Modeling Of Dynamic Systems Research Articles

Respiratory Diseases Prediction from a Novel Chaotic System

Pandemics can have a significant impact on international health systems. Researchers have found that there is a correlation between weather conditions and respiratory diseases. This paper focuses on the non-linear analysis of respiratory diseases and their relationship to weather conditions. Chaos events may appear random, but they may actually have underlying patterns. Edward Lorenz referred to this phenomenon in the context of weather conditions as the butterfly effect. This inspired us to define a chaotic system that could capture the properties of respiratory diseases. The chaotic analysis was performed and was related to the difference in the daily number of cases received from real data. Stability analysis was conducted to determine the stability of the system and it was found that the new chaotic system was unstable. Lyapunov exponent analysis was performed and found that the new chaotic system had Lyapunov exponents of (+, 0, -, -). A dynamic neural architecture for input-output modeling of nonlinear dynamic systems was developed to analyze the findings from the chaotic system and real data. A NARX network with inputs (maximum temperature, pressure, and humidity) and one output was used to to overcome any delay effects and analyze derived variables and real data (patients number). Upon solving the system equations, it was found that the correlation between the daily predicted number of patients and the solution of the new chaotic equation was 90.16%. In the future, this equation could be implemented in a real-time warning system for use by national health services.

Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results

This paper discusses recent developments in the data-based modeling and control of nonlinear chemical process systems using sparse identification of nonlinear dynamics (SINDy). SINDy is a recent nonlinear system identification technique that uses only measurement data to identify model dynamical systems in the form of first-order nonlinear differential equations. In this work, the challenges of handling time-scale multiplicities and noisy sensor data when using SINDy are addressed. Specifically, a brief overview of novel methods devised to overcome these challenges are described, along with modeling guidelines for using the proposed techniques for process systems. When applied to two-time-scale systems, to overcome model stiffness, which leads to ill-conditioned controllers, a reduced-order modeling approach is proposed where SINDy is used to model the slow dynamics, and nonlinear principal component analysis is used to algebraically “slave” the fast states to the slow states. The resulting model can then be used in a Lyapunov-based model predictive controller with guaranteed closed-loop stability provided the separation of fast and slow dynamics is sufficiently large. To handle high levels of sensor noise, SINDy is combined with subsampling and co-teaching to improve modeling accuracy. The challenges of modeling and controlling large-scale systems using noisy industrial data are then addressed by using ensemble learning with SINDy. After summarizing the advances, a nonlinear chemical process is used to provide an end-to-end demonstration of process modeling using sparse identification with guidelines for chemical engineering practitioners. Finally, several future research directions for the incorporation of SINDy into process systems engineering are proposed.

Methods of numerical analysis for some integral dynamical systems with delay arguments

The aim of this work is to construct direct and iterative numerical methods for solving functional equations with hereditary components. Such equations are a convenient tool for modeling dynamical systems. In particular, they are used in population models structured by age with a finite life span. Models based on integro-differential and integral equations with various kinds of delay arguments are considered. For nonlinear equations, the operators are linearized according to the modified Newton-Kantorovich scheme. Direct quadrature and simple iteration methods are used to discretize linear equations. These methods are constructed in the paper: an iterative method for solving a nonlinear integro-differential equation on the semiaxis (−∞,0] , a direct method for solving the signal recovery problem, and iterative methods for solving a nonlinear Volterra integral equation with a constant delay. Special quadrature formulas based on orthogonal Lagger polynomials are used to approximate improper integrals on the semiaxis. The results of numerical experiments confirm the convergence of suggested methods. The proposed approaches can also be applied to other classes of nonlinear equations with delays.

Differential Elimination for Dynamical Models via Projections with Applications to Structural Identifiability

Elimination of unknowns in a system of differential equations is often required when analyzing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from the literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available online as a Julia package.

A deep generative framework for data-driven surrogate modeling and visualization of parameterized nonlinear dynamical systems

A deep generative framework for data-driven surrogate modeling and visualization of parameterized nonlinear dynamical systems

Data-Driven pH Model in Raceway Reactors for Freshwater and Wastewater Cultures

The industrial production of microalgae is a process as sustainable as it is interesting in terms of its diverse applications, especially for wastewater treatment. Its optimization requires an exhaustive knowledge of the system, which is commonly achieved through models that describe its dynamics. Although not widely used in this field, artificial neural networks are presented as an appropriate technique to develop this type of model, having the ability to adapt to complex and nonlinear problems solely from the process data. In this work, neural network models have been developed to characterize the pH dynamics in two different raceway reactors, one with freshwater and the other with wastewater. The models are able to predict pH profiles with a prediction horizon of up to eleven hours and only using available measurable process data, such as medimum level, CO2 injection, and solar radiation. The results demonstrate the potential of artificial neural networks in the modeling of continuous dynamic systems in the field of industry, obtaining accurate, fast-running models that can adapt to different circumstances. Moreover, these models open the field to the design of data-driven model-based control algorithms to account for the nonlinear dynamics of this biological system.

Neural network modeling and dynamic behavior prediction of nonlinear dynamic systems

Neural network modeling and dynamic behavior prediction of nonlinear dynamic systems

Quantitative study on steam system thermal inertia based on a dynamic hydraulic analytical model

Integrated energy system (IES) in industrial parks is pivotal to China's carbon neutrality path, where steam plays a critical role as an energy carrier and raw materials in the production process. Utilization of the thermal inertia of steam systems may become a means to address challenges in industrial park IES dispatch. However, researchers have less discussed the dynamic modeling and inertia quantification of industrial steam systems compared to district heating. This work proposes a dynamic hydraulic analytical model (DHAM) of steam systems reflecting the spatial and temporal transportation of steam by introducing the reference temperature and momentum linearization assumptions. Further, a steam thermal inertia model (STIM) which comprises five storage key parameters and two indexes, is developed to quantify the thermal inertia based on DHAM. Validation results of DHAM in an industrial park demonstrate that the relative error is less than 3%, achieving high accuracy. Whilst the thermal inertia of a 163-node steam system in two operation conditions is quantified and compared. Results show that the net heat storage of the steam system could reach 7440.30 kg while the positive utilization rate in both scenarios never rises above 3%. It indicates that the thermal inertia as virtual storage can fully cover the dispatching demand while is not utilized and lacks the regulation strategy of active charging in operation. DHAM and STIM proposed in this study lay the quantitative basis for steam system analysis and operation optimization of industrial park IES.

INVESTIGATION OF OPTIMAL CONTROL OF VARIABLE SYSTEMS IN THE DYNAMIC SPECTRUM

The article presents a study of systems of difference equations, their role and application in modeling and analysis of dynamical systems in various fields. The purpose of the work is to analyze and develop methods for solving difference equations with a special emphasis on their application in automation and mechanics. Difference equations are mathematical models describing the evolution of variables in a discrete time space. Their study allows for a deeper understanding of complex dynamic processes and effective modeling of systems of diverse nature. The paper presents an overview of various methods of analysis and solution of difference equations. Numerical integration methods, approximation methods and stabilization methods of systems of difference equations are considered. Special attention is paid to the properties of stability, convergence and controllability of such systems. The results of the study contribute to a deep understanding of the dynamics of systems of difference equations and the development of effective numerical methods for their solution. The solution of difference equations is widely used in automatic control, robotics, aviation, mechatronics and other industries. It plays an important role in modeling and controlling various systems, including electromechanical systems, robots, autopilots, automation processes, and others.

Data-Driven Dynamical System Models of Roughness-Induced Secondary Flows in Thermally Stratified Turbulent Boundary Layers

AbstractThe goal of this work is to investigate the feasibility of constructing data-driven dynamical system models of roughness-induced secondary flows in thermally stratified turbulent boundary layers. Considering the case of a surface roughness distribution which is homogeneous and heterogeneous in the streamwise and spanwise directions, respectively, we describe the streamwise averaged in-plane motions via a stream function formulation, thereby reducing the number of variables to the streamwise velocity component, an appropriately introduced stream function, and the temperature. Then, from the results of large eddy simulations, we perform a modal decomposition of each variable with the proper orthogonal decomposition and further utilize the temporal dynamics of the modal coefficients to construct a data-driven dynamical system model by applying the sparse identification of nonlinear dynamics (SINDy). We also present a novel approach for enforcing spanwise reflection symmetry within the SINDy framework to incorporate a physical bias.

ИДЕНТИФИКАЦИЯ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ТАНКЕРА «NORDIC ARCTIC TANKER AT 19» С ИСПОЛЬЗОВАНИЕМ ДАННЫХ НАТУРНЫХ ЭКСПЕРИМЕНТОВ

The problem of identifying a mathematical model of a ship considered in this paper is easily immersed in the general problem of modeling and identifying models. From a general standpoint, the main content of sciencec an be recognized as the formation of models of one type or another based on the results of observations and the study of their behavior. Models can be formalized to varying degrees, but they all have one main property - they link observations into some general picture. Solving the problems of constructing mathematical models of dynamic systems based on observational data on their behavior is the subject of identification theory.

Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses

AbstractIdentifying dynamical system models from measurements is a central challenge in the structural dynamics community. Nonlinear system identification, in particular, is a big challenge as there are many possible combinations of model structures, which requires expert knowledge to construct an appropriate model. Furthermore, traditional nonlinear system identification methods require a steady excitation input that is not always available in many practical applications. Recently, a technique referred to as the sparse identification of nonlinear dynamics (SINDy) algorithm was developed to discover mathematical models of general nonlinear systems. The SINDy method finds a generalized linear state-space model for an autonomous nonlinear system by analyzing the collected response data. In this work, the SINDy method is adapted and combined with the shooting method and the numerical continuation technique to form a system identification framework that can predict the nonlinear modal properties of mechanical oscillators. The proposed framework predicts the nonlinear normal modes (NNMs) of these systems by processing the noised data of the systems' free vibration response. In addition, the NNMs and the internal resonance of nonlinear systems at a high energy level can be captured using the proposed framework by processing the response data at a lower energy level. The proposed method is numerically demonstrated on a 2-degree-of-freedom mechanical oscillator. Furthermore, the effects of the measurement error and the excitation condition on NNM prediction are investigated. The NNM prediction framework presented in this paper is fairly general and is applicable to a variety of nonlinear systems.

LUCC Simulation Based on RF-CNN-LSTM-CA Model with High-Quality Seed Selection Iterative Algorithm

Land use/cover change (LUCC) models are essential for studying the profound impact of land use/cover dynamics on various aspects of the natural and social environment. Cellular Automata (CA) is widely used in the dynamic modeling of complex LUCC systems. In the traditional machine learning CA model, when using statistical methods to obtain neighborhood features, there is usually the problem that the spatio-temporal feature learning of neighborhood factors is insufficient. At the same time, the CA dynamic iteration module using the random seed selection mechanism often has the problem that the seed selection efficiency is very low. In this paper, taking the Chongqing Metropolitan Area as an example, convolutional neural networks (CNN)-Long Short-Term Memory Network (LSTM) is introduced to improve the learning effect of the traditional random forest (RF)-CA model in the spatial and temporal characteristics of neighborhood factors. CNN is used to extract the spatial dimension features of LUCC in the neighborhood, and the LSTM model is used to extract the time dimension features and long-term dependencies. At the same time, a high-quality seed selection iterative algorithm (HQSSIA) is used to improve the accuracy of the multi-land-use dynamic change model and the efficiency of the iterative algorithm. The results show that, the proposed model performs better than other models in simulating the LUCC from 2015 to 2020 (Kappa = 0.9684, FOM = 0.1744, Accuracy = 0.9829, F1 = 0.9641, Hamming = 0.0171) and from 2010 to 2020 (Kappa = 0.9599, FOM = 0.4662, Accuracy = 0.9785, F1 = 0.8113, Hamming = 0.0214). After introducing the CNN-LSTM model, the Figure of Merit (FOM) increased by 1.56% and 18.88% for 2015–2020 and 2010–2020. Compared with the CA model-based random seed selection algorithm, the FOM of the model using HQSSIA in the dynamic iteration module are improved by 11.60% and 24.79% for 2015–2020 and 2010–2020, and the operation efficiency of the dynamic iteration module is improved by about 19 times. Compared with the current mainstream LUCC models PLUS and FLUS, the proposed model has improved 14.38%, 37.55%, and 14.93%, 37.74% in FOM, respectively, for 2015–2020 and 2010–2020. The research shows that: (1) RF-CNN-LSTM-CA model not only retains the interpretability advantage of the traditional RF-CA model, but also improves the accuracy of the whole model by improving the spatio-temporal characteristics of neighborhood factors through in-depth learning; (2) the HQSSIA can quickly and accurately search for cells to be converted with higher conversion probability in the observed data, which can not only significantly reduce the time complexity of the model, but also improve the accuracy of LUCC simulation.

Barrier Lyapunov function-based adaptive fuzzy control for general dynamic modeling of affine and non-affine systems

Barrier Lyapunov function-based adaptive fuzzy control for general dynamic modeling of affine and non-affine systems

Combining generalized modeling and specific modeling in the analysis of ecological networks.

The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems.

Curriculum learning for data-driven modeling of dynamical systems.

The reliable prediction of the temporal behavior of complex systems is key in numerous scientific fields. This strong interest is however hindered by modeling issues: Often, the governing equations describing the physics of the system under consideration are not accessible or, when known, their solution might require a computational time incompatible with the prediction time constraints. Not surprisingly, approximating complex systems in a generic functional format and informing it ex-nihilo from available observations has become common practice in the age of machine learning, as illustrated by the numerous successful examples based on deep neural networks. However, generalizability of the models, margins of guarantee and the impact of data are often overlooked or examined mainly by relying on prior knowledge of the physics. We tackle these issues from a different viewpoint, by adopting a curriculum learning strategy. In curriculum learning, the dataset is structured such that the training process starts from simple samples toward more complex ones in order to favor convergence and generalization. The concept has been developed and successfully applied in robotics and control of systems. Here, we apply this concept for the learning of complex dynamical systems in a systematic way. First, leveraging insights from the ergodic theory, we assess the amount of data sufficient for a-priori guaranteeing a faithful model of the physical system and thoroughly investigate the impact of the training set and its structure on the quality of long-term predictions. Based on that, we consider entropy as a metric of complexity of the dataset; we show how an informed design of the training set based on the analysis of the entropy significantly improves the resulting models in terms of generalizability and provide insights on the amount and the choice of data required for an effective data-driven modeling.

Model-Predictive Control Design for Power System Oscillation Damping via Excitation – A Data-Driven Approach

This paper presents a novel power system oscillation damping controller design based on a data-driven model-predictive control (MPC) approach. The system dynamics are extracted from the measurements and applied to the synthesis of control actions in an equation-free manner, without requiring explicit knowledge of the underlying system model. Dynamic mode decomposition with control (DMDc), originating from the Koopman operator theory, connects the collected data with the nonlinear dynamical system modeling. The discrepancy between the model identified by DMDc and the real plant is labeled as a total disturbance. It is estimated in real time by an extended state observer (ESO) and mitigated via a linear MPC, assuming the estimate to be constant over the prediction horizon. The overall control framework is referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ESO-Koopman-MPC (EKM)</i> . Two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EKM</i> -based oscillation damping controllers are proposed - a standalone PSS and an integrated AVR+PSS. The controller operation is illustrated on the single machine infinite bus system (SMIB), Kundur two-area system and IEEE 39-bus system, and the performance is compared with conventional power system stabilizers (CPSSs) under various test scenarios.

DEVELOPMENT OF ALGORITHMS AND SOFTWARE FOR MODELING CONTROLLED DYMAMIC SYSTEMS USING SYMBOLIC COMPUTATIONS AND STOCHASTIC METHODS

The development of software for synthesizing and analyzing models of controlled systems taking into account their deterministic and stochastic description is an important direction of research. Results of the development of software for modeling dynamic systems the behavior of which can be described by onestep processes are presented. Models of population dynamics are considered as an example. The software uses a deterministic description of the model at its input to obtain a corresponding stochastic model in symbolic form and also analyze the model in detail (calculate trajectories in the deterministic and stochastic cases, find control functions, and visualize the results). An important aspect of the development is the use of computer algebra for analyzing the model and synthesizing controls. Methods and algorithms based on deterministic and stochastic Runge–Kutta methods, stability and control theory, methods for designing self-consistent stochastic models, numerical optimization algorithms, and artificial intelligence are implemented. The software was developed using high-level programming languages Python and Julia. As the basic tools, high-performance libraries for vector–matrix computations, symbolic computation libraries, libraries for the numerical solution of ordinary differential equations, and libraries of global optimization algorithms are used.

Autonomous Underwater Vehicle Path Tracking Based on the Optimal Fuzzy Controller with Multiple Performance Indexes

Autonomous underwater vehicles (AUVs) are increasingly being used in missions involving submarine cable detection, underwater archaeology, pipeline inspection, military reconnaissance, and so on. It is very important to realize AUV path tracking to accomplish these missions. In this paper, a fuzzy controller based on the established kinematic and dynamic models of AUV systems is presented to solve the AUV path-tracking problem. In order to design the fuzzy controller to exhibit good performance, we select the path length, smoothness, and cross-track position error as the multiple optimization performance indexes for the fuzzy controller. We propose the particle swarm optimization (PSO) algorithm to determine the parameters of the membership functions. Different scenarios are presented to test the performance of the proposed algorithm, including the straight line, sine curve, half-moon shape, Archimedean spiral, and practical paths. The results are given to illustrate the effectiveness and feasibility of the fuzzy controller with the optimization of multiple performance indexes.

Generative Music with Partitioned Quantum Cellular Automata

Cellular automata (CA) are abstract computational models of dynamic systems that change some features with space and time. Music is the art of organising sounds in space and time, and it can be modelled as a dynamic system. Hence, CA are of interest to composers working with generative music. The art of generating music with CA hinges on the design of algorithms to evolve patterns of data and methods to render those patterns into musical forms. This paper introduces methods for creating original music using partitioned quantum cellular automata (PQCA). PQCA consist of an approach to implementing CA on quantum computers. Quantum computers leverage properties of quantum mechanics to perform computations differently from classical computers, with alleged advantages. The paper begins with some explanations of background concepts, including CA, quantum computing, and PQCA. Then, it details the PQCA systems that we have been developing to generate music and discusses practical examples. PQCA-generated materials for Qubism, a professional piece of music composed for London Sinfonietta, are included. The PQCA systems presented here were run on real quantum computers rather than simulations thereof. The rationale for doing so is also discussed.