Continuous Dynamic Model Research Articles

Galloping of Iced Transmission Lines Considering Multi-Torsional Modes and Experimental Validation on a Continuous Model

This study aims to determine the galloping trend of iced transmission lines. A mathematical model considering the first three torsional modes is first established by applying the Galerkin method to the continuous dynamic model. The Hopf bifurcation theory is applied to the linear part of the mathematical model to calculate the critical stability conditions for each mode. Numerical procedures are then implemented on the mathematical model to simulate the galloping feature. An experiment on a continuous model for conductor galloping is designed to validate the above-mentioned galloping feature. The phenomena observed in the wind tunnel test are in good agreement with the theoretical observations. The results show that torsional galloping modifies the numbers of bifurcation points for the in-plane modes. A lower in-plane mode is gradually substituted by a higher one with increasing wind velocity. The theoretical and experimental results are then compared in terms of the galloping frequency and wind velocity range of galloping. By applying the experimental parameters to the theoretical model, the consistency between the theory and the experiment is proven. A convenient method is proposed to predict the wind speed range of galloping and is expected to be applicable for predictions of other critical parameters.

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways.

The complexity of the human respiratory system causes that one of the main methods of analyzing the dynamic pulmonary phenomena and interpreting experimental results are simulations of its computational models. Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time-varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.

Study on Microstructure Evolution and Continuous Dynamic Recrystallization Constitutive Model of Dual-Phase Mg-Li Alloy LA103Z during Hot Deformation

Study on Microstructure Evolution and Continuous Dynamic Recrystallization Constitutive Model of Dual-Phase Mg-Li Alloy LA103Z during Hot Deformation

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Continuous Model and Analytical Solution for Unbalance Responses

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.

Algebraic Systems with Positive Coefficients and Positive Solutions

The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it.

A continuous dynamic constitutive model for normal- and high-strength structural steels

The use of numerical models in the advanced analysis and design of steel structures, particularly under extreme loading conditions, is becoming increasingly widespread. A crucial component of such models is an accurate description of the material response. A systematic study into the dynamic constitutive modelling of structural steels is presented herein. The key features of the dynamic stress–strain characteristics of structural steels at various strain rates, i.e., test methods, material strength, strain-rate effect index and strain-rate effect models, are examined and discussed. Supplementary SHPB tests on both normal- and high-strength structural steels (Q235, Q355, Q460, and S960) under a wide range of strain rates up to 5000 s−1, filling gaps in existing datasets, are then carried out. A database of dynamic test results, containing 453 stress–strain curves, is systematically established and analyzed. Finally, a continuous dynamic constitutive model, capturing the dependency of both yield strength and strain rate, is proposed to predict the dynamic stress–strain response for structural steels, from normal- to high-strength material (235–960 MPa), and from static to high strain rate loading conditions (up to 5000 s−1).

Virtual labs for the study of enzymatic stirred tank bioreactors

AbstractVirtual laboratories have successfully proven to be very versatile and intuitive when simulating experiments in science, biotechnology, and engineering. These tools must complement the experiments carried out in real labs or pilot plants. This study describes the creation of a virtual laboratory through the Easy JavaScript Simulation platform. A web‐based simulation of an enzymatic stirred‐tank bioreactor has been built using a dynamic model. This simulation reproduces the behavior of a continuous bioreactor, including the deviations of ideal mixing conditions as by the use of an in tanks‐in‐series model for nonideal flow. This article describes the continuous dynamic model in a stirred tank bioreactor, as well as the operation of a tool capable of carrying out virtual practice with students. Practice scripts have been developed that should be used by students during the practical classes. This interactive tool is powerful and useful to develop many experiments by varying the different input parameters, saving time and resources. In addition, the tool allows following teaching sessions in specific situations such as the health situation derived from the pandemic caused by COVID‐19.

The Quantitative Features Analysis of the Nonlinear Model of Crop Production by Hybrid Soft Computing Paradigm

In this study, we provide a discretized system of a continuous dynamical model for enhancing crop production in the presence of insecticides and insects. Crops are assumed to grow logistically but are limited by an insect population that entirely depends on agriculture. To protect crops from insects, farmers use insecticides, and their overmuch use is harmful to human health. We assumed that external efforts are proportional to the gap between actual production and carrying capacity to increase the field’s development potential. We use the Levenberg–Marquardt algorithm (LMA) based on artificial neural networks (NNs) to investigate the approximate solutions for different insecticide spraying rates. “NDSolve” tool in Mathematica generated a data collection for supervised LMA. The NN-LMA approximation’s value is achieved by the training, validation, and testing reference data sets. Regression, error histograms, and complexity analysis help to validate the technique’s robustness and accuracy.

Dynamics of adolescents\u2019 smartphone use and well-being are positive but ephemeral

Well-being and smartphone use are thought to influence each other. However, previous studies mainly focused on one direction (looking at the effects of smartphone use on well-being) and considered between-person effects, with self-reported measures of smartphone use. By using 2548 assessments of well-being and trace data of smartphone use collected for 45 consecutive days in 82 adolescent participants (Mage = 13.47, SDage = 1.62, 54% females), the present study disentangled the reciprocal and individual dynamics of well-being and smartphone use. Hierarchical Bayesian Continuous Time Dynamic Models were used to estimate how a change in frequency and duration of smartphone use predicted a later change in well-being, and vice versa. Results revealed that (i) when participants used the smartphone frequently and for a longer period, they also reported higher levels of well-being; (ii) well-being positively predicted subsequent duration of smartphone use; (iii) usage patterns and system dynamics showed heterogeneity, with many subjects showing reciprocal effects close to zero; finally, (iv) changes in well-being tend to persist longer than changes in the frequency and duration of smartphone use.

ДИНАМІЧНИЙ СИНТЕЗ МОБІЛЬНОЇ ЗЕМЛЕРИЙНОЇ МАШИНИ БЕЗПЕРЕРВНОЇ ДІЇ З ЛАНЦЮГОВО-БАЛКОВИМ РОБОЧИМ ОРГАНОМ

This article depics the mobile continuous earth-moving machine dynamic model with a chain-type trenching equipment in order to determine the effect of changes in the elastic-inertial system parameters on its own resonant frequencies. The object of the research: natural resonant transmission frequencies of the soil-working working equipment drive in the mobile earth-moving continuous action machine with a chain-beam working body. The purpose of the work: to determine the system elements, in which the elastic-inertial parameters affect the lower natural resonant frequencies. To give practical recommendations on the parameter choice of such elements in order to deviate from the resonant frequency. Creation of strong, reliable and durable machines depends on the dynamic load accuracy and ways to reduce it. Modern earthmoving machine structure formation can be realized using the modular principle, but always with taking into account the full picture of possible machine loads and their drives in the process, these load magnitude and their dynamic characteristics. In accordance with the dynamic synthesis conditions, the dynamic system machine parameters should be selected so that the external load machine change frequency in its maximum productivity mode doesn’t coincide with the dynamic system natural frequency. According to the theoretical and strain gauge research results, it is established that the frequency of the first form of earth-moving machine drive torsional oscillations is close to 9 Hz. The first frequency oscillation shape has a node between the gearbox masses, which can lead to fatigue shaft destruction, joints or gears of the base tractor transmission part destruction. The frequency of the natural oscillation system is close to the traction chain link engagement frequency with the sprocket teeth in the earth-moving machine maximum productivity mode.

Consensus, polarization, and coexistence in a continuous opinion dynamics model with quenched disorder.

A model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that consensus, polarization and a spread of moderate opinions are all possible within this model. Using dynamic mean-field theory, we are able to identify the statistical features of the interactions between individuals that give rise to each of the aforementioned emergent phenomena. The nature of the transitions between each of the observed macroscopic states is also studied. It is demonstrated that heterogeneity of interactions between individuals can lead to polarization, that mostly antagonistic or contrarian interactions can promote consensus at a moderate opinion, and that mostly reinforcing interactions encourage the majority to take an extreme opinion.

A novel, scalable, and modular bioreactor design for dynamic simulation of the digestive tract.

In vitro gut model systems permit the growth of gut microbes outside their natural habitat and are essential to the study of gut microbiota. Systems available today are limited by a lack of scalability and flexibility in the mode of operation. Here, we describe the development of a versatile bioreactor module that can be easily adjusted for culture size and capable of sensing and controlling of environmental parameters such as pH control of culture medium, rate of influx and efflux of the culture medium, and aerobic/anaerobic atmosphere. Bioreactor modules can be operated as single units or linked in series to construct a model of a digestive tract with multiple compartments to allow the growth of microbiota in vitro. We tested the growth of synthetic and natural bacterial communities in a multicompartment continuous dynamic culture model simulation of the mammalian gut. The distal compartments of a sterile system inoculated with the synthetic bacterial community at the proximal module attained a stable bacterial density by 24 h, and all the genera present in the inoculum were firmly established in the distal modules simulating the large intestine at 5 days of continuous culture. A natural bacterial community simultaneously inoculated into the distal modules attained a stable bacterial composition at the phylum level by Day 7 of continuous culture. The findings illustrate the utility of the system to culture mixed bacterial communities which can be used to study the collective biological activities of the cultured microbiota in the absence of host influence.

Construction of Continuous Dynamic Model for River Networks and Its Application in Simulation of Spatiotemporal Migration of Typical Biocides

Biocides are widely added to personal care products and enter the environment through sewage treatment plant (STP) discharge, which affects ecological health. This paper evaluated the pollution characteristics of triclosan and triclocarban in a river network during the COVID-19 epidemic. Moreover, a continuous dynamic river network model coupling a one-dimensional hydrodynamic model and four-level fugacity model was established to address the temporal and spatial heterogeneity of pollutants in the river network migration process; then, this model was applied to evaluate two biocides in the Shima River Basin. The model passed calibration and in-field concentration verification tests and yielded satisfactory simulation results. The results of the study showed that the concentration of biocides in the river network during the new crown epidemic was twice that of the non-epidemic period. The concentration of triclosan and triclocarban in the river channel first increased and then decreased with the increase of the river migration distance after STP discharge. The time variation characteristics of the concentrations were affected by the river flow. The biocide concentration in the river network of the low flow upstream area first increased and then decreased, gradually stabilizing in about 20 h. The pollution concentration in the high flow downstream area was increased, and the concentration did not stabilize at 24 h. These results indicate the necessity of evaluating the temporal and spatial characteristics of migration of typical biocides in the river network by stages and time on the premise of distinguishing the flow.

Electrode kinetics of porous Ni-3YSZ cermet operated in fuel cell and electrolysis modes for solid oxide cell application

The electrochemical reactions of hydrogen oxidation and steam reduction have been investigated for a porous cermet electrode made of Ni and 3YSZ. The electrochemical characterizations have been performed over a large range of gas compositions at 700°C. It has been shown that the fuel electrode response is activated by the potential under anodic current while a limiting current density appears under cathodic polarization. Moreover, the impedance diagrams exhibit a shape representative of a kind of finite-length Gerischer element with a low-frequency contribution sensitive to the steam content. To interpret these experimental results, a continuous dynamic model has been developed by describing the mass and charge transfers within the electrode. The reaction has been divided into a sequence of elementary steps considering two scenarios of charge transfer based on the oxygen and hydrogen spillover mechanisms. Three-dimensional reconstructions obtained by synchrotron X-ray nano-holotomography have been used to provide the cermet structural properties for the simulations. The numerical computations have shown that the hydrogen spillover scenario is the most appropriate mechanism to reproduce correctly the experiments. Besides, the electrode response is controlled by the charge transfer at triple phase boundary lengths, the oxygen vacancies migration in the 3YSZ network and a pure chemical surface process depending on the polarization. In fuel cell mode, desorption of water molecules from 3YSZ would co-limit the electrode response, while in electrolysis mode, the steam adsorption on Ni would become one of the rate determining steps. Finally, a sensitivity analysis has shown that surface diffusion would also play a key role in the electrode response.

Continuous Self-Attention Models with Neural ODE Networks

Stacked self-attention models receive widespread attention, due to its ability of capturing global dependency among words. However, the stacking of many layers and components generates huge parameters, leading to low parameter efficiency. In response to this issue, we propose a lightweight architecture named Continuous Self-Attention models with neural ODE networks (CSAODE). In CSAODE, continuous dynamical models (i.e., neural ODEs) are coupled with our proposed self-attention block to form a self-attention ODE solver. This solver continuously calculates and optimizes the hidden states via only one layer of parameters to improve the parameter efficiency. In addition, we design a novel accelerated continuous dynamical model to reduce computing costs, and integrate it in CSAODE. Moreover, since the original self-attention ignores local information, CSAODE makes use of N-gram convolution to encode local representations, and a fusion layer with only two trainable scalars are designed for generating sentence vectors. We perform a series of experiments on text classification, neural language inference (NLI) and text matching tasks. With fewer parameters, CSAODE outperforms state-of-the-art models on text classification tasks (e.g., 1.3% accuracy improved on SUBJ task), and has competitive performances for NLI and text matching tasks as well.

Coupling Epidemiological Models with Social Dynamics.

In this work we study a Susceptible-Infected-Susceptible model coupled with a continuous opinion dynamics model. We assume that each individual can take measures to reduce the probability of contagion, and the level of effort each agent applies can change due to social interactions. We propose simple rules to model the propagation of behaviors that modify the level of effort, and analyze their impact on the dynamics of the disease. We derive a two dimensional set of ordinary differential equations describing the dynamic of the proportion of the number of infected individuals and the mean value of the effort parameter, and analyze the equilibria of the system. The stability of the endemic phase and disease free equilibria depends only on the mean value of the levels of efforts, and not on the initial distribution of levels of effort.

Imitation Learning of Hierarchical Driving Model: From Continuous Intention to Continuous Trajectory

One of the challenges to reduce the gap between the machine and the human level driving is how to endow the system with the learning capacity to deal with the coupled complexity of environments, intentions, and dynamics. In this letter, we propose a hierarchical driving model with explicit models of continuous intention and continuous dynamics, which decouples the complexity in the observation-to-action reasoning in the human driving data. Specifically, the continuous intention module takes perception to generate a potential map encoded with obstacles and intentions. Then, the potential map is regarded as a condition, together with the current dynamics, to generate a continuous trajectory as output by a continuous function approximator network, whose derivatives can be used for supervision without additional parameters. Finally, our method is validated by both datasets and stimulation, demonstrating that our method has higher prediction accuracy of displacement and velocity and generates smoother trajectories. Our method is also deployed on the real vehicle with loop latency, validating its effectiveness. To the best of our knowledge, this is the first work to produce the driving trajectory using a continuous function approximator network. Our code is available at https://github.com/ZJU-Robotics-Lab/CICT.

Dynamical system learning using extreme learning machines with safety and stability guarantees

SummaryThis article presents a continuous dynamical system model learning methodology that can be used to generate reference trajectories for the autonomous systems to follow, such that these trajectories are invariant to a given closed set and uniformly ultimately bounded with respect to an equilibrium point inside the closed set. The autonomous system dynamics are approximated using extreme learning machines (ELM), the parameters of which are learned subject to the safety constraints expressed using a reciprocal barrier function, and the stability constraints derived using a Lyapunov analysis in the presence of the ELM reconstruction error. This formulation leads to solving a constrained quadratic program (QP) that includes a finite number of decision variables with an infinite number of constraints. Theorems are developed to relax the QP with infinite number of constraints to a QP with a finite number of constraints which can be practically implemented using a QP solver. In addition, an active sampling methodology is developed that further reduced the number of required constraints for the QP by only evaluating the constraints at a smaller subset of points. The proposed method is validated using a motion reproduction task on a seven degree‐of‐freedom Baxter robot, where the task space position and velocity dynamics are learned using the presented methodology.

Hybrid Petri nets-based Flow modeling and application on hybrid system.

Flow management is necessary in several application areas, in the optimization of industrial production lines, in IT to manage data flows and in the automation of industrial systems. Physical systems in general consist of continuous processes interacting with discrete processes forming a hybrid dynamic system constituted by continuous dynamic type models and discrete events. The application of the hybrid Petri nets tool in the modeling, study and performance evaluation of these systems helps to analyze the dynamic properties by acting on the parameters and the structure of the models in order to evaluate their behavior. This work is focused on the application of this tool to model a material flow management system between a rotary kiln and a clinker cooler in a production line (cement process). The implementation of the modeling and the analysis of the results obtained by simulation on a software platform (Visual Object Net ++), aims to study industrial processes with mathematical tools and to follow their behavior on software, this allows us an optimal analysis of complex systems in dangerous environments, and to try practical and effective solutions by simple means before moving on to the implementation and programming of actions that require more expensive means.

Hybrid Petri nets-based Flow modeling and application on hybrid system.

Flow management is necessary in several application areas, in the optimization of industrial production lines, in IT to manage data flows and in the automation of industrial systems. Physical systems in general consist of continuous processes interacting with discrete processes forming a hybrid dynamic system constituted by continuous dynamic type models and discrete events. The application of the hybrid Petri nets tool in the modeling, study and performance evaluation of these systems helps to analyze the dynamic properties by acting on the parameters and the structure of the models in order to evaluate their behavior. This work is focused on the application of this tool to model a material flow management system between a rotary kiln and a clinker cooler in a production line (cement process). The implementation of the modeling and the analysis of the results obtained by simulation on a software platform (Visual Object Net ++), aims to study industrial processes with mathematical tools and to follow their behavior on software, this allows us an optimal analysis of complex systems in dangerous environments, and to try practical and effective solutions by simple means before moving on to the implementation and programming of actions that require more expensive means.