Modeling Of Dynamic Systems Research Articles

Invariant forms and control dimensional parameters in complexity quantification

Non-equilibrium dynamics is omnipresent in nature and technology and can exhibit symmetries and order. In idealistic systems this universality is well-captured by traditional models of dynamical systems. Realistic processes are often more complex. This work considers two paradigmatic complexities—canonical Kolmogorov turbulence and interfacial Rayleigh-Taylor mixing. We employ symmetries and invariant forms to assess very different properties and characteristics of these processes. We inter-link, for the first time, to our knowledge, the scaling laws and spectral shapes of Kolmogorov turbulence and Rayleigh-Taylor mixing. We reveal the decisive role of the control dimensional parameters in their respective dynamics. We find that the invariant forms and the control parameters provide the key insights into the attributes of the non-equilibrium dynamics, thus expanding the range of applicability of dynamical systems well-beyond traditional frameworks.

On the adaptation of recurrent neural networks for system identification

This paper presents a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network (RNN) models of dynamical systems. A nominal RNN model is first identified using available measurements. The system dynamics are then assumed to change, leading to an unacceptable degradation of the nominal model performance on the perturbed system. To cope with the mismatch, the model is augmented with an additive correction term trained on fresh data from the new dynamic regime. The correction term is learned through a Jacobian Feature Regression (JFR) method defined in terms of the features spanned by the model’s Jacobian with respect to its nominal parameters. A non-parametric view of the approach is also proposed, which extends recent work on Gaussian Process (GP) with Neural Tangent Kernel (NTK-GP) to the RNN case (RNTK-GP). This can be more efficient for very large networks or when only few data points are available. Implementation aspects for fast and efficient computation of the correction term, as well as the initial state estimation for the RNN model are described. Numerical examples show the effectiveness of the proposed methodology in presence of significant system variations.

Some thoughts on dynamic systems modeling of L2 learning

The aim of this article is to present a very basic dynamic systems model of L2 learning based on a number of basic principles 1) at any moment in time, a learner’s L2 proficiency is a distribution of potentialities (possible levels of L2 production), 2) the distribution changes as a result of experienced L2-events such as conversations, 3) L2 proficiency and L2 events are represented on the same underlying array of linguistic proficiency (from 0, i.e., inexistent, to 1, i.e., maximal under the currently available linguistic resources); 4) learning processes are “normative” in the sense that they are governed by a process of convergence on the language spoken by a particular L2 community, this process depends on an optimum between familiarity and novelty; 5) the parameters governing the systems dynamic differ among individual learners and L2 learning contexts (e.g., highly adaptive versus non-adaptive communicative interactions with native L2 speakers).

GLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

MULTI-MOTOR DRIVE NON-PARAMETRIC BLACK-BOX FUZZY MODEL

The multi-motor drives, the typical examples of which are continuous lines (CL) for tension processing of various materials are complex and coupled MIMO higher-order nonlinear systems, which parameters are difficult to identify. The article focuses on a method for the design of a non-parametric black-box fuzzy model of a continuous production line with emphasis on minimal knowledge on the modelled system. The proposed fuzzy model structure is based on the state space representation of the dynamic system in discrete form, which only requires a suitable set of information on its input/output relations. The properties of the proposed CL fuzzy model were verified by experimental measurements on a CL laboratory model. The obtained results have confirmed the rightness and effectiveness of the fuzzy model design method that can be applied not only in the field of industry technologies with CL but also in modeling and control of nonlinear dynamic systems.

Evaluation of Equivalent Dynamic Active Distribution Network Models with Individual and Aggregated Consideration of Grid Forming Converters

Detailed active distribution network modeling in the context of stability studies of future power systems can be avoided by applying complexity‐reduced equivalent dynamic models. Previous work developed an approach to derive such equivalent dynamic network models of systems dominated by grid following and grid forming converters. Nevertheless, this approach lacks an investigation of the aggregation of multiple grid forming converters to one equivalent component. Also, the approach needs to be evaluated for a closed ring topology to substantiate its validity independent of the detailed network topology. This work applies and validates the developed approach on active distribution networks in the context of three scenarios. The detailed and equivalent network models are simulated for three events and the results are used to compare the models with respect to accuracy and complexity. The derived equivalent dynamic network models with an individual representation of grid forming converters reproduce the dynamic behavior of the corresponding detailed networks very well. The aggregation of grid forming converters results in an adequate reproduction of the detailed network's dynamic behavior under the constraint of aggregating only neighboring grid forming converters of one branch. This allows for the consideration of the detailed network's topology in the corresponding equivalent dynamic model.

Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

A continuous-time dynamical system with parameter varepsilon is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as varepsilon approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

Drag crisis analysis of a high-altitude balloon in critical transition

Drag coefficient is one of the crucial parameters in the dynamic modeling of position control systems for high-altitude super-pressure balloons. Numerical simulations with Transition SST model are conducted to analyze the drag characteristics of a typical shape of super-pressure balloons. A series of the freestream Reynolds numbers in the range of 103 to 107 are considered, covering the subcritical, critical, and supercritical regimes of the flow transition. The relationship of the drag coefficient to the Reynolds number is obtained to present the drag crisis in the critical regime. The precipitous drop of the drag coefficient is observed as the Reynolds number increases. Accordingly, a fitted formula of the drag coefficient with respect to the Reynolds number is proposed, which is able to effectively predict the drag coefficient in the critical regime. Complex Flow phenomena at the critical Reynolds number are further analyzed by the flowfield and wall properties around the balloon. Flow transition is observed at the flat top area and the leeward side. Downstream of the transition, the flow separation occurs with the formation of a separation bubble. In the transition regions, substantial changes in pressure and skin friction coefficients are demonstrated.

Anxiety and depression: A top-down, bottom-up model of circuit function.

A functional interplay of bottom-up and top-down processing allows an individual to appropriately respond to the dynamic environment around them. These processing modalities can be represented as attractor states using a dynamical systems model of the brain. The transition probability to move from one attractor state to another is dependent on the stability, depth, neuromodulatory tone, and tonic changes in plasticity. However, how does the relationship between these states change in disease states, such as anxiety or depression? We describe bottom-up and top-down processing from Marr's computational-algorithmic-implementation perspective to understand depressive and anxious disease states. We illustrate examples of bottom-up processing as basolateral amygdala signaling and projections and top-down processing as medial prefrontal cortex internal signaling and projections. Understanding these internal processing dynamics can help us better model the multifaceted elements of anxiety and depression.

V Workshop on Modeling and Simulation for Science and Engineering

This volume presents the written contributions of the participants of the V Workshop on Modeling and Simulation for Science and Engineering (V WMSSE) which was held from July 25 to 26, 2022, at the Bogotá city, Colombia, organized by the Foundation Of Researchers In Science And Technology Of Materials (FORISTOM).The Proceedings volume includes 12 manuscripts that were presented as plenary talks at the conference; the abstracts of all participants’ contributions were published in the Book with ISSN 2745-1496. The website of the conference is available at https://foristom.org/5wmsse.The two-day scientific program of the V WMSSE consisted of 5 plenary lectures, 12 oral on-site presentations, and 26 virtual presentations, with the participation of undergraduate and graduate students, professors, researchers, and entrepreneurs from Spain, Mexico, Uruguay, Brazil, Ecuador, and Colombia.Likewise, the main aim of V WMSSE was to bring together national and international researchers in order to show scientific progress and to highlight the strong correlation of research in modeling and simulation on science, engineering, nanotechnology, and industrial applications; besides, to promote the exchange of creative ideas and the effective transfer of scientific knowledge, from fundamental research to innovation applied to industrial solutions with of purpose to advance in the development of the society by means of efficient transference of the knowledge between sectors academia and industry.All papers in these Proceedings volume refer to one of the following topics covered in the V WMSSE:✓ Computer Science.✓ Mechatronic Systems.✓ Dynamic Systems Modeling.✓ Physical-Chemistry Modeling.✓ Physics-Mathematical Modeling.✓ Modeling, Simulation, and Diagnostics.✓ Education on Science, Engineering, and Technology.On behalf of the organizing committee of the V WMSSE, we are extremely thankful to all authors and participants for providing their valuable contributions for this Proceedings volume as well as the reviewers for their constructive recommendations and criticism aiding to improve the presented articles.List of Organizing Committee, National Scientific Committee, International Scientific Committee, Invited Speakers, Sponsor, Partners are available in this Pdf.

A quadratic decoder approach to nonintrusive reduced‐order modeling of nonlinear dynamical systems

AbstractLinear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection‐dominated problems. Nonlinear approaches have shown to outperform linear methods in terms of dimension reduction versus accuracy but, typically, come with a large computational overhead. In this work, we consider a quadratic reduction scheme which induces nonlinear structures that are well accessible to tensorized linear algebra routines. We discuss that nonintrusive approaches can be used to simultaneously reduce the complexity in the equations and propose an operator inference formulation that respects dynamics on nonlinear manifolds.

Learning a Low-Dimensional Representation of a Safe Region for Safe Reinforcement Learning on Dynamical Systems.

For the safe application of reinforcement learning algorithms to high-dimensional nonlinear dynamical systems, a simplified system model is used to formulate a safe reinforcement learning (SRL) framework. Based on the simplified system model, a low-dimensional representation of the safe region is identified and used to provide safety estimates for learning algorithms. However, finding a satisfying simplified system model for complex dynamical systems usually requires a considerable amount of effort. To overcome this limitation, we propose a general data-driven approach that is able to efficiently learn a low-dimensional representation of the safe region. By employing an online adaptation method, the low-dimensional representation is updated using the feedback data to obtain more accurate safety estimates. The performance of the proposed approach for identifying the low-dimensional representation of the safe region is illustrated using the example of a quadcopter. The results demonstrate a more reliable and representative low-dimensional representation of the safe region compared with previous works, which extends the applicability of the SRL framework.

Computer Model of Pump–Well–Reservoir System Based on the New Concept of Imitational Modeling of Dynamic Systems

Computer Model of Pump–Well–Reservoir System Based on the New Concept of Imitational Modeling of Dynamic Systems

UNCERTAINTY VISUALIZATION FOR CHARACTERIZING HETEROGENEOUS HUMAN BEHAVIORS IN DISCRETE DYNAMICAL SYSTEM MODELS

When modeling human behavior in multi-player games, it is important to understand heterogeneous aspects of player behaviors. By leveraging experimental data and agent-based simulations, various data-driven modeling methods can be applied. This provides a great opportunity to quantify and visualize the uncertainty associated with these methods, allowing for a more comprehensive understanding of the individual and collective behaviors among players. For networked anagram games, player behaviors can be heterogeneous in terms of the number of words formed and the amount of cooperation among networked neighbors. Based on game data, these games can be modeled as discrete dynamical systems characterized by probabilistic state transitions. In this work, we present both Frequentist and Bayesian approaches for visualizing uncertainty in networked anagram games. These approaches help to elaborate how players individually and collectively form words by sharing letters with their neighbors in a network. Both approaches provide valuable insights into inferring the worst, average, and best player performance within and between behavioral clusters. Moreover, interesting contrasts between the Frequentist and Bayesian approaches can be observed. The knowledge and inferences gained from these approaches are incorporated into an agent-based simulation framework to further demonstrate model uncertainty and players’ heterogeneous behaviors.

A variational Bayesian inference technique for model updating of structural systems with unknown noise statistics

Dynamic models of structural and mechanical systems can be updated to match the measured data through a Bayesian inference process. However, the performance of classical (non-adaptive) Bayesian model updating approaches decreases significantly when the pre-assumed statistical characteristics of the model prediction error are violated. To overcome this issue, this paper presents an adaptive recursive variational Bayesian approach to estimate the statistical characteristics of the prediction error jointly with the unknown model parameters. This approach improves the accuracy and robustness of model updating by including the estimation of model prediction error. The performance of this approach is demonstrated using numerically simulated data obtained from a structural frame with material non-linearity under earthquake excitation. Results show that in the presence of non-stationary noise/error, the non-adaptive approach fails to estimate unknown model parameters, whereas the proposed approach can accurately estimate them.

Full Bayesian identification of linear dynamic systems using stable kernels

System identification learns mathematical models of dynamic systems starting from input-output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.

Dynamic energy flow analysis of electricity-heating based integrated energy system

With the development of integrated energy system, energy flow analysis of coupling energy network has attracted much attention. In this study, based on the unified energy path theory, energy flow analysis of electricity-heating coupled energy system is implemented considering different time characteristic of each system. Considering the instantaneous change process of heat transfer in the heating system, the dynamic model of heat network is constructed based on unified energy path theory. On this basis, the dynamic models of electric and heating systems are coupled, and the dynamic energy flow calculation method of the coupling system is proposed. Through a case study, the feasibility of the proposed model and calculation method are verified. In addition, the effect of heat source on the dynamic process of heat transfer in the heating system is analyzed.

Fuzzy Graph Modeling and Clustering Analysis of Nonlinear Dynamical Systems

Analyzing stability and designing control strategies for interconnected nonlinear dynamical systems poses mathematical challenges due to combinatorial growth in complexity. This paper develops a methodology integrating fuzzy graph theory with spectral clustering techniques to enable tractable certification of stability properties. Fuzzy similarity relations between state variables model imprecise couplings within the nonlinear dynamics. Representing these relations through graph adjacency matrices facilitates partitioning strongly connected states using spectral algorithms. Stability of the overall fuzzy state graph is inferred from the spectral radii of decoupled fuzzy subgraphs. The graph-theoretic abstraction provides a coarse-grained lens into nonlinear stability properties while circumventing computational barriers. The fuzzy graph modeling and spectral partitioning pipeline ultimately streamlines control synthesis targeting local clustered subdynamics. Case studies on power network stabilization, swarm navigation, and process operations showcase scalable applications to high-dimensional complex systems. The integrated fuzzy graph and spectral clustering approach provides a systematic toolkit for analysis and control of heavily interconnected nonlinear dynamical systems across engineering domains.

Gait optimization and energy-based stability for biped locomotion using large-scale programming

AbstractThis paper presents a gait optimization method to generate the locomotion pattern for biped and discuss its stability. The main contribution of this paper is a newly proposed energy-based stability criterion, which permits the dynamic stable walking and could be straight-forwardly generalized to different locomotion scenarios and biped robots. The gait optimization problem is formulated subject to the constraints of the whole-body dynamics and kinematics. The constraints are established based on the modelling of bipedal hybrid dynamical systems. Following the whole-body modelling, the system energy is acquired and then applied to create the stability criterion. The optimization objective is also established on the system energy. The gait optimization is solved by being converted to a large-scale programming problem, where the transcription accuracy is improved via the spectral method. To further reduce the dimensionality of the large-scale problem, the whole-body dynamics is re-constructed. The generalization of the optimized gait is improved by the design of feedback control. The optimization examples demonstrate that the stability criterion naturally leads to a cyclic biped locomotion, though the periodicity was not previously imposed. Two simulation cases, level ground walking and slope walking, verify the generalization of the stability criterion and feedback control. The stability analyses are carried out by investigating the motions of centre of gravity and centre of pressure. It is revealed that if the tracked speed is above 0.3 m/s or the biped accelerates/climbs the slope, the stability criterion accomplishes the dynamic stable walking, where zero moment point criterion is not strictly complied.

Variations of Rotating Savings and Credit Associations for Community Development

Informal financial cooperation strategies have emerged as a solution to improve the resilience of low-income communities, being one of the most popular ones the rotating savings and credit associations (ROSCAs). In this article, using computational tools and dynamical systems modeling, we study the performance of two variations of ROSCAs that can potentially increase the resilience of communities. First, we propose a strategy that saves a percentage of the contributions of each member of the ROSCA to reduce the impact of individuals who stop contributing to the association and study how this strategy impacts the financial life of the individuals and trust among community members. Second, we study a decentralized version of the ROSCA in which individuals contribute to more than one association and analyze the impact of the size of the cooperation scheme and the number of associations where each individual participates. Through mathematical and simulation analyses, we show how the cooperation strategies impact the resilience of low-income communities.