Search Results (21)

Event detection is the most important element of eye movement analysis. Deep learning approaches have recently demonstrated superior performance across various fields, so researchers have also used them to identify eye movement events. In this study, a combination of two-dimensional convolutional neural networks (2D-CNN) and long short-term memory (LSTM) layers is proposed to simultaneously classify input data into fixations, saccades, post-saccadic oscillations (PSOs), and smooth pursuits (SPs). The first step involves calculating features (i.e., velocity, acceleration, jerk, and direction) from positional points. Various combinations of these features have been used as input to the networks. The performance of the proposed method was evaluated across all feature combinations and compared to state-of-the-art feature sets. Combining velocity and direction with acceleration and/or jerk demonstrated significant performance improvement compared to other feature combinations. The results show that the proposed method, using a combination of velocity and direction with acceleration and/or jerk, improves PSO identification performance, which has been difficult to distinguish from short saccades, fixations, and SPs using classic algorithms. Finally, heuristic event measures were applied, and performance was compared across different feature combinations. The results indicate that the model combining velocity, acceleration, jerk, and direction achieved the highest accuracy and most closely matched the ground truth. It correctly classified 82% of fixations, 90% of saccades, and 88% of smooth pursuits. However, the PSO detection rate was only 73%, highlighting the need for further research. Full article

Brownian motion has been studied since 1827, leading to numerous important advances in many branches of science and to it being studied primarily as a stochastic dynamical system. In this paper, we present a deterministic model for the Brownian motion for a particle in a constant force field based on the Ornstein–Uhlenbeck model. By adding one degree of freedom, the system evolves into three differential equations. This change in the model is based on the Jerk equation with commutation surfaces and is analyzed in three cases: overdamped, critically damped, and underdamped. The dynamics of the proposed model are compared with classical results using a random process with normal distribution, where despite the absence of a stochastic component, the model preserves key Brownian motion characteristics, which are lost in stochastic models, giving a new perspective to the study of particle dynamics under different force fields. This is validated by a linear average square displacement and a Gaussian distribution of particle displacement in all cases. Furthermore, the correlation properties are examined using detrended fluctuation analysis (DFA) for compared cases, which confirms that the model effectively replicates the essential behaviors of Brownian motion that the classic models lose. Full article

By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also features two-dimensional offset boosting, where a single parameter can realize direct offset boosting while another provides interlocked cross-dimensional offset boosting. Furthermore, this jerk system has a parameter-dominated symmetric attractor, which means that symmetric attractors appear successively as the parameter changes from positive to negative. Circuit experiments confirm the feasibility of analog fractional exponentiation using the 444 circuit and the complete control, including amplitude control and offset boosting, of the resulting system. The proposed circuit may facilitate applications of chaotic signal generators where signal versatility is important and exemplifies the generative potential of analog fractional exponentiation. Full article

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

In this paper, we construct a family of Hamilton–Poisson jerk systems. We show that such a system has infinitely many Hamilton–Poisson realizations. In addition, we discuss the stability and we prove the existence of periodic orbits around nonlinearly stable equilibrium points. Particularly, we deduce conditions for the existence of homoclinic and heteroclinic orbits. We apply the obtained results to a family of anharmonic oscillators. Full article

Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system. Full article

In the case of electric vehicle drives, faults in the drive system or in the traction inverter, which controls the vehicle drive unit, could lead to abrupt and unpredictable motion as well as acceleration of the vehicle. In terms of functional safety, the typically existing, permanent mechanical connection of the drive machine with the drive wheels poses a high safety risk. In particular, unintended motion of the vehicle from a standstill is especially critical due to the high risk of injury to traffic participants. To reduce this risk, appropriate monitoring algorithms can be applied for the rapid detection of faulty operation. A corresponding algorithm for fault detection in the electric drive of a vehicle is presented in this paper. In addition to the description of the algorithms, various driving maneuvers of an electric single-wheel drivetrain are simulated in fault-free and faulty operation on a hardware-in-the-loop test bench. The focus here is on the consideration of driving-off operations. Full article

The time that a vehicle merges in a lane reduction can significantly affect passengers’ safety, comfort, and energy consumption, which can, in turn, affect the global adoption of autonomous electric vehicles. In this regard, this paper analyzes how connected and automated vehicles should cooperatively drive to reduce energy consumption and improve traffic flow. Specifically, a model-free deep reinforcement learning approach is used to find the optimal driving behavior in the scenario in which two platoons are merging into one. Several metrics are analyzed, including the time of the merge, energy consumption, and jerk, etc. Numerical simulation results show that the proposed framework can reduce the energy consumed by up to 76.7%, and the average jerk can be decreased by up to 50%, all by only changing the cooperative merge behavior. The present findings are essential since reducing the jerk can decrease the longitudinal acceleration oscillations, enhance comfort and drivability, and improve the general acceptance of autonomous vehicle platooning as a new technology. Full article

In recent years, many methods have been developed to calculate the trajectory of a robotic arm in the joint-space. These methods have many advantages, such as a soft motion and infinite jerk avoidance. Nevertheless, these methods present other problems that must be avoided, such as an unnatural motion while generating the trajectory and producing unsafe planning. In this sense, this work presents a numerical method named iterative optimal solution trajectory via ${\left(\zeta \right)}_v$-homotopy former (IOSTV ${\left(\zeta \right)}_v$-HF). It is proposed to reduce and avoid oscillation while obtaining trajectories with different shapes to perform better, reliable, smooth, and long-life robotic systems. The algorithm with the proposed method is described, and examples of the trajectories obtained with different parameters are presented. In addition, these were mapped and a trajectory with a continuous velocity and a reduced oscillation and another trajectory with the same restrictions but with a continuous acceleration and zero oscillations were shown; the method is versatile since it allows for choosing and finding the most optimal solutions according to the application. Finally, the article ends with a critical discussion of the experimental results. Full article

In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and the multiple scales method. Both the first- and second-order approximations for the unforced and forced jerk Van-der Pol oscillatory equations are derived in detail using the proposed methods. Comparative analysis is performed between the analytical approximations using the proposed methods and the numerical approximations using the fourth-order Runge–Kutta scheme. Additionally, the global maximum error to the analytical approximations compared to the Runge–Kutta numerical approximation is estimated. Full article

Electric vehicle drivetrains are considered a way to reduce greenhouse gas emissions from road traffic. The use of electric drives in automotive vehicles offers advantages, such as the potential to recover energy during braking (regenerative braking). The limitation of the maximum air gap torque of the vehicle drive machine by several factors requires a temporary standalone or simultaneous use of the conventional vehicle wheel brake. In several studies, it is shown that during braking operations, the drive machine and the vehicle wheel brake can induce torsional oscillations in the drivetrain, which have a negative influence on the driving comfort and lead to a high mechanical load. To reduce these oscillations, the simultaneous use of an active anti-jerk control is necessary. Due to the problem of oscillation excitations caused by a brake intervention, the used drivability function (integrated prefilter, anti-jerk control) is investigated and optimized with regard to brake blending maneuvers and the effectiveness for damping torsional oscillations. Therefore, the dynamics of the drivetrain are adapted to the dynamics of the braking system using the prefilter, which leads to precise fulfilment of the driver’s braking desire, even during dynamic brake blending maneuvers. All investigations are carried out with a hardware-in-the-loop test bench to create reproducible results. Full article

The subject of this paper is the existence, uniqueness and stability of solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. The arguments are based upon the Banach contraction principle, Krasnoselskii fixed-point theorem and Ulam–Hyers stabilities. As applications, one illustrative example is included to show the applicability of our results. Full article

This paper deals with a method for generating symmetrical trapezoidal acceleration profiles for the motor of a vibrating system in rest-to-velocity motion. The aim was to significantly reduce the acceleration time and residual load vibration of lightly damped systems. Under undamped conditions, the analytical values of the jerk time are found to be in relation to the estimated natural frequency and the minimum value of the acceleration time is provided, also taking into account a limit value for motor acceleration. The analysis of the sensitive curves allows the designer to understand the magnitude of the residual vibration generated by an incorrect estimate of the natural frequency. Numerical simulations, with a closed-chain controlled motor and a zero or very small structural damping coefficient of the oscillating system, confirm the validity of the proposed method. Full article

Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been applied to the target tracking field, the precision and stability of SHAKF remain to be improved. In this paper, a square root Sage–Husa adaptive robust Kalman filter (SR-SHARKF) algorithm together with the constant jerk model is proposed, which can not only solve the problem of filtering divergence triggered by numerical rounding errors, inaccurate system mathematics, and noise statistical models, but also improve the filtering accuracy. First, a novel square root decomposition method is proposed in the SR-SHARKF algorithm for decomposing the covariance matrix of SHAKF to assure its non-negative definiteness. After that, a three-segment approach is adopted to balance the observed and predicted states by evaluating the adaptive scale factor. Finally, the unbiased and the biased noise estimators are integrated while the interval scope of the measurement noise is constrained to jointly evaluate the measurement and observation noise for better adaptability and reliability. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm in eliminating white noise triggered by the USV and target oscillations. Full article

Flight control electro-mechanical actuators (EMAs) are among the primary onboard systems that significantly influence the reliability and safety of unmanned aerial vehicles. Recent reliability studies have shown that the ball-screw element of a flight control EMA is subject to oscillating operating conditions that may initiate rapid degradation, such as fatigue spall defects. Accordingly, detecting and quantifying such faults are crucial for developing efficient fault prognostic and remaining useful life estimation capabilities. In this study, a vibration-based fault quantification method is developed to quantify the fatigue faults of a ball-screw mechanism of an EMA. The method is based on identifying the ball passing instants through a localized surface defect on the vibrational jerk rather than the vibrational acceleration measurement. The jerk is numerically determined from conventional accelerometers using a Savitzky–Golay differentiator. This method was successfully tested for ball bearings and it is adjusted in this paper for ball-screw faults. The experimental validation is investigated on a set of fault-seeded samples on NASA’s Ames Research Center Flyable Electro-Mechanical Actuator test stand. Full article