A 3-D spherical chaotic attractor

Abstract: A simple smooth chaotic system, which showed a 3-layer sphere chaotic attractor, is investigated. It is found that this chaotic attractor is a limit cycle instead of chaotic attractor. This situation was caused by the simulation time which is too short to reach its real status. It also shows that it is not reliable to construct chaotic system based only on the Šhilnikov criterion without finding the exact homoclinic orbits. Then a chaotic system with the real sphere shape is proposed. This proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagrams and Poincaré section

Tube Shear Hydro-bending of Titanium Alloys

AbstractA shear hydro-bending process was proposed to form the titanium alloys tubes with small bending radius, which can not be integrally formed by the conventional bending methods. Numerical simulation and experimental research were conducted to investigate effects of internal pressure and feeding ratio on defects, strain state and thickness distribution. The results show that the sound part can be successfully manufactured as the internal pressure ranges from 0.2σs to 0.6σs and the feeding ratio ranges from 1.0 to 1.3, while the defects occur if the internal pressure and the feeding ratio exceed to these scopes. The strain state of the inner and outer sides of the bend are tensile and compressive, and the thicknesses are thinning and thickening, respectively, which is influenced prominently by the internal pressure and the feeding ratio. The strain state of the lateral side is shear and the thickness is generally invariable. It can be conducted that shear hydro-bending method is suitable to manufacture the titanium alloys tube with small bending radius. There is a process window for the internal pressure and the feeding ratio, in which the tubes can be successfully formed without defects

Identification of discrete-time output error model for industrial processes with time delay subject to load disturbance

In this paper, a bias-eliminated output error model identification method is proposed for industrial processes with time delay subject to unknown load disturbance with deterministic dynamics. By viewing the output response arising from such load disturbance as a dynamic parameter for estimation, a recursive least-squares identification algorithm is developed in the discrete-time domain to estimate the linear model parameters together with the load disturbance response, while the integer delay parameter is derived by using a one-dimensional searching approach to minimize the output fitting error. An auxiliary model is constructed to realize consistent estimation of the model parameters against stochastic noise. Moreover, dual adaptive forgetting factors are introduced with tuning guidelines to improve the convergence rates of estimating the model parameters and the load disturbance response, respectively. The convergence of model parameter estimation is analyzed with a rigorous proof. Illustrative examples for open- and closed-loop identification are shown to demonstrate the effectiveness and merit of the proposed identification method

Single-pixel imaging of a translational object

Image-free tracking methods based on single-pixel detectors (SPDs) can track a moving object at a very high frame rate, but they rarely can achieve simultaneous imaging of such an object. In this study, we propose a method for simultaneously obtaining the relative displacements and images of a translational object. Four binary Fourier patterns and two differential Hadamard patterns are used to modulate one frame of the object and then modulated light signals are obtained by SPD. The relative displacements and image of the moving object can be gradually obtained along with the detection. The proposed method does not require any prior knowledge of the object and its motion. The method has been verified by simulations and experiments, achieving a frame rate of 3332 Hz to acquire relative displacements of a translational object at a spatial resolution of $128 \times 128$ pixels using a 20000-Hz digital micro-mirror device. This proposed method can broaden the application of image-free tracking methods and obtain spatial information about moving objects.Comment: 15 pages, 9 figures, 1 tabl

Tracking and fast imaging of a translational object via Fourier modulation

The tracking and imaging of high-speed moving objects hold significant promise for application in various fields. Single-pixel imaging enables the progressive capture of a fast-moving translational object through motion compensation. However, achieving a balance between a short reconstruction time and a good image quality is challenging. In this study, we present a approach that simultaneously incorporates position encoding and spatial information encoding through the Fourier patterns. The utilization of Fourier patterns with specific spatial frequencies ensures robust and accurate object localization. By exploiting the properties of the Fourier transform, our method achieves a remarkable reduction in time complexity and memory consumption while significantly enhancing image quality. Furthermore, we introduce an optimized sampling strategy specifically tailored for small moving objects, significantly reducing the required dwell time for imaging. The proposed method provides a practical solution for the real-time tracking, imaging and edge detection of translational objects, underscoring its considerable potential for diverse applications.Comment: 6 figure