APPLICATION OF CONVOLUTIONAL NEURAL NETWORK AND CHAOS THEORY IN FAULT DIAGNOSIS OF ROLLING BEARINGS by JIN JiangTao, XU ZiFei, LI Chun, MIAO WeiPao, ZHANG WanFu, LI Gen

“…In order to solve the traditional methods in the process of judging the fault type of the bearing caused by signal strongly nonlinear misjudgment wrongly, based on the chaos theory, the phase space reconstruction method（PSR） is used to restore the system dynamics characteristics and the convolution neural network（CNN） is used to learn and extract the effective nonlinear information from the chaotic sequence, proposes the PSR-CNN intelligent fault diagnosis method, visualizes the attractor trajectory, and analyzes the nonlinear characteristics of each fault signal. …”
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Topological phases and non-Hermitian topology in photonic artificial microstructures by Liu Hui, Lai Pengtao, Wang Haonan, Cheng Hua, Tian Jianguo, Chen Shuqi

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An Inelastic Theoretical Model regarding the Load-Carrying Capacity of PSL Bending Component by Baolu Sheng, Yuling Bian, Dong He, Aiping Zhou

“…To predict the nonlinear bending performance of the PSL beams, a theoretical model that could consider the nonlinear stress-strain relations of PSL and predict the damage modes of the PSL beams was developed. …”
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Local existence result of the single dopant diffusion including cluster reactions of high order by R. Bader, W. Merz

“…The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. …”
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Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method by Fei Wu, Lan-Lan Huang

“…The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. …”
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Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization by Abdelkrim El Mouatasim

“…In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. …”
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Asymptotic Methods for Solitary Solutions and Compactons by Ji-Huan He

“…This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. …”
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Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series by Liu Hai, Song Yong, Du Qingfu

“…Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. …”
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Design of an Anti-Windup PID Algorithm for Differential Torque Steering Systems by Dengzhi Peng, Bin Huang, Hao Huang

“…Based on the built 8 DOF model, the vehicle performance indicators are calculated and compared, the gap between the models with linear and nonlinear tires is non-negligible, and a reference model with a nonlinear tire model is recommended for the relevant research. …”
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Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping by Xiaojuan Sun, Jianrun Zhang

“…Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. …”
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Plasma Parameters Effects on Dust Acoustic Solitary Waves in Dusty Plasmas of Four Components by Abeer A. Mahmoud, Essam M. Abulwafa, Abd-alrahman F. Al-Araby, Atalla M. Elhanbaly

“…The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. …”
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Finite-Time Synchronization and Synchronization Dynamics Analysis for Two Classes of Markovian Switching Multiweighted Complex Networks from Synchronization Control Rule Viewpoint by Bin Yang, Xin Wang, Yongju Zhang, Yuhua Xu, Wuneng Zhou

“…This paper is mainly concerned with how nonlinear coupled one impacts synchronization dynamics of a class of nonlinear coupled Markovian switching multiweighted complex networks (NCMSMWCNs). …”
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Multimodel Modeling and Predictive Control for Direct-Drive Wind Turbine with Permanent Magnet Synchronous Generator by Lei Wang, Tao Shen, Chen Chen

“…The desired trajectory of the nonlinear system is decomposed to be suitable for the reference trajectory of multiple models that are presented by the linear models of the nonlinear system, which simplifies the nonlinear optimization problems and decreases the calculation difficulty. …”
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Holomorphic embedding method for large-scale reverse osmosis desalination optimization by Junzhi Chen, Tao Wang, Jiu Luo, Hongbo Chen, Yi Heng

“…Abstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. …”
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Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation by Xian Li, Yao Wang, Meidan Chen, Biao Li

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Vehicle Stability Control Based on Model Predictive Control Considering the Changing Trend of Tire Force Over the Prediction Horizon by Shaosong Li, Guodong Wang, Bangcheng Zhang, Zhixin Yu, Gaojian Cui

“…Moreover, its performance was close to that of the nonlinear controller, whereas its calculation speed is much faster than that of the nonlinear model predictive controller.…”
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Inclined Magnetic Field on Mixed Convection Darcy–Forchheimer Maxwell Nanofluid Flow Over a Permeable Stretching Sheet With Variable Thermal Conductivity: The Numerical Approach by Gossaye Aliy Adem, Adamu Gizachew Chanie

“…In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. …”
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DAMAGE DETECTION OF COMPOSITE PLATE BASED ON LOCAL DEFECT RESONANCE INTER-MODULATION EFFECT by CHEN WenJian, QU WenZhong, XIAO Li

“…Comparing with nonlinear ultrasonic nondestructive testing method using harmonic signals and modulation methods, the local defect resonance（LDR） inter-modulation effect can greatly enhance the nonlinear behavior between the damaged interfaces,also,it uses the modulation between input signal and LDR frequency thus the input signal is simplified. …”
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Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods by Özkan Güner, Dursun Eser

“…As a result, these methods can also be applied to other nonlinear fractional differential equations.…”
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Stability, Bifurcation, and Quenching Chaos of a Vehicle Suspension System by Chun-Cheng Chen, Shun-Chang Chang

“…This study investigated the dynamics and control of a nonlinear suspension system using a quarter-car model that is forced by the road profile. …”
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