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This paper introduces an innovative approach to address the distribution network reconfiguration (DNR) challenge, aiming to reduce power loss through an advanced hyperbolic tangent particle swarm optimization (HT-PSO) method. This approach is distinguished by the adoption of a novel hyperbolic tangent function, which effectively limits the rate of change values, offering a significant improvement over traditional sigmoid function-based methods. A key feature of this new approach is the integration of a tunable parameter, δ, into the HT-PSO, enhancing the curve’s adaptability. The careful optimization of δ ensures superior control over the rate of change across the entire operational range. This enhanced control mechanism substantially improves the efficiency of the search and convergence processes in DNR. Comparative simulations conducted on 33- and 94-bus systems show an improvement in convergence, demonstrating a more exhaustive exploration of the search space than existing methods documented in the literature based on PSO and variations where functions are proposed for the rate of change of values.

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle’s Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet, successfully simplified post-processing and integrated post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent (HTBNet). First of all, we propose the Binarization of Hyperbolic Tangent (HTB), optimized along with which the segmentation network can expedite the initial convergent speed by reducing the number of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention (MSCA). Meanwhile, considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial (FMCS), which can fuse the multi-scale feature maps from channel and spatial dimensions. Finally, we adopt cross-entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet, compared with lightweight models, has achieved competitive performance and speed on Total-Text (F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

The Grey Wolf Optimization Algorithm (GWO) replicates the leadership and foraging mechanisms of the natural grey wolf and excels in solving problems in a variety of domains. However, the algorithm tends to converge to a local optimal and has a slow convergence rate. This paper proposes an enhanced Grey Wolf optimization algorithm (HTGWO) based on hyperbolic tangent inertia weights to solve this problem. HTGWO employs inertia weights based on hyperbolic tangent functions to balance GWO’s global and local search capabilities of the GWO. HTGWO has a faster convergence rate and more accurate solutions than GWO. Five classical test functions were used to construct comparative experiments between the HWGWO and five classical intelligent optimization algorithms. The comparison results indicate that HWGWO has superior convergence speed, solution precision, and stability compared with the other five classical intelligent optimization algorithms. Moreover, experimental evidence suggests that the HWGWO is more effective at solving multimodal functions than unimodal functions. In addition, HTGWO can balance exploration and exploitation by adjusting the parameters according to the characteristics of different problems.

This research investigates two-dimensional MHD incompressible boundary layer Hyperbolic Tangent nanofluid flow across a non-linear stretching plate. Similarity transformations are employed to convert the governing non-linear partial differential equations (PDEs) into coupled non-linear ordinary differential equations (ODEs). The MATLAB built-in routine bvp4c has been used for finding the numerical solutions of the dimensionless velocity, temperature, and concentration profiles. The current findings are validated with already published results. The influence of some important parameters on the velocity, temperature, and concentration profiles are displayed through graphs and tables. It is observed that for increasing values of magnetic parameter M and hyperbolic Tangent parameter We, the boundary layer thickness of the velocity profile decreases while it increases for the temperature profile.

In machine learning, the input data is often given in different dimensions. As a result of the scientific papers review, it is shown that the initial data described in different types of scales and units of measurement should be converted into a single representation by normalization or standardization. The difference between these operations is shown. The paper systematizes the basic operations presented in these scales, as well as the main variants of the function normalization. A new scale of parts is suggested and examples of the data normalization for correct analysis are given. Analysis of publications has shown that there is no universal method of data normalization, but normalization of the initial data makes it possible to increase the accuracy of their classification. It is better to perform data clustering by methods using distance functions after converting all features into a single scale. The results of classification and clustering by different methods can be compared with different scoring functions, which often have different ranges of values. To select the most accurate function, it is reasonable to normalize several functions and to compare their estimates on a single scale. The rules for separating features of tree-like classifiers are invariant to scales of quantitative features. Only comparison operation is used. Perhaps due to this property, the random forest classifier, as a result of numerous experiments, is recognized as one of the best classifiers in the analysis of data of different nature.

Toughness and the transition from ductile to brittle behavior are long-standing concerns for applications of ferritic steel such as line-pipe. Three algorithms have been developed to fit a hyperbolic tangent curve to any Charpy V-notch dataset and estimate the uncertainty for (1) the 85% shear appearance area transition temperature and (2) the upper shelf absorbed energy. To fit the hyperbolic tangent curve to the data the (I) first algorithm relied on iterative estimation of four-parameters; (II) the second algorithm on two parameters (after simplification based on physical assumptions); and (III) the third algorithm on only one parameter (after further simplification). The algorithms were written using the open-source programing language, R. The minimum input requirements for the algorithm are experimental data for shear appearance area and absorbed energy from at least four temperatures for the four-parameter algorithm, two temperatures for the two-parameter algorithm, and one temperature for the one-parameter algorithm. The test temperatures and quantity of tests at each temperature can vary. The algorithms are described in detail and demonstrated using a data set of 12 Charpy test results (shear area and absorbed energy) from one API-5L grade X52 pipe with 4.5 mm thick Charpy bars. A future paper will test and compare the algorithms using a wide variety of Charpy V-notch data sets to clarify their applicability and possible limitations.

We present smooth approximations to the absolute value function |x| using sigmoid functions. In particular, x erf(x/μ) is proved to be a better smooth approximation for |x| than x tanh(x/μ) and x2+μ\sqrt {{x^2} + \mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.

We propose that in some papers (4 maybe 5 !) to present a model of teaching and learning in secondary education of hyperbolic functions, giving many properties (starting with fundamental ones and finishing with development in Tayler series), and then to present some of their applications in algebra and mathematical analysis. The papers addresses teachers in the teaching of these issues in the classroom, but also in preparing students to the school competitions .

The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form ∫ 0 ∞ log ( 1 ± e − α y ) R ( k , a , y ) d y in terms of a special function, where R ( k , a , y ) is a general function and k, a and α are arbitrary complex numbers, where R e ( α ) > 0 .

This work establishes a 2D numerical model to simulate the cutting process of workpieces made of Ti⁻6Al⁻4V, by applying an improved Smoothed Particle Hydrodynamics algorithm together with a modified constitutive model based on the Johnson⁻Cook model known as Hyperbolic Tangent (TANH). The location information of the surface particles obtained by the SPH cutting model are used to evaluate the variation trend of surface roughness with different parameters. Parameters that affect the surface roughness are investigated in detail by using the Taguchi method and the SPH cutting model. The present work provides an efficient and cost-effective approach to determine the optimal parameters for cutting processes for Ti⁻6AL⁻4V workpieces, through computer simulations in virtual environments, instead of expensive and time-consuming cutting experiments using actual workpieces.