Parameters Of Dynamic System Research Articles

Dynamic Optimal ANFIS Parameters Tuning with Particle Swarm Optimization

This paper presents dynamic modification parameters of the Adaptive Neuro-Fuzzy Inference System (ANFIS) using the Particle Swarm Optimization (PSO) algorithm. In the proposed ANFIS_PSO, each particle dynamically adjusts its weight to the optimal states of the particles using a nonlinear fuzzy model. Tests of the model were performed using the "Signal-Time Series". The methods are tested simultaneously until the best method to solve the problem is found. The proposed model takes advantage of PSO to tune ANFIS parameters by minimizing mean square error (MSE), root mean square error (RMSE), R-Squared (R2) and Mean Absolute Error (MEA) metrics. The main contribution is a strategy for dynamically finding the best result, which identifies methods for solving a given problem using different performance metrics depending on the problem. The proposed structure's results were compared with several machine learning algorithms. Simulation results show the effectiveness of the proposed algorithm.

Real-time state estimation of low-frequency plasma oscillations in Hall effect thrusters

An extended Kalman filter (EKF) is developed to estimate unobserved states and parameters in plasma dynamical systems. Physical constraints are satisfied by adapting the process and measurement noise covariances to account for consistency between the estimates and the physical processes. First, the EKF is tested using the Lorenz system to demonstrate the robustness of the EKF with sparse measurement data. Then, the capabilities of the EKF are applied to investigate discharge current oscillations in a Hall effect thruster. It is demonstrated that the dynamics of the electron temperature can be estimated using the discharge current fluctuation as the measurement data. The propagation of the uncertainties of such estimates is also quantified.

Emergency control of cyber-physical systems in the technological environment

The task how to increase the industrial object crucial infrastructure reliability and safety is being studied formed with cyber-physical systems. To solve this task they represent a cyber-physical production as a complicated dynamic systems with tide and continuous conveyor cycles, which behavior is under control in the state parameters space. The cyber-physical systems actions of the inner technological environment factors and cyber-physical production external factors must be analyzed to study single and systematic actions of chaos creating character in equipment, which add some components to the control error. The emergency control is a directed cyber-physical action to maintain the cyber-physical production dynamic system in a non-variant state to the equipment failures and interferences. The control method and parameters are determined as a result of the assessment of the state of cyber-physical production performed in its phase space according to the predicted trajectories, probably indicating the dynamics of the technological environment and the risks of uncontrolled situations. The actual information of the cyber-physical production states includes the cyber-physical systems functionality modes data, which is proposed to be accumulated in a virtual environment to which the technological automatics of different hierarchy levels is connected to. The parametric states space dynamic system behavior trajectory forming principle is defined to make concrete separate cyber-physical systems and the cyber-physical production in general.

Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.

Potential Analysis of the Attention-Based LSTM Model in Ultra-Short-Term Forecasting of Building HVAC Energy Consumption

Predicting system energy consumption accurately and adjusting dynamic operating parameters of the HVAC system in advance is the basis of realizing the model predictive control (MPC). In recent years, the LSTM network had made remarkable achievements in the field of load forecasting. This paper aimed to evaluate the potential of using an attentional-based LSTM network (A-LSTM) to predict HVAC energy consumption in practical applications. To evaluate the application potential of the A-LSTM model in real cases, the training set and test set used in experiments are the real energy consumption data collected by Kitakyushu Science Research Park in Japan. Pearce analysis was first carried out on the source data set and built the target database. Then five baseline models (A-LSTM, LSTM, RNN, DNN, and SVR) were built. Besides, to optimize the super parameters of the model, the Tree-structured of Parzen Estimators (TPE) algorithm was introduced. Finally, the applications are performed on the target database, and the results are analyzed from multiple perspectives, including model comparisons on different sizes of the training set, model comparisons on different system operation modes, graphical examination, etc. The results showed that the performance of the A-LSTM model was better than other baseline models, it could provide accurate and reliable hourly forecasting for HVAC energy consumption.

Observation of Dynamic State Parameters and Yaw Stability Control of Four-Wheel-Independent-Drive EV

Vehicle yaw stability control is an important part of the active safety of electric vehicles. In order to realize the yaw stability control of vehicles, this paper takes 4-WID electric vehicles as the research object, studies the nonlinear estimation of the state parameters of the lateral stability dynamic system and the yaw stability control strategy. The vehicle state parameter estimation strategy, based on the unscented Kalman filter (UKF) algorithm and the model predictive control algorithm, are designed to control the vehicle yaw stability, which realizes the safe and stable driving of the vehicle. Through CarSim–Simulink joint simulation and hardware-in-the-loop (HIL) experiments based on MicroAutoBox, the effectiveness and real-time performance of the designed control strategy are fully verified, which accelerate the development process of the vehicle controller, and realizes the safe and stable driving of the vehicle.

Вычислительная диагностика неустойчивых по Якоби динамических систем с использованием гибридных алгоритмов глобальной оптимизации

The study focuses on the problems of restoration and analysis of free parameters of dynamical systems from indirect, approximately given information. In the context of the Kosambi --- Cartan --- Chern theory, a geometric description of the time-evolution of the system is introduced. Five geometric invariants are determined for the system under study. The eigenvalues of the second invariant estimate the Jacobi stability of the system. Such a study is of interest in practical applications, where it is required to identify the regions in which both Lyapunov stability and Jacobi stability occur simultaneously. The inverse problem of computational diagnostics of the system is formulated for approximately given eigenvalues of the second invariant. The solution to the regularized inverse problem is determined using an optimization approach. Scalar criterion functions are assumed to be continuous, multidimensional, locally Lipschitzian, and not necessarily everywhere differentiable. When searching for global solutions, we used new hybrid algorithms that integrate stochastic algorithms for scanning the space of variables and a deterministic local minimization procedure. The numerical scanning procedure is implemented with the use of two modified versions: quasi-opposition-based and rotation-based learning mechanisms. In the phase of local search, two-parameter smoothing approximations of criterion functions are introduced. Examples of solving problems of computational diagnostics of Jacobi unstable dynamical systems are given: the Lorentz system and a controllable elliptical pendulum

Adaptive 3D Visual Servoing of a Scara Robot Manipulator with Unknown Dynamic and Vision System Parameters

In the present work, we develop an adaptive dynamic controller based on monocular vision for the tracking of objects with a three-degrees of freedom (DOF) Scara robot manipulator. The main characteristic of the proposed control scheme is that it considers the robot dynamics, the depth of the moving object, and the mounting of the fixed camera to be unknown. The design of the control algorithm is based on an adaptive kinematic visual servo controller whose objective is the tracking of moving objects even with uncertainties in the parameters of the camera and its mounting. The design also includes a dynamic controller in cascade with the former one whose objective is to compensate the dynamics of the manipulator by generating the final control actions to the robot even with uncertainties in the parameters of its dynamic model. Using Lyapunov’s theory, we analyze the two proposed adaptive controllers for stability properties, and, through simulations, the performance of the complete control scheme is shown.

Structure-preserving interpolation for model reduction of parametric bilinear systems

In this paper, we present a projection-based interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear systems, and then provide conditions on projection spaces for the interpolation of structured subsystem transfer functions such that the system structure and parameter dependencies are preserved in the reduced-order model. Two benchmark examples with different parameter dependencies are used to demonstrate the theoretical analysis.

Stability of inverter-interfaced power systems with multi-scale-free properties

Scale-free networks are proven to have many distinct properties and numerous statistical studies have shown that most large power systems have the scale-free topology. However, the overall system behavior is also constrained by node dynamics, of which the interaction effects with network topology remain unknown. Here, we investigate the individual and mutual effects of network degree distribution, with two system dynamic parameters, on system small-disturbance angle stability. We show that network degree distribution and active power injection distribution are critical in determining system small-disturbance angle stability while frequency coefficient shows relatively less significant influence. Further, the scale-free level for degree distribution positively interacts with active power injection distribution on the overall system behavior. Consequently, not only network topology but also system dynamic parameters and, importantly, their synergistic effects matter in determining system behavior. Based on the results, we further provide guidance for the coordination of the various parameters to improve system small-disturbance angle stability.

SEIR order parameters and eigenvectors of the three stages of completed COVID-19 epidemics: with an illustration for Thailand January to May 2020

By end of October 2020, the COVID-19 pandemic has taken a tragic toll of 1150 000 lives and this number is expected to increase. Despite the pandemic is raging in most parts of the world, in a few countries COVID-19 epidemics subsided due to successful implementations of intervention measures. A unifying perspective of the beginnings, middle stages, and endings of such completed COVID-19 epidemics is developed based on the order parameter and eigenvalue concepts of nonlinear physics, in general, and synergetics, in particular. To this end, a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model is used. It is shown that COVID-19 epidemic outbreaks follow a suitably defined SEIR order parameter. Intervention measures switch the eigenvalue of the order parameter from a positive to a negative value, and in doing so, stabilize the COVID-19 disease-free state. The subsiding of COVID-19 epidemics eventually follows the remnant of the order parameter of the infection dynamical system. These considerations are illustrated for the COVID-19 epidemic in Thailand from January to May 2020. The decay of effective contact rates throughout the three epidemic stages is demonstrated. Evidence for the sign-switching of the dominant eigenvalue is given and the order parameter and its stage-3 remnant are identified. The presumed impacts of interventions measures implemented in Thailand are discussed in this context.

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

This paper considers a relevant issue related to the influence exerted by the fuzziness in linear dynamic system parameters on its stability. It is known that the properties of automated control systems can change under the influence of parametric disturbances. To describe the change in such properties of the system, the concept of roughness is used. It should be noted that taking into consideration the fuzziness in the parameters of mathematical models could make it possible at the design stage to assess all the risks that may arise as a result of an uncontrolled change in the parameters of dynamic systems during their operation. To prevent negative consequences due to variance in the parameters of mathematical models, automated control systems are designed on the basis of the requirement for ensuring a certain margin of stability of the system in terms of its amplitude and phase. At the same time, it remains an open question whether such a system would satisfy the conditions of roughness. Parameters of the mathematical model of a system are considered as fuzzy quantities that have a triangular membership function. This function is inconvenient for practical use, so it is approximated by the Gaussian function. That has made it possible to obtain formulas for calculating the characteristic polynomial and the transfer function of the open system, taking into consideration the fuzziness of their parameters. When investigating the system according to Mikhailov’s criterion, it was established that the dynamic system retains stability in the case when the parameters of the characteristic equation are considered as fuzzy quantities. It has been determined that the quality of the system significantly deteriorated in terms of its stability that could make it enter a non-steady state. When using the Nyquist criterion, it was established that taking into consideration the fuzziness in the parameters of the transfer function did not affect the stability of the closed system but there was a noticeable decrease in the system stability reserve both in terms of phase and amplitude. The relative decrease in the margin of stability for amplitude was 16 %, and for phase ‒ 17.4 %.

A new model of Hopfield network with fractional-order neurons for parameter estimation

In this work, we study an application of fractional-order Hopfield neural networks for optimization problem solving. The proposed network was simulated using a semi-analytical method based on Adomian decomposition,, and it was applied to the on-line estimation of time-varying parameters of nonlinear dynamical systems. Through simulations, it was demonstrated how fractional-order neurons influence the convergence of the Hopfield network, improving the performance of the parameter identification process if compared with integer-order implementations. Two different approaches for computing fractional derivatives were considered and compared as a function of the fractional-order of the derivatives: the Caputo and the Caputo–Fabrizio definitions. Simulation results related to different benchmarks commonly adopted in the literature are reported to demonstrate the suitability of the proposed architecture in the field of on-line parameter estimation.

COMPREHENSIVE STUDY OF THE DYNAMICS OF THE RETAINING MECHANISM OF THE AUTOMATIC MILL

The results of the study of the dynamics of the mechanism for holding the mandrel of an automatic TPA mill are presented. The value of the axial force acting on the mandrel and the rod system of the mechanism of its holding is determined. Developed models of the mandrel retention mechanism have been developed, which made it possible to establish the nature of the development of dynamic processes on the output side of the automatic mill, taking into account the force parameters of the longitudinal rolling process of the sleeve and the parameters of the output side of the automatic mill. Mathematical models of the mandrel retention mechanism have been developed, taking into account the parameters of the technological process and the inertness of the rolled sleeve. The solution of the system of differential equations with variable coefficients is implemented numerically using the Runge-Kutta method for the corresponding dynamic models of the mandrel retention mechanism on the example of calculating the automatic mill TPA 350. The picture of the formation of dynamic processes in the mandrel retention mechanism during the implementation of the entire technological process of pipe production on an automatic mill has been clarified. taking into account the variable impact from the deformation zone and the change in the mass of the rolled sleeve. For various dynamic models, numerical solutions of problems were implemented, which made it possible to select the necessary technological and dynamic parameters of the mechanical system, to assign stable modes of rolling the sleeves on the automatic mill TPA 350. It is shown that the refined solution of the problem for three developed dynamic models of the mechanical system differs significantly from the previously known mathematical models. It has been established that the dynamics of the mechanism for holding the mandrel of the automatic TPA 350 mill is equivalent to the formation of the mechanism for the formation of different wall thickness of pipes. A mechanism for stabilizing the dynamics of the mandrel holding mechanism by separating the sections of the output side of the mill is proposed.

Fractional-Order Adaptive Fault-Tolerant Synchronization Tracking Control of Networked Fixed-Wing UAVs Against Actuator-Sensor Faults via Intelligent Learning Mechanism.

This article presents an enhanced fault-tolerant synchronization tracking control scheme using fractional-order (FO) calculus and intelligent learning architecture for networked fixed-wing unmanned aerial vehicles (UAVs) against actuator and sensor faults. To increase the flight safety of networked UAVs, a recurrent wavelet fuzzy neural network (RWFNN) learning system with feedback loops is first designed to compensate for the unknown terms induced by the inherent nonlinearities, unexpected actuator, and sensor faults. Then, FO sliding-mode control (FOSMC), involving the adjustable FO operators and the robustness of SMC, are dexterously proposed to further enhance flight safety and reduce synchronization tracking errors. Moreover, the dynamic parameters of the RWFNN learning system embedded in the networked fixed-wing UAVs are updated based on adaptive laws. Furthermore, the Lyapunov analysis ensures that all fixed-wing UAVs can synchronously track their references with bounded tracking errors. Finally, comparative simulations and hardware-in-the-loop experiments are conducted to demonstrate the validity of the proposed control scheme.

Parameter extraction with reservoir computing: Nonlinear time series analysis and application to industrial maintenance.

We study the task of determining parameters of dynamical systems from their time series using variations of reservoir computing. Averages of reservoir activations yield a static set of random features that allows us to separate different parameter values. We study such random feature models in the time and frequency domain. For the Lorenz and Rössler systems throughout stable and chaotic regimes, we achieve accurate and robust parameter extraction. For vibration data of centrifugal pumps, we find a significant ability to recover the operating regime. While the time domain models achieve higher performance for the numerical systems, the frequency domain models are superior in the application context.

A Method of Increasing the Accuracy of Controlling the Parameters of Dynamic Systems and Regulating the Parameters of the Elastic-Deformable State in the Process of Treating Low-Rigidity Shafts

A Method of Increasing the Accuracy of Controlling the Parameters of Dynamic Systems and Regulating the Parameters of the Elastic-Deformable State in the Process of Treating Low-Rigidity Shafts

Dynamics of exit section of automatic mill of pipe rolling line

Nonuniformity of pipe wall thickness is one of significant indices, determining quality of hot-rolled seamless pipes. One of the reasons of increased nonuniformity arising is dynamics of exit section mechanisms of pipe rolling line (PRL). Results of study of mandrel holding mechanism dynamics of PRL presented. Dynamic models of exit section, accounting parameters of technological process and inertia of a rolled hollow billet elaborated, which enabled to determine the character of dynamic processes at the exit section of PRL automatic mill. Differential equations of exit section elements motion at the exit section of PRL automatic mill were made up. The solution of the differential equations system was obtained in a numerical form by application of Runge‒Kutta method for correspondent dynamic models of exit section based on the example of calculations for ТПА-350 automatic mill. The pattern of dynamic processes arising at the exit section was specified at realization of the whole technological process of a hollow billet rolling at automatic mill, taking into consideration alternative action from the side of deformation center and mass of the rolled hollow billet. It was shown, that the specified solution of the task for three advanced dynamic models of mechanical system considerably differs from those of the known mathematical models. It was established, that the dynamics of the mandrel holding mechanism of ТПА-350 automatic mill equivalently form the mechanism of finished pipes geometry forming. Analysis of dynamic models of the mill exit section enabled to select the necessary technological and dynamic parameters of the mechanical system, to determine stable modes of hollow billets rolling at the ТПА-350 automatic mill. Results of the study of dynamics of exit section ТПА-350 automatic mill presented. A scheme of modernization of the exit section ТПА-350 automatic mill proposed, which enables to realize rational modes of operation accounting level of mechanical system dynamics and to control quality (geometric parameters) of the rolled pipes.

Statistics of Voltage Processes in Random Environment

Abstract A method is developed to characterize the performance of voltage processes X(t) harvested from primary-absorber dynamical systems subjected to Gaussian forcing functions. The method is based on properties of the Slepian model of X(t) and Monte Carlo simulation. Statistics are calculated for excursions of X(t) above levels which can be related to energy demand. The duration and the area of these excursions are used as metrics for the voltage process. Their statistics depend on the topology and the parameters of primary-absorber dynamical systems, which can be optimized to maximize the output voltage.

Calibration and Improvement of an Odometry Model with Dynamic Wheel and Lateral Dynamics Integration.

Localization is a key part of an autonomous system, such as a self-driving car. The main sensor for the task is the GNSS, however its limitations can be eliminated only by integrating other methods, for example wheel odometry, which requires a well-calibrated model. This paper proposes a novel wheel odometry model and its calibration. The parameters of the nonlinear dynamic system are estimated with Gauss–Newton regression. Due to only automotive-grade sensors are applied to reach a cost-effective system, the measurement uncertainty highly corrupts the estimation accuracy. The problem is handled with a unique Kalman-filter addition to the iterative loop. The experimental results illustrate that without the proposed improvements, in particular the dynamic wheel assumption and integrated filtering, the model cannot be calibrated precisely. With the well-calibrated odometry, the localization accuracy improves significantly and the system can be used as a cost-effective motion estimation sensor in autonomous functions.