Third-order Model Research Articles

Cooperative Finite-time Control for autonomous vehicles platoons with nonuniform V2V communication delays

In this paper we introduce a novel fully distributed finite-time cooperative control law able to solve the platoon formation control problem for a network of autonomous vehicles, whose dynamics is represented via the third-order drivetrain linear model. Internet of Vehicle (IoV) communication latencies have been considered and modeled via heterogeneous time-varying delays. The resulting control protocol is computed via outdated information and embeds vehicles acceleration error, which allows improving control reactivity during sudden acceleration/deceleration maneuvers. The finite-time stability of the vehicular network has been analyzed and proved by leveraging Multi-Agent Systems (MASs) paradigm along with Lyapunov-Krasovskii method. This latter leads to stability conditions in the forms of Linear Matrix Inequalities, whose solution allows finding control gains and state trajectories threshold. Simulation results confirm the effectiveness of the theoretical derivation in guaranteeing the cooperative driving despite the presence of IoV communication latencies.

Multilevel organisational learning in a project-based organisation: computational analysis based on a 3rd-order adaptive network model

This paper describes how the recently developed self-modeling network modeling approach for multilevel organisational learning has been tested on applicability for a real-world case of a project-based organisation. The modeling approach was able to successfully address this complex case by designing a third-order adaptive network model. Doing this, as a form of further innovation three new features have been added to the modeling approach: recombination of selected high-quality mental model parts, refinement of mental model parts, and distinction between context-sensitive detailed control and global control.

Bayesian Robust Tensor Factorization for Angle Estimation in Bistatic MIMO Radar With Unknown Spatially Colored Noise

In this paper, we propose a robust tensor-based scheme for joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic multiple-input multiple-output (MIMO) radar with unknown spatially colored noise. To eliminate the colored noise, the proposed algorithm first denoises the received signal from the temporal cross-correlation approach and constructs a third-order complex tensor model. Then, a real-valued compressed tensor model is developed by utilizing the characteristic of radar antenna arrays. Finally, Bayesian tensor factorization is derived to fit the constructed real-valued model and approximate factor matrices, from which DOD and DOA can be extracted. We also derive Cramér-Rao bound (CRB) results for angle estimation. The proposed algorithm is suitable for both uniform linear array (ULA) and uniform planar array (UPA) manifolds. Compared with existing angle estimation methods, the proposed one has better estimation accuracy and more stable performance. In addition, the proposed algorithm works well even if the number of targets is unknown. Simulation results demonstrate the effectiveness and improvement of the proposed angle estimation algorithm.

Application of the ARMA Model to Describe and Forecast the Flotation Feed Solids Flow Rate

The flow rate of solids is subject to random disturbances of the changing feed and can significantly affect the quantitative and qualitative parameters of the coal flotation products. This quantity can be described as a stochastic process. The paper presents the results of the solids flow rate model for coal flotation identification calculations, treated as a disturbance to the process. This is an innovative approach to modelling those quantitative parameters of the flotation feed that are measurably available and whose random changes have a significant impact on the enhancement process under industrial conditions. These include the volumetric flow rate of the feed and, in particular, concentration of solids in the feed. Therefore, it is suggested that random changes of these two parameters of the feed should be mapped using a model of one quantity—the flow rate of solids. This solution is advantageous because this quantity, as a quantitative parameter of the feed, has a significant impact on the course of the coal flotation process. The model is necessary in the process of designing an automatic control system through simulation tests. It allows us to generate a data string simulating random changes to this quantitative parameter of the feed. On this basis, in the simulation model, the correct functioning of the automatic control system is tested, the task of which is to compensate the influence of this disturbance. To determine the empirical model of the feed solids flow rate, measurement data obtained during the registration of the solids concentration and volumetric flow rate of the feed were used in four consecutive periods of operation of an industrial facility of one of the Polish coal processing plants. The time courses of the solids flow rate in the feed were described by ARMA (autoregressive–moving-average model) means, and the two-stage least squares method was used to estimate the model parameters. The results of the identification and verification of the designated model showed the correctness of adopting the third-order ARMA model, with parameters a1 = −1.0682, a2 = −0.2931, a3 = 0.3807, c1 = −0.1588, c2 = −0.2301, c3 = 0.1037, and variance σ2ε = 0.0891, white noise sequence εt, determined on the basis of a series of residuals described by the fifth-order model. It has been shown that the identified model of the flow rate of solids of the feed to flotation as disturbances can be used to develop a predictive model that allows forecasting the modelled quantity with a prediction horizon equal to the sampling period. One-step forecasting based on the determined predictor equation was found to give results consistent with the recorded values of the solid part flow rate of the feed and the extreme values of the prediction error are within the range from −1.08 to 2.90 kg/s.

Adaptive Smooth Variable Structure Filter Strategy for State Estimation of Electric Vehicle Batteries

Battery Management Systems (BMSs) are used to manage the utilization of batteries and their operation in Electric and Hybrid Vehicles. It is imperative for efficient and safe operation of batteries to be able to accurately estimate the State of Charge (SoC), State of Health (SoH) and State of Power (SoP). The SoC and SoH estimation must remain robust and accurate despite aging and in presence of noise, uncertainties and sensor biases. This paper introduces a robust adaptive filter referred to as the Adaptive Smooth Variable Structure Filter with a time-varying Boundary Layer (ASVSF-VBL) for the estimation of the SoC and SoH in electrified vehicles. The internal model of the filter is a third-order equivalent circuit model (ECM) and its state vector is augmented to enable estimation of the internal resistance and current bias. It is shown that system and measurement noise covariance adaptation for the SVSF-VBL approach improves the performance in state estimation of a battery. The estimated internal resistance is then utilized to improve determination of the battery’s SoH. The effectiveness of the proposed method is validated using experimental data from tests on Lithium Polymer automotive batteries. The results indicate that the SoC estimation error can remain within less than 2% over the full operating range of SoC along with an accurate estimation of SoH.

Linear and non-linear wave theories coupled with a modified BEM model for quantifying dynamic loads of a tidal stream turbine

Dynamic loads resulted from wave-current interaction is a serious problem facing tidal current turbines (TCTs), which may lead to catastrophic results. The main issue in such environments is the accelerated fatigue, which likely results from the cyclic loading especially in the axial direction. For investigating the current effects on the wave field and evaluating the resulted dynamic loads, a modified Blade Element Momentum (BEM) model was presented and coupled with linear and non-linear wave theories.Firstly, a validation study has been performed between the present modified BEM model coupled with linear wave theory and previous numerical and experimental results. A previously introduced dynamic inflow model was reemployed in the present BEM model during this validation to assess its applicability and accuracy. Very good agreements were seen between the present model and the experimental data at different wave properties and operational conditions, which emphasized the precision of the present unsteady BEM model and its corrections for further investigations.Comparing with other operational conditions, the intrinsic wave period and wave height had significant effects on the resulted hydrodynamic loading ranges of both the blade root bending moments. By the use of linear wave theory, the resulted out-of-plane bending moment was under predicted. Linear wave and second-order models had similar bending moments at all wave and flow conditions. Due to considering the current effects on wave properties, Dean's, third-order and fifth-order models had dynamic loadings differed in phase, frequency and amplitude from the experimental data. Fifth-order model was finally considered the best choice for simulating the wave-current velocity at different wave conditions and immersion depths.An additional complete time series runs were performed to assess the effect of dynamic stall correction inclusion in the present BEM model on the resulted hydrodynamic loads. It had minor effects on the bending moments, while had noticeable influence on the turbine thrust.

Predicting indoor particle dispersion under dynamic ventilation modes with high-order Markov chain model.

Mechanical and natural ventilations are effective measures to remove indoor airborne contaminants, thereby creating improved indoor air quality (IAQ). Among various simulation techniques, Markov chain model is a relatively new and efficient method in predicting indoor airborne pollutants. The existing Markov chain model (for indoor airborne pollutants) is basically assumed as first-order, which however is difficult to deal with airborne particles with non-negligible inertial. In this study, a novel weight-factor-based high-order (second-order and third-order) Markov chain model is developed to simulate particle dispersion and deposition indoors under fixed and dynamic ventilation modes. Flow fields under various ventilation modes are solved by computational fluid dynamics (CFD) tools in advance, and then the basic first-order Markov chain model is implemented and validated by both simulation results and experimental data from literature. Furthermore, different groups of weight factors are tested to estimate appropriate weight factors for both second-order and third-order Markov chain models. Finally, the calculation process is properly designed and controlled, so that the proposed high-order (second-order) Markov chain model can be used to perform particle-phase simulation under consecutively changed ventilation modes. Results indicate that the proposed second-order model does well in predicting particle dispersion and deposition under fixed ventilation mode as well as consecutively changed ventilation modes. Compared with traditional first-order Markov chain model, the proposed high-order model performs with more reasonable accuracy but without significant computing cost increment. The most suitable weight factors of the simulation case in this study are found to be (λ1 = 0.7, λ2 = 0.3, λ3 = 0) for second-order Markov chain model, and (λ1 = 0.8, λ2 = 0.1, λ3 = 0.1) for third-order Markov chain model in terms of reducing errors in particle deposition and escape prediction. With the improvements of the efficiency of state transfer matrix construction and flow field data acquisition/processing, the proposed high-order Markov chain model is expected to provide an alternative choice for fast prediction of indoor airborne particulate (as well as gaseous) pollutants under transient flows.

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

A unique feature of flexible cantilevered beams, which is used in a range of applications from energy harvesting to bio-inspired actuation, is their capability to undergo motions of extremely large amplitudes. The well-known third-order nonlinear cantilever model is not capable of capturing such a behaviour, hence requiring the application of geometrically exact models. This study, for the first time, presents a thorough experimental investigation on nonlinear dynamics of a cantilever under base excitation in order to capture extremely large oscillations to validate a geometrically exact model based on the centreline rotation. To this end, a state-of-the-art in vacuo base excitation experimental set-up is utilised to excite the cantilever in the primary resonance region and drive it to extremely large amplitudes, and a high-speed camera is used to capture the motion. A robust image processing code is developed to extract the deformed state of the cantilever at each frame as well as the tip displacements and rotation. For the theoretical part, a geometrically exact model is developed based on the Euler–Bernoulli beam theory and inextensibility condition, while using Kelvin–Voigt material damping. To ensure accurate predictions, the equation of motion is derived for the centreline rotation and all terms are kept geometrically exact throughout the derivation and discretisation procedures. Thorough comparisons are conducted between experimental and theoretical results in the form of frequency response diagrams, time histories, motion snapshots, and motion videos. It is shown that the predictions of the geometrically exact model are in excellent agreement with the experimental results at both relatively large and extremely large oscillation amplitudes.

Design of Gudermannian Neuroswarming to solve the singular Emden-Fowler nonlinear model numerically.

The current investigation is related to the design of novel integrated neuroswarming heuristic paradigm using Gudermannian artificial neural networks (GANNs) optimized with particle swarm optimization (PSO) aid with active-set (AS) algorithm, i.e., GANN-PSOAS, for solving the nonlinear third-order Emden–Fowler model (NTO-EFM) involving single as well as multiple singularities. The Gudermannian activation function is exploited to construct the GANNs-based differential mapping for NTO-EFMs, and these networks are arbitrary integrated to formulate the fitness function of the system. An objective function is optimized using hybrid heuristics of PSO with AS, i.e., PSOAS, for finding the weights of GANN. The correctness, effectiveness and robustness of the designed GANN-PSOAS are verified through comparison with the exact solutions on three problems of NTO-EFMs. The assessments on statistical observations demonstrate the performance on different measures for the accuracy, consistency and stability of the proposed GANN-PSOAS solver.

Barrier height study of two-well resonant-phonon terahertz quantum cascade lasers. I. The third-order tunneling current theory

The third-order tunneling current model, reflecting the effect of carrier leakage from bound to continuum states, is modeled based on the second-order tunneling current and semi-classical leakage current theories and is incorporated in a simulation based on the rate equation. GaAs/AlGaAs-based two-well resonant-phonon terahertz quantum cascade lasers, published in the past, are theoretically examined by this method. Based on the latest recorded device, the influence of barrier height is investigated by changing the Al-composition from 12.5% to 45% with a fixed-layer thickness. As a result, there are carrier dynamics that diminish the carrier density of lasing subbands in both high and low barrier conditions. On the one hand, carrier leakage into continuum states increases drastically below 25% Al-composition. On the other hand, in high barrier conditions, substantial carriers accumulate in the ground state due to a strong confinement effect in addition to oscillator strength lowering.

An oscillation damping method for frequency-detector-less virtual synchronous generators

This paper presents an active power oscillation damping method for frequency-detector-less virtual synchronous generator (VSG) to enhance its transient stability and to avoid the ill effect of frequency detector. In the paper, first, the mechanism and the low-frequency oscillation model of a conventional VSG is derived and reduced to a second-order model. Then, a new way to obtain the damping power without using frequency detector is proposed in order to simplify the conventional one, which includes frequency detector. The new approach presents an equivalent third-order model, and based on small-signal state-space analysis, the dominant poles are assigned to the same place as the original one, so that we can fairly compare their dynamic performances. Finally, experimental results are performed to compare the proposed approach with some other VSG control methods. The experimental results show that the proposed approach does better in transient stability and power-sharing ability than other conventional VSG control methods.

Geometrically exact dynamics of cantilevered pipes conveying fluid

In this paper, the global dynamics of a hanging fluid conveying cantilevered pipe with a concentrated mass attached at the free end is investigated. The problem is of interest not only for engineering applications, but also because it displays interesting and often surprising dynamical behaviour. The widely used nonlinear models based on the transverse motion of the pipe are not able to accurately capture the dynamical behaviour of the system at very high flow velocities. Thus, a high-dimensional geometrically-exact model is developed for the first time, utilising Hamilton’s principle together with the Galerkin modal decomposition technique. Extensive numerical simulations are conducted to investigate the influence of key system parameters. It is shown that at sufficiently high flow velocities past the first instability (Hopf bifurcation), the system undergoes multiple bifurcations with extremely large oscillation amplitudes and rotations, beyond the validity of third-order nonlinear models proposed to-date. In the presence of an additional tip mass, quasi-periodic and chaotic motions are observed; additionally, it is shown that for such cases an exact model is absolutely essential for capturing the pipe dynamics even at relatively small flow velocities beyond the first instability.

ДОСЛІДЖЕННЯ РЕЖИМУ НАПРУГИ В ДАЛЬНІХ ЛІНІЯХ ЕЛЕКТРОПЕРЕДАЧІ ЗМІННОГО СТРУМУ

The charging currents of EHV transmission lines cause the Ferranti effect, which causes an increase in voltage at intermediate points transmission line. The work aims to study the laws of the voltage distribution along the line route and to develop a method for determining the coordinates of a point with extreme voltage. Methodology. Mathematical modeling of long-distance transmission lines in Wolfram Mathematica allowed to form the laws of the voltage distribution along the line and determine the coordinate of the extreme point on the voltage. Results. It is shown that the application of the traditional model of idealized power transmission causes high modeling accuracy only in the modes of unloaded line and low loads. In the range of medium and high loads, the simulation error reaches unacceptably large values. The paper proposes more accurate models for determining the coordinate of an extreme voltage point: linearized and second- and third-order models. It is shown that the proposed models are characterized by higher accuracy in a wide range of loads. Increasing the degree of the model results in higher accuracy, but is associated with an increase in the cumbersomeness of the mathematical model. It is shown that first and second-order models provide sufficient accuracy for typical designs of 750 kV power transmission lines. It is shown that neglecting the losses on the corona has almost no effect on the accuracy of calculating the coordinates of the extreme point on the voltage, which simplifies the linear calculation model and models of the second and third-order. Originality. Mathematical models of the first, second and third orders have been developed for high-precision determination of the coordinate of a voltage-extreme point along a long-distance transmission line. Practical significance. The offered mathematical models are intended for application in problems of regulation and adjustment of parameters of flexible power transmissions. Ref. 12, figure, tables 4.

Periodic Third-Order Problems with a Parameter

This work concerns with the solvability of third-order periodic fully problems with a weighted parameter, where the nonlinearity must verify only a local monotone condition and no periodic, coercivity or super or sublinearity restrictions are assumed, as usual in the literature. The arguments are based on a new type of lower and upper solutions method, not necessarily well ordered. A Nagumo growth condition and Leray–Schauder’s topological degree theory are the existence tools. Only the existence of solution is studied here and it will remain open the discussion on the non-existence and the multiplicity of solutions. Last section contains a nonlinear third-order differential model for periodic catatonic phenomena, depending on biological and/or chemical parameters.

Extreme Multistability and Antimonotonicity in a Shinriki Oscillator with Two Flux-Controlled Memristors

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.

Event-Triggering Communication Based Distributed Coordinated Control of Multiple High-Speed Trains

This paper deals with the coordinated control of the multiple high-speed train system taking into account the sampled characteristic of the communication information. Considering the inertial lag of the servo motor/braking unit in practical scenarios, a third-order nonlinear model is adopted to capture the dynamics of a train, based on which the coordinated control problem is formulated. By virtue of the back-stepping linearization technique, the sampled-data communication based train coordination is transformed to the stabilization of a linear multiple-input system subject to periodic time-varying input delay. An event-triggering communication framework is constructed to lower the dependence on the communication resource. Furthermore, distributed low-gain feedback control protocols are established that, besides achieving coordination of the train operation, ensure the trains track the predefined train speed profile while avoiding unnecessary information transmission. Numerical experiments are carried out to verify the theoretical results.

Comparison of strongly and weakly nonlinear flame models applied to thermoacoustic instability

Weakly nonlinear flame (or heater) dynamic models, only accounting for heat release rate disturbances from the flame (or heater) at forcing frequencies and omitting harmonic terms due to nonlinear mechanisms, are widely used in low-order tools for the analysis and prediction of thermoacoustic instabilities, because they have a numerical cost much cheaper than tools based on Navier–Stokes equations, and are easier to develop and validate. However, these models may lead to errors under certain conditions. The present work considers a Rijke tube model combustor, in which a classical third-order model is used to describe the flame dynamic response to the oncoming flow disturbance. We call this model the strongly nonlinear flame model. The weakly nonlinear flame model is then introduced. The wave-based approach is adopted as a low-order tool. The weakly and strongly nonlinear flame models are embedded in the low-order tool to reproduce the thermoacoustic instability of the model combustor. The natural frequency and growth rate of thermoacoustic instability are then determined by mode extracted methods. The differences between the results predicted by using the weakly and strongly nonlinear flame models are compared for a set of operating conditions, in order to find the conditions under which the weakly nonlinear flame model works. Short-time Fourier transform is adopted to analyze the extracted frequencies and growth rates of four selected cases. When the dominant acoustic mode strength is much stronger than the remaining modes, the weakly nonlinear models perform well. However, these models fail to capture the mode frequency and growth rate when multiple unstable modes are present.

Nonlinear stability of axially compressed couple stress-based composite micropanels reinforced with random checkerboard nanofillers

In this investigation, by matching the moving Kriging meshfree formulations with the third-order shear flexible shell model together with the modified couple stress continuity, the size-dependent nonlinear stability characteristics of micropanels subjected to axial compression are analyzed. The random checkerboard model is employed for the micropanels made of graphene nanoplatelet random-reinforced composites. The associated material characteristics are evaluated via a probabilistic-based micromechanical scheme. Afterwards, proper meshfree functions are implemented to enforce the essential boundary conditions at the considered nodding system accurately. It is shown that the stiffening character of the couple stress size dependency coming from the rotation gradient tensor causes to rise the nonlinear critical stability load and the associated critical shortening of random reinforced composite micropanels. Moreover, for a specific value of the graphene nanofillers volume fraction, by reducing the length to width aspect ratio of them, the role of rotation gradient size dependency in the both critical stability load and critical shortening of an axially compressed random checkerboard reinforced composite micropanel becomes somehow more significant.

Microstructural Size Dependency in Nonlinear Lateral Stability of Random Reinforced Microshells via Meshfree-Based Applied Mathematical Modeling

The prime objective of this research work is to develop an efficient small scale-dependent computational framework incorporating microstructural tensors of dilatation gradient, rotation gradient, and deviatoric stretch gradient to analyze nonlinear lateral stability of cylindrical microshells. The numerical strategy is established based upon a mixed formation of the third-order shear deformable shell model and modified strain gradient continuum mechanics. The graphene nanoplatelet reinforcements are assumed to be randomly dispersed in a checkerboard scheme within the resin matrix. Accordingly, to extract the effective material properties, the Monte Carlo simulation together with a probabilistic technique are employed. The numerical solution for the microstructural-dependent nonlinear problem is carried out via the moving Kriging meshfree method having the capability to accommodate accurately the essential boundary conditions using proper moving Kriging shape function. It is represented that the role of the stiffening characters related to the effect of microstructural dilatation gradient, rotation gradient, and deviatoric stretch reduces continuously by going to deeper territory of the load-deflection stability path. Moreover, it is indicated that among various microstructural gradient tensors, the stiffening character of the rotation gradient is higher than deviatoric stretch gradient, and the stiffening character of the latter is more considerable than the dilatation gradient tensor.

Research on a modeling method of wing deformation under the influence of separation and compound multi-source disturbance

AbstractAn aircraft wing is the carrier of imaging payload (interferometric synthetic aperture radar (SAR) or array SAR) of a high-resolution aerial remote sensing system, and high-precision estimation of wing deformation is the key. There are two main traditional modelling methods for wing deformation, namely stochastic theory modelling and material mechanics modelling only dealing with single disturbance, of which the model parameters are derived from empirical values. Aiming at the complex multi-source disturbance of an aircraft wing, this paper separately probes the influence of external disturbance (air disturbance) and internal disturbance (engine vibration) based on the real-time observation of sensors and classifies the wing deformation on the basis of auto-regressive (AR) modelling for parameter identification. With the authentic flight data of a certain types of aircraft, the experimental analysis shows that the wing deformation under the influence of engine vibration is the 14th-order AR model, and the wing deformation under the influence of turbulence is the fifth-order AR model. Meanwhile, this paper also provides an experimental verification idea for the wing deflection modelling built on the second- or third-order Markov model.