Discrete-continuous System Research Articles

A Contrastive Plan Explanation Framework for Hybrid System Models

In artificial intelligence planning, having an explanation of a plan given by a planner is often desirable. The ability to explain various aspects of a synthesized plan to an end user not only brings in trust on the planner but also reveals insights of the planning domain and the planning process. Contrastive questions such as “Why action A instead of action B?” can be answered with a contrastive explanation that compares properties of the original plan containing A against the contrastive plan containing B. In this article, we explore a set of contrastive questions that a user of a planning tool may raise and propose a re-model and re-plan framework to provide explanations to such questions. Earlier work has reported this framework on planning instances for discrete problem domains described in the Planning Domain Definition Language (PDDL) and its variants. In this article, we propose an extension for planning instances described by PDDL+ for hybrid systems that portray a mix of discrete-continuous dynamics. Specifically, given a mixed discrete-continuous system model in PDDL+ and a plan describing the set of desirable actions on the same to achieve a destined goal, we present a framework that can integrate contrastive questions in PDDL+ and synthesize alternate plans. We present a detailed case study on our approach and propose a comparison metric to compare the original plan with the alternate ones.

Non-reciprocal wave propagation in time-modulated elastic lattices with inerters

Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.

Modeling of serpentine belt accessory drive system coupled vibrations and utilizing nonlinear tensioner to enhance performances

Serpentine belt accessory drive system (SBADS) is a complex hybrid discrete-continuous system and is a typical coupled vibration system with rigid body vibrations and belt vibrations, which consists of rotational vibrations of pulleys and tensioner arm and transverse vibrations of continuum belt spans. Taking an engine front end accessory drive system as an example, the coupling vibration model of belt, pulleys and tensioner arm is established. In the model, hysteretic behavior of tensioner is considered, and a calculation method for estimating the output torque versus the imposed angle of tensioner arm is proposed. In solving the coupled motion equations of the SBADS, transverse displacement of a belt span is discretized as the product of time function and space function by using Galerkin method, the steady-state deflections of belt spans are calculated by singular perturbation method, and the nonlinear dynamic responses of a SBADS are solved by numerical method. The nonlinear dynamic responses of the SBADS are calculated by the established method and validated by the experiment results. Benefits of nonlinear hysteretic behavior of a tensioner on the dynamic responses of a SBADS are studied, and the method for how to utilize nonlinear characteristics of tensioner to enhance the performances of a SBADS is proposed in the end of this paper.

Building a model of the process of shooting a mobile armored target with directed fragmentation-beam shells in the form of a discrete-continuous stochastic system

This paper describes the process of shooting a mobile armored combat vehicle with directed fragmentation-beam shells as a discrete-continuous random process. Based on this approach, a stochastic model has been proposed in the form of a system of Kolmogorov-Chapman differential equations. A universal model of the process of defeating a moving armored target with directed fragmentation-beam shells has been built, which would provide preconditions for experimental studies into the effectiveness of various variants of the components of the artillery system for three-shot firing. The execution of an artillery task is considered as a set of certain procedures characterized by the average value of its duration. They are dependent on the firing phases involving a prospective automatic gun and the explosive destruction of fragmentation-beam shells while the explosive destruction of each shell case is characterized by the self-propagation of the reaction of explosive transformations based on tabular data on the target. An indicator of the functionality of various design options for fragmentation-beam shells is the probability of causing damage by «useful fragments» in the vulnerable compartments of a combat armored vehicle. Devising universal models for the process of shooting a moving armored vehicle forms preconditions for further full-time experiments in accordance with the design solutions defined as a result of modeling. It is possible to use the developed discrete-continuous stochastic model in other modeling tasks to determine the optimal value of defeat. As regards the practical application of discrete-continuous stochastic models, one can argue about the possibility of reducing the cost of performing design tasks related to weapons by 25 % and decreasing the likelihood of making mistakes at the stage of system engineering design

A discrete-continuous multi-vehicle anticipation model of driving behaviour in heterogeneous disordered traffic conditions

This study proposes a multi-vehicle anticipation-based discrete-continuous choice modelling framework for describing driver behaviour in heterogeneous disordered traffic (HDT) conditions. To incorporate multi-vehicle anticipation, the concept of an influence zone around a vehicle (subject vehicle) is introduced. Vehicles within the influence zone can potentially influence the subject vehicle’s driving behaviour. Further, driving decisions are characterized as combination of discrete and continuous components. The discrete component involves the decision to accelerate, decelerate, or maintain constant speed and the continuous component involves the decision of how much to accelerate or decelerate. A copula-based joint modelling framework that allows dependencies between discrete and continuous components is proposed. Such a joint modelling framework recognizes that the discrete and continuous decisions are made simultaneously, and common unobserved factors influence both decisions. Additionally, truncated distributions are employed for the continuous model components to avoid the prediction of unrealistically high acceleration or deceleration values. The parameters of the proposed model are estimated using a trajectory dataset from Chennai, India. The empirical results underscore (a) the importance of considering multi-vehicle anticipation for describing driving behaviour in HDT conditions, and (b) the efficacy of the joint discrete-continuous system for modelling driving behaviour. Further, not all traffic environment variables found to influence the discrete decisions were found influential on continuous decisions and vice versa. Moreover, the influence of several variables was found to be stronger on the decision to accelerate or decelerate than on the decision of how much to accelerate or decelerate.

A framework for estimating bikeshare origin destination flows using a multiple discrete continuous system

Given the burgeoning growth in bikeshare system installations and their growing adoption for trip making, it is important to develop modeling frameworks to understand bikeshare demand flows in the system. The current study examines two choice dimensions for capturing the system level bikeshare system demand: (1) total station level demand and (2) distribution of bike flows from an origin station across the network. A linear mixed model is used to estimate the first choice and Multiple Discrete Continuous Extreme Value (MDCEV) model is used to analyze the latter. The data is drawn from the New York City bikeshare system (CitiBike) for six months (January through June 2017). For our analysis, we examine demand and distribution patterns on a weekly basis controlling for a host of independent variables (trip, socio-demographics, bicycle infrastructure, land use and built environment, temporal and weather). Model validation exercise results revealed that the proposed model performs well for low demand destinations. A policy exercise evaluating destination choice behavior demonstrated how the impact of distance is compensated by additional bicycling infrastructure in the farther locations. The results from the study help bikesharing system planners and operators to better evaluate and improve bikeshare systems.

ALGORITHMS FOR SYNTHESIS OF DISCRETE CONTROLLERS IN NONLINEAR CONTROL SYSTEMS WITH DELAY

Algorithms for the synthesis of discrete controllers in nonlinear control systems, taking into account the delay, have been proposed. The synthesized vector controller provides a solution to the control problem, for example, the translation of the image point of a closed system from arbitrary initial conditions to the origin of the phase space coordinates. Built on the basis of a series-parallel set of invariant manifolds, the dynamic discrete controller ensures the fulfillment of the specified technological requirements, the asymptotic stability of a closed discrete-continuous system, and has the property of predicting the behavior of the system after sampling. These algorithms have made it possible to effectively solve the problems of synthesis of discrete controllers, taking into account the delay in process control systems.

Self-Sustained Oscillations on the Back Branch of the Inverse Hysteresis in a Mathematical Model of Catalytic CO Oxidation over Palladium

Under study is the mathematical model describing the inverse temperature hysteresis as well as the self-sustained oscillations in the CO oxidation over a palladium catalyst in an chemical stirred tank reactor (CSTR). We consider the reaction dynamics under temperature-programmed conditions: At first, the temperature T of the CSTR monotonically increases (due to outside heating) and then it decreases to the initial value. As the temperature goes up, on the surface and in the bulk of the catalyst two palladium oxide forms appear and then, while the temperature decreases, the catalyst reduces to its original state. The mathematical model of nonstatinary processes in such a CSTR is the piecewise continuous system of nonlinear ordinary differential equations (ODE), i.e, a discrete-continuous system. Using the theory of dynamical systems and bifurcation theory as well as numerical methods, we study the structure of the maximal families of the steady states and periodic solutions in dependence on temperature. For the system under study some sufficient conditions are given under which an inverse hysteresis is observed on the dependence of the conversion of the main reagent versus T. Moreover, as temperature decreases, there are self-oscillations of the reaction rate and CO conversion on the lower back branch of the hysteresis. The parameters of the model are found such that the experimental data are qualitatively described.

In memory of Oded Maler

Hybrid automata are an elegant formal model seamlessly integrating differential equations representing continuous dynamics with automata capturing switching behavior. Since the introduction of the computational model more than a quarter of a century ago [Maler et al. 1992], its algorithmic verification has been an area of intense research. Within this note, which is dedicated to Oded Maler (1957--2018) as one of the inventors of the model, we are trying to delineate major lines of attack to the reachability problem for hybrid automata. Due to its relation to system safety, the reachability problem is a prototypical verification problem for hybrid discrete-continuous system dynamics.

THE INFLUENCE OF FRICTION FORCES ON LONGITUDINAL WAVE PROPAGATION IN A STUCK DRILL STRING IN A BOREHOLE

A mathematical model and the computer software for the analysis of dynamic processes occurring in the drilling pipes in the borehole under stuck drill string release by means of an impact mechanism (a jerking device) or a pulse-wave installation, equipped with electric linear pulse motor are presented. The drill string with an impact mechanism, which is inserted over the stuck section after failure, is detected and is activated by lowering and taking the non-stuck upper part of the string by means of the drilling rig drive and is considered as a discrete-continuous mechanical system. As a result of the impact of the hammer on the body of the impact mechanism, wave processes are formed in the drill string, which helps to release the stuck drill string. The influence of friction forces on propagation of longitudinal waves in the drill pipe string is investigated. Practical recommendations are developed regarding the above-mentioned efficiency of drilling for oil and gas.

Discrete-Continuous Approach and Terminology: Description of Energy-Information Interaction

The objective is to study definitions that describe energy-information interactions under a discrete-continuous approach to the model of person.
 Materials and methods. The research used the general scientific methodology of systems analysis. According to it, a scientific and theoretical study does not consider relatively independent components separately, but in a combination, in a system with others. A systems approach made it possible to reveal integrative, systematic features and qualitative characteristics absent in individual elements forming the system. To define the terminology that describes energy-information interactions, the research used a discrete-continuous approach. The research object was the existence of appropriate terminology that meets the requirements of modern science.
 Results. The paper presents a model describing a person in the form of a discrete-continuous system, with the focus on energy aspects and information technology. Information technology systemizes knowledge representation, creates logical and computational tools for establishing regularities from primary information arrays, constructs information systems. The research clarified the following terms: infotomation is obtaining information knowledge on the layer-by-layer structure of the study object organization; information indicators are natural indicators transformed into a normalized relative form, according to the natural indicator position on the scale of its change. The form makes it possible to obtain an information evaluation of the system state by this indicator; information model is an information knowledge in a formula or algorithmic form.
 Conclusions. The research studied the definitions that describe energy-information interactions for the systems of material points and continuous medium.

Lyapunov analysis of the spatially discrete-continuous system dynamics

The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

Peculiarities of Simulation of Biomechanical and Biological Systems

The objective is to combine the methods and principles of biomechanics and continuum mechanics in order to pose and solve problems that have practical application in extreme conditions. Materials & methods: the movement of blood through large vessels was studied on the basis of the Euler and Navier-Stokes equations. Analysis of the cardiovascular system was used for the examination of the functional state of the athlete. The initial experimentally measured heart rate (HR) was determined by the Polar RC800 cardiac monitor. The resulting time series is analyzed using the software package Kubios HRV. Results: the article proposes to consider a model describing human body as a discrete-continuous system. Using the Euler equation, a mathematical model of the movement of blood through large vessels is considered. A mathematical model of the process of pulse wave propagation in blood vessels is given. We found and interpreted hidden periodicities relative to the numerical series occurring during analysis of biological and heart rhythms of athletes during training and competitive activities. Conclusions: the use of methods and principles of continuum mechanics makes it possible to pose and solve the problems of mathematical physics for practical purposes. These include the movement of blood through large vessels, the issue of heat protection, and so on. The heart rate changes during the day and has a fluctuating character with certain periods. Periods of heart rate depend on the activity of a person and the time of day. Moreover, the heart rate tends to increase the amplitude and depend significantly on person’s workload.

Complex modal analysis of serpentine belt drives based on beam coupling model

Serpentine belt drive system is widely used as engine front end accessory drive system in automotive industry. It is a complex hybrid discrete-continuous system whose vibrations are mainly composed of rotational vibrations of pulleys and the tensioner arm, and transverse vibrations of continuum belt spans. In this paper, an efficient method to evaluate the natural vibration characteristics of serpentine belt drives is proposed and investigated. The equations of motion of an actual multiple pulley serpentine belt drive are established and reformulated into an extended operator form, in which belt spans are modeled as axial moving beams with bending stiffness so that the belt–pulley coupling is comprehensively quantified. The natural frequencies and modes of the system are comprehensively calculated. The model is verified by a real example. Furthermore, the influences of some parameters such as belt bending stiffness and belt axial speed on natural vibration characteristics and degree of coupling are investigated, and the applicability of the traditional single beam model is discussed. The proposed method can also be used to efficiently solve eigenvalue problems of other hybrid systems composed of continuums and discrete bodies.

Multi-cell model for pressure swing adsorption process

Pressure Swing Adsorption process is a discrete–continuous system by nature and it is extremely time consuming to simulate steady state performance for a given set of design and operating parameters. A multitude of design variations is offered by the configuration of Pressure Swing Adsorption cycle in terms of choice, sequence, and durations of various possible component steps implemented on two or more adsorber beds. Often, simplifying assumptions are made to speed up each simulation. These assumptions erode the quality of match between reality and simulation and make the resultant design approximate. Use of assumptions like no adsorption/desorption during the pressurization and blowdown steps, constancy in volumetric flow during the adsorption and purge steps makes the model computationally lighter but raises questions on its predictive power. A new modeling approach, namely Multi-cell Model is presented in this work. It is shown to avoid the extensive time taken with equation-based simulations and to have better predictive power. The model is used to study a representative Pressure Swing Adsorption process for nitrogen enrichment from the air. Numerical convergence with respect to the spatial and temporal step sizes and mass balance closure is verified. The model is generic in nature and is valid for any multi-bed, multi-adsorbent, multi-component Pressure Swing Adsorption process executing any combination of component steps.

On the synthesis of passive–adaptive systems for electric drive control

A new approach to synthesis of passive–adaptive electromechanical control systems is proposed. Decomposition of a control system structure into two subsystems, which solve a uniform problem of finite control, but have various functions, is a feature of the presented approach. The first subsystem is a control system of an electric drive, and it carries out the task of finite control that is invariant to the reference signals in the traditional statement of linear discrete–continuous systems. The second subsystem is an adaptive reference model that forms a criterion that is optimal in terms of performance and accuracy of the phase coordinate vector of an electric drive with restriction of them to acceptable levels. A discrete–continuous system of electric drive control and a functional structure of a passive–adaptive electromechanical system are set up in the MexBIOS Development Studio simulating the modeling environment. The results of simulation showed that there is an acceptable quality of system operation in both linear and nonlinear areas of operation when working out additive increments of setting the position of the drive shaft changing at random points of time. The synthesized system has low sensitivity to changes in the parameters of the object of electromechanical control.

Controllability and observability of hybrid discrete-continuous systems in the simplest function classes

We consider controllability problems for linear discrete dynamical systems in the class of outputs of linear discrete dynamic controllers. We obtain a number of necessary conditions, sufficient conditions, and necessary and sufficient conditions for such a controllability. In the case of the solvability of some controllability problem, we represent the form of an admissible control bringing the trajectory of the system from an initial state into a given terminal state. Dual observability problems are stated, and the duality principle in considered problems of control and observation is proved. The obtained results are analyzed and illustrated in detail by related examples and counterexamples and are applied to the study of the controllability and observability problems for quantized hybrid discrete-continuous systems in classes of functions piecewise constant on the quantization interval and described by discrete algebraic and trigonometric polynomials as well as solutions of difference equations. We consider an example of the controllability of a hybrid discrete-continuous system in the class of algebraic polynomials.

Необходимые условия оптимальности в задаче оптимального управления дискретно-непрерывной системой

Необходимые условия оптимальности в задаче оптимального управления дискретно-непрерывной системой

Necessary Conditions of Optimality of the First and Second Order in a Stepwise Optimal Control Problem with Discrete-Continuous System

Necessary Conditions of Optimality of the First and Second Order in a Stepwise Optimal Control Problem with Discrete-Continuous System

Effect of periodicity of railway track and wheel–rail interaction on wheelset–track dynamics

The paper deals with the investigation of some phenomena which are essential for dynamic interaction of a wheelset or bogie with the railways track. The track is modeled as discrete–continuous system composed of rails, fastening systems and sleepers interacting with ballast by means of viscous–elastic elements. Transient and stationary problems are investigated. The stationary periodic problems are connected with wave propagation in stopping bound, passing bound and mistuning. In this paper, a review of selected problems and exemplary results of simulation and experimental investigations is given supplemented by a few results of analysis and simulation.