Modeling Of Dynamic Systems Research Articles

Dynamic systems modeling of the spallation neutron source cryogenic moderator system to optimize transient control and prepare for power upgrades

Through support of the US Department of Energy’s Office of Basic Energy Sciences, Oak Ridge National Laboratory has begun applying machine learning methods to improve accelerator and target performance of the Spallation Neutron Source (SNS). These methods are being applied to the control optimization and power upgrade of the SNS Cryogenic Moderator System (CMS). A numerical model of the CMS has been developed to study these optimizations and system modifications using EcosimPro. This paper compares steady-state and transient numerical results with experimental data. Control optimization studies focused on dampening mass flow, temperature, and pressure fluctuations during sudden losses of accelerator beam power. This analysis was conducted by adjusting five proportional-integral-derivative controllers connected to four flow control valves and one heater. Future efforts include power uprate studies focused on increasing the CMS cooling capacity. The current accelerator power is 1.4 MW; the first target station is being upgraded to 2.0 MW as part of the Proton Power Upgrade effort. The CMS cooling capacity is sufficient for 2.0 MW operation.

An Implicit Factorized Transformer with Applications to Fast Prediction of Three-dimensional Turbulence

Transformer has achieved remarkable results in various fields, including its application in modeling dynamic systems governed by partial differential equations. However, transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence. In this paper, we propose an implicit factorized transformer (IFactFormer) model, which enables stable training at greater depths through implicit iteration over factorized attention. IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence (HIT), and is shown to be more accurate than the FactFormer, Fourier neural operator (FNO), and dynamic Smagorinsky model (DSM) in the prediction of the velocity spectra, probability density functions of velocity increments and vorticity, temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity. IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT. Furthermore, IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.

Intellectual capital and human resources: A 26-year thematic systematic review

Intellectual capital is the sum of whatever organization resources that contribute to value and competitiveness of a company. Though some metrics have been developed for measuring individual and collective capabilities, from Human Resources point of view, it is difficult to translate the concept of “intellectual capital” into, for example, financial terms. To better understand the field, the aim this study is to draw a thematic analysis on the relations between Intellectual Capital and Human Resources. We provide an overview of publications and their course in this subject. We accessed two widely used databases (Scopus and Web of Science) to produce the review. We set a period of 26 years marked by the subject’s theme entry. In order to handle duplicates, we used RStudio Software and to manage the data we used Bibliometrix package tools, said: biblioshiny and thematic map. Our analysis revealed how intellectual capital and human resources are important for generating value in organizations. Some results explores innovative ways of managing these resources, such as integrating technological, commercial, organizational and cultural aspects, using dynamic systems modeling, investing in long-term strategies and in education and training, and studying the relationship between green intellectual capital and green human resources management.

Plug‐and‐play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

AbstractWe present an algorithm for constructing efficient surrogate frequency‐domain models of (nonlinear) parametric dynamical systems in a non‐intrusive way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach combines rational approximation and smooth interpolation. In the approximation effort, locally adaptive sparse grids are applied to effectively explore the parameter domain even if the number of parameters is modest or high. Adaptivity is also employed to build rational approximations that efficiently capture the frequency dependence of the problem. These two features enable our method to build surrogate models that achieve a user‐prescribed approximation accuracy, without wasting resources in “oversampling” the frequency and parameter domains. Thanks to its non‐intrusiveness, our proposed method, as opposed to projection‐based techniques for model order reduction, can be applied regardless of the complexity of the underlying physical model. Notably, our algorithm for adaptive sampling can be used even when prior knowledge of the problem structure is not available. To showcase the effectiveness of our approach, we apply it in the study of an aerodynamic bearing. Our method allows us to build surrogate models that adequately identify the bearing's behavior with respect to both design and operational parameters, while still achieving significant speedups.

Constructing compartmental models of dynanic systems using a software package for symbolic computation in Julia

This paper considers the problem of constructing compartmental models of dynamic systems by using a software package for symbolic calculation written in Julia. The software package is aimed at unifying the formalized construction of compartmental models, taking into account the meaningful description of possible interactions among compartments and the influence of various factors on the evolution of systems. An approach to the development of the instrumental and methodological basis for modeling the dynamic systems the behavior of which can be described by one-step processes is developed. The proposed software package enables the symbolic representation of the differential equations of the model in both stochastic and deterministic cases. It is implemented in Julia and uses the Julia Symbolics computer algebra library. A comparison between the Julia Symbolics tools and some other computer algebra systems is carried out. The application of the developed software package to a compartmental model is considered. The results can be used to solve problems of constructing and studying dynamic models in natural sciences that are represented by onestep processes.

Robotic and Autonomous Systems (RAS): Dynamic Modeling of Cyber-physical Environments

Dynamic modeling of nonlinear systems in cyber-physical contexts is necessary for understanding and predicting complex behavior. Enabling accurate representation of intricate interactions between cyber and physical components is crucial for enhancing control systems, predicting maintenance requirements, and enhancing resilience. This article presents industrial automation and robotics, taking into account the circumstances in developing economies. The importance of studying and using industrial automation and robotics can be attributed to the complexity of today's industrial setup and the pressing demand for increased production quantity and quality. Finding current initiatives and chances for more research was the aim of the examination. When it reaches innovation maturity, there is a dearth of study on the application and adoption of automation technologies and even less on technology innovation or prototyping. A more recent development has been an increase in the amount of research being done on industrial production technologies, especially additive manufacturing. Research on non-robotic cyber-physical systems, such as IoT connection, drone technologies, and actuator and actuator technologies specifically geared towards the construction industry, is minuscule. This research significantly advances dynamic modeling methodologies by creating a comprehensive and adaptable strategy tailored to the complexities of cyber-physical systems.

Dynamic Systems Modeling and Integrated Transportation Demand-and-Supply Management with a Polynomial Arrival Queue Model

Dynamic Systems Modeling and Integrated Transportation Demand-and-Supply Management with a Polynomial Arrival Queue Model

Constructing Compartmental Models of Dynamic Systems Using a Software Package for Symbolic Computation in Julia

Constructing Compartmental Models of Dynamic Systems Using a Software Package for Symbolic Computation in Julia

Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems

An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems’ transfer functions are rewritten in different barycentric forms using different parametrizations. Loewner-like algorithms are developed for the explicit computation of second-order systems from data based on the developed barycentric forms. Numerical experiments show the performance of these new structured data-driven modeling methods compared to other interpolation-based data-driven modeling techniques from the literature.

Semi-supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary Differential Equations (NODE) have shown promising results by leveraging the expressive power of neural networks to model unknown dynamics. However, these approaches often suffer from limited labeled training data, leading to poor generalization and suboptimal predictions. On the other hand, semi-supervised algorithms can utilize abundant unlabeled data and have demonstrated good performance in classification and regression tasks. We propose TS-NODE, the first semi-supervised approach to modeling dynamical systems with NODE. TS-NODE explores cheaply generated synthetic pseudo rollouts to broaden exploration in the state space and to tackle the challenges brought by lack of ground-truth system data under a teacher-student model. TS-NODE employs an unified optimization framework that corrects the teacher model based on the student's feedback while mitigating the potential false system dynamics present in pseudo rollouts. TS-NODE demonstrates significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.

The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps

Piecewise-smooth maps are used as discrete-time models of dynamical systems whose evolution is governed by different equations under different conditions (e.g. switched control systems). By assigning a symbol to each region of phase space where the map is smooth, any period-p solution of the map can be associated to an itinerary of p symbols. As parameters of the map are varied, changes to this itinerary occur at border-collision bifurcations (BCBs) where one point of the periodic solution collides with a region boundary. It is well known that BCBs conform broadly to two cases: persistence, where the symbolic itinerary of a periodic solution changes by one symbol, and a nonsmooth-fold, where two solutions differing by one symbol collide and annihilate. This paper derives new properties of periodic solutions of piecewise-linear continuous maps on Rn to show that under mild conditions BCBs of mode-locked solutions on invariant circles must be nonsmooth-folds. This explains why Arnold tongues of piecewise-linear maps exhibit a sausage-string structure whereby changes to symbolic itineraries occur at codimension-two pinch points instead of codimension-one persistence-type BCBs. But the main result is based on the combinatorical properties of the itineraries, so the impossibility of persistence-type BCBs also holds when the periodic solution is unstable or there is no invariant circle.

Research on dynamic characteristics of railway side-cracked slab for train-track coupled system

The Ballastless track have been extensively implemented in high-speed railways. However, during the long-term operational process, degradation, such as side crack or defect phenomena produced on the slab inevitably, poses a threat to the stability and the durability of the track structure. Consequently, it is imperative to propose a dynamic approach that can effectively predict the impact of side-cracked slab (SCS) on the vehicle-track coupled system. This paper utilizes co-simulation technology to investigate the dynamic behavior of the slab with and without side crack. Firstly, the dynamic substructure of the finite element model of the SCS is obtained by eigenvalue analysis. Secondly, the SCS model has been applied to the classical vehicle-track coupled dynamic system, and the coupled dynamic model of the train-side cracked slab (TSCS) is established, which considers the multi-rigid-body vehicle subsystem, the flexible rail subsystem, the flexible SCS and subgrade foundation subsystem, and the wheel-rail nonlinear contact model. Later, the accuracy and reliability of the proposed model are verified by the comparison with field tests. Finally, the differences in the vibration characteristics of the vehicle and track structure with and without a side crack are compared and analyzed, and its dynamic stress of the slab as variable train speeds is revealed. The results indicate that the existence of a side crack will reduce the natural frequency of the slab, with a maximum decrease of 22.31%. Although the SCS has a minor effect on the vehicle responses, the existence of a side crack has a significant impact on the slab, especially on the root mean square (RMS) of the vibration acceleration of the slab, with a maximum difference of 74.10% laterally and an increase of 55.16% vertically. Meanwhile, the train speed remarkably affects the crack tip dynamic stress of the SCS, with a maximum increase of 76.07% in the longitudinal direction, 50.34% in the lateral direction and 49.09% in the vertical direction. Higher train speeds will further exacerbate crack propagation under long-term train loading. This study may contribute to the dynamic modeling of TSCS systems and the maintenance of the slab ballastless track.

Discover an accurate approximation of dynamical system without prior information and customized design

Modeling dynamical systems is fraught with challenges when data can be collected but thorough analysis of the mechanism is absent. We design a method to discover unknown dynamical systems from data. The method discovers an accurate approximation of the model without the prior information and the customized design for each problem. The identification steps are straightforward as bringing in the data and then obtaining the model. The method begins with the simple idea that the equations of motion of many practical problems are Riemann integrable functions. For this reason, the Fourier series can decompose the equations of motion. In order to improve the accuracy, we design an extension that helps us to approximate unknown functions by the Fourier series with a high rate of convergence. The idea converts the difficulty of modeling the dynamical system into finding its Fourier series approximation. Convenient procedures enable the modeling of different problems. Numerical examples show that the new method discovers linear and nonlinear dynamical systems in the same steps and without the prior information.

Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct structure-preserving Lagrangian ROMs by projecting the Euler–Lagrange equations of the full-order model (FOM) onto a linear subspace. This Galerkin projection step requires complete knowledge about the Lagrangian operators in the FOM and full access to manipulate the computer code. In contrast, the proposed Lagrangian operator inference approach embeds the mechanics into the operator inference framework to develop a data-driven model reduction method that preserves the underlying Lagrangian structure. The proposed approach exploits knowledge of the governing equations (but not their discretization) to define the form and parametrization of a Lagrangian ROM which can then be learned from projected snapshot data. The method does not require access to FOM operators or computer code. The numerical results demonstrate Lagrangian operator inference on an Euler–Bernoulli beam model, the sine-Gordon (nonlinear) wave equation, and a large-scale discretization of a soft robot fishtail with 779,232 degrees of freedom. The learned Lagrangian ROMs generalize well, as they can accurately predict the physical solutions both far outside the training time interval, as well as for unseen initial conditions.

Dietary mineral intakes predict Coronavirus-disease 2019 (COVID-19) incidence and hospitalization in older adults

BackgroundThe aim of this study was to determine the association between dietary mineral intake and Coronavirus-disease 2019 (COVID-19) infection and its associated hospitalization.MethodsThis cohort study utilized the MASHAD study population, which comprised individuals aged 35–65. Upon recruitment in 2007, dietary intake was documented using a validated 65-item food frequency questionnaire (FFQ). Data on COVID-19 PCR test results was collected from all relevant medical centers in Mashhad between February 2020 and June 2022. The regression model included dietary minerals and employed the backward variable selection method, along with advanced data analysis techniques.ResultsThe final analysis involved 1957 participants, including 193 COVID-19-positive patients. The mean age was 49.71 and 50.28 years in the COVID-19-positive and negative groups, respectively (p = 0.12). Dietary intakes of magnesium, iron, and potassium were notably lower in COVID-19-positive patients (P < 0.05). Following adjustments for age and sex, dietary iron remained significantly associated with COVID-19 incidence (OR = 0.94, 95% CI: 0.90–0.98). Furthermore, a statistically significant relationship was observed between dietary zinc and hospitalization due to COVID-19 (OR = 0.69, 95% CI: 0.51–0.93). In dynamical system models, intakes of calcium, zinc, and iron below the cut-offs of 1138, 9.7, and 8.17 mg/day, respectively, were linked to an increased risk of COVID-19 incidence.ConclusionHigher dietary iron and zinc intake are associated with decreased risk of COVID-19 infection and hospitalization, respectively.

Learning physics-based reduced-order models from data using nonlinear manifolds.

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

Mathematical modeling of dynamic processes of agricultural mobile energy vehicles on an electric drive

The article considers the issues of modeling the processes of agricultural mobile energy vehicles (MEV) with electric drive (ED). A review of modern literature on the problem under study as well as questions on modeling the functional properties of mobile machines and improving the quality indicators of MEV work are presented. A mathematical model of the motion of the MEV with an electric motor is presented, as well as a description of the method used and a sequence of actions for conducting research. Preliminary theoretical studies of motion in different modes of operation have been carried out. The proposed model is convenient for implementation and calculation in any of the applied software products that support the modeling of dynamic systems with an electromechanical drive. The proposed model, the solution of which is based on the methods of numerical integration of systems in the Matlab Simulink software environment, made it possible to simulate the dynamic processes of electromechanical power transmission of MEV during various agricultural operations. With the help of this model, the analysis of electromechanical processes in transient and steady-state operating modes, as well as dynamic processes in the power transmission were carried out. Graphs of changes in the studied parameters of the MEV power transmission are obtained and elastic moments in the joints of the 5-mass design scheme are determined. The use of the model allows you to track the change in statistical characteristics when the conditions of the experiment change. The model has shown its operability when performing simulation of agricultural operations: fertilization, cultivation and sowing, and it can be used at the design stage to study the characteristics of dynamic processes of small-class traction MEV power transmissions with an electromechanical drive. With different parameters of the model, there is a change in the mathematical expectation of the angular velocity of the ED from 147.89 to 156.87 rad/s, a change in the mathematical expectation of the speed of the MES from 4.51 to 4.79 m/s.

AI Institute in Dynamic Systems: Developing machine learning and AI tools for scientific discovery, engineering design, and data‐driven control

AbstractThe mission of the AI Institute in Dynamic Systems is to develop the next generation of advanced machine learning (ML) and AI tools for controlling complex physical systems by discovering physically interpretable and physics‐constrained data‐driven models through optimal sensor selection and placement. The research effort is anchored by a common task framework (CTF) that evaluates the performance of ML algorithms, architectures, and optimization schemes for the diverse tasks required in engineering applications. The aim is to push beyond the boundaries of modern techniques by closing the loop between data collection, control, and modeling, creating a unique and cross‐disciplinary architecture for learning physically interpretable and physics constrained models of complex dynamic systems from time series data. The CTF further supports sustainable and open‐source challenge datasets, which are foundational for developing interpretable, ethical, and inclusive tools to solve problems fundamental to human safety, society, and the environment.

WyNDA: A method to discover mathematical models of dynamical systems from data

This paper introduces a novel method called Wide-Array of Nonlinear Dynamics Approximation (WyNDA) for extracting mathematical models of dynamical systems from data. A key advantage of this method over existing approaches lies in its suitability for online implementation. Moreover, WyNDA stands out by not relying on optimization or machine learning, ensuring computational efficiency. The fundamental concept revolves around approximating the unknown function of a dynamical system through a diverse set of basis functions that encapsulate the available data. An adaptive observer is then employed to iteratively refine this approximation and estimate the associated parameters. The efficacy of the proposed method is demonstrated through numerical simulations encompassing linear systems, nonlinear systems, and control systems. The results underscore the method’s ability to successfully unveil the governing equations of dynamical systems, highlighting its potential for extracting intricate system dynamics from observational data.•WyNDA represents a novel approach for uncovering mathematical models of dynamical systems from data.•Utilizing a series of basis functions, WyNDA effectively approximates the unknown structure inherent in dynamical systems.•The validation of WyNDA involves benchmark equations of dynamical systems, confirming its efficacy in diverse scenarios.