Solving an Infectious Disease Model considering Its Anatomical Variables with Stochastic Numerical Procedures

The aim of the current work is to perform the numerical investigation of the infectious disease based on the nonlinear fractional order prey-predator model using the Levenberg–Marquardt backpropagation (LMB) based on the artificial neuron networks (ANNs), i.e., LMBNNs. The fractional prey-predator model is classified into three categories, the densities of the susceptible, infected prey, and predator populations. The statistics proportions for solving three different variations of the infectious disease based on the fractional prey-predator model are designated for training 80% and 10% for both validation and testing. The numerical actions are performed using the LMBNNs to solve the infectious disease based on the fractional prey-predator model, and comparison is performed using the database Adams–Bashforth–Moulton approach. The infectious disease based on the fractional prey-predator model is solved using the LMBNNs to reduce the mean square error (M.S.E). In order to validate the exactness, capability, consistency, and competence of the proposed LMBNNs, the numerical procedures using the correlation, M.S.E, regression, and error histograms are drawn.

Processing and Interpretation of UAV Magnetic Data: A Workflow Based on Improved Variational Mode Decomposition and Levenberg-Marquardt Algorithm

Unmanned aerial vehicles (UAVs) have become a research hotspot in the field of magnetic exploration because of their unique advantages, e.g., low cost, high safety, and easy to operate. However, the lack of effective data processing and interpretation method limits their further deployment. In view of this situation, a complete workflow of UAV magnetic data processing and interpretation is proposed in this paper, which can be divided into two steps: (1) the improved variational mode decomposition (VMD) is applied to the original data to improve its signal-to-noise ratio as much as possible, and the decomposition modes number K is determined adaptively according to the mode characteristics; (2) the parameters of target position and magnetic moment are obtained by Euler deconvolution first, and then used as the prior information of the Levenberg–Marquardt (LM) algorithm to further improve its accuracy. Experiments are carried out to verify the effectiveness of the proposed method. Results show that the proposed method can significantly improve the quality of the original data; by combining the Euler deconvolution and LM algorithm, the horizontal positioning error can be reduced from 15.31 cm to 4.05 cm, and the depth estimation error can be reduced from 16.2 cm to 5.4 cm. Moreover, the proposed method can be used not only for the detection and location of near-surface targets, but also for the follow-up work, such as the clearance of targets (e.g., the unexploded ordnance).

Artificial Neural Network Training Algorithms in Modeling of Radial Overcut in EDM

This chapter describes with the comparison of the most used back propagations training algorithms neural networks, mainly Levenberg-Marquardt, conjugate gradient and Resilient back propagation are discussed. In the present study, using radial overcut prediction as illustrations, comparisons are made based on the effectiveness and efficiency of three training algorithms on the networks. Electrical Discharge Machining (EDM), the most traditional non-traditional manufacturing procedures, is growing attraction, due to its not requiring cutting tools and permits machining of hard, brittle, thin and complex geometry. Hence it is very popular in the field of modern manufacturing industries such as aerospace, surgical components, nuclear industries. But, these industries surface finish has the almost importance. Based on the study and test results, although the Levenberg-Marquardt has been found to be faster and having improved performance than other algorithms in training, the Resilient back propagation algorithm has the best accuracy in testing period.

Levenberg-Marquardt method for absolute value equation associated with second-order cone

<p style='text-indent:20px;'>In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.</p>