Analysis Of Dynamical Systems Research Articles

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

Experimental Proof of Concept for Using Hybrid Paper Based on Silver Nanowires, Cellulose and Poly(dimethylsiloxane) in Systems Dynamic Analysis and Healthcare Applications

The research results and evaluation of the applicability of the original composition of hybrid paper based on silver nanowires (AgNWs), cellulose pulp (CP), and carbon nanotubes (CNTs) are presented and discussed. The material tested was used to manufacture sensors for mechanical deformation resulting from external influences or related to human activity interactions. The sensors were fabricated using an AgNWs + CP suspension and additives by the vacuum filtration method. The substrate obtained was machined and then laminated with a layer of poly(dimethylsiloxane) (PDMS). The recorded responses to selected types of imposed mechanical interactions in the form of changes in the relative resistance of the sensor throughout the tests showed a close cause-and-effect relationship. The response of the tested systems when applying an alternating magnetic field was also observed. The results indicate that the proposed solutions can find application in the monitoring of mechanical interactions resulting from the dynamic behavior of physical objects, as well as derived from selected human vital functions.

Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

DYNAMIC ANALYSIS OF SEITR MATHEMATICAL MODEL ON THE SPREAD OF HEPATITIS B DISEASE IN AMBON CITY

Hepatitis B is a disease caused by infection with the HBV (Hepatitis B Virus) virus that commonly infects the liver and can develop into liver cancer. The disease can be transmitted through blood, semen, breast milk, saliva, vaginal fluids, and sperm. One effective way to prevent Hepatitis B disease is by vaccination. This study will construct a mathematical model, such as the SEITR model, to study the spread of Hepatitis B disease in Ambon City. The SEITR epidemic model is a disease spread model that divides the population into five subpopulation classes, namely the susceptible individual subpopulation class, the exposed individual subpopulation class, the infected individual subpopulation class, the treatment individual subpopulation class, and the recovered individual subpopulation class. Based on the dynamic system analysis conducted, two equilibrium points were obtained, namely the disease-free equilibrium point and the endemic equilibrium point. In addition, based on the data and simulation results, it can be concluded that the spread of Hepatitis B in Ambon City depends on the transmission rate from infected individuals to susceptible individuals

Dynamical stability and phase space analysis of an emergent Universe with non-interacting and interacting fluids

Abstract We investigate the evolution of a flat Emergent Universe obtained with a non-linear equation of state (nEoS) in Einstein’s general theory of Relativity. The nEoS is equivalent to three different types of barotropic cosmic fluids, which are found from the nEoS parameter. The EU began expanding initially with no interactions among the cosmic fluids. However, one can assume an interaction that sets in at a time t ⩾ t i in the cosmic fluids, we study the evolution of the EU that accommodates the present observed Universe. We adopt dynamical system analysis to study the critical points of the autonomous system and the evolutionary behavior of an EU with or without interaction among the cosmic fluid components. We also study the stability of critical points and plot the phase portraits. The density parameters and the corresponding cosmological parameters are determined for both the non-interacting and interacting phases of the evolutionary dynamics of the Universe.

Dynamic response and stability analysis of vehicle systems with double time-delay feedback control

In this paper, the vehicle suspension dynamic response of time delay feedback control is analyzed considering the suspension of the seat. An active suspension vibration reduction control method based on double time-delay feedback control is proposed to further improve the ride comfort. Firstly, the double time-delay dynamic response equation of the system with three degrees of freedom is established. Then, the root mean square values of seat acceleration and body acceleration are used as the objective functions. Meanwhile, the RMS values of suspension dynamic deflection and tire dynamic displacement are used as constraints, and the optimal feedback parameters are obtained using particle swarm optimisation. The Routh-Hurwitz criterion and frequency domain scanning methods are used to verify the stability of the double time-delay system. Finally, simulation in the time domain and frequency domain is accomplished. It is verified that this feedback control method has strong robustness and anti-interference ability.

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Extension of dual equivalent linearization to analysis of deterministic dynamic systems: Part 2—multi-parameter equivalent linearization

Dynamic analysis of an infected predator-prey system with prey herd behavior

ABSTRACT To protect themselves from predation, sometimes prey starts roaming in groups and shows herd behavior. This paper addresses the predator-prey system dynamics with prey herd behavior and infection in predators. We explore the conditions under which all equilibria exist and the stability of each equilibrium point of the system. The outcomes of this work suggest that prey herd behavior is beneficial for the prey population when the predators are diseased. Under suitable conditions, the three populations can coexist and maintain the ecological balance of nature.

Observational constrained Weyl type [formula omitted] gravity cosmological model and the dynamical system analysis

Using the cosmological date sets, the cosmological parameters are constrained in this paper, with well known phantom behavioural Hubble parameter. To understand the dynamics of the Weyl type f(Q,T) gravity, functional form of f(Q,T) has been introduced, where Q and T respectively represents the nonmetricity scalar that depends on the Weyl vector (Q=−6w2) and trace of energy–momentum tensor. Using the constrained values of the parameters, the other geometrical parameters are analysed and the accelerating behaviour has been shown. The dynamical parameters and energy conditions are also analysed. Further to get the complete evolutionary behaviour of the Universe, the dynamical system analysis has been performed.

Investigation of the dynamic characteristics of the pneumatic-mechanical drive of the installation movements of machine mechanisms

The creation of new and improvement of existing machines and mechanisms requires the development of drive engineering and the creation of new drive systems capable of competing with currently known circuit solutions. Under these conditions, the creation of combined pneumatic-mechanical drives is an important scientific and technical task. The purpose of this work is to increase the speed at a given accuracy of auxiliary movements of the target mechanisms of technological machines by creating a pneumatic-mechanical drive with improved energy and dynamic characteristics. The technical solution of a positioning pneumatic-mechanical drive of executive movements of technological equipment is presented, mathematical and computer models are developed. In this case, the method of solving the differential equation in the SimInTech program is used. As a result, an oscillogram of transients is obtained. The developed models allow for dynamic analysis of pneumatic-mechanical systems.

Dynamical system analysis of quintessence dark energy model

Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables, the evolution equations are reduced to an autonomous system for exponential form of the scalar potential. The critical points are analyzed with center manifold theory and stability has been discussed by using Schwarzian derivative. Finally, cosmological implications of the critical points are discussed and it is found that the stability of the late-time attractor changes for quintessence dark energy model.

Dynamic performance analysis of a new low-temperature nuclear heating system with APROS

ABSTRACT Pool-type low-temperature heating reactor (PLTHR) has attracted considerable attention throughout the world due to its low operating parameters and satisfactory inherent safety in district heating. Exploring the dynamic performance of PLTHR is a prerequisite for designing control systems and developing operation strategies. Until now, the dynamic performance of the district heating system using a 400 MW pool-type low-temperature heating reactor (DHR-400) has not been fully discussed. Based on APROS software, a precise dynamic model for DHR-400 is constructed in this paper. The dynamic responses of DHR-400 under five external variables such as control rod reactivity, first loop flow rate, second loop flow rate, third loop flow rate, and return temperature at the third loop are investigated. The results revealed that the core power variation is not linear with the flow rate variation at the three loops. Core power variations are −16.27, −14.04, and −20.96 MW with a 30% reduction in flow rate at the first loop, the second loop, and the third loop, respectively. Considering safe operation, when there are minor fluctuations in the heating demand, the core power regulation method by adjusting the third loop’s flow rate should be given priority without altering the position of the control rods.

Dynamic analysis of spindle-bearing system considering bearing wear evolution

Dynamic analysis of spindle-bearing system considering bearing wear evolution

Photonic next-generation reservoir computer based on distributed feedback in optical fiber.

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the Rössler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, we show that it is possible to scale to high-dimensional systems while maintaining low latency and low power consumption.

A Survey on Energy Methods for Vibroacoustic Analysis of Random Dynamic Systems and Applications

Abstract Engineering can be considered a field of applied physics, as for the design of dynamic systems several aspects such as the strength, parameters of motion, among others, must be estimated for dimensioning, specifications of construction procedures, and operation. In the search for an appropriate model to estimate the dynamic response of a system to a prescribed input, several energy-based methods have been explored over the last decades to address three main issues. Firstly, it is quite rare that a solution for a purely analytical model exists, particularly for complex built-up structures. Secondly, numerical approaches to solve such complex equations of motion of a structure are computationally expensive. Lastly, even if a numerical or analytical solution can be found, there is no warranty that such estimation would be true for an ensemble of nominally identical built-up systems due to uncertainties that are not usually considered by the models. The aim of this work is to present a survey of existing approaches based on equations of energy rather than motion to simplify the computational process and include the effects of uncertainties in the dynamic response, and improvements to such models in regard of other engineering aspects. Additionally, several engineering applications are presented.

Stability analysis of discrete dynamical system using khan-iteration technique

Stability analysis of discrete dynamical system using khan-iteration technique

Dynamical heterogeneity and universality of power-grids

Electric power systems during transient states are extensively investigated using variations of the Kuramoto model to analyze their dynamic behavior. However, the majority of current models fail to capture the physics of power flows and the heterogeneity of the grids under study. This study addresses this gap by comparing the levels of heterogeneity in continent-sized power grids in Europe and North America to reveal the underlying universality and heterogeneity of grid frequencies, electrical parameters, and topological structures. Empirical data analysis of grid frequencies from the Hungarian grid indicates that q-Gaussian distributions best fit simulations, with spatio-temporally correlated noise evident in the frequency spectrum. Comparing European and North American power grids reveals that employing homogeneous transmission capacities to represent power lines can lead to misleading results on stability, and nodal behavior is heterogeneous. Community structures of the continent-sized grids are detected, demonstrating that Chimera states are more likely to occur when studying only subsystems. A topographical analysis of the grids is presented to assist in selecting such subsystems. Finally, synchronization calculations are provided to illustrate the occurrence of Chimera states. The findings underscore the necessity of heterogeneous grid models for dynamic stability analysis of power systems.

Flexible multitask computation in recurrent networks utilizes shared dynamical motifs

Flexible computation is a hallmark of intelligent behavior. However, little is known about how neural networks contextually reconfigure for different computations. In the present work, we identified an algorithmic neural substrate for modular computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses revealed learned computational strategies mirroring the modular subtask structure of the training task set. Dynamical motifs, which are recurring patterns of neural activity that implement specific computations through dynamics, such as attractors, decision boundaries and rotations, were reused across tasks. For example, tasks requiring memory of a continuous circular variable repurposed the same ring attractor. We showed that dynamical motifs were implemented by clusters of units when the unit activation function was restricted to be positive. Cluster lesions caused modular performance deficits. Motifs were reconfigured for fast transfer learning after an initial phase of learning. This work establishes dynamical motifs as a fundamental unit of compositional computation, intermediate between neuron and network. As whole-brain studies simultaneously record activity from multiple specialized systems, the dynamical motif framework will guide questions about specialization and generalization.

A dynamical system analysis of bouncing cosmology with spatial curvature

A dynamical system analysis of bouncing cosmology with spatial curvature