Nonlinear Simulation Model Research Articles

Surrogated modelling for structural reliability and safety assessments of high-strength concrete beams with industrial and recycled steel fibers

As a secondary material recycled from tyres, Recycled Steel Fibre Reinforced Concrete (RSF) aims to replace industrial steel fibres (ISF) to improve concrete matrix‘s severability, fracture toughness, and residual tensile stress. Despite the increasing attention on the mechanical properties of this material, RSF concrete’s influence on structural component strength is still neglected due to a lack of sufficient and reliable experimental data. This study looks into existing Crack mouth opening displacement (CMOD) experiment results of both types of steel fibre reinforced concrete beams together with nonlinear finite element model (FEM) simulations using the RILEM TC 162-TDF crack damage model(CDP) proposed for ISF in ABAQUS. Meanwhile, an additional parameter analysis of the experimental data related to shear capacity also examines the shear span ratio, fibre content, and fibre type of the two types of fibre reinforced concrete beams. Moreover, Kriging surrogate models (KSM) and Sobol global sensitivity analysis have been conducted. For the reference concrete beams with a fibre content of 0.4 %, the prediction accuracy ratios of ultimate strength, corresponding displacement, and stiffness between the FEM and the experiment results are 98 %, 88 %, and 100 %, respectively. This paper has been proved that the CMOD-based CDP model effectively elucidates the shear contribution of different steel fibres, which can be used in structural analysis of ISF or RSF concrete for structure components. Utilizing FEMs, a series of modified flexural strength prediction formulas based on TR63 standards are proposed to enhance structural applications with ISF and RSF. Moreover, the prediction ability of the proposed formulas is validated using the results of 183 real flexural capacity experiments of ISF reinforced concrete beams, achieving an improved R² value of 0.97.

Study on the 2D equivalent nonlinear dynamics simulation model related to high speed precision bearing and spindle

The stiffness and contact stress of the bearing spindle system are the key factors affecting its machining accuracy and service life under the condition of high-speed service, which will be affected by different structural parameters and service conditions. It is essential to establish an efficient and accurate computational simulation model to understand the influence of complex factors on the nonlinear dynamic characteristics of the bearing spindle system. Firstly, in the paper, a 2D axisymmetric finite element model of the bearing, aims at the relationship between stiffness and contact stress of the bearing under high-speed service, has been built based on a classical dynamic analysis model and the reversed method of material parameters of equivalent rolling balls. Additionally, for the BT30 spindle, the 2D axisymmetric finite element model of the bearing spindle system also has been built and applied in mechanical analysis of spindle under different conditions of assembly and service, based on the bearing model. The results show that the axial force of bearings decreases as the rotational speed increases, and an augmentation in speed will result in a reduction in the axial stiffness of the BT30 spindle. In addition, the maximum contact stress exhibits a slight decline as the rotational speed increases. Furthermore, with an escalating preload, the stiffness and contact stress of the spindle undergo substantial increments, however, these parameters will cease to alter once a certain threshold is reached.

Numerical simulation and experimental study on nonlinear ultrasonic characterization of graphite size in nodular cast iron

Graphite morphology has a significant influence on mechanical properties such as tensile strength and hardness in nodular cast iron (NCI). Compared to the detection of graphite nodularity, there is relatively less ultrasonic simulation and detection experiment research on the graphite size. Therefore, it is of great importance to study rapid nondestructive testing methods for the internal graphite size of NCI. This study establishes a simulation model of nonlinear ultrasonic penetration longitudinal wave detection for graphite size. The acoustic nonlinearity parameter (ANP) is used to characterize the graphite size. Nonlinear ultrasonic detection experiments on the internal graphite size are conducted to verify the reliability of the nonlinear ultrasonic simulation model. The simulation and experimental results show that the ANP of penetrating longitudinal waves decreases with the increase of average graphite diameter. The relationship between ANP and internal graphite size is established. Moreover, the experimental results verified the accuracy of the numerical model. The decrease in ANP may be related to the decrease in the number of grain boundaries. Therefore, the nonlinear ultrasonic technique is an effective method for characterizing the internal graphite size. The establishment of a nonlinear ultrasonic simulation model for graphite size in NCI lays the research foundation for nonlinear ultrasonic microstructure characterization experiments.

Variance-based global sensitivity analysis of the performance of a proton exchange membrane water electrolyzer

This study is threefold objective. First, a nonlinear one-dimensional steady-state simulation model for hydrogen production from proton exchange membrane water electrolyzer (PEMWE) is established. The model comprehensively addresses activation, diffusion overpotentials and ohmic potential drop, and particularly incorporating Nafion membrane properties in the presence of liquid water. The model is enhanced by analyzing the hydrogen crossover, introducing corresponding diffusion equations to evaluate Faraday efficiency. The model accurately quantifies voltage efficiency, hydrogen production rate and specific energy consumption, and it is validated with published experimental data found in the scientific literature. Second, a variance-based global sensitivity analysis (GSA) on the model, is employed as a metric to assess the impact of operating conditions and material characteristics on three objective functions: the hydrogen production rate; the voltage efficiency and the specific energy consumption. Third, to support the GSA analysis, genetic algorithm (GA) technique is performed to maximize hydrogen production rate while minimizing specific energy consumption. In the course of this novel investigation, it was discerned that the number of cells, the cross-sectional area of the electrolyzer, the current density and temperature all exerted a significant impact on the three objective functions. This combined approach GSA-GA provides a thorough exploration of parameter influences and an efficient optimization strategy for enhancing the model's performance. These findings provide valuable insights that can guide analysis of the performance and the optimization of the PEMWE system.

Research on non-linear dynamic simulation model of feeding system

Abstract The automatic gun feeding system is an important mechanism for achieving continuous shooting, but due to its complex structure, there is a lot of contact during firing, and its reliability is lower. To improve the reliability of the feeding system and its dynamic characteristics, a multi rigid body dynamic simulation model of the feeding system considering contact nonlinearity was established based on nonlinear dynamics theory. The dynamic characteristics of the feeding system were analyzed for single and continuous firing. The research results indicate that the presence of contact nonlinearity increases the interaction forces between components and also increases the uncertainty of component motion.

Wind Shear Response of Aircraft with C* and C*U Controller during Approach

This study investigates the impact of wind shear on the flight dynamics of commercial aircraft where C* and C*U control laws are employed during the approach phase. Given the high incidence of flight accidents during takeoff and landing attributed to wind shear, this research aims to enhance aviation safety by analyzing control law behavior under varying wind shear conditions. A nonlinear flight simulation model was developed, utilizing aerodynamic and engine data from a B737, to explore the aircraft’s response to different wind shear intensities. The simulation analysis was used to compare the response of the aircraft with C* and C*U controllers, respectively, under different wind shear, and to evaluate the effectiveness of its stability enhancement in wind shear. It was found that in most cases, the controller can achieve a good stabilization effect, but in some cases of wind fields, the aircraft suffered more significant oscillation.

Interaction Difference Hypothesis Test for Prediction Models

Machine learning research focuses on the improvement of prediction performance. Progress was made with black-box models that flexibly adapt to the given data. However, due to their increased complexity, black-box models are more difficult to interpret. To address this issue, techniques for interpretable machine learning have been developed, yet there is still a lack of methods to reliably identify interaction effects between predictors under uncertainty. In this work, we present a model-agnostic hypothesis test for the identification of interaction effects in black-box machine learning models. The test statistic is based on the difference between the variance of the estimated prediction function and a version of the estimated prediction function without interaction effects derived via partial dependence functions. The properties of the proposed hypothesis test were explored in simulations of linear and nonlinear models. The proposed hypothesis test can be applied to any black-box prediction model, and the null hypothesis of the test can be flexibly specified according to the research question of interest. Furthermore, the test is computationally fast to apply, as the null distribution does not require the resampling or refitting of black-box prediction models.

A study of nonlinear fractional-order biochemical reaction model and numerical simulations

This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.

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.

Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme

Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.

Linearized Models of the Coupled Rotorcraft Flight Dynamics and Acoustics for Real-Time Noise Prediction

This article demonstrates the linearization of the coupled rotorcraft flight dynamics and aeroacoustics to provide realtime acoustic predictions in generalized maneuvering flight. To demonstrate the methodology, the study makes use of a nonlinear simulation model of a generic utility helicopter (PSUHeloSim) that is coupled with an aeroacoustic solver based on a marching cubes algorithm. A periodic equilibrium of the coupled rotorcraft flight dynamics and acoustics is first found at a desired flight condition using a modified harmonic balance trim solution method. Next, the nonlinear time-periodic dynamics are linearized about that periodic equilibrium and transformed into an equivalent higher order linear time-invariant system in harmonic decomposition form. Composite aeroacoustic measures are included as an output of this system. To speed up runtime and make control design tractable, the order of these harmonic decomposition models is reduced via residualization to an 8-state model where the states are representative of the rigid-body dynamics of the aircraft. This 8-state model is shown to provide accurate acoustic response predictions for small-amplitude pilot inputs and to abate runtime by a factor of approximately 104, thus enabling acoustic predictions in generalized maneuvering flight that are significantly faster than real time. The 8-state model is subsequently used to demonstrate the use of linear system tools for the dynamic analysis of the coupled rotorcraft flight dynamics and acoustics.

A Numerical Method for the Dynamics Analysis of Blade Fracture Faults in Wind Turbines Using Geometrically Exact Beam Theory and Its Validation

In pursuit of China’s goals for carbon peak and carbon neutrality, wind turbines are continually evolving to achieve a lower levelized cost of energy. The primary technological focus in the wind power industry is on large-scale, lightweight designs for entire turbines to enhance cost competitiveness. However, this advancement has led to an increased risk of blade fractures under extreme operating conditions. This paper addresses this challenging issue by using geometrically exact beam theory to develop a nonlinear simulation model for long, flexible blades. The model accounts for sudden changes in blade properties at the moment of failure, covering both the extensive motions and deformations of the fractured blade. The validation of the proposed model is carried out by comparing the results from power production cases with bladed simulations and further validating the simulations of blade fracture load cases against measurement data. The methodologies and findings presented in this study offer valuable insights for diagnosing faults in wind turbines.

Passive-guaranteed modeling and simulation of a finite element nonlinear string model

This paper proposes to solve the dynamics of the Kirchhoff-Carrier nonlinear string model using the finite elements method. In order to ensure the power balance of the resulting finite dimensional model it is rewritten in the Port-Hamiltonian System (PHS) formalism. Using a discrete gradient and a quadratization of the Hamiltonian, an explicit power-preserving numerical scheme is proposed. Results of simulation are presented.

Estimation of airship states and model uncertainties using nonlinear estimators

This Airships are lighter than air vehicles and due to their growing number of applications, they are becoming attractive for the research community. Most of the applications require an airship autonomous flight controller which needs an accurate model and state information. Usually, airship states are affected by noise and states information can be lost in the case of sensor's faults, while airship model is affected by model inaccuracies and model uncertainties. This paper presents the application of nonlinear and Bayesian estimators for estimating the states and model uncertainties of neutrally buoyant airship. It is considered that minimum sensor measurements are available, and data is corrupted with process and measurement noise. A novel lumped model uncertainty estimation approach is formulated where airship model is augmented with six extra state variables capturing the model uncertainty of the airship. The designed estimator estimates the airship model uncertainty along with its states. Nonlinear estimators, Extended Kalman Filter and Unscented Kalman Filter are designed for estimating airship attitude, linear velocities, angular velocities and model uncertainties. While Particle filter is designed for the estimation of airship attitude, linear velocities and angular velocities. Simulations have been performed using nonlinear 6-DOF simulation model of experimental airship for assessing the estimator performances. 1−𝜎 uncertainty bound and error analysis have been performed for the validation. A comparative study of the estimator's performances is also carried out.

Energy-efficient torque distribution strategy for four wheel drive electric vehicles based on Traffic zone

This paper presents a four-wheel electric vehicle control system. It incorporates a two-level control strategy for stability and optimal torque distribution to improve fuel efficiency and extend the vehicle’s operational range. The control architecture is structured hierarchically, with a higher level responsible for determining yaw moment and traction forces based on the desired vehicle dynamics. At the lower level, a multi-criteria constrained optimization method is employed, considering both vehicle stability and energy consumption. Additionally, this study takes into consideration the vehicle’s operational context, such as the specific Traffic zone, and the adhesion properties of the tires. This ensures a delicate balance between instantaneous power consumption and overall vehicle stability. The control system’s performance is tested and assessed through three distinct scenarios within the Matlab/Simulink environment. The co-simulation involves the nonlinear vehicle model simulation software, Carsim, and the results are comprehensively compared to the literature.

Linear and Non-linear Regression Methods to Study the Adsorption of Cr(VI) from an Aqueous Solution Using Pomegranate Peel

In this study, the previous data of the adsorption of Chromium (VI) ions on the pomegranate peels (MPGP) as adsorbents were used. linear and non-linear equations for Langmuir, Freundlich, Dubinin-Radushkevich, Tempkin, Redlich-Peterson, Sips, and Toth adsorption isotherm models were applied. The five error functions ERRSQ, HYBRD, MPSD, ARE, and EABS were analyzed for non-linear isotherm equations and in each case a set of isotherm parameters were determined. The algorithms for the simulation of linear and non-linear isotherm models using error functions were achieved with the aid of Microsoft Excel solver Add-Ins for minimizing the respective error function across the concentration range studied. Linear and non-linear methods show comparable data for two-parameter models, also high R2 values were obtained for Langmuir, Freundlich, and Temkin models while the Dubinin-Radushkevich model reveals low R2 values, on the contrary, three-parameter models show different data between linear and non-linear methods with high R2 value for all. Which indicates that the error does not obey the Gaussian distribution.

Simulation and Measurement Analysis of an Integrated Flow Battery Energy-Storage System with Hybrid Wind/Wave Power Generation

This study aims to evaluate the power-system stability and the mitigation of fluctuations in a hybrid wind/wave power-generation system (HWWPGS) under different operating and disturbance conditions. This evaluation is performed by employing a vanadium redox flow battery-based energy storage system (VRFB-ESS) as proposed. The measurement results obtained from a laboratory-scale HWWPGS platform integrated with the VRFB-ESS, operating under specific conditions, are used to develop the laboratory-scale simulation model. The capacity rating of this laboratory-scale simulation model is then enlarged to develop an MW-scale power-system model of the HWWPGS. Both operating characteristics and power-system stability of the MW-scale HWWPGS power system model are evaluated through frequency-domain analysis (based on eigenvalue) and time-domain analysis (based on nonlinear-model simulations) under various operating conditions and disturbance conditions. The simulation results demonstrate that the fluctuations and stability of the studied HWWPGS under different operating and disturbance conditions can be effectively smoothed and stabilized by the proposed VRFB-ESS.

Numerical analysis and experimental validation of nonlinear broadband monostable and bistable energy harvesters

Vibration based piezoelectric energy harvesting has been receiving more and more attention for supplying usable electrical energy to low-power electronic devices. This type of energy can produce the desired voltage to power any low electronic device or wireless sensor. But most of them provide lower voltage and insufficient power. In this paper, the nonlinear magnetic field is introduced to broaden the effective resonant bandwidth for overcoming this issue. The dynamic linear and nonlinear model of magnetic coupling piezoelectric vibration energy harvester is established based on the Hamilton principle, Euler-Bernoulli beam theory, piezoelectric theory, and Kirchhoff's law and law of mechanics. Numerical solutions of nonlinear energy harvesting systems are studied by using the Runge-Kutta method. The bifurcation diagram, Poincare map, power spectrum, and phase trajectory of voltage output are investigated with different excitation amplitudes and frequencies. Simulation of linear and nonlinear model were illustrated at given excitation levels. Simulation results show the harvesting performance can be improved by proper external magnetic coupling and potential energy function. The theoretical harmonic balance analysis results verify the numerical solution and influence the mechanism of excitation levels and interface resistances. Experimental verification is carried out to measure the nonlinear restoring force and examine the performance of nonlinear bistable and monostable energy harvesters. The experiment results show the nonlinear bistable and monostable energy harvesters can provide larger voltage and more power.

Modeling and Hover Flight Control of a Micromechanical Flapping-Wing Aircraft Inspired by Wing–Tail Interaction

This article intends to give a comprehensive model to a brand new micromechanical flapping-wing aircraft inspired by wing–tail interaction. In this aircraft, the flapping-wing induced flow contributes to the tail control torque generation. However, this also makes the wing–tail interaction nonnegligible, and this flow would be disturbed by the relative flow produced by the body motion. The dominant unsteady aerodynamic effects of the flapping wing are considered. The flapping-wing induced flow over the tail is included when analyzing the tail aerodynamics. Especially, the aerodynamic–dynamic coupling effect of both the wing and the tail is considered to account for the force due to the body motion. A nonlinear and time-periodic simulation model of the aircraft is, thus, established. The model is averaged and linearized around hover status. Because of the combination of the wing–tail interaction with the aerodynamic–dynamic coupling, the state and control matrixes, including both the induced flow effect and the body motion effect, can be obtained. The pitch dynamics are analyzed, and it is found that the tail can push the two unstable oscillatory poles closer to the imaginary axis. The role of the tail is fully demonstrated by considering the induced flow. Cascade controllers are also designed according to the root-locus plot based on the built model. Due to the inclusion of the wing–tail interaction and the aerodynamic–dynamic coupling, the controllers are proved to be efficient in the attitude stabilization during statistic hover, descent, and ascent flights. Our proposed model can be easily applied to the modeling of other flapping-wing aircraft with similar structures, and it makes the controller design process more efficient and targeted.

Development and evaluation of a practical nonlinear elastic constitutive model for rockfill dam deformation simulation based on monitoring results

Development and evaluation of a practical nonlinear elastic constitutive model for rockfill dam deformation simulation based on monitoring results