Arctangent Function Research Articles

Parallel Parking Path Planning Based on Improved Arctangent Function Optimization

Parallel Parking Path Planning Based on Improved Arctangent Function Optimization

An energy-based model for the generation of excess pore water pressure in saturated coral sand

A series of undrained cyclic shear tests was carried out on saturated coral sands, with different initial physical states, as they were subjected to rotations of 90° in the paths of cyclic stress with various initial orientations under isotropic conditions. An important finding is that the cumulative dissipated energy required for liquefaction (W s) was significantly affected by their fines content (FC), relative density (D r), and effective stress of consolidation ( p ′ 0 ), but was independent of the conditions of cyclic loading. W s increased significantly with the increase in p ′ 0 . When FC was less than the threshold fines content, W s increased with FC and decreased with an increase in D r. The equivalent intergranular void ratio (e*) was introduced to reflect the effects of FC, physical states of the particles, and inter-particle contact on the physical properties of coral sand. The results revealed a unique relationship between e* and W s at p ′ 0 = 100 kPa. Furthermore, the unified model of the relation between the normalized cumulative dissipated energy and the ratio of excess pore water pressure (EPWP) followed an arc-tangent function. This model can be used to characterize the generation of EPWP with the cumulative dissipated energy of fine-grained sand under isotropic consolidation conditions.

Accurate Power Allocation of Multienergy Storage Island DC Microgrid Based on Virtual Power Rating

For isolated island dc microgrid connected with multidistributed energy storage, the initial state of charge (SOC) of energy storage is inconsistent and the power distribution of distributed energy storage unit (DESU) may be affected by the mismatched line impedance. Therefore, an adaptive droop coefficient control method based on virtual power rating is designed, which can quickly equalize SOC and eliminate the influence of mismatched line impedance. In the proposed control strategy, the arctangent function is introduced to combine the droop coefficient with the SOC of the energy storage unit, and the characteristic of the arctangent function is used to ensure the fast SOC equilibrium and limit the adaptive adjustment range of the droop coefficient. Considering the actual operating point together with the virtual operating point of the energy storage unit, the virtual power rating is used to construct the compensation term, which can automatically eliminate the output power deviation according to the line impedance difference of the DESU. In addition, the stability analysis is given theoretical support for the proposed control strategy. Finally, the reliability and effectiveness of the proposed strategy are verified by the RTLAB experiment.

Revealing Land Surface Deformation Over the Yineng Backfilling Mining Area, China, by Integrating Distributed Scatterer SAR Interferometry and a Mining Subsidence Model

Monitoring the surface deformation of filling coal mines regularly and understanding their spatiotemporal evolution characteristics for mining management and disaster warning is greatly significant. However, there is a lack of research on extracting spatiotemporal evolution characteristics of large-scale and high-resolution surface deformation in backfill mining areas and on evaluating filling effectiveness of subsidence restraint. In this study, we took the Yineng Coal Mine in Shandong Province of China and the surrounding area of the coal mine as the study area. The advanced Distributed scatterer InSAR (DS InSAR) technique was adopted for time-series analysis. The probability integral method (PIM) model for backfilling mining and an arctangent time function were integrated with DS InSAR to overcome the sparsity of InSAR observation points due to the temporal decorrelation caused by vegetation coverage. The results show that the proposed integration strategy is helpful in improving the number of effective monitoring points and obtaining the complete spatiotemporal information of the surface deformation of the working face. The whole study area has eight key deformation zones. All six working faces in the Yineng initial minery display different degrees of deformation during the study period. The comparison between the deformation results of backfill mining and the simulated deformation of nonbackfill mining in the CG1312 working face shows that backfilling mining technology effectively reduces the range (22.00%) and magnitude (61.50%) of surface subsidence and significantly reduces the potential threat to surface buildings.

A Heterogeneous Time-Tracking Fusion and Application to Health Evaluation of Aerospace Engines

Heterogeneous information fusion has long been a difficult problem due to the differences in the representation and feature of various physical information. Besides, the multi-sensor signals of large mechanical equipment such as aerospace engines often change in a complicated way during the start-up stage and long-term operation, which makes the multi-sensor fusion based health assessment research impending. To explore a suitable fusion method for the multi-physical signals with different change rates, as well as to monitor the health state of large mechanical equipment based on multi-sensor information, this paper proposes a heterogeneous time-tracking fusion algorithm. Firstly, the time-domain indexes and instantaneous frequencies of the fast-varying harmonic-like signals are obtained by employing index extraction and second-order synchrosqueezing transform respectively, by which the overall and detailed characteristics of the signals are thus obtained. Secondly, after structuring a dynamic time-tracking function consisting of the hyperbolic tangent function and modified arctangent function, the time-dynamic confidence upper limit for fast-varying signals and confidence interval for slow-varying signals are obtained creatively. Finally, the different varying-rate signals are fused into a dynamic normalized time-varying index representing the health state through the aforementioned functions. By applying the proposed method to the health evaluation for ignition start-up stage of gas generators and the long-term performance of the turbopump, its effectiveness and practicability in the aerospace engine health analysis have been validated.

Wavelet based tone mapping (TM) enhancement to a detection system for faint and compact sources in HDR and large FOV radio scenes

For high dynamic range (HDR) and large field-of-view (FOV) radio scenes, detection of faint sources with compact support and tiny sizes in comparatively extensive celestial areas is a challenging task. In the era of the Square Kilometer Array (SKA), it will be of particular concern, and data-targeted systematic methods are put on the agenda. This paper proposes a systematic method to solve this problem. From the perspective of image processing, a multiscale image contrast enhancement (ICE) is proposed to normalize the HDR. Source representation is realized by a starlet framework, where a two-step tone mapping (TM) including an arc-tangent function compression and an aggregated gain function enhancement are embedded. According to two bionic principles, the gain function is designed to highlight faint sources, remove artifacts (e.g., halos), and avoid feature distortions. For source detection, an integration method is proposed for projections between the celestial and the planar coordinate systems. It serves for coordinate transform and source location. A detection indicator system is built, and elaborate discrimination principles are drawn up. In the experiments, this method is dedicated to the dataset of the TIFR GMRT Sky Survey (TGSS) alternative data release 1 (ADR1) to facilitate the scientific goal of discovering new sources. Results show its advantages over the state of the art methods in visual inspections and detection ratios, and preliminarily prove that it has prospects for future HDR and large FOV radio data.

Study and Design of Ratiometric Inductive Position Sensors Using Area-of- Overlap Functions

This article presents a theoretical study of an absolute, ratiometric inductive position sensor (IPS) based on eddy currents. The aim is to describe the working principle of the sensor, having as key components a transmitting coil, the receiving coils, and the conductive target, by introducing area-of-overlap functions. We show that each target–receiver pair needs the adoption of a different reconstruction formula for the identification of the target position, whereas in the literature the usual inverse tangent function is applied for every possible pair. Then, we seek the target–receiver pair that maximizes the amplitude of the induced voltages on the receivers. The results show that to achieve the maximum value of the induced voltages, the best choice is to have a rectangular target and rectangular receivers. To verify the theory, a simulation and optimization method has been applied to the rectangular receiver coils on two rotary IPS realized with printed circuit board (PCB) technology. Measurements performed on the prototypes have shown an increment of the induced voltage of more than 57% with respect to the commonly used sinusoidal receivers. However, a linearity error of 1.5%FS is obtained by using the inverse tangent reconstruction formula. When using the formula provided by the theory, the linearity error becomes 0.6%FS for the nonoptimized prototype and below 0.15%FS for the optimized one.

An Indirect State-of-Health Estimation Method Based on Improved Genetic and Back Propagation for Online Lithium-Ion Battery Used in Electric Vehicles

Lithium-ion battery state of health (SOH) estimation technology is an important part of the design of a battery monitoring system (BMS) for electric vehicles. People often use battery capacity and internal resistance as SOH estimation indicators. However, due to actual working conditions, it is difficult for electric vehicles to achieve complete charge and discharge, so the battery capacity and internal resistance cannot be monitored online. In view of the above questions, this article proposes an indirect SOH estimation method for online EV lithium-ion batteries based on arctangent function adaptive genetic algorithm combination with back propagation neural network (ATAGA-BP). Firstly, constant current drop time (CCDT), constant current drop capacity (CCDC) and maximum constant current drop rate (MCCDR) in constant voltage charging stage are used as health indicator (HI) to evaluate battery SOH in order to indirectly quantify the degradation process of lithium-ion batteries. Error point optimization and correlation verification are also carried out. Secondly, an ATAGA-BP algorithm is proposed to establish the relationship between HI and available battery capacity, and SOH estimate is made for lithium-ion batteries according to the proposed algorithm. Finally, simulation results with NASA data show the correlation between the proposed HI and lithium-ion battery capacity is above 85%, the error of SOH estimation method proposed is 3.7%, and the iteration efficiency is increased by 17.8%.

Rigorous spherical bearing with Soldner coordinates and azimuth angles on sphere

Meridian systems, called Soldner coordinates (parallel coordinate) systems, have found wide application in geodesy. In particular, the meridian system constitutes a suitable base for the Gauss-Kruger projection of the ellipsoid and the sphere. Soldner coordinates can be used in Cassini-Soldner projection without any processing. As it is known, the directions of the edges are shown with azimuth angles in the geographic coordinate system and the bearing angles in the Soldner coordinate system. Bearing or azimuth angles are frequently used in geodetic calculations. These angles give the direction of sides in the clockwise direction from a certain initial direction. Both angle values range from 0 to 360 degrees and are usually calculated from the arctan function. But the arctan function returns an angle value between -90 and +90 degrees. Therefore, it is necessary to analyze the quarter for the angle found. For practical computations, the quadrants of the arctangents are determined by the signs of the numerator and denominator in the tangent formulas. Determining the quarter of the angles is done with if…, then…, end..., blocks on the computer. It should be noted that each comparison requires a separate processing time. This study will be given how to calculate both bearing and azimuth angles with direct formulas without any need to examine them. In addition, a solution proposal will be given against the division by zero errors in the bearing and azimuth angles calculations.

The Method of Probabilistic Nodes Combination in Biomechanics

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve modeling and handwriting identification by using the set of key points. Nodes are treated as characteristic points of signature or handwriting for modeling and writer recognition. Identification of handwritten letters or symbols need modeling and the model of each individual symbol or character is built by a choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter γ as probability distribution function enables curve parameterization and interpolation for each specific letter or symbol. Two-dimensional curve is modeled and interpolated via nodes combination and different functions as continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function.

High-fidelity quantum control via Autler-Townes splitting

We propose quantum control protocols for the high-fidelity preparation of target states in systems with Autler-Townes splitting. We investigate an approximated three-level system obtained from a four-level one by adiabatically eliminating a state that does not participate in the evolution. In our work we use linear, arctan, and Roland-Cerf functions for transferring population between two eigenstates of the system obtaining a high fidelity for long evolution times. Additionally, in order to overcome the restriction given by the lifetimes of the experimental setup, we propose an accelerated adiabatic evolution with a shortcut to adiabaticity protocol, which allows us to reach fidelities close to one but much faster.

Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

Fixed‐time fault‐tolerance attitude tracking control for spacecraft without unwinding

In this paper, the attitude tracking control problem is investigated for rigid spacecraft subjected to external disturbance, inertia uncertainties, and actuator faults. The rotation matrix is used to model the spacecraft attitude control system which can get rid of the unwinding problem. A nonlinear observer is developed to achieve a high accuracy estimation for the lumped disturbance in fixedtime without the awareness of the boundary of disturbance. To restrain measurement noise, a tracking differentiator is used in the observer to construct signals instead of using the polluted measurement values. Based on the estimation provided by the disturbance observer, a fixed-time attitude tracking controller is proposed by backstepping technique to stabilize attitude tracking errors in fixed time regardless of initial values. The singularity problem in traditional fixed-time controllers based on signal function is eliminated with the help of the arctangent function in the proposed controller. The feature of the designed fixed-time attitude controller is that it can suppress actuator faults, measurement noises and has no unwinding problem. Theoretical analysis based on Lyapunov theory and numerical simulations are presented to illustrate the robustness and effectiveness of the proposed control strategy.

The Method of Probabilistic Nodes Combination in Handwritten Character Reconstruction

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve modeling and handwriting identification by using the set of key points. Nodes are treated as characteristic points of signature or handwriting for modeling and writer recognition. Identification of handwritten letters or symbols need modeling and the model of each individual symbol or character is built by a choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter γ as probability distribution function enables curve parameterization and interpolation for each specific letter or symbol. Two-dimensional curve is modeled and interpolated via nodes combination and different functions as continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function.

Adaptive nonsingular fixed-time sliding mode control for manipulator systems’ trajectory tracking

In this paper, an adaptive fixed-time controller is raised for the manipulator system with uncertain disturbances to boost the rate and precision of its trajectory tracking and solve the convergence time dependence on the system's initial conditions. First, a nonsingular fixed-time sliding mode (SM) surface and a reaching law based on an arctangent function are constructed to enhance the control scheme performance. Second, the upper bound is difficult to obtain because of the uncertainty of the disturbance. The disturbance upper bound is estimated by adaptive techniques, which do not require a priori knowledge about the upper bound and effectively inhibit the effect of disturbance on the system. Finally, the fixed-time convergence of the states is analyzed by rigorous theoretical proof, and the validity of the presented control scheme is demonstrated by simulation.

General multivariate arctangent function activated neural network approximations

Here we expose multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or \(\mathbb{R}^{N}\), \(N\in \mathbb{N}\), by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Frechet derivatives.
 Our multivariate operators are defined by using a multidimensional density function induced by the arctangent function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

Infrared and low-light visible image fusion based on hybrid multiscale decomposition and adaptive light adjustment

Most traditional infrared and visible image fusion methods often ignore weak texture details, especially for the low-light visible images in which the weak details are easily drowned due to noise or ill-illumination. To address this problem, we propose a novel infrared and low-light visible image fusion method from the perspective of low-light visible image enhancement, weak feature extraction strategy and detail preserved fusion rules. By combining both local and global contrast enhancements, an adaptive light adjustment algorithm is proposed to improve the brightness and texture details of low-light visible images. In addition, we design a hybrid multiscale decomposition model based on guided filters (GFs) and side window guided filters (SWGFs) to decompose the source images into the base layer, large-scale detail layers and small-scale detail layers. The three layers reflects the background, large edge structures and weak texture details of source images respectively. Subsequently, the visual saliency retention, normalized arctan function, and edge preservation-based consistency verification are applied to highlight salient targets and retain weak details for three layers fusion. Qualitative and quantitative experimental results on publicly available datasets prove the superiority of our method over state-of-the-art methods in terms of highlight salient targets, avoiding edge blurring, and retaining weak details.

High-efficiency and low-energy ship recognition strategy based on spiking neural network in SAR images.

Ship recognition using synthetic aperture radar (SAR) images has important applications in the military and civilian fields. Aiming at the problems of the many model parameters and high-energy losses in the traditional deep learning methods for the target recognition in the SAR images, this study has proposed a high-efficiency and low-energy ship recognition strategy based on the spiking neural network (SNN) in the SAR images. First, the visual attention mechanism is used to extract the visual saliency map from the SAR image, and then the Poisson encoder is used to encode it into a spike train, which can suppress the background noise while retaining the visual saliency feature of the SAR image. Besides, an SNN model integrating the time-series information is constructed by combining the leaked and integrated firing spiking neurons with the convolutional neural network (CNN), which can use the firing frequency of the spiking neurons to realize the ship recognition in SAR images. Finally, to solve the problem that SNN model is difficult to train, the arctangent function is used as the surrogate gradient function of the spike emission function during the backpropagation. Hence, applying this backpropagation method to the training process can optimize the SNN model. The experimental results show the following: (1) the proposed strategy can more accurately recognize the ship in the SAR image, and the F1 score can reach 98.55%, which has a better recognition performance than the other traditional deep learning methods; (2) the proposed strategy has the least amount of model parameters (only 3.11MB), which is far less than the model parameters of the other traditional deep learning methods; (3) the proposed strategy has fewer operations (only 17.97M) and can reach 1/30 time of operands of the other traditional deep learning methods, which shows the high efficiency of the proposed strategy using the spike emission signals; (4) the proposed strategy has the energy loss of 1.38 × 10−6J, which can achieve the low energy advantage of nearly three orders of the magnitude compared to the other traditional deep learning methods, indicating that the proposed strategy has a significant energy efficiency.

Near infrared spectroscopic variable selection by a novel swarm intelligence algorithm for rapid quantification of high order edible blend oil

The quantification of single oil in high order edible blend oil is a challenging task. In this research, a novel swarm intelligence algorithm, discretized whale optimization algorithm (WOA), was first developed for reducing irrelevant variables and improving prediction accuracy of hexanary edible blend oil samples. The WOA is inspired by hunting strategy of humpback whales, which mainly includes three behaviors, i.e., encircling prey, bubble-net attacking and searching for prey. In discretized WOA, positions of whales were updated and then discretized by arctangent function. The whale population performance, iteration number and whale number of WOA were investigated. To validate the performance of selected variables, partial least squares (PLS) was used to build model and predict single oil contents in hexanary blend oil. Results show that WOA-PLS can provide the best prediction accuracy compared with full-spectrum PLS, continuous wavelet transform-PLS (CWT-PLS), uninformative variable elimination-PLS (UVE-PLS), Monte Carlo uninformative variable elimination-PLS (MCUVE-PLS) and randomization test-PLS (RT-PLS). Furthermore, CWT-WOA-PLS can further produce better results with fewer variables compared with WOA-PLS.

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets.