Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach by Mrinal Kanti Rajak, Rajen Pudur

“…A comprehensive mathematical model is developed, incorporating the nonlinear dynamics of the PLL system through differential equations and transfer functions. …”
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A Group Rotate-Vector Algorithm for Mixed-Variable Optimization Problems by Zhongming Li, Lutao Yan, Haiyuan Li, Lianxin Wang

“…To address the simultaneous search and optimization of multiple variable types in nonlinear mixed integer programming problems, a grouping and comprehensive processing method is employed. …”
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Scattered Data Processing Approach Based on Optical Facial Motion Capture by Qiang Zhang, Xiaoying Liang, Xiaopeng Wei

“…To recover missing data, given the nonlinear relationships among neighbors with the current missing marker, we propose an improved version of a previous method, where we use the motion of three muscles rather than one to recover the missing data. …”
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Synthesis, Structural, Spectroscopic, and Hirshfeld Surface Analysis, and DFT Investigation of Benzaldehyde Semicarbazone by N. Sudha, S. Anbuselvi, Sudhakar Jyothula, A. Thiruppathi, B. Vijayakumar, Kartikeya Parmar, G. Puthilibai, Leevesh Kumar

“…By using single-crystal XRD, the nonlinear characteristics of the material were studied. …”
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Using Electrocardiogram Signal Features and Heart Rate Variability to Predict Epileptic Attacks by Ying Jiang, Yuan Feng, Danni Lu, Lin Yang, Qun Zhang, Haiyan Yang, Ning Li

“…In the proposed method, 12 features are extracted from the heart rate variability signal in time, frequency, time-frequency, and nonlinear domains to predict epileptic seizures. We used a multivariate statistical process control algorithm for abnormality detection. …”
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Experimental Research on Internal Behaviors of Caved Rocks under the Uniaxial Confined Compression by Yu-jiang Zhang, Guo-rui Feng, Ting-ye Qi

“…A stratification phenomenon of breakage was discovered, which presents breakage concentration in the middle of the sample. The nonlinear movement and shear dislocation induced by shifts among caved rocks are the reason of the breakage stratification phenomenon. …”
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Shear Behavior of RC Beams Strengthened by External Vertical Prestressing Rebar by Ying Li, Meizhong Wu, Weiqi Wang, Xingwei Xue

“…The objectives of this study are to simulate EVPR strengthening of concrete beams using a nonlinear three-dimensional finite element model and to explore its shear enhancement features under different EVPR stirrup ratios, vertical compressive stress degrees, and optimal arrangements of EVPRs. …”
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Translation Invariance-Based Deep Learning for Rotating Machinery Diagnosis by Wenliao Du, Shuangyuan Wang, Xiaoyun Gong, Hongchao Wang, Xingyan Yao, Michael Pecht

“…Although deep learning algorithms can automatically learn a good set of features without manual intervention, the lack of domain knowledge greatly limits the performance improvement, especially for nonstationary and nonlinear signals. This paper develops a multiscale information fusion-based stacked sparse autoencoder fault diagnosis method. …”
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A Review of Optical Interferometry for High-Precision Length Measurement by Guangyao Huang, Can Cui, Xiaoyang Lei, Qixue Li, Shuhua Yan, Xinghui Li, Guochao Wang

“…With regard to discussion on enhancement of measurement precision, special attention is given to periodic nonlinear errors and phase demodulation methods. This review offers insights into current challenges and potential future directions for improving interferometric measurement systems, and also emphasizes the role of innovative technologies in advancing precision metrology technology.…”
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Fast Transient Thermal Analysis of Non-Fourier Heat Conduction Using Tikhonov Well-Conditioned Asymptotic Waveform Evaluation by Sohel Rana, Jeevan Kanesan, Ahmed Wasif Reza, Harikrishnan Ramiah

“…The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML), another well-conditioned scheme, called mass effect (ME) T-WCAWE, is introduced. …”
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Rolling Bearing Fault Diagnosis Method based on EEMD Denoising and Correlation Coefficient Identification by Pei Junfeng, Sun Jianhua, Song Chuanzhi, Song Yupeng, Ge Huizhong

“…In view of the nonlinear,non-stationary and massive noise features of reciprocating pump power of rolling bearing vibration signal,a fault diagnosis method of rolling bearing based on EEMD,distance factor,correlation coefficient and wavelet packet decomposition is proposed. …”
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Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization by Aynur Ali, Atanas Ilchev, Vanya Ivanova, Hristina Kulina, Polina Yaneva, Boyan Zlatanov

“…The additional analysis confirms that there are no dependencies, even of a nonlinear type, in the constructed models that are not included. …”
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Kinematics Analysis of a Planar Symmetric (CRR)₂S-(3R)₂R Parallel Mechanism by Jie Li, Linxian Che, Li Du, Xin Zheng

“…The coordinate transformation method is applied to establish a set of nonlinear equations for the positive solution of the mechanism position，and the differential evolution algorithm is used to find the set of equations. …”
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Novel Adaptive Bacteria Foraging Algorithms for Global Optimization by Ahmad N. K. Nasir, M. O. Tokhi, N. Maniha Abd. Ghani

“…In order to overcome such problems, novel linear and nonlinear mathematical relationships based on the index of iteration, index of bacteria, and fitness cost are adopted which can dynamically vary the step size of bacteria movement. …”
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Suspended Load Path Tracking Control Strategy Using a Tilt-Rotor UAV by M. A. Santos, B. S. Rego, G. V. Raffo, A. Ferramosca

“…An unscented Kalman filter (UKF) is designed for nonlinear state estimation of all the system states, assuming that available information is provided by noisy sensors with different sampling rates that do not directly measure the load’s attitude. …”
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Distributed Analytical Formation Control and Cooperative Guidance for Gliding Vehicles by Shengwei Jia, Xiao Wang, Fugui Li, Yulin Wang

“…The proposed method takes full consideration of the characteristics of hypersonic gliding vehicle, such as complex nonlinear dynamics, no thrust, and quasi-equilibrium gliding condition, and no online numerical iteration is needed, which is well applicable for hypersonic gliding vehicles. …”
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Tipping point-induced abrupt shifts in East Asian hydroclimate since the Last Glacial Maximum by Fuzhi Lu, Huayu Lu, Yao Gu, Pengyu Lin, Zhengyao Lu, Qiong Zhang, Hongyan Zhang, Fan Yang, Xiaoyi Dong, Shuangwen Yi, Deliang Chen, Francesco S. R. Pausata, Maya Ben-Yami, Jennifer V. Mecking

“…Our findings underscore the nonlinear behavior of the EASM and its coupling with other tipping elements.…”
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The tolerance balancing optimization with multiple constraints on the form and function of the discrete functional surface by Chuanyuan Zhou, Xiaomei Guo, Xiaoxiao Wei

“…The tolerance contribution is incorporated into the nonlinear inertial weight particle swarm algorithm. …”
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Nanometer‐Scale 1D Negative Differential Resistance Channels in Van Der Waals Layers by Qirong Yao, Jae Whan Park, Choongjae Won, Sang‐Wook Cheong, Han Woong Yeom

“…This result would be important for nanoscale device applications based on strong nonlinear resistance within van der Waals material architectures.…”
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Influence of Body Mass Index on Inflammatory Profile at Admission in Critically Ill Septic Patients by Fernando G. Zampieri, Vanessa Jacob, Hermes V. Barbeiro, Fabiano Pinheiro da Silva, Heraldo P. de Souza

“…We found that levels of epidermal growth factor, vascular endothelial growth factor, and interleukins 4, 5, and 13 were associated with BMI in a complex, nonlinear way, independently of illness severity. Higher BMI was associated with higher levels of anti-inflammatory interleukins. …”
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