Parameters Of Dynamic System Research Articles

Bayesian sequential data assimilation for COVID-19 forecasting

We introduce a Bayesian sequential data assimilation and forecasting method for non-autonomous dynamical systems. We applied this method to the current COVID-19 pandemic. It is assumed that suitable transmission, epidemic and observation models are available and previously validated. The transmission and epidemic models are coded into a dynamical system. The observation model depends on the dynamical system state variables and parameters, and is cast as a likelihood function. The forecast is sequentially updated over a sliding window of epidemic records as new data becomes available. Prior distributions for the state variables at the new forecasting time are assembled using the dynamical system, calibrated for the previous forecast. Epidemic outbreaks are non-autonomous dynamical systems depending on human behavior, viral evolution and climate, among other factors, rendering it impossible to make reliable long-term epidemic forecasts. We show our forecasting method’s performance using a SEIR type model and COVID-19 data from several Mexican localities. Moreover, we derive further insights into the COVID-19 pandemic from our model predictions. The rationale of our approach is that sequential data assimilation is an adequate compromise between data fitting and dynamical system prediction.

Fault diagnosis of active magnetic bearings

Active magnetic bearings (AMBs) are intrinsically unstable systems and require feedback control to ensure stable operation. Further, sensors, actuators, and the rotor need to operate under normal conditions, and a fault detection and diagnostics system is necessary to ensure a safe and reliable operation. Accordingly, several studies have developed methods to detect failures associated with the rotor or the electrical system (i.e., AMB). However, prior identification of the dynamic system parameters or the magnetic forces is usually desired, which can be impractical for real machines. To overcome this problem, this study proposes a failure detection method based on a mathematical model and the correlation between the measured states related to the rotor and the control. Artificial neural networks are used to map the states that cannot be measured, and faults are determined by comparing the output correlations of neural networks. Faults in the AMB/rotor system are identified considering various rotor unbalance configurations (mechanical failures) and failures in the position sensor gain and in the magnetic actuator current (electrical failures). Various fault configurations were explored for each case cited. A comparison of the theoretical and experimental results showed good agreement, which demonstrates the adequacy of the method in detecting mechanical and electrical failures in industrial machines.

The Modelling and Analysis of Micro-Milling Forces for Fabricating Thin-Walled Micro-Parts Considering Machining Dynamics

In the fabrication process of thin-walled micro-parts, both micro-cutting tools and thin-walled micro-parts have the characteristics of small size and low stiffness. Therefore, the regenerative chatter during the machining process cannot be ignored. The influence of the tool runout error and actual trochoidal trajectories of the cutting edge on micro-milling forces should also be considered comprehensively. In this paper, the tool runout error in the micro-milling process is first analysed, and an instantaneous undeformed chip thickness model is established considering the runout error. On this basis, the dynamic deformation of the micro-cutting tool and thin-walled micro-part is studied, and an instantaneous, undeformed, chip-thickness model is proposed with the consideration of both the runout error and dynamic deformation. The dynamic parameters of the machining system are obtained using the receptance coupling method. Finally, thin-walled micro-part machining experiments are carried out, and the obtained results of micro-milling force simulation based on the proposed model are compared with the experimental results. The results indicate that the micro-milling force modelling, by taking the influence of machining dynamics into account, has better prediction accuracy, and the difference between the predicted resultant forces and the experimental results is less than 11%.

Coordination and matching of tire system of new straddle-type rapid transit vehicle

Under the trend of promoting economy, environmental protection and high efficiency in the urban rail transit industry, this paper proposes a new type of straddle-type rapid transit system. Compared with most straddle-type monorail systems, it has the advantages of low construction cost and low operating cost, which makes it more suitable for urban rail transit system in small and medium-sized cities. In the process of vehicle development and design, in order to achieve the coordination and matching of tire systems and reduce the wear of tire systems, this work uses a multi-objective optimisation method to reduce the guiding torque of each tire system when the vehicle passes through the curve. Based on the vehicle dynamics model, the multi-body dynamics simulation model of the vehicle is established. The guiding torque of each tire system is taken as the optimisation objective, and the position and dynamic parameters of each tire system are taken as the optimisation parameter. Based on the NSGA-II algorithm, the ISIGHT and SIMPACK software are used for co-simulation. Finally, the guiding torque of each tire system is effectively reduced, and the coordination and matching of tire system is realised.

A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

AbstractIn this paper, the robustness of a recently validated linearization approach is demonstrated with the linear stability analysis of a waveboard, a human-propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a differential-algebraic system of equations (DAE system), are linearized along the steady forward motion. With this approach, the minimal set of linearized equations of motion of the waveboard multibody model with toroidal wheels is derived. The procedure enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

Index Matrices—Based Software Implementation of Power Electronic Circuit Design

This article aims to present a comprehensive approach with corresponding software that uses index matrices. They have been developed by the authors for an automated model-based design. One of the main goals of this paper is to propose a simple model solving technique for powering electronic devices (particularly, for all subsystems: power supplies, static power converters, electric filters, electrical loads, control systems, etc.). Index matrices, which contain first-order discrete dynamical system parameters, with real numbers as elements, are constructed in order so that voltages, amperages, and discrete values can be calculated. Simulations on a three-phase converter, as well as simulations on buck and boost DC-DC converters with PI controllers, are presented. The function of the proposed software (with examples on the aforementioned devices) is considered, and diagrams of its basic programming classes are shown. The latter draws electronic schemes and their respective graphics, and provides important characteristics. Simulink is used to verify results. Advantages of the proposed approach are a higher speed of calculations (compared to Simulink, due to a lack of differential equations) and a simpler handling of various electronic components. Additionally, a computational scalability is demonstrated.

Dynamic Parameter Identification of a Human-Exoskeleton System With the Motor Torque Data

The objective of this paper is to identify dynamic parameters of the human-exoskeleton system (HES) with the motor torque data considering modeling the passive elastic joint torque of the user. Based on a lower limb exoskeleton prototype we recently developed, the dynamics of the joint actuators and two degrees of freedom link-based swing leg are firstly modeled. The passive elasticity of the human joint is modeled by double-exponential equations. Systematic experiments are then conducted, during which the motor current is measured to compute the motor torque for identification. Finally, the dynamic parameters of the joint actuators, the exoskeleton leg and the human-exoskeleton leg are successively identified. The identification is implemented through the off-line inverse dynamic model simulation with the measured motor torque data. A consistent tendency is found between the simulated motor torque after identification and the measured one. This demonstrates the validity of the identification method proposed. This paper provides a systemic method of identifying the HES with the motor torque data and enriches the experimental proof that the double-exponential model is feasible to describe the passive elastic joint torque.

Estimating the Spin of the Black Hole Candidate MAXI J1659-152 with the X-Ray Continuum-fitting Method

Abstract As a transient X-ray binary, MAXI J1659-152 contains a black hole candidate as its compact star. MAXI J1659-152 was discovered on 2010 September 25 during its only known outburst. Previously published studies of this outburst indicate that MAXI J1659-152 may have an extreme retrograde spin, which, if confirmed, would provide an important clue as to the origin of black hole spin. In this paper, utilizing updated dynamical binary system parameters (i.e., the black hole mass, the orbital inclination, and the source distance) provided by Torres et al., we analyze 65 spectra of MAXI J1659-152 from RXTE/PCA, in order to assess the spin parameter. With a final selection of nine spectra matching our f sc ≲ 25%, soft state criteria, we apply a relativistic thin disk spectroscopic model kerrbb2 over 3.0–45.0 keV. We find that inclination angle correlates inversely with spin, and, considering the possible values for inclination angle, we constrain spin to be −1 < a * ≲ 0.44 at a 90% confidence interval via X-ray continuum fitting. We can only rule out an extreme prograde (positive) spin. We confirm that an extreme retrograde solution is possible and is not ruled out by considering accretion torques given the young age of the system.

Persistence Curves: A canonical framework for summarizing persistence diagrams

Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to be challenging as the space lacks an inner product. For that reason, transforming these diagrams in a way that is compatible with machine learning is an important topic currently researched in TDA. In this paper, our main contribution consists of three components. First, we develop a general and unifying framework of vectorizing diagrams that we call the Persistence Curves (PCs), and show that several well-known summaries, such as Persistence Landscapes, fall under the PC framework. Second, we propose several new summaries based on PC framework and provide a theoretical foundation for their stability analysis. Finally, we apply proposed PCs to two applications—texture classification and determining the parameters of a discrete dynamical system; their performances are competitive with other TDA methods.

Dynamic parameter identification of the rigid body model of an elastic laser cutting machine

Identifying dynamic parameters of an elastic robotic system can be a quite challenging task. This is because elastic robotic systems are often highly underactuated and sensor data may only be available for the driven states. To overcome this shortcoming, the identification process can be addressed by different experiments based on different reduced models. However, reducing a model leads almost always to redundant dynamic parameters. This work addresses a method how to deal with these redundant parameters and how to combine the results of different experiments based on confidence weights.

Dynamic Identification of Equivalent Parameters of Mathematical Models of Power Electrical Equipment of Electromechanical Power Systems

The article describes a method for dynamic identification of AC and DC hybrid power network parameters. The inaccuracy of the parameters of the electromechanical transient simulation model of the power system has caused the obvious difference between the simulation results and the actual measurement, which has restricted its online application. Over the years, the dynamic parameter identification technology based on field test and test has made great progress, but it is far from satisfactory and accurate. There is still a long research journey for the requirements of performance. The online identification method based on the actual dynamic parameters of the power system is a way to solve the problem. The article includes the main microprocessor modules for system parametric identification of load (SIP L) and an overhead power transmission line (SIP TL). The article will analyze the active electrical network and passive electrical network

Influence of surface textures on the dynamic stability and performance parameters of hydrodynamic two-lobe journal bearings

Surface texturing can improve the performance of journal bearing system. The present study theoretically investigates the impact of surface textures on the dynamic stability and performance parameters of two-lobe journal bearing system. Galerkin's finite element method is used to solve the Reynolds equation governing the flow of lubricant in the gap between the bearing and the journal. Reynolds boundary conditions are applied in the simulation study of plain, full-textured, partially textured-I and partially textured-II configurations of two-lobe journal bearing. The dynamic stability and performance parameters of textured two-lobe journal bearings are computed with the variation of eccentricity ratio and dimple depth and compared with circular bearing results. The results indicate that the existence of surface textures in the pressure build-up zone ranging from 126°–286° and at unity dimple aspect ratio can significantly improve the dynamic stability and performance parameters of two-lobe bearing system.

Quality improvement of manufacturing rolling mill rolls

At present time grinding operations for rolling mills rolls, providing the final quality parameters, are the most labour-intensive ones. It is caused first of all via their complex stochastic nature, which leads to a spread of quality indicators, lowering of reliability, productivity and efficiency of technological process. Development of the dynamic process models which can adequately describe the changes occurring in the technological system is considered as one of the ways for solving these problems. The models allowing to assess the influence of random components of the tool profile deviations as factors disturbing the grinding process dynamics are presented in the article. This assessment makes it possible to select the dynamic system parameters (such as mass, damping and stiffness) in order to ensure the maximal possible tool life, the permissible spread of the product quality parameters, as well as the maximal efficiency and productivity of the operation.

Adaptive preassigned finite‐time stability of nonlinear systems with time‐varying powers and full‐state constraints

AbstractThis article discusses adaptive preassigned finite‐time stability of nonlinear systems with unknown time‐varying powers and full‐state constraints. By introducing a concept of practical preassigned finite‐time stable, constructing finite‐time performance functions and nonlinear transformed functions, and integrating high‐power and low‐power terms into dynamic surface control design, an adaptive state‐feedback controller is designed to eliminate the effects of unknown powers and serious unknown parameters in system dynamics, and decrease the computational burden in previous design methods. It is proved that all the signals of the closed‐loop system are bounded, asymmetric time‐varying full‐state constraints are not transgressed, and system states converge to a prescribed arbitrarily small region around zero after a preassigned settling time. Two simulation examples show the effectiveness and advantages of this control scheme.

A machine learning approach for identifying an effective dimension in parametric dynamical systems

AbstractWe consider dynamical systems including physical parameters. An operator maps a realisation of the parameters to a trajectory of a quantity of interest. The operator is approximated by an artificial neural network, i.e., an approach of machine learning. We arrange modified neural networks, which determine a kind of effective dimension in the parameter space.

Practical identifiability of mathematical models of biomedical processes

The paper is devoted to a numerical study of the uniqueness and stability of problems of determining the parameters of dynamical systems arising in pharmacokinetics, immunology, epidemiology, sociology, etc. by incomplete measurements of certain states of the system at fixed time. Significance of parameters difficult to measure is very high in many areas, as their definition will allow physicians and doctors to make an effective treatment plan and to select the optimal set of medicines. Due to the fact that the problems under consideration are ill-posed, it is necessary to investigate the degree of ill-posedness before its numerical solution. One of the most effective ways is to study the practical identifiability of systems of nonlinear ordinary differential equations that will allow us to establish a set of identifiable parameters for further numerical solution of inverse problems. The paper presents methods for investigating practical identifiability: the Monte Carlo method, the matrix correlation method, the confidence intervals method and the sensitivity based method. There is presented two mathematical models of the pharmacokinetics of the C-peptide and mathematical model of the spread of the COVID — 19 epidemic. The identifiability investigation will allow us to construct a regularized unique solution of the inverse problem.

A long short-term memory based deep learning algorithm for seismic response uncertainty quantification

The application of metamodeling technique to overcome computational challenge of Monte Carlo simulation (MCS) technique for response uncertainty quantification under stochastic earthquake load is a difficult task due to the high-dimensional nature of stochastic load. Recent developments in the sequential models for forecasting and prediction have opened a new avenue in this regard. Various deep learning algorithms, particularly the convolutional neural network and recurrent neural network are quite suitable for response uncertainty quantification of nonlinear stochastic dynamic system. However, most of the existing studies consider stochastic load as the only source of uncertainty assuming the parameters characterizing a structure as deterministic. The present study proposes a long short-term memory (LSTM) based deep learning algorithm for seismic response uncertainty quantification by duly addressing both the stochastic nature of dynamic load and structural system parameter uncertainty. The functional application program interface feature of Keras that allows layers sharing to form more complex model is explored to form a response approximation model. It incorporates more than one input source i.e., stochastic dynamic excitation sequence as well as structural system parameter uncertainty. The proposed algorithm is elucidated through two numerical examples i.e., a proof-of-concept example and one realistic structural engineering problem by considering the direct MCS based results as the benchmark. The results of accuracy matrices, regression analysis results, comparison of seismic response statistics and reliability results with the results of direct MCS technique clearly revealed the enhanced prediction capability of the proposed LSTM model.

Structural Design and Dynamics Simulation Analysis of A Certain Type of Co-frame Launcher

To study the dynamic response of a certain type of co-frame launcher during launch, this article uses the 3D modeling software Pro/E to import the model into Adams from the perspective of launch dynamics. the launch dynamics model of the shared-frame launcher is established. We apply the ejection thrust of the two types of missiles to the corresponding ejection devices and measure and collect the dynamic parameters of the cartridge system. The simulation results show that the dynamic parameters of the A and B missiles are in line with the available overload design requirements. The B-type missiles are superior to the A-type missiles in terms of ballistic orbit contact force and ejection attitude.

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.