Search Results (6,822)

To address a key issue in functional time series analysis on testing the randomness of an observed series, we propose an IID test for functional time series by generalizing the Brock–Dechert–Scheinkman (BDS) test, which is commonly used for testing nonlinear independence. Similarly to the BDS test, the proposed functional BDS test can be used to evaluate the suitability of prediction models as a model specification test and to detect nonlinear structures as a nonlinearity test. We establish asymptotic results for the test statistic of the proposed test in a generic separate Hilbert space and show that it enjoys the same asymptotic properties as those for the univariate case. To address the practical issue of selecting hyperparameters, we provide the recommended range of the hyperparameters. Using empirical data on the VIX index, empirical studies are conducted that feature the applications of the proposed test to evaluate the adequacy of the fAR(1) and fGARCH(1,1) models in fitting the daily curves of cumulative intraday returns (CIDR) of the index. The results reveal that the proposed test remedies some shortcomings of the existing independence test. Specifically, the proposed test can detect nonlinear temporal structures, while the existing test can only detect linear structures. Full article

Wearable devices have gained increasing attention for use in multifunctional applications related to health monitoring, particularly in research of the circadian rhythms of cognitive functions and metabolic processes. In this comprehensive review, we encompass how wearables can be used to study circadian rhythms in health and disease. We highlight the importance of these rhythms as markers of health and well-being and as potential predictors for health outcomes. We focus on the use of wearable technologies in sleep research, circadian medicine, and chronomedicine beyond the circadian domain and emphasize actigraphy as a validated tool for monitoring sleep, activity, and light exposure. We discuss various mathematical methods currently used to analyze actigraphic data, such as parametric and non-parametric approaches, linear, non-linear, and neural network-based methods applied to quantify circadian and non-circadian variability. We also introduce novel actigraphy-derived markers, which can be used as personalized proxies of health status, assisting in discriminating between health and disease, offering insights into neurobehavioral and metabolic status. We discuss how lifestyle factors such as physical activity and light exposure can modulate brain functions and metabolic health. We emphasize the importance of establishing reference standards for actigraphic measures to further refine data interpretation and improve clinical and research outcomes. The review calls for further research to refine existing tools and methods, deepen our understanding of circadian health, and develop personalized healthcare strategies. Full article

Deep learning has become indispensable for identifying hierarchical spatial features (SFs), which are crucial for linking neurological disorders to brain functionality, from functional Magnetic Resonance Imaging (fMRI). Unfortunately, existing methods are constrained by architectures that are either linear or nonlinear, limiting a comprehensive categorization of spatial features. To overcome this limitation, we introduce the Semi-Nonlinear Deep Efficient Reconstruction (SENDER) framework, a novel hybrid approach designed to simultaneously capture both linear and nonlinear spatial features, providing a holistic understanding of brain functionality. In our approach, linear SFs are formed by directly integrating multiple spatial features at shallow layers, whereas nonlinear SFs emerge from combining partial regions of these features, yielding complex patterns at deeper layers. We validated SENDER through extensive qualitative and quantitative evaluations with four state-of-the-art methods. Results demonstrate its superior performance, identifying five reproducible linear SFs and eight reproducible nonlinear SFs. Full article

In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear system. As an auxiliary system, we consider a system of two scalar fractional equations with CFDF and define a strict stability in the couple. We illustrate both definitions with several examples and, in these examples, we show that the applied function in the fractional derivative has a huge influence on the stability properties of the solutions. In addition, we use Lyapunov functions and their CFDF to obtain several sufficient conditions for strict stability. Full article

The web-wrinkle phenomenon always occurs in the roll-to-roll coating production process, which leads to the decline of coating quality and an increase in waste. A theoretical analysis of the phenomenon is presented, and a simulation research method is proposed for the study. The method is outlined as follows: Initially, the web’s surface on the guide roll is modeled as a thin shell, with the relationship between web displacement and strain established through the nonlinear large deflection theory. The differential equations of the web are derived based on the internal-force equilibrium relationship. Subsequently, the boundary conditions are established according to the transfer of the web on the guide roller’s surface, and the deflected surface functions satisfying these conditions are obtained. The static method was used to determine the critical load for a web wrinkle, considering the friction between the web and the guide roll. Finally, finite element simulation analysis was conducted to ascertain the factors affecting the critical wrinkling load of the web. Through the analysis, the accuracy of the formulas used to calculate the critical compression load of the web was determined. The critical wrinkling load increases with the web thickness, web tension, and modulus of elasticity. The critical compressive stress of a web wrinkle was found to be proportional to the web thickness, modulus of elasticity, tension, and coefficient of friction. The rational selection of these parameters provides a theoretical foundation for improving the quality of coating production. Full article

This study delves into the synchronization issues of the impulsive fractional-order, mainly the Caputo derivative of the order between 0 and 1, bidirectional associative memory (BAM) neural networks incorporating the diffusion term at a fixed time (FXT) and a predefined time (PDT). Initially, this study presents certain characteristics of fractional-order calculus and several lemmas pertaining to the stability of general impulsive nonlinear systems, specifically focusing on FXT and PDT stability. Subsequently, we utilize a novel controller and Lyapunov functions to establish new sufficient criteria for achieving FXT and PDT synchronizations. Finally, a numerical simulation is presented to ascertain the theoretical dependency. Full article

Background: Arterial mechanics are crucial to cardiovascular functionality. The pressure–strain elastic modulus often delineates mechanical properties. Emerging methods use non-linear continuum mechanics and non-convex minimization to identify tissue-specific parameters in vivo. Reliability of these methods, particularly their accuracy in representing the in vivo stress state, is a significant concern. This study aims to compare the predicted stress state and the collagen-attributed load-bearing fraction with the stress state from in silico experiments. Methods: Our team has evaluated an in vivo parameter identification method through in silico experiments involving finite element models and demonstrated good agreement with the parameters of a healthy abdominal aorta. Results: The findings suggest that the circumferential stress state is well represented for an abdominal aorta with a low transmural stress gradient. Larger discrepancies are observed in the axial direction. The agreement deteriorates in both directions with an increasing transmural stress gradient, attributed to the membrane model’s inability to capture transmural gradients. The collagen-attributed load-bearing fraction is well predicted, particularly in the circumferential direction. Conclusions: These findings underscore the importance of investigating both isotropic and anisotropic aspects of the vessel wall. This evaluation advances the parameter identification method towards clinical application as a potential tool for assessing arterial mechanics. Full article

Abstract: Hydropower is a vital strategic component of China’s clean energy development. Its construction and optimized water resource allocation are crucial for addressing global energy challenges, promoting socio-economic development, and achieving sustainable development. However, the optimization scheduling of cascade hydropower stations is a large-scale, multi-constrained, and nonlinear problem. Traditional optimization methods suffer from low computational efficiency, while conventional intelligent algorithms still face issues like premature convergence and local optima, which severely hinder the full utilization of water resources. This study proposed an improved whale optimization algorithm, the Black-winged Differential-variant Whale Optimization Algorithm (BDWOA), which enhanced population diversity through a Logistic-Sine-Cosine combination chaotic map, improved algorithm flexibility with an adaptive adjustment strategy, and introduced the migration mechanism of the black-winged kite algorithm along with a differential mutation strategy to enhance the global search ability and convergence capacity. The BDWOA algorithm was tested using test functions with randomly generated simulated data, with its performance compared against five related optimization algorithms. Results indicate that the BDWOA achieved the optimal value with the fewest iterations, effectively overcoming the limitations of the original whale optimization algorithm. Further validation using actual runoff data for the cascade hydropower station optimization scheduling model showed that the BDWOA effectively enhanced power generation efficiency. In high-flow years, the average power generation increased by 8.3%, 6.5%, 6.8%, 4.1%, and 8.2% compared to the five algorithms while achieving the shortest computation time. Significant improvements in power generation were also observed in normal-flow and low-flow years. The scheduling solutions generated by the BDWOA can adapt to varying inflow conditions, offering an innovative approach to solving complex hydropower station optimization scheduling problems. This contributes to the sustainable utilization of water resources and supports the long-term development of renewable energy. Full article

The rehabilitation exoskeleton represents a typical human–robot system featuring complex nonlinear dynamics. This paper is devoted to proposing an adaptive impedance control strategy for a rehabilitation exoskelton. The patient’s motion intention is estimated online by the neural network (NN) to cope with the intervention of the patient’s subjective motor awareness in the late stage of rehabilitation training. Due to the differences in impedance parameters for training tasks in individual patients and periods, the least square method was used to learn the impedance parameters of the patient. Considering the uncertainties of the exoskeleton and the safety of rehabilitation training, an adaptive neural network impedance controller with output constraints was designed. The NN was applied to approximate the unknown dynamics and the barrier Lyapunov function was applied to prevent the system from violating the output rules. The feasibility and effectiveness of the proposed strategy were verified by simulation. Full article

This paper investigates the state estimation problem for nonlinear cyber–physical systems (CPSs). To conserve system resources, we propose a novel hybrid dynamic event-triggered mechanism (ETM) that prevents the occurrence of Zeno behavior. This work is based on designing an interval observer under the hybrid dynamic ETM to solve the state reconstruction problem of Lipschitz nonlinear CPSs subject to disturbances. That is, the designed triggering mechanism is integrated into the design of the Interval Observer (IO), resulting in a hybrid dynamic event-triggered interval observer (HDETIO), and the system stability and robustness are proved using a Lyapunov function, demonstrating that the observer can effectively provide interval estimation for CPSs with nonlinearity and disturbances. Compared to existing work, the primary contribution of this work is its ability to pre-specify the minimum inter-event time (MIET) and apply it to interval state estimation, enhancing its practicality for real-world physical systems. Finally, the correctness and effectiveness of the designed hybrid dynamic ETM and IO framework are validated with an example. Full article

This study aims to explore the optimal power allocation problem under Distributed Denial of Service (DDoS) attack in wireless communication networks. The Starkberg Equilibrium (SE) framework is employed to analyze the strategic interactions between defenders and attacker under conditions of incomplete information. Considering the energy constraints of both sensors and attacker, this paper also proposes an Intrusion Detection System (IDS) based on remote estimation to achieve an optimal defense strategy, with Packet Reception Rate (PPR) serving as a criterion for intrusion detection. Targeting leaders and followers, the optimal power allocation solution is derived with Signal-to-Interference-Noise Ratio (SINR) and transmission cost as the objective functions. By combining the Adaptive Penalty Function (APF) method with the Differential Evolution (DE) algorithm, the study effectively addresses related non-linear and non-convex optimization problems. Finally, the effectiveness of the proposed method is verified through case studies. Full article

This paper presents a class of proximal alternating direction multiplier methods for solving nonconvex, nonsmooth optimization problems with nonlinear coupled constraints. The key feature of the proposed algorithm is that we use a linearized proximal technique to update the primary variables, followed by updating the dual variables using a discounting approach. This approach eliminates the requirement for an additional proxy function and then simplifies the optimization process. In addition, the algorithm maintains fixed parameter selection throughout the update process, removing the requirement to adjust parameters to ensure the decreasing nature of the generated sequence. Building on this framework, we establish a Lyapunov function with sufficient decrease and a lower bound, which is essential for analyzing the convergence properties of the algorithm. We rigorously prove both the subsequence convergence and the global convergence of the algorithm and ensure its robustness and effectiveness in solving complex optimization problems. Our paper provides a solid theoretical foundation for the practical application of this method in solving nonconvex optimization problems with nonlinear coupled constraints. Full article

This study presents a method for the active control of a follow-up lower extremity exoskeleton rehabilitation robot (LEERR) based on human motion intention recognition. Initially, to effectively support body weight and compensate for the vertical movement of the human center of mass, a vision-driven follow-and-track control strategy is proposed. Subsequently, an algorithm for recognizing human motion intentions based on machine learning is proposed for human-robot collaboration tasks. A muscle–machine interface is constructed using a bi-directional long short-term memory (BiLSTM) network, which decodes multichannel surface electromyography (sEMG) signals into flexion and extension angles of the hip and knee joints in the sagittal plane. The hyperparameters of the BiLSTM network are optimized using the quantum-behaved particle swarm optimization (QPSO) algorithm, resulting in a QPSO-BiLSTM hybrid model that enables continuous real-time estimation of human motion intentions. Further, to address the uncertain nonlinear dynamics of the wearer-exoskeleton robot system, a dual radial basis function neural network adaptive sliding mode Controller (DRBFNNASMC) is designed to generate control torques, thereby enabling the precise tracking of motion trajectories generated by the muscle–machine interface. Experimental results indicate that the follow-up-assisted frame can accurately track human motion trajectories. The QPSO-BiLSTM network outperforms traditional BiLSTM and PSO-BiLSTM networks in predicting continuous lower limb motion, while the DRBFNNASMC controller demonstrates superior gait tracking performance compared to the fuzzy compensated adaptive sliding mode control (FCASMC) algorithm and the traditional proportional–integral–derivative (PID) control algorithm. Full article

This paper studies nonlinear mixed variational-like inequalities under generalized quasimonotone mappings in Banach spaces. The main objective of this work is to relax the well-known KKM (Knaster–Kuratowski–Mazurkiewicz) condition which is extensively used in the literature to prove the existence of solutions for variational inequalities and equilibrium problems, and to establish the existence of solutions for the nonlinear mixed variational-like inequalities, which uncovers another approach of solving variational inequalities. Further, we propose an iterative algorithm to find approximate solutions to our problem and to study its convergence criteria. Finally, as an application, we find a gap function for nonlinear mixed variational-like inequalities, which uncovers another way of solving our variational-like inequalities using the methods of solutions and algorithms of the optimization problems. Full article

This study focuses on the problems of poor control performance, synchronization performance and stability in multi-motor permanent magnet drive systems in mining belt conveyors when a Proportional Integral Derivative (PID) controller is used to control the multi-motor. In this paper, a system model for three-motor synchronous control of a mine belt conveyor is established. On this basis, an Enhanced first-order Active Disturbance Rejection Controller (Efal_ADRC) is designed based on an optimized nonlinear function. Additionally, a weighted arithmetic mean is used to enhance the compensator of the ring coupling control structure. Finally, the system model is evaluated and simulated using various algorithms. Results show that synchronous control of a multi-Permanent Magnet Synchronous Motor (multi-PMSM) drive system based on the Efal_ADRC ring coupling control structure has better anti-interference ability, control accuracy and synchronization, which is conducive to the stable and efficient safe operation of the belt conveyor. Full article