Nonlinear Dynamic Model Research Articles

Nonlinear dynamic modeling and analysis of the fluid-transporting cracked pipe using the hybrid semi-analytical and finite element method

The fatigue cracks may develop in the pipe systems due to long-term cyclic loading, which may cause catastrophic accidents. The finite element method (FEM) is usually adopted to simulate the stress singularity and breathing effect, resulting in expensive computational costs. Therefore, in this paper, an efficient hybrid semi-analytical and finite element (SA-FE) method is proposed to study the nonlinear dynamic characteristics of the fluid-transporting cracked pipe (FTCP) considering the breathing effect. Furthermore, the crack sensitivity parameters are obtained through bending-bending and bending-axial vibration analysis. For the SA-FE method, the semi-analytical method (SAM) and FEM are separately used to construct the dynamic models of the non-cracked and cracked regions, and the connection at the interface is performed by constraint equations. Subsequently, the validity of the modeling method is substantiated through both FEM and experimental tests. Finally, the effects of crack and fluid parameters on the dynamic characteristics of the FTCP are analyzed. The results indicate that changes in crack positions may trigger different-order mode switching, and continuous switching may occur between higher-order modes. In addition, the bending-bending and bending-axial coupling responses can effectively detect crack failures of the FTCP with varying levels of damage. The proposed model can offer valuable insights for fault diagnosis and health monitoring of FTCP.

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.

Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method

The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model for the novel coronavirus (COVID-19), which includes susceptible, exposed, asymptomatic infected, symptomatic infected, and recovered individuals, and the concentration of COVID-19 in the environment is indicated by S(t), E(t), A(t), I(t), R(t), and B(t), respectively. We present the series solution of this model by varying the controlling parameters and representing them graphically. Additionally, we verify the accuracy of the series solution (up to the (n−1)th-degree polynomial) that satisfies both the initial conditions and the model, with all coefficients correct at 18 decimal places. Furthermore, we have compared our results with the Runge–Kutta fourth-order method. Based on our findings, we conclude that the homotopy perturbation method is a promising approach to solve nonlinear dynamical models, particularly those associated with pandemics. This method provides valuable insight into how the control of various parameters can affect the model. We suggest that future studies can expand on our work by exploring additional models and assessing the applicability of other analytical methods.

Backstepping Control Design in Conjunction with an EKF-based Sensorless Field-Oriented Control of an IPMSM

The collector and brushless electronic commutation machines have gained widespread utilization in industrial applications. Among these machines, internal permanent magnet synchronous motors (IPMSMs) have become increasingly popular due to their numerous advantages, including high torque/current and torque/inertia ratios, robust construction, high efficiency, and reliability. However, the incorporation of position sensors in IPMSMs has introduced challenges concerning their application, performance, mass production, and cost. Consequently, the implementation of sensorless control techniques has become essential in drive systems and various applications. This paper proposes a backstepping control approach for achieving speed sensorless control of IPMSMs, employing an extended Kalman filter (EKF). The first step involves developing a comprehensive nonlinear dynamical model of the IPMSM in the direct and quadrature (d-q) rotor frame and obtaining its corresponding state-space representation. Subsequently, backstepping controllers for rotor speed and current tracking are designed to ensure precise tracking and anti-disturbance performance. These controllers are integrated into the field-oriented control (FOC) scheme. The Lyapunov stability theorem is employed to guarantee the asymptotic stability condition of the backstepping controller. To address the challenge of estimating immeasurable mechanical parameters of the IPMSM and accurately tracking the system states, an EKF is designed. This filter enables the estimation of mechanical parameters and achieves high steady-state precision within a finite time. The effectiveness of the proposed methodology is demonstrated through simulations conducted under various dynamic operating conditions, including sudden torque load changes, command speed changes, and parameter variations.

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 change of torsional damping between stages would 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 motion states across excitation frequencies. Notably, it mitigates the unstable motion state caused by high-frequency excitation when tooth side clearance is minimal.

Forecasting Oil Prices with Non-Linear Dynamic Regression Modeling

The recent energy crisis has renewed interest in forecasting crude oil prices. This paper focuses on identifying the main drivers determining the evolution of crude oil prices and proposes a statistical learning forecasting algorithm based on regression analysis that can be used to generate future oil price scenarios. A combination of a generalized additive model with a linear transfer function with ARIMA noise is used to capture the existence of combinations of non-linear and linear relationships between selected input variables and the crude oil price. The results demonstrate that the physical market balance or fundamental is the most important metric in explaining the evolution of oil prices. The effect of the trading activity and volatility variables are significant under abnormal market conditions. We show that forecast accuracy under the proposed model supersedes benchmark specifications, including the futures prices and analysts’ forecasts. Four oil price scenarios are considered for expository purposes.

Desirable banking competition and stability

Every financial crisis raises questions about how the banking market structure affects the real economy. Although low bank concentration may reduce markups and foster riskier behavior, concentrated banking systems appear more resilient to financial shocks. We use a nonlinear dynamic stochastic general equilibrium model with financial frictions to compare the transmissions of shocks under different competition and concentration configurations. The results reveal that oligopolistic competition amplifies the effects of the shocks relative to monopolistic competition. The transmission mechanism works through the markups, which are amplified when banking concentration is increased. The desirable banking market structure is determined according to financial stability and social welfare objectives. Moreover, we find that depending on policymakers’ preferences, a banking concentration of five to eight banks balances social welfare and bank stability objectives in the United States.

Asset prices in a production network

The relative importance of sectoral and aggregate productivity shocks in asset pricing is examined using a nonlinear dynamic equilibrium model where heterogenous sectors interact in a production network. The model accounts for the heterogeneity in sectoral stock returns and endogenously generates conditional heteroskedasticity and fat tails. The equity risk premium is shown to be driven by sectoral shocks—specially to investment good producers and mining—with a limited contribution from the aggregate shock. SMM estimates of the elasticities of substitution between material inputs and between investment goods support the assumption of gross complementarity employed by previous network literature.

A Nonlinear Dynamic Analysis of Skidding Behavior in Rolling Bearings Using Lubricant Traction Coefficients and Cage Flexibility

Skidding is a primary cause of rolling element bearing (REB) failure, which is influenced by operating conditions, lubricant properties, and bearing design. This paper presents an improved nonlinear dynamic model of REBs to analyze the impact of lubricant characteristics on REB skidding at different speed states. The model considers time-varying traction coefficient, cage flexibility, and cage pocket clearance. The selected tested lubricants include lithium grease (LGT2), compound calcium sulfonate (CCS) grease, and 4109 Chinese aviation oil. Simulation results show that CCS grease effectively reduces cage skidding, with the lowest load limits (300N at 2000 RPM) under constant speed conditions and the highest stable limit (2932 RPM) during acceleration. LGT2 grease exhibits minimal sensitivity to acceleration and fluctuation speed parameters change.

Maintenance and transformation method for a multi-AUV dense formation

Accurate formation maintenance and safe formation transformations are significant challenges for multiple autonomous underwater vehicle (multi-AUV) dense formations. To address these problems, an innovative control method for a multi-AUV dense formation is proposed. First, a model predictive controller (MPC) that considers AUV input constraints and external disturbances is designed such that a multi-AUV dense formation can accurately maintain a desired formation while tracking a reference trajectory. After that, at the kinematics level, an optimal path for a safe and efficient multi-AUV dense formation transformation is generated based on the Hungarian method. Furthermore, considering an underactuated and nonlinear AUV dynamics model at the dynamics level, a potential function based on collision avoidance is established. It is added to the MPC objective function to further guarantee the potential of the formation transformation. Finally, a multi-AUV dense formation maintenance simulation shows that the proposed method can guarantee higher trajectory tracking accuracy than other algorithms. A multi-AUV dense formation transformation simulation shows that the proposed method avoids the occurrence of cross paths and a safe distance between AUVs is always maintained. The above results demonstrate that multi-AUV dense formations can achieve accurate maintenance and safe transformations, and the proposed method is feasible and effective.

Study on lateral stability control of carrier-based aircraft towbarless tractor system

The lateral stability and control of carrier-based aircraft towbarless tractor system are analysed. Considering the coupled motion effects of carrier roll, pitch and heave, a four degree of freedom time-varying nonlinear dynamic model of the carrier-based aircraft towbarless tractor system is established. The lateral stability of the traction system is analysed, and the discrimination method of the system instability form is proposed. The yaw rate of the tractor and the lateral speed of the carrier-based aircraft are selected as variables, the lateral stability controller is designed using sliding mode control (SMC) theory and the compensation torque and lateral force required for the lateral stability control of the traction system are obtained, thereby achieving tracking of the ideal values. The simulation results show that the designed control scheme can effectively controls the yaw rate of the target tractor and the lateral speed of the carrier-based aircraft, ensuring the lateral stability of the carrier-based aircraft towbarless tractor system.

Informing policy via dynamic models: Cholera in Haiti.

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

Sideslip Angle Estimation for Distributed Drive Electric Vehicles Based on Robust Unscented Particle Filter

An accurate and reliable sideslip angle is crucial for active safety control systems and advanced driver-assistance systems (ADAS). The direct measurement method of the sideslip angle suffers from challenges of high costs and environmental sensitivity, so sideslip angle estimation has always been a significant research issue. To improve the precision and robustness of sideslip angle estimation for distributed drive electric vehicles (DDEV) in extreme maneuvering scenarios, this paper presents a novel robust unscented particle filter (RUPF) algorithm based on low-cost onboard sensors. Firstly, a nonlinear dynamics model of DDEV is constructed, providing a theoretical foundation for the design of the RUPF algorithm. Then, the RUPF algorithm, which incorporates the unscented Kalman filter (UKF) to update importance density and utilizes systematic random resampling to mitigate particle degradation, is designed for estimation. Eventually, the availability of the proposed RUPF algorithm is validated on the co-simulation platform with non-Gaussian noises. Simulation results demonstrate that RUPF algorithm attains a higher precision and stronger robustness compared with the traditional PF and UKF algorithms.

Flight control design for a hypersonic waverider configuration: A non-linear model following control approach

AbstractDLR is currently investigating the potential of hypersonic flight systems in the context of different mission scenarios. One configuration type of higher interest for civil and military purposes is the hypersonic glide vehicle (HGV). Such HGVs operate over broad flight envelopes and pose complex flight dynamic characteristics. This article presents DLR’s generic hypersonic glide vehicle 2 (GHVG-2) and proposes an integrated non-linear flight control architecture that is based on the idea of the non-linear dynamic inversion and non-linear model following control methodologies. The proposed control scheme is designed to sufficiently and robustly handle the system dynamics of the over-actuated flight vehicle. The approach is first discussed, and the performance of the suggested control laws is later investigated via simulations of a high-fidelity non-linear flight dynamic model in the nominal case and under the presence of parametric uncertainties. The presented results demonstrate that the proposed NMFC approach provides benefits for the robust control of the regarded hypersonic system.

Passivity-based control of fluid flow networks with capacitance

Fluid flow networks (FFNs) widely exist in industrial energy systems tightly related with the industrial production and residents living, such as district heating networks (DHN), mine-ventilation systems and gas transportation systems. The FFN operation is to drive the flowrates and pressures to their desired values, and the flowrate-pressure coordinated control of FFN is crucial in providing safe, stable and efficient operation. Although fluid capacitance has the same importance as fluid resistance and fluid inductance in giving dynamical characteristics of FFN, fluid capacitance is still not fully considered in the flowrate and pressure control design of FFN. In this paper, a nonlinear dynamic model of general FFN with fluid resistance, inductance and capacitance is first given. By using this nonlinear model, it is shown that the general FFN dynamics is strictly passive, and the corresponding generalized Hamiltonian form (GHF) is also given. Based on the passivity of FFN, a decentralized adaptive flowrate-pressure coordinated control is newly proposed, taking a simple proportional-integral (PI) form while providing globally asymptotic regulation for network flowrates and pressures. This FFN control method is applied to design the flowrate-pressure controller of an auxiliary startup circuit (ASC) equipped to a modular high temperature gas-cooled reactor (mHTGR), and simulation results in the cases of heating-up and cooling-down show the feasibility of control design.

Study on safety gap between fuel channels in NHR200-II

This paper presents a novel method for estimating the safety gap between deformed fuel channels. The irradiation causes deformation of the fuel channel, which narrows the control rod channel, directly affecting the safety of the reactor. Investigating the critical safety gap between fuel channels can be utilized for safety assessments in design. Specifically, we first define the safety gap and three typical dropping cases. Next, we analyze the forces on the control rod, including flow resistance and channel resistance. Then, we establish a nonlinear dynamic model and simulate three dropping cases. Finally, we explore the influence of the friction coefficient and the fuel rod bundle. We find that the critical safety gap for the NHR200-II reactor is -5.0∼-3.1 mm (standard case) and -4.2∼-2.5 mm (arbitrary case), respectively. Our study provides a novel solution to accurately evaluate the effect of deformed boxed channels on the control rod’s dropping.

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

In this current work, a new nonlinear dynamic model based on the forced Van der Pol oscillator is introduced to demonstrate the time-domain sensitivities of the micro-cantilever to the varying properties of the surrounding fluids. Effects of diverse multi-frequency excitations on the hydrodynamically forced displacements are investigated for the Glycerol-water solutions with different concentrations. Driving forces at the eigenmode frequencies are applied simultaneously to actuate the micro-cantilever in multi-modal operations. The hydrodynamic force induces notable variations in the observables of high-frequency steady-state vibrations. To illustrate, the frequency of the displacements decreases with increasing dynamic viscosity and density of the fluids (among 55% and 85% Glycerol-water solutions) in bimodal- and trimodal-frequency excitations. Essentially, the observable responses are often used to distinguish the surrounding fluids in which the micro-cantilever operates. In addition, steady-state observables are achieved at only particular eigenmodes in single- and multi-frequency operations. It is highlighted that the periodic oscillations are obtained for the first and second eigenmodes with the highest value of forced Van der Pol parameter (μ = 1030). Clearly, higher eigenmodes require different values of the nonlinearity parameter to acquire periodic vibrations in multi-modal operations. In general, achieving steady-state observables is substantially critical in quantifying sensitivity to varying fluid properties. For instance, the vibration frequency of around 7.33 MHz and amplitude of around 0.03 pm are obtained at the first eigenmode for 75% Glycerol-water solution in tetra-modal operations. Note that femtometer amplitudes of deflections can be measured using quantum-enhanced AFM techniques. The frequency responses obtained in this work are compared with the measured ones in the literature and the results show satisfactory agreements. Therefore, a novel multi-modal nonlinear dynamic model enables to quantify observable sensitivity to micro-rheological properties at higher eigenmodes of the micro-cantilever.

Plug‐and‐play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

AbstractWe present an algorithm for constructing efficient surrogate frequency‐domain models of (nonlinear) parametric dynamical systems in a non‐intrusive way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach combines rational approximation and smooth interpolation. In the approximation effort, locally adaptive sparse grids are applied to effectively explore the parameter domain even if the number of parameters is modest or high. Adaptivity is also employed to build rational approximations that efficiently capture the frequency dependence of the problem. These two features enable our method to build surrogate models that achieve a user‐prescribed approximation accuracy, without wasting resources in “oversampling” the frequency and parameter domains. Thanks to its non‐intrusiveness, our proposed method, as opposed to projection‐based techniques for model order reduction, can be applied regardless of the complexity of the underlying physical model. Notably, our algorithm for adaptive sampling can be used even when prior knowledge of the problem structure is not available. To showcase the effectiveness of our approach, we apply it in the study of an aerodynamic bearing. Our method allows us to build surrogate models that adequately identify the bearing's behavior with respect to both design and operational parameters, while still achieving significant speedups.

Modeling and Analysis of 1:3 Internal Resonance of Suspension Bridge Under Boundary Excitations

This study investigated the nonlinear dynamic behavior of suspension bridge subjected to multi-frequency boundary excitations. Firstly, the nonlinear dynamic model of the suspension bridge subjected to multi-frequency boundary excitations is established. The in-plane vibration equations are derived based on Hamilton’s principle, taking into account the effects of geometric nonlinearity of the girder-deck and main cable as well as the stiffness of hangers. Secondly, the Galerkin method is used to solve for the frequencies and corresponding mode shape functions. Thirdly, the corresponding modulation equations are obtained based on the multiple scales method, and the 3:1 internal resonance between two symmetrical modes is analyzed. Combined with numerical analysis, the nonlinear dynamic behavior between modes of the suspension bridge is demonstrated through the frequency–response, force–response, and time history curves. The results indicate that the drift phenomenon appears when perturbing the amplitude and frequency of the different excitations, and the system exhibits intricate dynamic responses.