Vol. 5, No. 2 (2021): Regular Issue

Many control systems incorporate input from actuators. The actuators can be represented as force or displacement input. When an actuator is modeled as a displacement input, there are many practical applications for which the displacement is not smooth and its time derivative, i.e. the velocity, is not continuous everywhere. Numerical study for such displacement input becomes tedious since the state variables experience a finite jump at the time of acceleration singularity. Although the acceleration singularity can be avoided if the actuator dynamics is modeled by a force input, such an approach increases the order of the overall system. To preserve the simplicity of the displacement input of the actuators, we propose transforms of state variables so that only the velocity of the displacement input appears explicitly in the equations of the dynamical system. In short, we introduce transforms that reduce the order of time derivatives of the input. This approach simplifies the numerical solutions for non-smooth displacement input. Moreover, when the transform is applied to a parametrically excited pendulum, the stabilizing effect of the parametric excitation is shown explicitly.

Image fusion is a branch of multi-source information fusion, which plays an increasingly significant role in the military field. Since the environment is full of many interference factors, including light, dust, etc., the target object cannot be clearly identified. Image fusion based on visible image and infrared image is attractive and promising for the object detection applications. This paper analyzes and compares pixel-level, feature-level and decision-level image fusion, and summarizes the performance-gains of image fusion at different levels with examples. It is concluded that pixel-level fusion can be used to process more delicately than feature-level fusion, and the result of feature-level fusion is more delicate than decision-level fusion. Furthermore, we conclude a creative idea, that is pixel-level and feature-level methods can be combined in the future.

This paper presented the dynamics of an infinite-equilibrium system based on a quadratic oscillator. equilibria, stability and singularity of such an infinite equilibrium system are discussed through the local analysis, and numerical studies of the periodically perturbed infinite-equilibrium systems are completed. The infinite-equilibrium boundaries in infinite-equilibrium systems can be artificially designed to control motions in the corresponding non-infinite-equilibrium systems. Through this study, one can have a better understanding of dynamics of infinite-equilibrium nonlinear systems. The authors believe infinite-equilibrium systems will have extensive applications in science and engineering.

By solving the three one-dimensional (1D) nonlinear dynamic differential equations analytically, it has been proved that unless the nonlinear terms are in first order, a nonlinear dynamic system never has a vibration natural frequency. For an elastic solid with nonlinear deformation and with static loads including a rotational angular velocity, a virtual small factor has been introduced to ensure a small deformation, a generalized formulation to predict vibration frequencies has been developed. Tapered rotating cantilever beams have been used to validate the formulation against FE analysis, and the analytical and FE results are in a good agreement.

This paper constructs a theoretical framework to analyze stability of higher order nonlinear implicit fractional differential equations. The main theorem asserts the stability and asymptotic stability by making use of Krasnoselskii's fixed point technique. Results are established in a weighted Banach space to arrive at the compactness requirements directly. Two examples are provided to illustrate the theory.

This research is dedicated to developing an analytical physics-based model of a reciprocating compressor based on a bond graph approach. At first, a mathematical model is developed for one-cylinder reciprocating compressor based on multi-body dynamics, particularly considering planar motion of the rigid bodies using body fixed reference frames. All the dynamical equations of motions are represented and linked altogether by the bond graph that simulates a complete system model. The model has unique capability to show forces at various joints, which enhances our understanding of complex system behavior. Moreover, the consequences of changing coefficients of those forces are accentuated. The utility of the model in fault diagnosis and condition monitoring are emphasized by highlighting the effects of a crack in a joint and a dent on cylinder wall. Nonlinear differential equations extracted from bond graph model are solved efficiently using a MATLAB stiff solver. Responses of the model parts are analyzed later by force analysis along with a comparison with a previous research to examine model validity.

In order to enhance the texture details of images and preserve the complete structure of images, we propose a novel image detail enhancement method based on spectral total variation, which combines the total variation method and spectral analysis method. Firstly, the total variation flow, as a non-ideal high-pass filter, decomposes image and obtains the spectral characteristics of different time scales in the transform domain. The transform domain can be regarded as a frequency domain. Then, we construct a special filter in the transform domain, and the spectrum features are filtered and enhanced by the filter. Finally, according to the proposed reconstruction method, the filtering results in the transform domain are inversely converted to the spatial domain, that is, the final enhanced image is obtained. The experimental results show that the proposed spectral total variation method can effectively use the spectral information of the image to enhance the local details, so that the enhanced image can obtain more prominent texture information, while maintaining the integrity of the image structure.