Time-continuous System Research Articles

Transparent boundary condition and its high frequency approximation for the Schrödinger equation on a rectangular computational domain

This paper addresses the numerical implementation of the transparent boundary condition (TBC) and its various approximations for the free Schrödinger equation on a rectangular computational domain. In particular, we consider the exact TBC and its spatially local approximation under high frequency assumption along with an appropriate corner condition. For the spatial discretization, we use a Legendre–Galerkin spectral method where Lobatto polynomials serve as the basis. Within variational formalism, we first arrive at the time-continuous dynamical system using spatially discrete form of the initial boundary-value problem incorporating the boundary conditions. This dynamical system is then discretized using various time-stepping methods, namely, the backward-differentiation formula of order 1 and 2 (i.e., BDF1 and BDF2, respectively) and the trapezoidal rule (TR) to obtain a fully discrete system. Next, we extend this approach to the novel Padé based implementation of the TBC presented by Yadav and Vaibhav (2024). Finally, several numerical tests are presented to demonstrate the effectiveness of the boundary maps (incorporating the corner conditions) where we study the stability and convergence behaviour empirically.

Continuous short-term pain assessment in temporomandibular joint therapy using LSTM models supported by heat-induced pain data patterns.

This study aims to design a time-continuous pain level assessment system for temporomandibular joint therapy. Our objectives cover verifying literature suggestions on pain stimulus, protocols for collecting reference data, and continuous pain recognition models. We use two types of pain data acquired during (1) heat stimulation and (2) temporomandibular joint therapy. Thirty-six electrodermal activity (EDA) features are determined to build a binary classification model. The experimental dataset is used to train the initial model that produces pseudo-labels for weakly-labeled clinical data. In training the final long short-term memory (LSTM) model, we propose a novel multivariate loss involving, i.a., dynamometer data. Significant differences are found between EDA features extracted from experimental and clinical datasets in pain and no pain events. The classification model is validated at different stages of the model development. The final model classifies each four-second frame with a mean accuracy of 0.89 and an F1 score of 0.85. Our study introduces the dynamometer as a novel source of pain-feeling indications that meets the challenges given in the literature: data can be acquired in various procedures and from patients with limited abilities. The main contribution of the study is to design the first time-continuous and short-term pain assessment system for a clinical setting.

Research on a Space-Time Continuous Sensing System for Overburden Deformation and Failure during Coal Mining.

Underground coal mining can cause the deformation, failure, and collapse of the overlying rock mass of a coal seam. If the mining design, monitoring, early warning, or emergency disposal are improper, in that case, it can often lead to mining disasters such as roof falls, water inrush, surface collapse, and ground fissures, seriously threatening the safety of mine engineering and the geological environment protection in mining areas. To ensure the intrinsic security of the entire coal mining process, aspace-time continuous sensing system of overburden deformation and failure was developed, which breaks through the limitations of traditional monitoring methods that characterize the evolution process of overlying rock deformation and ground subsidence. This paper summarizes the classification of typical overburden deformation and failure modes. It researches the space-time continuous sensing of rock-soil mass above the coal seam based on Distributed Fiber Optic Sensing (DFOS). A multi-range strain optical fiber sensing neural series from micron to meter was developed to achieve synchronous sensing of overburden separation, internal micro-cracks, and large rock mass deformation. The sensing cable-rock mass coupling test verified the reliability of the optical fiber monitoring data. The sensing neural network of overburden deformation was constructed using integrated optical fiber layout technology on the ground and underground. Different sensing nerves' performance and application effects in overburden deformation and failure monitoring were compared and analyzed with field monitoring examples. A physical model was used to carry out the experimental study on the overburden subsidence prediction during coal mining. The results showed that the optical fiber monitoring data were reliable and could be used to predict overburden subsidence. The reliability of the calculation model for overlying rock subsidence based on space-time continuous optical fiber sensing data was verified in the application of mining subsidence evaluation. A systematic review of the shortcomings of current overburden deformation observation technology during coal mining was conducted, and a space-time continuous sensing system for overburden deformation and failure was proposed. This system integrated sensing, transmission, processing, early warning, decision-making, and emergency response. Based on the fusion of multi-parameter sensing, multi-method transmission, multi-algorithm processing, and multi-threshold early warning, the system realized the real-time acquisition of space-time continuous information for the overburden above coal seams. This system utilizes long-term historical monitoring data from the research area for data mining and modeling, realizing the prediction and evaluation of the evolution process of overburden deformation as well as the potential for mining subsidence. This work provides a theoretical reference for the prevention and control of mining disasters and the environmental carrying capacity evaluation of coal development.

Adaptive finite-time parameter estimation for grid-connected converter with LCL filter

This study proposes an online finite-time adaptive parameter estimation method for grid-connected voltage source inverter (VSI) with LCL filter. In this framework, a time-continuous state-space system model is first developed, which is different from the nonparametric frequency-response-based method. Then, the parameter estimation error information is extracted by introducing a series of filter operations. Moreover, a sliding mode term is studied and cooperated with the obtained parameter estimation error to design the parameter estimation error-based finite-time adaptive parameter estimation algorithm. With the help of this novel adaptive law, the physical parameters of electrical components can be driven to their true values accurately and fast. Theoretical analysis is conducted in terms of the Lyapunov theory to demonstrate the convergence of the parameter estimation error. Finally, numerical simulation results are provided to illustrate the superiority of the proposed method over the conventional method.

Networked control systems with probabilistic time-varying delay based on event-triggered non-fragile [formula omitted] control

The non-fragile H∞ problem for networked control systems with probabilistic time-varying delay, stochastic nonlinear, controller gain fluctuation and adaptive event-triggered mechanism is studied. The random interval delay, nonlinear fluctuation and gain fluctuation of the controller all obey a certain uncorrelated Bernoulli distribution white noise sequence. An improved time continuous delay system model for networked control systems is constructed by using input delay method. A two-sided closed-loop Lyapunov–Krasovskii functional is constructed considering the sawtooth structure of artificial time delay, and the asymptotically stable conditions of closed-loop system with little conservatism are obtained. A non-fragile H∞ control strategy based on adaptive event-triggered is proposed and the co-design method for gain matrix of the non-fragile controller and event-triggered matrix is obtained. Finally, the effectiveness of the proposed method is verified by two simulation examples.

An Adaptive Framework for Optimization and Prediction of Air Traffic Management (Sub-)Systems with Machine Learning

Evaluating the performance of complex systems, such as air traffic management (ATM), is a challenging task. When regarding aviation as a time-continuous system measured in value-discrete time series via performance indicators and certain metrics, it is important to use sufficiently targeted mathematical models within the analysis. A consistent identification of system dynamics at the evaluation level, without dealing with the actual physical events of the system, transforms the analysis of time series into a system identification process, which ensures control of an unknown (or only partially known) system. In this paper, the requirements for mathematical modeling are presented in the form of a step-by-step framework, which can be derived from the formal process model of ATM. The framework is applied to representative datasets based on former experiments and publications, for whose prediction of boarding times and classification of flight delays with machine learning (ML) the framework presented here was used. While the training process of neural networks was described in detail there, the paper shown here focuses on the control options and optimization possibilities based on the trained models. Overall, the discussed framework represents a strict guideline for addressing data and machine learning (ML)-based analysis and metaheuristic optimization in ATM.

Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics

In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.

Effects of Sampling and Prediction Horizon in Reinforcement Learning

Plain reinforcement learning (RL) may be prone to loss of convergence, constraint violation, unexpected performance, etc. Commonly, RL agents undergo extensive learning stages to achieve proper functionality. This is in contrast to classical control algorithms, which are typically model-based. A direction of research is the fusion of RL with such algorithms, especially model-predictive control (MPC). This, however, introduces new hyper-parameters related to the prediction horizon. Furthermore, RL is usually concerned with Markov decision processes. Nevertheless, most of the real environments are not time-discrete. The factual physical setting of RL consists of a digital agent and a time-continuous dynamical system. There is thus, in fact, yet another hyper-parameter – the agent sampling time. In this paper, we investigate the effects of prediction horizon and sampling of two hybrid RL-MPC agents in a case study with a mobile robot parking, which is, in turn, a canonical control problem. We benchmark the agents with a simple variant of MPC. The sampling showed a “sweet spot” behavior, whereas the RL agents demonstrated merits at shorter horizons.

ROBUST MATHEMATICAL FORMULATION AND PROBABILISTIC DESCRIPTION OF AGENT-BASED COMPUTATIONAL ECONOMIC MARKET MODELS

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy–Levy–Solomon model and the Franke–Westerhoff model. We derive time-continuous formulations of both models, and in particular, we discuss the impact of the time-scaling on the model behavior for the Levy–Levy–Solomon model. For the Franke–Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time-continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic descriptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy–Levy–Solomon and Franke–Westerhoff model.

Multi-model estimation using neural network and fault detection in unknown time continuous fractional order nonlinear systems

In this paper, multi-model estimation and fault detection using neural network is proposed for an unknown time continuous fractional order nonlinear system. Fractional differentiation is considered based on Caputo concept and the fractional order is considered to be between 0 and 1. In order to estimate a time continuous fractional order nonlinear system with unknown term in its dynamic, single-layer and double-layer RBF neural network is used. First, a parallel-series neural network observer is designed for state estimation. Weights of the neural network are updated adaptively and updating laws are presented in fractional order form. Using Lyapunov method, it is proved that state estimation error and weight estimation error of the neural network are bounded. Parameters of the neural estimator converge to ideal parameters which satisfy excitation condition stability. Then, multi-model estimation structure of fractional order nonlinear systems is presented and its application in fault detection is investigated. Finally, simulation results are presented to show efficiency of the proposed method.

Blood pressure monitoring system: real time-continuous and noninvasive-electronic, based on magnetic dipole moment of the proton spin of hydrogen atoms in the blood

This research is motivated by the fact that blood pressure monitoring devices currently available cannot be integrated practically with other electronic health monitoring devices. The research is aimed to obtain a real time-continuous and noninvasive-electronic blood pressure monitoring system with a magnetic coil technique. This technique is a simplified form of the nuclear magnetic resonance (NMR) technique because the induced EMF that is obtained does not involve resonance but rather by sudden population changes and relaxation of the magnetic dipole moments of the proton spin of hydrogen atoms in the blood, both when systole and diastole. The benefit of this research output is that it can obtain noninvasive-electronic blood pressure monitoring devices, and the monitoring process does not interfere with blood flow in the branchial artery samples, so that the monitoring equipment can be integrated with other health monitoring equipment practically. The methodology of this research was carried out by placing a sample arm between two poles of a permanent magnet with a magnitude (7,300±200) gauss and his or her hand inside the receiver coil (involving 2,000 turns), after going through a 500 times voltage gain an induction EMF (in volts) was displayed on digital storage oscilloscope screen. This is done when the sample is relaxed (17 volts is obtained), shortly after jogging (26 volts), and the relaxed state a few moments later (12 volts). The result is that the induced EMF signal enlarges and widens shortly after jogging but slides back when the sample return to relaxed. It was concluded that this blood pressure monitoring equipment of the magnetic-coil technique could be used as a blood pressure monitor.

378-P: Human Voice Is Modulated by Hypoglycemia and Hyperglycemia in Type 1 Diabetes

Anecdotal evidence suggests that high pitched voice may be a clinical symptom of hypoglycemia. We conducted a pioneer study aiming at assessing voice variables during hypoglycemia and hyperglycemia. We recruited 10 non-smoking individuals with type 1 diabetes (4 women, 6 men; mean [±SD] age 40.2±10.4 years, diabetes duration 21.4±9.9 years, HbA1c 8.0±1.8%) who were using real time continuous glucose monitoring system (rt-CGM, Guardian Connect, Medtronic) for mean 5.2±0.6 days in controlled hospital setting. At regular intervals during normoglycemia and additionally at blood glucose <70 mg/dl or >200 mg/dl each patient was instructed to record with a professional voice recorder (LS-14, Olympus) a standardized sentence and the sound of vowel ‘a’ for 3 seconds. The voice samples (n=177) were analyzed against CGMS data with the DiagnoScope software (DiagNova, Wroclaw, Poland). Number of fundamental PERiods (PER), time of fundamental PERiods (PERTime), fundamental frequency (F0), energy (E), amplitude of fundamental frequency (AF0), indicator of voiced/phonation probability (Voiced), simple voice quality (SimpleQ), relative average perturbation (RAP), shimmer (Shimm), amplitude perturbation quotient (APQ), four formant frequencies (F1-F4), harmonic perturbation quotients (HPQ), residual to harmonic ratio (R2H), unharmonic to harmonic ratios (U2H), subharmonic to harmonic ratio (S2H), noise to harmonics ratio (NHR), 1st to 4th harmonic to all energy ratio (Fx1-Fx4) were analyzed. In women during hypoglycemia E, AF0, Voiced, F1, F4, R2H, Fx3, Fx4, while in hyperglycemia - RAP and F2 were significantly altered when compared to normoglycemia. In men in hypoglycemia the differences were found in PER, PERTime, Voiced, SimpleQ, Shimm, APQ, F2, U2H, S2H, Fx2, NHR, while in hyperglycemia - PERTime, F1, HPQ, U2H, Fx2 (all p<0.05). We report for the first time that hypoglycemia and hyperglycemia modulate human voice. This phenomenon may offer potential for early detection and prevention of hypoglycemia. Disclosure L. Czupryniak: None. E. Sielska-Badurek: None. A. Niebisz: None. M. Sobol: None. M. Kmiecik: None. K. Jedra: None. E. Szymanska-Garbacz: None. K. Niemczyk: None. Funding Polish Ministry of Science and Higher Education

Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials

According to the theory of stable and unstable manifolds of an equilibrium point, we firstly find out some geometrical properties of orbits on the stable and unstable manifolds of a saddle point under some brief conditions of nonlinear terms composed of polynomials for [Formula: see text]-dimensional time continuous system. These properties show that the orbits on stable and unstable manifolds of the saddle point will stay on the corresponding stable and unstable subspaces in the [Formula: see text]-neighborhood of the saddle point. Furthermore, the necessary conditions of existence for orbit homoclinic to a saddle point are exposed. Some examples including homoclinic bifurcation are given to indicate the application of the results. Finally, the conclusions are presented.

Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants

Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system coupled to non-linear diffusion equations that describe the diffusion of the surfactant in the bulk phases as well as along the diffuse interface. Moreover, the surfactant concentration influences the free energy and therefore the surface tension of the diffuse interface. For this system existence of weak solutions globally in time for general initial data is proved. To this end a two-step approximation is used that consists of a regularization of the time continuous system in the first and a time-discretization in the second step.

State Estimation for Coupled Output Complex Dynamical Networks with Stochastic Sampled-Data

In this paper, the problem of the state estimation on complex dynamical networks coupled with stochastically sampling is studied. By using the input delay approach, the sampled-data system is transformed into a time-continuous system where the data at sampling periods have two different time-varying delays randomly happening between two intervals which have different known lower and upper bounds. The sampling points occur with two known probabilities and satisfy Bernoulli distribution. There are two different types of stochastically-sampled-data considered in this complex dynamical network. One of the stochastically-sampled-data is used to data exchange over the dynamical network, the other is used to construct the Luenburger state estimator as feedback data. We derive the state estimator for the complex dynamical network with new models which combined with two types of above stochastic-sampled-data, and delay-dependent asymptotical stabilities of the estimation error has been solved by constructing a Lyapunov–Krasovskii functional and the linear matrix inequality toolbox in MATLAB. Finally, a numerical example has been illustrated to demonstrate the effectiveness of the proposed results.

Prediction of flow dynamics using point processes.

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

Metriplectic integrators for the Landau collision operator

We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonic behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.

Evaluation of the impact of orally administered carbohydrates on postprandial blood glucose levels in different pre-clinical models

We developed a pre-clinical model in which to evaluate the impact of orally administered carbohydrates on postprandial blood glucose levels. For this purpose, we compared the effects of different carbohydrates with well-established glycemic indexes. We orally administered (gavage) increasing amounts (0.2, 0.4, 0.6, 0.8, and 1.0 g/kg) of sucrose and lactose to rats which had been fasted for 6 h or 15 h, respectively. In part of the experiments we administered frutose (gavagem). Three different models were compared for measuring postprandial blood glucose levels: a) evaluation of interstitial glucose concentrations by using a real time continuous glucose monitoring system; b) evaluation of glucose levels in blood obtained from the rat tail; c) evaluation of serum glucose levels in blood collected after decapitation. Our results showed that blood obtained from the tails of 15-h fasted rats was the best model in which to evaluate the effect of carbohydrates on postprandial blood glucose levels.

A double window state observer for detection and isolation of abrupt changes in parameters

Abstract The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T. These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window zT (t − T) and the initial value of the state z 0(t − T) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment tA = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

Use of a real time continuous glucose monitoring system as an educational tool for patients with gestational diabetes.

BackgroundWomen with gestational diabetes mellitus (GDM) are required to control their blood glucose shortly after GDM diagnosis to minimize adverse pregnancy outcomes. A real time-continuous glucose monitoring system (RT-CGMS) provides the patient with continuous information about the alterations in levels of the blood glucose. This visibility may empower the patient to modify her lifestyle and engage in therapeutic management. The aim of this study was to determine whether a single application of RT-CGMS to pregnant women shortly after GDM diagnosis is useful as an educational and motivational tool.MethodsThis study was a prospective open label randomized controlled study conducted at Maternity and Children Hospital, Medina, Saudi Arabia. A total of 130 pregnant women with GDM were randomised to either blood glucose self-monitor alone (SMBG group) (n = 62) or in addition to SMBG, patients wore a Guardian® REAL-Time Continuous Glucose Monitoring System (Medtronic MiniMed) once for 3–7 days, within 2 weeks of GDM diagnosis (RT-CGMS group) (n = 68). The primary outcomes were maternal glycemic control and pregnancy outcomes. Secondary outcomes were the changes in parameters of glucose variability, which includes mean sensor readings, standard deviation (SD) of blood glucose, and area under the curve for hyper and hypoglycaemia at the end of the RT-CGMS application.ResultsHbA1c, mean fasting and postprandial glucose levels were similar in both groups at the end of the pregnancy. Pregnancy outcomes were comparable. However, there was significant improvement in the parameters of glucose variability on the last day of sensor application; both mean glucose and the SD of mean glycaemia were reduced significantly; P = 0.016 and P = 0.034, respectively. The area under the curve for hyper and hypoglycaemia were improved, however, the results were not statistically significant.ConclusionAlthough a single application of RT-CGMS shortly after GDM diagnosis is helpful as an educational tool, it was not associated with improvement in glycemic control or pregnancy outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s13098-016-0161-5) contains supplementary material, which is available to authorized users.