Nonlinear Dynamics Research Articles

Nonlinear Dynamics of Two-Directional Functionally Graded Beam Under a Moving Load with Influence of Homogenization Scheme

Nonlinear Dynamics of Two-Directional Functionally Graded Beam Under a Moving Load with Influence of Homogenization Scheme

Nonlinear dynamics and forced vibrations of simply-supported fractional viscoelastic microbeams using a fractional differential quadrature method

Nonlinear dynamics and forced vibrations of simply-supported fractional viscoelastic microbeams using a fractional differential quadrature method

Smoothed naturally stabilized RKPM for non-linear explicit dynamics with novel stress gradient update

Smoothed naturally stabilized RKPM for non-linear explicit dynamics with novel stress gradient update

Nonlinear Dynamics of an Axially Moving Plate Submerged in Fluid with Parametric and Forced Excitation

Nonlinear Dynamics of an Axially Moving Plate Submerged in Fluid with Parametric and Forced Excitation

Artificial Neural Network Modeling in the Presence of Uncertainty for Predicting Hydrogenation Degree in Continuous Nitrile Butadiene Rubber Processing

The transition from batch to continuous production in the catalytic hydrogenation of nitrile butadiene rubber (NBR) into hydrogenated NBR (HNBR) marks a significant advance for applications under demanding conditions. This study introduces a continuous process utilizing a static mixer (SM) reactor, which notably achieves a hydrogenation conversion rate exceeding 97%. We thoroughly review a mechanistic model of the SM reactor to elucidate the internal dynamics governing the hydrogenation process and address the inherent uncertainties in key parameters such as the Peclet number (Pe), dimensionless time (θτ), reaction coefficient (R), and flow rate coefficient (q). A comprehensive dataset generated from varied parameter values serves as the basis for training an artificial neural network (ANN), which is then compared against traditional models including linear regression, decision tree, and random forest in terms of efficacy. Our results clearly demonstrate the ANN’s superiority in predicting the degree of hydrogenation, achieving the lowest root mean squared error (RMSE) of 3.69 compared to 21.90 for linear regression, 4.94 for decision tree, and 7.51 for random forest. The ANN’s robust capability for modeling complex nonlinear relationships and dynamics significantly enhances decision-making, planning, and optimization of the reactor, reducing computational demands and operational costs. In other words, this approach allows users to rely on a single ML-based model instead of multiple mechanistic models for reflecting the effects of possible uncertainties. Additionally, a feature importance study validates the critical impact of time and element number on the hydrogenation process, further supporting the ANN’s predictive accuracy. These findings underscore the potential of ML-based models in streamlining and enhancing the efficiency of chemical production processes.

Theoretico-experimental analysis of bistability in the oscillatory response of a TaOx ReRAM to pulse train stimuli

Fading memory is the capability of a physical system to approach a unique asymptotic behaviour, irrespective of the initial conditions, when stimulated by an input from a certain class. Standard stimuli from the AC periodic class typically induce fading memory effects in non-volatile memristors, as uncovered for the first time back in 2016. Very recently, a deep investigation of resistance switching phenomena in a TaOx resistive random access memory cell revealed the capability of the nano-device to exhibit one of two possible oscillatory behaviours, depending upon the initial condition, when subject to a particular periodic excitation. This interesting finding was, however, left unexplained. Bistability is the simplest form of local fading memory. In a system, endowed with local fading memory under a given stimulus, the initial condition does not affect the long-term behaviour of the state as long as it is drawn from the basin of attraction of either of the distinct coexisting state-space attractors (two limit cycles for the periodically forced memristor acting as a bistable oscillator). Here, the history of the system, encoded in the initial condition, is, thus, erasable only locally through ad hoc stimulation. Motivated by the discovery of local history erase effects in our resistive random access memory cell, this study applies a powerful system-theoretic tool, enabling the analysis of the response of first-order systems to square pulse train-based periodic stimuli, known as the time-average state dynamic route, to an accurate physics-based mathematical model, earlier fitted to the nano-device, to determine a strategy for specifying the parameters of an excitation signal, consisting of the sequence of two square pulses of opposite polarity per period so as to induce various forms of monostability or multistability in the non-volatile memristor. In particular, as an absolute novelty in the literature, experimental measurements validate the theoretical prediction on the capability of the device to operate as one of two distinct oscillators, depending upon the initial condition, under a specific pulse train excitation signal. The coexistence of multiple oscillatory operating modes in the periodically forced resistive random access memory cell, an example par excellence of their unique non-linear dynamics, may inspire the development and circuit implementation of novel sensing and mem-computing paradigms.

Atmospheric Chemistry Surrogate Modeling With Sparse Identification of Nonlinear Dynamics

AbstractModeling atmospheric chemistry is computationally expensive and limits the widespread use of chemical transport models. This computational cost arises from solving high‐dimensional systems of stiff differential equations. Previous work has demonstrated the promise of machine learning (ML) to accelerate air quality model simulations but has suffered from numerical instability during long‐term simulations. This may be because previous ML‐based efforts have relied on explicit Euler time integration—which is known to be unstable for stiff systems—and have used neural networks which are prone to overfitting. We hypothesize that parsimonious models combined with modern numerical integration techniques can overcome this limitation. Using a small‐scale mechanism to explore the potential of these methods, we have created a machine‐learned surrogate by (a) reducing dimensionality using singular value decomposition to create an interpretably‐compressed low‐dimensional latent space and (b) using Sparse Identification of Nonlinear Dynamics (SINDy) to create a differential‐equation‐based representation of the underlying dynamics in the compressed latent space with reduced stiffness. The root mean square error of ML model prediction for ozone concentration over 9 days is 37.8% of the root mean square concentration across all simulations in our testing data set. The surrogate model is 10× faster with 12× fewer integration timesteps compared to reference model and is numerically stable in all tested simulations. Overall, we find that SINDy can be used to create fast, stable, and accurate surrogates of a simple photochemical mechanism. In future work, we will explore the application of this method to more detailed mechanisms and their use in large‐scale simulations.

Nonlinear evolution characteristics and seepage mechanical model of fluids in broken rock mass based on the bifurcation theory

With the deep extension of coal mining in China, fault water inrush has become one of the major disasters threatening the safety production of coal mine. Based on the control equations of steady state and non-Darcy seepage in fractured rock mass, the multi-parameter nonlinear dynamic seepage equations of fractured rock mass are established in this paper. Based on the nonlinear dynamics theory, the function of the state variable in the system is derived, and the influence of the gradual change of non-Darcy flow factors on the structural stability of seepage system is studied. The research achievements show that there are three branches in the equilibrium state of the seepage system. Specifically, the stability of the equilibrium state changes abruptly near the limit parameter. The seepage dynamic system of fractured rock mass has the delayed bifurcation, and the coal mine disaster such as fault water inrush occurs easily at the bifurcation point. The research results are of great significance to enrich the theory of fault water inrush in coal mine, and to reveal the disastrous mechanism of fault water inrush and guide its prevention and control technology in coal mine, which can provide the theoretical reference for predicting the water seepage stability in fractured rock mass.

An enhanced hybrid scheme for ship roll prediction using support vector regression and TVF-EMD

In order to represent the complex characteristics of ship roll motion such as nonlinearity, uncertainty, and time-varying dynamics thus improving the ship roll prediction accuracy, an enhanced hybrid prediction scheme is proposed by using improved swarm intelligent optimization, time series decomposition, and machine learning. Firstly, the novel time-varying filtering-based empirical mode decomposition (TVF-EMD) is employed to decompose the ship roll motion data into multiple mode components with dynamic time-varying characteristics, which immunes of the mode mixing and intermittency problems of traditional empirical mode decomposition (EMD). Then, the support vector regression is utilized to train and predict mode components. Finally, the predicted results of individual components are reconstructed to achieve the final ship roll prediction angles. To avoid the unfavorable influence of manual parameter selection for TVF-EMD, an improved black widow optimization algorithm is employed to optimize the parameter configuration. The feasibility and effectiveness of the enhanced hybrid model are validated by ship roll prediction simulation based on the measured data of M.V. YuKun at sea. The experimental results show that the enhanced hybrid scheme can improve the prediction accuracy of ship roll motion and outrank those by using methods of EMD, ensemble empirical mode decomposition, and variational mode decomposition.

The relationship between weight-adjusted-waist index and suicidal ideation: evidence from NHANES

BackgroundAmidst growing evidence of the intricate link between physical and mental health, this study aims to dissect the relationship between the waist-to-weight index (WWI) and suicidal ideation within a representative sample of the US population, proposing WWI as a novel metric for suicide risk assessment.MethodsThe study engaged a sample of 9500 participants in a cross-sectional design. It employed multivariate logistic and linear regression analyses to probe the association between WWI and suicidal ideation. It further examined potential nonlinear dynamics using a weighted generalized additive model alongside stratified analyses to test the relationship's consistency across diverse demographic and health variables.ResultsOur analysis revealed a significant positive correlation between increased WWI and heightened suicidal ideation, characterized by a nonlinear relationship that persisted in the adjusted model. Subgroup analysis sustained the association's uniformity across varied population segments.ConclusionsThe study elucidates WWI's effectiveness as a predictive tool for suicidal ideation, underscoring its relevance in mental health evaluations. By highlighting the predictive value of WWI, our findings advocate for the integration of body composition considerations into mental health risk assessments, thereby broadening the scope of suicide prevention strategies.

Non-stationary SQM/IST correspondence and CPT/PT-invariant paired hamiltonians on the line

Abstract We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.

Nonlinear dynamics of a double pendulum energy harvesting device for continuously rotating systems

Nonlinear dynamics of a double pendulum energy harvesting device for continuously rotating systems

Effect of Interstage Torsional Damping on Nonlinear Dynamic Characteristics of Two-Stage Planetary Gear System

Abstract This paper explores the influence of interstage torsional damping on the nonlinear dynamics of a two-stage planetary gear transmission system. A comprehensive nonlinear dynamic model is developed, incorporating interstage torsional damping, stiffness, time-varying meshing parameters, damping, and tooth side clearance. The nonlinear equations are derived and solved using the fourth-order Runge–Kutta method. The investigation reveals that the changes in torsional damping between stages significantly affect the nonlinear dynamic characteristics of the system, especially under load fluctuations. Bifurcation characteristics are analyzed using phase diagrams, Poincaré diagrams, time history diagrams, and frequency–domain spectrograms. The simulation results demonstrate that heightened torsional damping between stages distinctly affects the motion states across excitation frequencies. Notably, it mitigates the unstable motion state caused by high-frequency excitation when tooth side clearance is minimal.

Parameter Tuning Approach for Incremental Nonlinear Dynamic Inversion-Based Flight Controllers

Incremental nonlinear dynamic inversion (INDI) is a widely used approach to controlling UAVs with highly nonlinear dynamics. One key element of INDI-based controllers is the control allocation realizing pseudo controls using available actuators. However, the tracking of commanded pseudo controls is not the only objective considered during control allocation. Since the approach only works locally due to linearization and the solution is often ambiguous, additional aspects like control efforts or penalizing the deviation of certain states must be considered. Conducting the control allocation by solving a quadratic program this results in a considerable number of weighting parameters, which must be tuned during control design. Currently, this is conducted manually and is therefore time consuming. An automated approach for tuning these parameters is therefore highly beneficial. Thus, this paper presents and evaluates a model-based approach automatically tuning the control allocation parameters of a tiltrotor VTOL using an optimization algorithm. This optimization algorithm searches for optimal parameters minimizing a cost functional that reflects the design target. This cost functional is calculated based on a test mission for the VTOL which is conducted within a simulation environment. The test mission represents the common operating range of the VTOL. The simulation environment consists of an aircraft model as well as a model of the INDI-based controller which is dependent on the control allocation parameters. On this basis, model-based optimization is conducted and the optimal parameters are identified. Finally, successful real-world tests on a 4-degrees-of-freedom testbench using the identified parameters are presented. Since the control allocation parameters can significantly influence the aircraft’s stability, the 4-DOF testbench for the aircraft is required for rapid validation of the parameters at a minimum amount of risk.

Flocks with Nonlinear Inherent Dynamics under Fixed and Switching Digraphs

Flocks with Nonlinear Inherent Dynamics under Fixed and Switching Digraphs

Exploring the physical characteristics and nonlinear wave dynamics of a (3+1)-dimensional integrable evolution system

This study comprehensively explores the [Formula: see text]-dimensional Mikhailov–Novikov–Wang [Formula: see text] integrable equation, with the primary objective of elucidating its physical manifestations and establishing connections with analogous nonlinear evolution equations. The investigated model holds significant physical meaning across various disciplines within mathematical physics. Primarily, it serves as a fundamental model for understanding nonlinear wave propagation phenomena, offering insights into wave behaviors in complex media. Moreover, its relevance extends to nonlinear optics, where it governs the dynamics of optical pulses and solitons crucial for optical communication and signal processing technologies. Employing analytical methodologies, namely the unified [Formula: see text], Khater II ([Formula: see text]hat.II) method, and He’s variational iteration [Formula: see text] method, both numerical and analytical solutions are meticulously examined. Through this investigation, the intricate behaviors of the equation are systematically unveiled, shedding illuminating insights on various physical phenomena, notably including wave propagation in complex media and nonlinear optics. The outcomes not only underscore the efficacy of the analytical techniques deployed but also accentuate the equation’s pivotal role in modeling a broad spectrum of nonlinear wave dynamics. Consequently, this research significantly advances our comprehension of complex physical systems governed by nonlinear dynamics, thereby contributing notably to interdisciplinary pursuits in mathematical physics.

Analyzing physical activity impact based on ubiquitous nonlinear dynamics and electroencephalography data.

Understanding complex systems is made easier with the tools provided by the theory of nonlinear dynamic systems. It provides novel ideas, algorithms, and techniques for signal processing, analysis, and classification. Presently, these ideas are being applied to the investigation of how physiological signals evolve. The study applies nonlinear dynamics theory to electroencephalogram (EEG) signals to better comprehend the range of alcoholic mental states. One of the main contributions of this paper is an algorithm for automatically distinguishing between sober and drunken EEG signals based on their salient features. The study utilized various entropy-based features, including ApEn, SampEn, Shannon and Renyi entropies, PE, TS, FE, WE, and KSE, to extract information from EEG signals. To identify the most relevant features, the study employed ranking methods like T-test, Wilcoxon, and Bhattacharyya, and trained SVM classifiers with the selected features. The Bhattacharyya ranking method was found to be the most effective in achieving high classification accuracy, sensitivity, and specificity. Classification accuracy of 95.89%, the sensitivity of 94.43%, and specificity of 96.67% are achieved by the SVM classifier with radial basis function (RBF) for polynomial Kernel using the Bhattacharyya ranking method. From the result, it is clear that the model serves as a cost-effective and accurate decision-support tool for doctors in diagnosing alcoholism and for rehabilitation centres to monitor the effectiveness of interventions aimed at mitigating or reversing brain damage caused by alcoholism.

Cement production and CO2 emission cycles in the USA: evidence from MS-ARDL and MS-VARDL causality methods with century-long data.

The cement industry is among the top three polluters among all industries and the examination of the nonlinear and cointegration dynamics between cement production and CO2 emissions has not been explored. Focusing on this research gap, the study employs a novel Markov-switching autoregressive distributed lag (MS-ARDL) model and its generalization to vector error correction, the MS-VARDL model, for regime-dependent causality testing. The new method allows the determination of nonlinear long-run and short-run relations, regime duration, and cement-induced-CO2 emission cycles in the USA for a historically long dataset covering 1900-2021. Empirical findings point to nonlinearity in all series and nonlinear cointegration between cement production and cement-induced CO2 emissions. The phases of regimes coincide closely with NBER's official economic cycles for the USA. The second regime, characterized by expansions, lasts twice as long relative to the first, the contractionary regime, which contains severe economic recessions, as well as economic crises, the 1929 Great Depression, the 1973 Oil Crisis, the 2009 Great Recession, and the COVID-19 Shutdown and Wars, including WWI and II. In both regimes, the adverse effects of cement production on CO2 emissions cannot be rejected with varying degrees both in the long and the short run. Markov regime-switching vector autoregressive distributed lag (MS-VARDL) causality tests confirm unidirectional causality from cement production to CO2 emissions in both regimes. The traditional Granger causality test produces an over-acceptance of causality in a discussed set of cases. Industry-level policy recommendations include investments to help with the shift to green kiln technologies and energy efficiency. National-level policies on renewable energy and carbon capture are also vital considering the energy consumption of cement production.

Landing cushioning analysis of new generation heavy airborne armored vehicles

Purpose The purpose of this study is to ensure the successful implementation of a landing cushion for the new generation armored vehicles with significantly enhanced quality. Furthermore, to introduce a high-precision landing cushioning analysis model. Design/methodology/approach To accurately analyze the cushioning performance of the new generation armored vehicles, a nonlinear finite element dynamics model considering the complex travel system was established. The model considered the influence of various nonlinear factors to measure the dynamic response difference between the proposed and traditional models. The cushioning performance of airbags under different landing conditions and their various influence factors were analyzed. Findings The travel system has a large influence on the key points of the vehicle, whose rear end of the upper deck has a larger acceleration fluctuation compared with the traditional model. The increase in the body material stiffness is helpful to reduce this fluctuation. The established nonlinear finite element model can effectively analyze the landing cushioning performance of airborne armored vehicles. The area of the external airbag vent has a large influence on the cushioning performance, and the cushioning system has excellent cushioning performance under various operating conditions. Practical implications This study introduces the travel system, which is ignored by traditional analytical models. The interactions between various types of complex structures are included in the analysis process in its entirety, leading to valuable new conclusions. Quantitatively reveals the analytical errors of traditional simulation models in multiple dimensions and the reasons for their formation. Based on a high-precision simulation model, it is verified that the designed airbag cushioning system has an excellent cushioning effect for the new generation of heavy airborne armored vehicles. Originality/value The novelty of this work comes from the need for smooth landing with low overload for a new type of large-load airborne armored vehicle and provides a high-precision model that quantifies the traditional analytical modeling errors and error principle.

Path tracking with personalized handling stability constraints matched to driving styles

In the path-tracking control process, drivers have different expectations of the lateral response of vehicles. To meet drivers’ expectations of handling stability, this paper proposes a model predictive control (MPC)-based path-tracking controller with personalized handling stability constraints matched to driving style. Firstly, the categories of driving styles are obtained by applying the K-Means algorithm to the collected driving data. Then the sideslip angle-longitudinal velocity map is constructed based on the nonlinear dynamics model of the vehicle to generate the front-wheel steering angle constraints that are matched with the maximum sideslip of the vehicle expected by drivers of different styles. After that, an MPC-based path-tracking controller has been built, and the front-wheel steering angle is incorporated into the MPC controller. Furthermore, compared to the strategy of directly using sideslip angle constraints for handling stability control, this approach avoids introducing additional constraint variables, leading to improved real-time performance. Simulation experiments are conducted to compare the dynamic vehicle responses between the handling stability control that takes into account the driving style and the control system that does not consider the driving style. In addition, the subjective evaluation is conducted to verify the proposed path-tracking control method that considers the stability constraints of driving style. The evaluation results show that the proposed method can obtain better subjective evaluation results than a path-tracking controller that does not consider the driving style. Finally, through the hardware-in-the-loop experiments, the real-time computational capability of the proposed controller is verified.