognition systems use multiple sensors and one or more servers to process data. All sensor data from initial methods was sent to the central server for processing, raising concerns about sensitive data disclosure. The main concern was that all data from all sectors that could contain confidential information was placed in a central server. Federated learning can solve this problem by using several local model training servers for each region and a central aggregation server to form a global model in IoT networks. This article presents a novel approach to optimize data transfer and convergence time in federated learning for a face recognition task using Non-dominated Sorting Genetic Algorithm II (NSGA II). The aim of the study is to balance the trade-off between training time and model accuracy in a federated learning environment. The results demonstrate the effectiveness of the proposed approach in reducing data transfer and convergence time, leading to improved performance in face recognition accuracy. This research provides insights for researchers and practitioners to enhance the efficiency of federated learning in real-world applications.

In this paper we propose a new method for ranking Z-numbers and generalizations. This method is based on the internal structure of the artificial neural network, which suggests that the structure of this network consists of inputs weights and the transfer function linear, nonlinear and sometimes linear and nonlinear. It is shown that the proposed method while possessing the ranking properties for Z-numbers whose components of the limiting part are equal and their confidence interval having the same center of gravity has a more logical ranking than those using the center of gravity. While some of the available methods for Z numbers whose boundaries are equal but not equal to their reliability but have the same focal gravity they rank equally which can not be logical in all cases. Therefore, the proposed method overcomes this problem. In some examples the correctness of the subject is shown. the results are compared with some existing methods.