Dynamic Model Research Articles

A Unified Collision Avoidance Trajectory Planning with Dual Variables for Collaborative Aerial Transportation Systems

As an essential application of unmanned aerial vehicle (UAV) systems, payload transportation has garnered significant attention in recent years. Collaborative payload transportation utilizing multiple UAVs can effectively increase the payload capacity of the transportation system. Nevertheless, the incorporation of multiple UAVs makes the dynamic model of the transportation system more complex due to the coupled UAV and payload states. In the immediate disaster relief response, the collaborative system is often required to promptly deliver supplies to the target site while avoiding obstacles to ensure the system’s safety. Consequently, devising fast delivery trajectories that avoid collisions for such complicated systems poses a considerable challenge. To this end, a novel trajectory planning method is presented for collaborative transportation systems. Specifically, the dynamic model of the collaborative transportation system is derived by utilizing the Euler–Lagrange method. Then, the trajectory planning problem is formulated as an optimization problem with considerations of dynamics, actuation, safety, and formation constraints. To expedite the optimization process, the collision avoidance safety constraint is constructed using dual variables. The efficacy of this trajectory planning approach is confirmed through multiple real-world flight experiments involving collaborative aerial transportation systems of two and three UAVs.

Post-earthquake train operation safety assessment model based on machine learning

Abstract Assessing the seismic risk to high-speed rail systems with limited structural damage data is a challenging task. This study employs machine learning algorithms to predict the wheel-rail forces of high-speed trains operating under post-earthquake conditions, particularly when infrastructure along the railway is damaged. By developing a post-earthquake train operation safety assessment model, this paper effectively predicts the impact of track irregularities induced by different earthquake intensities on wheel-rail interactions. The results obtained through feature selection and regression analysis using the Random Forest algorithm provide valuable insights into key safety indicators for post-earthquake train operations. Compared to traditional multibody dynamic models, this approach significantly improves the efficiency of analysis and computation. An analysis of the results across multiple speed levels reveals that trains operating at 250 km/h face derailment risks when subjected to high-intensity earthquakes (PGA > 0.6 g). The proposed predictive safety assessment model demonstrates that adjusting train speeds according to seismic intensity can effectively enhance operational safety, offering critical support for post-earthquake emergency recovery efforts.

Deep adversarial learning models for distribution patterns of piezoelectric plate energy harvesting

This paper presents a novel approach utilizing piezoelectric plate structures with random electrode distribution patterns for energy harvesting applications across various vibration modes. For the first time, leveraging electromechanical Finite Element Analysis (eFEA) and data extraction techniques, we investigate the integration of conditional Generative Adversarial Networks (cGAN)-based dynamic models for this purpose. The cGAN offers an effective technique for generating realistic synthetic data conditioned on input parameters, thereby enabling the creation of diverse and representative datasets for training energy harvesting systems. The integration of eFEA with cGAN opens up new possibilities for optimizing the design and performance of piezoelectric energy harvesters across various applications. Specifically, we explore four distinct cGAN models-based mechanics of energy harvesters by deploying distribution patterns. These models include training data generated by stacking simultaneously mode images, utilizing separate cGAN models for each mode, labeling images by mode, and concatenating all mode images into one. Our study focuses on assessing the effectiveness of these models in minimizing loss in cGAN-based power generation and predicting Structural Similarity Index Measure (SSIM) values, and more importantly, identifying the predicted data point outputs from the generated pixel image extractions. By analyzing the generated data from numerical model and its application in deep learning, we aim to enhance the understanding of the effects of distribution patterns and image processing techniques for optimal power generation and the effectiveness of piezoelectric energy harvesting systems across different vibration modes. The studies explore how different distribution patterns affect the power harvesting efficiency and frequency bandwidth, utilizing the generated datasets.

Towards a dynamic model of indispensable amino acid requirements of the adult human: A factorial estimate of oxidative amino acid losses

BackgroundConsensus regarding the required intake of indispensable amino acids (IDAAs) and protein (representing total AAs) in the adult is lacking. Oxidation is a major, though not exclusive, source of IDAA loss in the human body and a primary factor determining requirements; a quantitative understanding of oxidative IDAA losses is required. ObjectiveTo develop a factorial diurnal model of total oxidative IDAA and protein losses in the adult human. MethodsA factorial diurnal model of oxidative losses of protein and each IDAA at maintenance was developed by estimating the magnitude and variability of sources of oxidative loss from existing literature: inevitable catabolism (constitutive oxidation of each absorbed dietary AA), and protein turnover in the postprandial and postabsorptive states. Total oxidative losses were calculated by summing individual losses, validated against published independent nitrogen balance data and compared to current IDAA requirements. ResultsThe factorial model predicted minimum oxidative total AA losses of 390±60 mg.kgBW-1.day-1, 59% of the EAR for protein. Inevitable AA oxidation and oxidation associated with postabsorptive protein turnover were the major sources of the oxidative loss for protein, at 40% and 44%, respectively. Summed oxidative IDAA losses ranged from 64% (isoleucine) to 91% (tryptophan) of current requirements. Total oxidative losses predicted by the model were significant predictors of actual experimental oxidative losses obtained by nitrogen balance (R2=0.66; p=0.049). ConclusionsThe use of a factorial model for estimation of minimum IDAA and protein oxidative losses in the adult human provides an essential starting point for an updated understanding of protein and IDAA requirements. Further iterations of the model will estimate total protein and IDAA requirements, and account for variations in dietary protein quantity and quality, as well as different populations and physiological states. Additional data, especially for inevitable oxidation in humans, and particularly with respect to individual IDAAs, are needed.

Research on the climate change and prediction of the temperature in Beijing

Abstract. Over the past few years, global warming has become a growing threat to the human living environment. Thus, preventing extreme temperature changes is a crucial area of study for the global community. However, temperature changes have diverse causes, making it hard to accurately calculate the data that impacts subsequent temperature forecasts. The ARIMA model is widely favoured by researchers as a typical time series prediction model. Additionally, it holds significant research value in forecasting dynamic models. This paper will use the ARIMA model to forecast temperature changes in Beijing for the next month, starting on 21 July. The findings show that the temperature remains relatively stable in the upcoming month, with minimal fluctuations. Based on historical data, this is the peak temperature in Beijing for the year. So, if the temperatures are not extremely high now, they might not get higher later. This forecast can be used as a guide for managing extreme temperatures in Beijing in the future.

Dynamic policy in the presence of social norms

AbstractIndividual actions can depend on prevailing social norms. We investigate how optimal policy to promote pro‐social action should exploit the underlying social dynamics. We develop a dynamic model of prosocial action in which conformist consumers repeatedly choose whether to engage in some prosocial activity. Whereas individual behavior is not observed, the overall participation rate in the previous period is common knowledge. We demonstrate how conformity can lead to multiple steady states and how their selection depends on starting conditions and discount factors. We further show that the optimal subsidy path can be non‐monotonic and can decrease before reaching the steady state‐level. Our model thus provides a rationale for introductory subsidies to promote environmentally friendly behavior from a behavioral perspective.

Nonlinear vibration characteristics and damage detection method of blade with breathing fatigue crack

In aero-engine, blades operate under harsh conditions for extended periods, which makes them highly susceptible to fatigue cracks. The localized and nonlinear structural changes caused by blade crack lead to complex vibration characteristics that are not well understood, posing challenges to the identification of these cracks. This paper proposes an approach for identifying breathing fatigue crack in compressor blade, leveraging the nonlinear features induced by the cracks. Crucial sensitive characteristics are extracted and a crack indicator for accurate crack detection is defined. Initially addressing the typical morphology of fatigue breathing cracks, a dynamic model of blade with cracks is developed to analyze their impact on the natural frequencies. Nonlinear contact forces are introduced to characterize the "breathing" effect of the fatigue crack, allowing for the determination of the harmonic distribution patterns in the blade's vibration response under various excitation conditions. A finite element model is then established considering the crack morphology, by adopting the contact element. Based on that, the nonlinear response characteristics associated with the blade's primary, sub-harmonic, and super-harmonic resonances are explored. A crack-sensitive parameter is defined and extracted from the nonlinear responses, under different crack propagation stages. At last, effectiveness and reliability of the defined parameter for identifying cracks is validated through a vibration fatigue test.

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

Numerical investigation on transonic flutter characteristics of an airfoil with split drag rudder

In this paper, a series of flutter simulations are carried out to investigate the effects of split drag rudder (SDR) on the transonic flutter characteristic of rigid NACA 64A010. A structural dynamic model addressing two-degree-of-freedom pitch-plunge aeroelastic oscillations was coupled with the unsteady Reynolds-averaged Navier-Stokes equations to perform flutter simulation. Meanwhile, the influence mechanism of SDR on flutter boundary is explained through aerodynamic work and the correlated shock wave location. The results show that the SDR delays the shock wave shifting downstream, and the Mach number corresponding to reaching freeze region increases as the split angle increases. Therefore, the peak value of aerodynamic moment coefficient amplitude and the sharp ascent process of phase occurs at higher Mach number, which leads to the delay in the occurrence of the transonic dip. Besides, before the transonic dip of airfoil without SDR occurs, the aerodynamic moment phase of airfoil with the SDR decreases slowly due to the decrease in the speed of shock wave moving downstream. This results in an increased flutter speed when employing the SDR before the transonic dip of airfoil without SDR occurs. Meanwhile, the effects of asymmetric split angles on the transonic flutter characteristics are also investigated. Before the transonic dip of airfoil without SDR occurs, the flutter characteristic is dominated by the smaller split angle.

Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators

In this paper, for addressing the safe control problem of modular robot manipulators (MRMs) system with uncertain disturbances, an approximate optimal control scheme of nonzero-sum (NZS) differential games is proposed based on the control barrier function (CBF). The dynamic model of the manipulator system integrates joint subsystems through the utilization of joint torque feedback (JTF) technique, incorporating interconnected dynamic coupling (IDC) effects. By integrating the cost functions relevant to each player with the CBF, the evolution of system states is ensured to remain within the safe region. Subsequently, the optimal tracking control problem for the MRM system is reformulated as an NZS game involving multiple joint subsystems. Based on the adaptive dynamic programming (ADP) algorithm, a cost function approximator for solving Hamilton–Jacobi (HJ) equation using only critic neural networks (NN) is established, which promotes the feasible derivation of the approximate optimal control strategy. The Lyapunov theory is utilized to demonstrate that the tracking error is uniformly ultimately bounded (UUB). Utilizing the CBF’s state constraint mechanism prevents the robot from deviating from the safe region, and the application of the NZS game approach ensures that the subsystems of the MRM reach a Nash equilibrium. The proposed control method effectively addresses the problem of safe and approximate optimal control of MRM system under uncertain disturbances. Finally, the effectiveness and superiority of the proposed method are verified through simulations and experiments.

Identification of heart rate dynamics during treadmill and cycle ergometer exercise: the role of model zeros and dead time

Background The response of heart rate to changes in exercise intensity is comprised of several dynamic modes with differing magnitudes and temporal characteristics. Investigations of empirical identification of dynamic models of heart rate showed that second-order models gave substantially and significantly better model fidelity compared to the first order case. In the present work, we aimed to reanalyse data from previous studies to more closely consider the effect of including a zero and a pure delay in the model. Methods This is a retrospective analysis of 22 treadmill (TM) and 54 cycle ergometer (CE) data sets from a total of 38 healthy participants. A linear, time-invariant plant model structure with up to two poles, a zero and a dead time is considered. Empirical estimation of the free parameters was performed using least-squares optimisation. The primary outcome measure is model fit, which is a normalised root-mean-square model error. Results A model comprising parallel connection of two first-order transfer functions, one with a dead time and one without, was found to give the highest fit (56.7 % for TM, 54.3 % for CE), whereby the non-delayed component appeared to merely capture initial transients in the data and the part with dead time likely represented the true dynamic response of heart rate to the excitation. In comparison, a simple first-order model without dead time gave substantially lower fit than the parallel model (50.2 % for TM, 47.9 % for CE). Conclusions This preliminary analysis points to a linear first-order system with dead time as being an appropriate model for heart rate response to exercise using treadmill and cycle ergometer modalities. In order to avoid biased estimates, it is vitally important that, prior to parameter estimation and validation, careful attention is paid to data preprocessing in order to eliminate transients and trends.

Dynamic tensile behaviors and crack propagation in fiber-reinforced cementitious composites: Experimental investigation and Peridynamic simulation

Fiber-Reinforced Cementitious Composites (FRCC) have gained significant attention in engineering applications due to their superior mechanical properties and toughness, particularly under high strain rate conditions. This study performed dynamic tensile tests on FRCC at high strain rates (35-110 s⁻¹) using a Split Hopkinson Tensile Bar (SHTB) apparatus. Additionally, a novel Peridynamic (PD) model was developed for the SHTB and FRCC system, leveraging the advanced capabilities of the emerging PD theory. The study compared and analyzed dynamic tensile strength, ultimate tensile strain, strain rate effects, failure modes, and crack development in FRCC with different fiber ratios at various high strain rates, using both experimental data and PD simulations. The results show that the PD-SHTB-FRCC dynamic model developed in this study exhibits high consistency between numerical simulations and experimental findings, effectively capturing the processes of crack initiation, propagation, and complete failure in FRCC specimens. The dynamic tensile properties of FRCC improve significantly with increased strain rates, with polyethylene (PE) fibers providing superior reinforcement compared to steel fibers. Notably, the dynamic tensile strength, peak tensile stress, and ultimate tensile strain of FRCC increase significantly with rising strain rates, with specimens containing higher PE fiber content showing a more pronounced enhancement effect. For strain rates between 42.6 s⁻¹ and 76.1 s⁻¹, considering dynamic tensile strength, ultimate tensile strain, and peak tensile stress, the optimal combination for resisting dynamic tensile loads was 1.5% PE fibers and 0.5% steel fibers. At a strain rate of 99.8 s⁻¹, a 2% PE fiber ratio alone provided the best performance.

Assessment of a coupled electricity and hydrogen sector in the Texas energy system in 2050

Due to its ability to reduce emissions in the hard-to-abate sectors, hydrogen is expected to play a significant role in future energy systems. This study modifies a sector-coupled dynamic modeling framework for electricity and hydrogen by including policy constraints, carbon prices, and possible hydrogen pathways and applies it to Texas in 2050. The impact of financial policies, including the US clean hydrogen production tax credit, on required infrastructure and costs are explored. Due to low natural gas prices, financial levers are necessary to promote low-carbon hydrogen production as the optimized solution. The Levelized Costs of Hydrogen are found to be $1.50/kg in the base case (primarily via steam methane reformation production) and lie between $2.10 - 3.10/kg when production is via renewable electrolysis. The supporting infrastructure required to supply those volumes of renewable hydrogen is immense. The hydrogen tax credit was found to be enough to drive production via electrolysis.

Dynamic modeling of air–metal plasma mixture of single-turn coil with erosion at megaGauss magnetic field

Single-turn coil (STC) is a destructive pulsed magnet aiming at 100–300 T magnetic field. Due to the high discharge current, the conductor of STC is heated rapidly and undergoes melting and vaporization, leading to the generation of supersonic air–metal vapor mixed plasma jet and the magneto-fluid effect. In this study, the mixed plasma mass-transfer and fluid dynamic characteristics are modeled at megaGauss magnetic field, high temperature, high pressure, and supersonic conductor shock deformation. The collision integral method is employed to calculate the fluid transport properties. In addition, a boundary constraint model of fluid–structure interaction (FSI) compatible with both fluid wall boundary condition and plasma jet entrance condition and a model to simultaneously solve the thermal ionization and high electric field ionization of the mixed vapor are proposed. As the result, the distributions of plasma electrical conductivity, current density, electron, heavy particles, temperature, air body load, and velocity are derived. Especially, the region of highest electrical conductivity is not the air domain near the inner surface of the conductor with the highest electron density and the highest magnetic field, but the air domain near the outer surface of the conductor with the relatively higher electron density and lower magnetic field.

Comparison of synergy extrapolation and static optimization for estimating multiple unmeasured muscle activations during walking

BackgroundCalibrated electromyography (EMG)-driven musculoskeletal models can provide insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unknown.MethodsThis study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing “gold standard” muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) applied to a scaled generic musculoskeletal model was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to “gold standard” muscle activations and forces.ResultsOn average, compared to SO, SynX with simultaneous model calibration produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15, r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4 N, r value 0.53 vs. 0.07). SynX yielded calibrated Hill-type muscle–tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to “gold standard” calibrated model parameter values.ConclusionsThese findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

Probing Populations of Dark Stellar Remnants in the Globular Clusters 47 Tuc and Terzan 5 Using Pulsar Timing

We present a new method to combine multimass equilibrium dynamical models and pulsar timing data to constrain the mass distribution and remnant populations of Milky Way globular clusters (GCs). We first apply this method to 47 Tuc, a cluster for which there exists an abundance of stellar kinematic data and which is also host to a large population of millisecond pulsars. We demonstrate that the pulsar timing data allow us to place strong constraints on the overall mass distribution and remnant populations even without fitting on stellar kinematics. Our models favor a small population of stellar-mass black holes (BHs) in this cluster (with a total mass of 446−72+75M⊙ ), arguing against the need for a large (>2000 M ⊙) central intermediate-mass BH. We then apply the method to Terzan 5, a heavily obscured bulge cluster that hosts the largest population of millisecond pulsars of any Milky Way GC and for which the collection of conventional stellar kinematic data is very limited. We improve existing constraints on the mass distribution and structural parameters of this cluster and place stringent constraints on its black hole content, finding an upper limit on the mass in BHs of ∼4000 M ⊙. This method allows us to probe the central dynamics of GCs even in the absence of stellar kinematic data and can be easily applied to other GCs with pulsar timing data, for which data sets will continue to grow with the next generation of radio telescopes.

Simplified assessment of structures with clutching inertia-friction systems by equivalent linearization methods

The innovative Clutching Inertia System (CIS), has garnered increasing recognition for its effectiveness in mitigating structural vibrations. To enhance the efficiency of passive CIS, introducing suitable energy dissipation mechanisms for the rotation inertia component is imperative. This study delves into the dynamic behavior of CIS, augmented with additional friction damping. Initially, the influence of supplementary friction damping within the CIS framework is examined through a dynamic model of a Single-Degree-of-Freedom (SDOF) system, integrated with the CIS and incorporating the Coulomb friction model. Subsequently, to streamline the dynamic analysis of the CIS and optimize the friction force thereby enhancing control efficiency while minimizing inactive durations, the paper introduces two distinct Equivalent Linearization Methods (ELMs). Furthermore, an assessment of the CIS’s dynamic performance, subjected to various external excitations, is presented. The findings highlight the crucial role of supplemental friction damping in reducing the inactivity of CIS and enhancing its overall control effectiveness. The employed ELMs demonstrate commendable accuracy and practicality for both response assessment and CIS performance optimization. In essence, the CIS, when integrated with supplemental friction damping, exhibits superior performance in suppressing structural displacement responses across diverse excitations, particularly in longer-period structures. Conversely, a more pronounced efficacy in managing structural acceleration responses is observed in structures with shorter periods. The study concludes that for specific structural applications, enhancing supplemental friction damping is more advantageous for vibration control than increasing the CIS’s inertia.

Data-Assisted Dynamic Modeling of Bionic Robotic Fish and Its Precise Speed Control

Data-Assisted Dynamic Modeling of Bionic Robotic Fish and Its Precise Speed Control

Hydrogen-fueled PFI SI engine investigation for near-zero NOx emissions in de-throttled and supercharged ultra-lean burn conditions

This study investigates the efficiency and combustion characteristics of a hydrogen port fuel injection (PFI) spark ignition (SI) engine under various load levels, excess air ratios and intake pressures. Experiments were conducted on a single-cylinder research engine to evaluate the effects of throttle opening and supercharging on pumping work and combustion parameters. The key findings indicate that abnormal combustion events are more closely related to the relative air-fuel ratio (λ) than to load, further limiting load increases during de-throttled operation. Additionally, combustion variability compromised mixture enleanment in both naturally aspirated and supercharged conditions. The gross indicated efficiency was approximately 40.7% across the range of 2.2 < λ < 3.5 with minimal variation. Efficiency gains were linked to reduced heat transfer losses in lean conditions, as validated by computational heat transfer, thermodynamic and fluid dynamic models on Gamma Technologies GT-ISE software. Moreover, nitrogen oxides (NOx) emissions were nearly zero for all test conditions when λ was above 2.2. These findings provide crucial insights into optimizing hydrogen engine performance under various intake pressures, highlighting the potential for achieving high efficiency and low emissions.

Computation and analysis of optimal disturbances of periodic solution of the hepatitis B dynamics model

Abstract Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of the immune response and severity of the disease, namely, activation of antiviral immune reactions, attenuation of reactions, peak and minimum viral load. The possibility of using optimal disturbances to exit the domain of attraction of the considered periodic solution using minimal impact is studied. The components of disturbances that may underlie the phenomenon of spontaneous recovery from chronic hepatitis B observed in clinical practice are identified.