Nonlinear Description Research Articles

Linking multi-level population dynamics: state, role, and population.

The dynamics of an ecological community can be described at different focal scales of the species, such as individual states or the population level. More detailed descriptions of ecological dynamics offer more information, but produce more complex models that are difficult to analyze. Adequately controlling the model complexity and the availability of multiple descriptions of the concerned dynamics maximizes our understanding of ecological dynamics. One of the central goals of ecological studies is to develop links between multiple descriptions of an ecological community. In this article, starting from a nonlinear state-level description of an ecological community (generalized McKendrick–von Foerster model), role-level and population-level descriptions (Lotka–Volterra model) are derived in a consistent manner. The role-level description covers a wider range of situations than the population-level description. However, using the established connections, it is demonstrated that the population-level description can be used to predict the equilibrium status of the role-level description. This approach connects state-, role-, and population-level dynamics consistently, and offers a justification for the multiple choices of model description.

Influence of Fluid Viscosity and Compressibility on Nonlinearities in Generalized Aerodynamic Forces for T-Tail Flutter

The numerical assessment of T-tail flutter requires a nonlinear description of the structural deformations when the unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, a linear deformation description of the vertical tail plane (VTP) out-of-plane bending results in a spurious stiffening proportional to the steady lift forces, which is corrected by incorporating second-order deformation terms in the equations of motion. While the effect of these nonlinear deformation components on the stiffness of the VTP out-of-plane bending mode shape is known from the literature, their impact on the aerodynamic coupling terms involved in T-tail flutter has not been studied so far, especially regarding amplitude-dependent characteristics. This term affects numerical results targeting common flutter analysis, as well as the study of amplitude-dependent dynamic aeroelastic stability phenomena, e.g., Limit Cycle Oscillations (LCOs). As LCOs might occur below the linear flutter boundary, fundamental knowledge about the structural and aerodynamic nonlinearities occurring in the dynamical system is essential. This paper gives an insight into the aerodynamic nonlinearities for representative structural deformations usually encountered in T-tail flutter mechanisms using a CFD approach in the time domain. It further outlines the impact of geometrically nonlinear deformations on the aerodynamic nonlinearities. For this, the horizontal tail plane (HTP) is considered in isolated form to exclude aerodynamic interference effects from the studies and subjected to rigid body roll and yaw motion as an approximation to the structural mode shapes. The complexity of the aerodynamics is increased successively from subsonic inviscid flow to transonic viscous flow. At a subsonic Mach number, a distinct aerodynamic nonlinearity in stiffness and damping in the aerodynamic coupling term HTP roll on yaw is shown. Geometric nonlinearities result in an almost entire cancellation of the stiffness nonlinearity and an increase in damping nonlinearity. The viscous forces result in a stiffness offset with respect to the inviscid results, but do not alter the observed nonlinearities, as well as the impact of geometric nonlinearities. At a transonic Mach number, the aerodynamic stiffness nonlinearity is amplified further and the damping nonlinearity is reduced considerably. Here, the geometrically nonlinear motion description reduces the aerodynamic stiffness nonlinearity as well, but does not cancel it.

Non-linear and multi-domain modelling of a permanent magnet linear synchronous machine for free piston engine generators

• The motivations for continued FPE and LEM development are established. • A non-linear and multi-domain model of the PMLSM is presented. • Incorporation of the PMLSM in an FPEG multi-domain model is demonstrated. • Model validation with data captured from an experimental FPEG is conducted. • Simulation results indicate the model captures the dominant dynamics of the PMLSM. The Free Piston Engine (FPE) can be considered a viable and promising option in future low-carbon technology development. When coupled to the Linear Electric Machine (LEM) to produce electrical energy, its characteristic non-linear dynamics typically have been described as linear when considering a systems-level modelling approach. This paper presents a multi-domain model of a Permanent Magnet Linear Synchronous Machine (PMLSM) for Free Piston Engine Generators (FPEG) and offers a detailed non-linear mathematical description of the machine dynamics. The model was implemented in a free-piston expander system and validated against experimental data from a test rig that has identical parameters. The simulation results indicate a strong correlation to the experimental data, which captured the dominant dynamics of the PMLSM and prove the satisfactory accuracy and performance of the model, together with a similar voltage and current output trace, indicating a cyclic energy output error of approximately 10 %. This paper aims to extend the current knowledge and literature within FPEG PMLSM design by considering the inherent non-linearity and multi-directional nature of the system dynamics and its interactions with multi-physical domains.

2D CFTs: Large charge is not enough to control the dynamics

In this note we study two-dimensional conformal field theories at large global charge. Since the large-charge sector decouples from the dynamics, it does not control the dynamics and an effective field theory construction that works in higher-dimensional theories fails. It is however possible to use large charge in a double-scaling limit when another controlling parameter is present. We find some general features of the spectrum of models that admit a nonlinear sigma model description in a Wentzel-Kramers-Brillouin approximation and use the large-charge sector of the solvable $SU(2{)}_{k}$ Wess-Zumino-Witten model to argue the regimes of applicability of both the large-$Q$ expansion and the double-scaling limit.

Travelling wave solutions for hierarchy of nonlinear evolution equation description propagation pulse in optical fibers

Travelling wave solutions for hierarchy of nonlinear evolution equation description propagation pulse in optical fibers

Topological Descriptors of Gait Nonlinear Dynamics Toward Freezing-of-Gait Episodes Recognition in Parkinson’s Disease

Gait complexity analysis and nonlinear dynamics descriptions were widely used in abnormal state detection in disease studies. Recent development in algebra topology brought novel tools to describe dynamical systems, which inspired us a novel insight toward gait complexity analysis. This work investigates the gait complexity variations in Parkinson’s disease patients with a topological nonlinear dynamics analysis approach toward detecting the Freezing-of-Gait episode. In this work, we use 3-dimensional acceleration data from eight subjects with FoG symptoms and extract the FoG features from the accelerometer signals through topological analysis of the reconstructed phase space. Descriptors of Betti curves, persistence landscapes, silhouette landscapes were extracted to form feature vector toward FoG detection tasks, which achieve a sensitivity of 91.93% (94.49%), specificity of 87.61% (93.10%), the accuracy of 89.76% (93.75%), and the receiver operating characteristic curve (AUC) score of 0.956 (0.977) in the generic (person-specific) FoG recognition model. We also found that the proposed approach outperforms the traditional complexity parameters in the FoG recognition task, showing that the topological descriptions are promising in gait analysis. This work is supposed to be the first topological validation work in gait complexity analysis. Our findings are also relevant to risk stratification and continuous monitoring of Parkinson’s disease, which bring a promising approach for automated FoG detection for better healthcare.

Impact of intrinsic charm amount in the nucleon and saturation effects on the prompt atmospheric nu _{mu } flux for IceCube

The predictions for the atmospheric neutrino flux at high energies strongly depend on the contribution of prompt neutrinos, which are determined by the production of charmed mesons in the atmosphere at very forward rapidities. In this paper we estimate the related cross sections taking into account the presence of an intrinsic charm (IC) component in the proton wave function and the QCD dynamics modified by the onset of saturation effects. The impact on the predictions for the prompt neutrino flux is investigated assuming different values for the probability to find the IC in the nucleon (P_{ic}). We demonstrate that for P_{ic} sim 1%, the IC component dominates the high-energy prompt neutrino flux. A first comparison with the IceCube data is performed and upper limits on the amount of IC are obtained for the linear and nonlinear descriptions of the QCD dynamics.

Geometrically nonlinear formulation of Generalized Beam Theory for the analysis of thin-walled circular pipes

In this paper, the formulation of Generalized Beam Theory (GBT) for the geometrically nonlinear analysis of thin-walled circular pipes is presented. GBT is a computationally efficient numerical method which is especially formulated for thin-walled members with a capacity of determining the cross-sectional deformation through a combination of a set of pre-determined cross-sectional deformation modes. In this study, the current GBT analysis of circular pipes which is limited to buckling analysis is enhanced to a full geometrically nonlinear analysis. This new formulation considers the nonlinear membrane kinematic description based on the Green–Lagrange strain definition. The nonlinear tangent stiffness matrices and the internal force vectors are derived from the variation of the internal energy which results in third and fourth-order GBT deformation mode coupling tensors. These tensors can predetermine the type of GBT deformation modes needed for the nonlinear analysis based on the applied loading conditions. In addition to the classical GBT deformation modes, the non-conventional GBT deformations modes have a vital role since without these modes the coupling tensors and the nonlinear stiffness matrix related to the transverse and the shear membrane energy will be lost. Here, to illustrate the application and capabilities of the developed GBT formulation, two numerical examples involving transverse and longitudinal bending are presented to show the nonlinear relationship between bending, cross-sectional ovalization, and higher local deformation modes. For the purpose of validation, these examples are compared with refined shell finite element models in both displacement and stress fields.

Design of optimal controller for photovoltaic maximum power point tracking applications

ABSTRACT Photovoltaic (PV) maximum power point tracking (MPPT) technology is one of the key technologies that affect the energy utilization of PV power generation systems. How to achieve PV maximum power output quickly, accurately, and simply during the process of changing insolation and temperature conditions is a key problem in current research. At present, the traditional model-free maximum power tracking algorithm suffers from slow response, steady-state oscillations, and large influence of control parameters, whereas the model-based maximum power point tracking algorithm has the advantages of a simple control rate calculation and excellent control performance; however, the nonlinear characteristics of PV cells and power electronic converters lead to difficult controller design and often require a reference value of the maximum power point to be given. In this study, a mathematical model of a PV system was used, and a new PV maximum power tracking algorithm that does not require a reference value to be specified was proposed. The algorithm maps the nonlinear state-space description of the PV power generation system into a linear space through the state feedback linearization design. This solves the problem of difficult controller design for a nonlinear PV power generation system. Starting with the PV maximum power point as the extreme value point of the U-P curve, optimal control theory is applied to derive the PV maximum power tracking control rate, which overcomes the difficulty caused by the model-based control method requiring a reference to be specified. Compared with the traditional method, the proposed maximum power point tracking method improves the response speed by approximately 3–20 times and the tracking accuracy by approximately 3% or less. In addition, the method has a certain amount of immunity to DC bus voltage fluctuations.

Numerical simulation of deployable ultra-thin composite shell structures for space applications and comparison with experiments

In the present article, the geometrical nonlinear behavior of deployable booms undergoing large displacements and rotations is investigated. The triangular rollable and collapsible boom made of fiber-reinforced composite materials is considered along with a metallic tape spring. The mathematical model makes use of higher-order 1D structural theories based on the Carrera unified formulation, which allows the description of moderate nonlinearities to deep post-buckling mechanics of ultra-thin shells in a hierarchical and scalable manner. Particular attention is focused on the study of equilibrium paths of the booms subjected to coiling bending. Dedicated experimental tests reveal the validity of the proposed finite element approach, whereas the investigation of different lamination sequences offer a valuable perspective for possible future designs.

Soliton Molecule Dynamics Evolution Prediction Based on LSTM Neural Networks

In this article, we design a long short-term memory ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LSTM</i> ) scheme, combined with dense networks, to realize soliton dynamics prediction in passively mode-locked fiber lasers. Based on the particle characteristic of soliton interaction, we propose to use the separation and relative phase between solitons as characteristic parameters to model and predict the dynamics. The network predicted soliton collision and soliton molecule dynamics accurately. This scheme of precoding physical information with subsequent dynamics prediction not only introduces new prospects for the laser self-optimization algorithm, but also brings new insights for the modeling of nonlinear systems and description of soliton interactions.

Energetic formulation of large‐deformation poroelasticity

AbstractThe modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy‐based continuum mechanics framework to model large‐deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas–liquid phase‐changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data‐driven models in a Bayesian framework.

A Simulation and Experimental Study on Identification of an Electromechanical System

The current applications in electromechanical energy conversion demand highly accurate speed and position control. For this purpose, a better understanding of the motion characteristics and dynamic behavior of electromechanical systems including nonlinear effects is needed. In this paper, a suitable model of Permanent Magnet Direct Current (PMDC) motor rotating in two directions is developed for identification purposes. Model is parameterized and identified via simulation and using real experimental data. Linear and nonlinear models for the system are built for identification, and the effective nonlinearities in the system, which are Coulomb friction and dead zone, are integrated into the nonlinear model. A Weiner- Hammerstein nonlinear system description is used for identification of the model. MATLAB is selected as the investigating tool, and a simulation model is used to observe the error between the simulated and estimated outputs. Identification of the linear and nonlinear system models using experimental data is performed using the least squares (LS) and recursive least squares (RLS) methods. Performance of the model and identification method with the real time experiments are presented numerically and graphically, revealing the advantages of the proposed nonlinear identification approach.

Discrepancy-based control of particle processes

The production of goods in particulate form is important in many industries such as the chemical, pharmaceutical and food industry. For the subsequent use, specific particle properties determine the quality of the product. In order to ensure high quality and furthermore a constant production rate, process control methods can be applied. Here we present discrepancy-based control for a generic agglomeration process with additional particle breakage. The advantage of this control approach is the direct and simple control design using the nonlinear and infinite-dimensional system description as well as guaranteed stability for the chosen process variables. Two practically relevant scenarios are investigated. First, it is shown that control laws for two moments of the particle size distribution ensure the production of agglomerates with a constant Sauter mean diameter. Then, control laws for the production rate are designed. The resulting closed-loop behavior is investigated by means of dynamic simulation. It is shown that the control laws improve systems convergence speed for both set point tracking and disturbance rejection and achieve zero steady state error even under the occurrence of non-vanishing disturbances.

A toy model for the auditory system that exploits stochastic resonance

The transduction process that occurs in the inner ear of the auditory system is a complex mechanism which requires a non-linear dynamical description. In addition to this, the stochastic phenomena that naturally arise in the inner ear during the transduction of an external sound into an electro-chemical signal must also be taken into account. The presence of noise is usually undesirable, but in non-linear systems a moderate amount of noise can improve the system’s performance and increase the signal-to-noise ratio. The phenomenon of stochastic resonance combines randomness with non-linearity and is a natural candidate to explain at least part of the hearing process which is observed in the inner ear. In this work, we present a toy model of the auditory system which shows how stochastic resonance can be instrumental to sound perception, and suggests an explanation of the frequency dependence of the hearing threshold.

A two-level macroscale continuum description with embedded discontinuities for nonlinear analysis of brick/block masonry

A great proportion of the existing architectural heritage, including historical and monumental constructions, is made of brick/block masonry. This material shows a strong anisotropic behaviour resulting from the specific arrangement of units and mortar joints, which renders the accurate simulation of the masonry response a complex task. In general, mesoscale modelling approaches provide realistic predictions due to the explicit representation of the masonry bond characteristics. However, these detailed models are very computationally demanding and mostly unsuitable for practical assessment of large structures. Macroscale models are more efficient, but they require complex calibration procedures to evaluate model material parameters. This paper presents an advanced continuum macroscale model based on a two-scale nonlinear description for masonry material which requires only simple calibration at structural scale. A continuum strain field is considered at the macroscale level, while a 3D distribution of embedded internal layers allows for the anisotropic mesoscale features at the local level. A damage-plasticity constitutive model is employed to mechanically characterise each internal layer using different material properties along the two main directions on the plane of the masonry panel and along its thickness. The accuracy of the proposed macroscale model is assessed considering the response of structural walls previously tested under in-plane and out-of-plane loading and modelled using the more refined mesoscale strategy. The results achieved confirm the significant potential and the ability of the proposed macroscale description for brick/block masonry to provide accurate and efficient response predictions under different monotonic and cyclic loading conditions.

Prediction of Multiple Molten Iron Quality Indices in the Blast Furnace Ironmaking Process Based on Attention-Wise Deep Transfer Network

Molten iron quality (MIQ) indices prediction based on data-driven models is an important way to monitor product quality and smelting status in the blast furnace ironmaking process. However, some challenges still place in the MIQ prediction: 1) limited nonlinear and dynamic description capabilities and interpretability of data-driven models; 2) high demand on the number of the labeled samples; 3) insufficient exploration of the underlying relationship between MIQ indices. In this case, we propose a novel data-driven deep model for the online prediction of MIQ indices. First, we design an attention-wise module to self-learn the nonlinear and dynamic relationship between process variables and prediction targets and enhance interpretability. Then, the minute-level molten iron temperature data detected by our previously developed equipment is used to pre-train the attention-wise deep network to obtain the improved weights and reduce dependence on labeled samples. Finally, the pre-trained model is extended to a structure with a weight-shared attention-wise module and task-separated prediction networks to explore the relationship between multiple prediction tasks. The effectiveness of the proposed attention-wise deep network is verified in an industrial ironmaking plant, which shows a significant improvement in performance, i.e., high accuracy and interpretability.

A Control Concept for Battery Emulators Using a Reference Governor With a Variable PT1-Element for Constraint Handling

This paper presents a method for highly dynamic nonlinear control of DC-DC converters with constraints used in battery emulators. Controlling this system is particularly challenging as the connected units-under-test often behave like constant power loads (CPLs), which introduce unstable system dynamics and render the system nonlinear. In order to achieve fast output dynamics with the DC-DC converters over a large operating range, a special control architecture is proposed where feedback equivalence is established between a nonlinear system description and a linear description. The nonlinear system dynamics can then be transformed into linear ones for controller synthesis by exploiting the flatness property of the system. Additionally, constraints have to be met at any time during operation to prevent damage to components. In order to satisfy the constraints, a reference governor (RG) is added to the loop. This novel RG concept uses a low-pass filter in the shape of a PT1-element to modify the voltage reference. By changing the time constant of the PT1-element, the RG is able to generate smooth constraints-aware trajectories for setpoint changes. Finally, the capabilities of the control concept are demonstrated and discussed based on high-fidelity simulations.

A Review of Multitemporal and Multispatial Scales Photovoltaic Forecasting Methods

Reliable photovoltaic(PV) forecasting can provide important data support for power system operation, which is the key to realize the large-scale consumption of solar energy resources. PV forecasting task becomes crucial to ensure power system stability and economic operation. This paper reviews the existing research of PV forecasting methods from the perspective of multi-temporal scale and multi-spatial scale. Firstly, according to the forecasting process, demand, temporal and spatial scale, the forecasting methods are classified and the evaluation indicators involved in the research are listed. Secondly, based on the temporal scale of PV power generation, the results are combed through the three kind of scale of ultra-short-term, short-term and medium and long-term prediction. Thirdly, on each kind of temporal scale, the results are subdivided into single-site prediction and regional prediction to sort out in detail. Finally, the results are analyzed on the basis of the predicted temporal scale, spatial scale and input data. It has been observed that most recent papers highlight the importance of short-term predictions. The machine learning method shows excellent nonlinear description ability in short-term prediction, the prediction results are satisfactory. The spatial average effect of regional prediction reduces the variability of solar energy, the prediction results are reliable.

A Three-Dimensional Anisotropic Diffusion Equation-Based Video Recognition Model for Classroom Concentration Evaluation in English Language Teaching

In this paper, a three-dimensional anisotropic diffusion equation is used to conduct an in-depth study and analysis of students’ concentration in video recognition in English teaching classrooms. A multifeature fusion face live detection method based on diffusion model extracts Diffusion Kernel (DK) features and depth features from diffusion-processed face images, respectively. DK features provide a nonlinear description of the correlation between successive face images and express face image sequences in the temporal dimension; depth features are extracted by a pretrained depth neural network model that can express the complex nonlinear mapping relationships of images and reflect the more abstract implicit information inside face images. To improve the effectiveness of the face image features, the extracted DK features and depth features are fused using a multicore learning method to obtain the best combination and the corresponding weights. The two features complement each other, and the fused features are more discriminative, which provides a strong basis for the live determination of face images. Experiments show that the method has excellent performance and can effectively discriminate the live nature of faces in images and resist forged face attacks. Based on the above face detection and expression recognition algorithms, the classroom concentration analysis system based on expression recognition is designed to achieve real-time acquisition and processing of classroom images, complete student classroom attendance records using face detection and face recognition methods, and analyze students’ concentration from the face integrity and facial expression of students facing the blackboard by combining face detection and expression recognition to visualize and display students’ classroom data for teachers, students, and parents with more data support and help.