Dynamic Behaviour Of System Research Articles

Bullwhip effect in closed-loop supply chains with multiple reverse flows: a simulation study

Due to the complex nature of some products and the different quality of returns, in closed-loop supply chains there might be different types of reverse processes and reverse flows, including repaired, refurbished, remanufactured, or recycled goods. These reprocessed goods return to different echelons of the supply chain according to their quality, and the volume of each type of reverse flow (i.e. the returns share) may significantly vary between different supply chains, affecting the dynamic behaviour of the entire system. The aim of this work is to explore the impact of the volume of returns among multiple reverse flows in a closed-loop supply chain where each member can have its own reverse flow. We analyse a four-echelon closed-loop supply chain, where a collector is in charge of collecting and inspecting the returns and sending them to the different echelons depending on their quality. An agent-based simulation model considering different return rates, coefficient of variations for the forward lead times, and returns share is developed and evaluated in terms of bullwhip effect. We observe that considerable volume and medium–low quality of the returns enable bullwhip effect reduction in systems where returns are shared among all the members of the supply chain. However, in single reverse flow closed-loop supply chains, moderate volume and high quality of the returns are preferable to gain improvements both in terms of order and inventory variability. From a managerial point of view, we provide useful recommendations for companies adopting closed-loop.

Assessing performance using maturity model: a multiple case study of public health supply chains in Nigeria

PurposeThis study aims to determine the factors and dynamic systems behaviour of essential medicine stockout in public health-care supply chains. The authors examine the constraints and effects of mental models on medicine stockout to develop a dynamic theory of medicine availability towards saving patients’ lives.Design/methodology/approachThis study uses a mixed-method approach. Starting with a survey method, followed by in-depth interviews with stakeholders within five health-care supply chains to determine the dynamic feedback leading to stockout and conclude by developing a network mental model for medicines availability.FindingsThe authors identified five constraints and developed five case mental models. The authors develop a dynamic theory of medicine availability across cases and identify feedback loops and variables leading to medicine availability.Research limitations/implicationsThe need to include mental models of stakeholders like manufacturers and distributors of medicines to understand the system completely. Group surveys are prone to power dynamics and bias from group thinking. This survey’s quantitative output could minimize the bias.Originality/valueThis study uniquely uses a mixed-method of survey method and in-depth interviews of experts to assess the essential medicine stockout in Nigeria. To improve medicine availability, the authors develop a dynamic network mental model to understand the system structure, feedback and behaviour driving stockouts. This research will benefit public policymakers and hospital managers in designing policies that reduce medicine stockout.

A Dynamic Response Analysis of Vehicle Suspension System

Automotive engineering is a very important branch of design and development in mechanical engineering devoted to vehicle manufacturing. It demands solid knowledge focusing on the kinematics and dynamics of mechanical systems, either using structural analysis or modelling techniques. In this manuscript, a model based on the application of the fundamentals of the static and dynamic behaviour of the suspension system of a bus vehicle is developed. Therefore, a set of mathematical equations is expanded following the structural dynamic formulations to obtain an analytical solution on natural frequencies and the displacement under an external load. The problem is also solved using the Finite Element Method (FEM) to confirm the analytical results. Equivalent material parameters and boundary conditions were used for the FEM simulation. This work aims to propose a methodology based on modal analysis with a simplified model to predict the dynamic response of an automotive structure.

Non-linear dynamics and stability of rolling bearing–axle coupling system of a railway freight wagon with the change of axle rotating speed

PurposeThe purpose of this paper is to investigate the non-linear characteristics and stability of the rolling bearing–axle coupling system under the excitation of the axle/wheel speed of railway freight cars, so as to put forward a rationale for judging the vibration law and running stability of railway freight wagon.Design/methodology/approachConsidering the effects of eccentric force of the railway wagon axle, the non-linear resistance of the wagon and non-linear support forces of axle box rolling bearings, a centralized mass model of rolling bearing-axle coupling system of railway freight wagon is presented on the basis of the theory of rotor dynamics and non-linear dynamics. Then the Runge-Kutta method is adopted to solve the non-linear response of the proposed system, and numerical simulation including bifurcation diagrams, axis trajectory curves, phase plane plots, Poincaré sections and amplitude spectras are analysed when the axle rotating speed is changed. Meantime, the relation curve between Floquet multiplier and axle rotating speed, which affects the stability of coupling system, is plotted by numerical method based on the Floquet theory and method.FindingsThe simulation results of the dynamic model reveal the abundant dynamic behaviour of the coupling system when the axle rotating speed changes, including single period, quasi period, multi-period and chaotic motion, as well as the evolution law from multi-period motion to chaotic motion. And especially, the bearing–axle coupling system is in stable state with a single period motion when the axle rotating speed changes from 410 rpm to 510 rpm, in which the running speed of railway freight wagon is changed from 62 km/h to 80 km/h, the vibration displacement of the coupling system in X direction is between 1.2 mm and 1.8 mm, and the vibration displacement of the coupling system in Y direction is between 1.0 mm and 1.45 mm. Meanwhile, the influence law of axle rotating speed on the stability is obtained by comparing the bifurcation diagram and Floquet multiplier graph of the coupling system.Originality/valueThe numerical simulation data obtained in this study can provide a theoretical evidence for designing the running speed of railway freight wagon, utilizing or controlling the non-linear dynamic behaviours of the proposed coupling system, and ensuring the stability of railway freight wagons.

Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects

In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive R0s as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients.

Complexity And Chaos Control of A Cournot Duopoly Game With Relative Profit Maximization And Heterogeneous Expectations

The paper considers a Cournot-type duopoly game, in which linear demand and cost functions are used. The two players produce differentiated goods and offer them at discrete times on a common market. In the cost functions of the players, in addition to the production cost, the cost of transporting the products is also included. Each firm does not care only about its profits but also about the percentage of its opponents’ profits, using a generalized relative profit function. In this model, the players follow different strategies. More specifically, the first player is characterized as a bounded rational player while the second player follows an adaptive mechanism. The existence of the Nash Equilibrium is proved, and its stability conditions are found. The complexity that appears for some values of the game’s parameters is shown. A mechanism by which the chaotic behavior of the discrete dynamical system is presented, importing a new parameter m. The algebraic results are verified, and the apparent complexity is shown by plotting bifurcation diagrams and strange attractors, computing the Lyapunov numbers, and checking the system’s sensitivity on its initial conditions.
 Keywords: Cournot duopoly game, discrete dynamical system, heterogeneous expectations, stability, chaotic behavior, chaos control

Comparative Study of the Non-Linear Dynamic Behaviour of Different Seismic Isolation Systems

To mitigate the effect of earthquake on the structure, the base isolation technique is the best alternative as a seismic protection system. In this research, a two-degree-of-freedom (2DOF) equivalent model is modelled based on a real eight-level reinforced concrete structure damaged by the Boumerdes earthquake in 2003 is presented. The basic isolation systems considered are four models namely: the first system is a high damping isolator (HDBR), the second system is the friction pendulum isolator (FPS). The third model of the base isolation system is a non-linear model with two horizontal and rotational stiffness springs (SHRS), and finally the last model presents a bilinear spring (SB). The isolators are designed according to the UBC-97 code. Earthquake recordings from Dar-El-Beida of the 2003 Boumerdes earthquake were used as seismic load. A dynamic analysis of the comparative temporal responses of the structure was performed by comparing its dynamic behaviour with that of the fixed base structure. The results obtained reveal a reduction in base shear, stage drift and stage acceleration and an increase in displacement and time period for the structure isolated at the base. The results are presented in tables and graphs.

Dynamical behaviour of a prey-predator system in a destructive environment incorporating prey refuge

Degradation of habitat is a direct outcome of anthropogenic activities, which includes urbanization, mining, the emission of industrial waste, and many others. Many living organisms experience severe surviving challenges as a result of habitat degradation. Here, we have studied the impact of habitat destruction caused by human activities on the dynamics of a prey-predator interaction with prey refuge. Our analyses reveal that a higher rate of habitat destruction than the habitat regeneration rate is always detrimental to the survival of predators. Predator species may still be threatened with extinction even if the rate of habitat degradation is slightly lower than the habitat recovery rate. So, in order to maintain biodiversity, we must appropriately step up our efforts to slow down the rate of habitat degradation as well as accelerate the habitat restoration. Further, our investigation suggests that in order to achieve cohabitation, we should effectively control the habitat deterioration caused by human activity, rather than artificially introducing or eliminating the hiding places of prey species.

Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique

<abstract><p>In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number $ {\bf R}_{0}^{s} $ that can predict pathogen extermination and mean persistence. Furthermore, we show that if $ {\bf R}_{0}^{s} > 1 $, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.</p></abstract>

CHAOTIC BEHAVIOR OF FINANCIAL DYNAMICAL SYSTEM WITH GENERALIZED FRACTIONAL OPERATOR

In this paper, we analyzed the chaotic complexity of a financial mathematical model in terms of a new generalized Caputo fractional derivative. There are three components in this nonlinear financial model: price indexes, interest rates, and investment demand. Our analysis is based on applying the fixed point hypothesis to determine the existence and uniqueness of the solutions. The bifurcation of the proposed financial system has been analyzed at various parameters of the system. Dynamical phase portraits of the proposed financial model are demonstrated at various fractional-order values. We investigated the possibility of finding new complex dynamical behavior with generalized Caputo fractional derivative. This economic model is solved numerically using a predictor–corrector (PC) algorithm with a generalized Caputo derivative. This algorithm can be viewed as a non-integer extension of the classical Adams–Bashforth–Moulton (ABM) algorithm. Additionally, this numerical algorithm has been studied for stability. A number of diverse dynamic behaviors have been observed in numerical simulations of the system, including chaos. Over a broad range of system parameters, bifurcation diagrams indicate that the system behaves chaotically.

PMA models for nonlinear control: Nonlinear Damping and Limit-Cycle Induction for Reference Tracking

Piecewise multiaffine (PMA) controller design is straightforward, as it is possible to design a controller based on a desired close-loop plant model. The inherent robustness and simplicity involved in the design of PMA controllers, make it an attractive control scheme. PMA model based control of dynamic systems offers a rich variety of design alternatives. This paper aims at showing the advantages to use PMA models for nonlinear control. Thus, (a) a case of Nonlinear Damping for static reference signal and (b) a case of Limit-Cycle induction for dynamic reference signal so that tracking is greatly improved, are presented. The dynamic behaviour of the controlled system will be totally determined by the nature of the nonlinear surface induced by the PMA model.

Dynamic analysis of the effects of self-weight induced structural and damping nonlinearity on the performance of an origami-inspired vibration isolator

Origami-inspired structure has shown strong nonlinearity on its force response during morphing process between phases. When the origami-inspired structure is applied as vibration isolation system, the structural weight is rare to be considered and discussed in the modelling and analysis of vibration isolation system. The effects of the structural self-weight on the dynamic behaviour of the isolation system is not yet fully understood. Thus, this study aims to investigate the influence of the self-weight induced structural and damping nonlinearity on the dynamic performance of an origami-based vibration isolator. A three-mass body, which includes the payload mass, top facets’ mass and bottom facets’ mass, with multiple degree-of-freedom (DOF) motion is proposed to describe the vibration isolation system. First, a quasi-zero-stiffness feature is designed and its static performance is discussed for a set of specifically selected system parameters. Then, the equation of motion for such three-mass body with spring damping considered is derived by using the harmonic balance method (HBM) on its Lagrange's formulation, where the effects of strong nonlinearity on its dynamic performance can be investigated. The analytical expression is verified with the numerical solutions, which are obtained using the Newmark numerical integration method. The influences of each important system parameter on the dynamic nonlinearity are also discussed. It is expected that this study would provide valuable insights to the effects of structural self-weight in a quasi-zero-stiffness isolation system.

Seismic Fragility Assessment of RC Building Using HAZUS Methodology and Incremental Dynamic Analysis

The technique of coupled building strategy is more viable to protect the adjacent buildings of dissimilar in characteristics against seismic hazards. The philosophy of coupled building control in which adjacent buildings are allowed to exerts counter-acting forces one upon another. This study includes the seismic performance of various Coupled Buildings with respect to Uncoupled Buildings for which two models of Coupled Building are considered that is, first one is the two-shear type adjacent buildings connected in-line with MR dampers and second one is same as first with taller building is isolated by Resilient-Friction Base Isolator at its foundation. The seismic response analysis of RC coupled buildings are studied in terms of peak responses subjected to unidirectional excitation due to Kobe 1995 earthquake. The governing equation of motion of various coupled buildings is solved numerically by Newmark’s step-by-step method. The dynamic behaviour of semiactive MR damper and R-FBI base isolation system has been predicted by modified Bouc-Wen model and Wen’s model respectively. This study employed the Lyapunov direct approach as a control algorithm for the stability analysis and design of semiactive MR controller. The responses of various coupled buildings and uncoupled buildings are simulated through MATLABâ computing software. This study outlined that model of Coupled Building-2 performs more effective in controlling the seismic responses whereas model of Coupled Building-1 performs well not only in reducing the responses but also avoid pounding from the adjacent buildings. Further, there is significant reduction in responses of taller building isolated by base isolation system whereas marginal reduction takes place in shorter building which is not isolated.

Data-Driven and Model-Based Control Techniques for a Wind Turbine Benchmark Model

Abstract: Wind turbine plants are complex dynamic and uncertain processes driven by stochastic inputs and disturbances, as well as different loads represented by gyroscopic, centrifugal, and gravitational forces. Moreover, as their aerodynamic models are nonlinear, both modelling and control become challenging problems. On one hand, high–fidelity simulators should contain different parameters and variables in order to accurately describe the main dynamic system behaviour. Therefore, the development of modelling and control for wind turbine systems should consider these complexity aspects. On the other hand, these control solutions have to include the main wind turbine dynamic characteristics without becoming too complicated. The main point of this paper is thus to provide two practical examples of development of robust control strategies when applied to a simulated wind turbine plant. Extended simulations with the wind turbine benchhmark model and the Monte–Carlo tool represent the instruments for assessing the robustness and reliability aspects of the developed control methodologies when the model–reality mismatch and measurement errors are also considered. Advantages and drawbacks of these regulation methods are also highlighted with respect to different control strategies via proper performance metrics.

A numerical assessment of a latent heat storage system for district heating substations

This work deals with the development and sizing of a latent heat storage system for an urban district heating system (UDHS). The investigated system is a cylindrical tank containing spherical phase change material (PCM) capsules. A physical model based on the apparent specific capacity method was adopted and validated to describe the phase transition within the capsules. The effects of various designs and operating factors on storage performance are detailed and addressed, including the thermal energy provided by the system during the discharge period, the melting temperature, tank volume, and water return temperature. The results show that the energy efficiency of such a device can be enhanced only through a judicious choice of the mentioned parameters. For example, it was found that increasing the UDHN thermal power demand influences the system's performance and leads to reduce the discharging duration. Based on the presented analyses, it can be concluded that the proposed numerical tool can be used by thermal designers of urban heating networks to size, optimise, and predict the actual dynamic behaviour of the storage system under real exploitation conditions.

What could we have learnt from the previous flood data to predict losses caused by the 1980, 1986, and 1998 catastrophic floods in Ukrainian Transcarpathian?

This paper explores some aspects relating to retrospective predicting the confirmed monetary losses caused by the disastrous floods of 1980, 1986, and 1998 in the Tisza River basin within the Transcarpathian region of Ukraine. The research was based on two time series – the losses because of past floods and the maxima water discharges gauged at the hydrological station near the village of Vylok, Vynohradiv district. The main aim of the research was to make out whether it had been the possibility to predict the losses due to those floods in advance.In solving the task, there was revealed and modelled the dependence of the risk of losses due to the floods in Transcarpathia on the maximum water discharges of the Tisza River gauged at the “Vylok” hydrological station. Predicting was based on the hypothesis of the stationary random process for maximum water discharges, which allowed using an empirical distribution function of a random variable regarding flood water discharges assessing the risk of flood losses.Retrospective predicting of the losses caused by the floods of 1980, 1986, and 1998 was carried out by means of a combined situational-inductive predictive modelling method (CSIPMM), being an original author’s development. The method relates to predicting the behaviour of complex dynamic systems based on monitoring findings presented as time series data reflecting evolutions of a resulting (dependent) variable and an explaining (independent) variable (predictor). The method uses extrapolation-regression type models. According to this method, the prediction task is performed in two stages. The first stage realises the retrospective situational modelling task aiming to obtain a set of simple regressions (situational models) built on data of sample time series. The situational models are accepted to be adequate or relevant ones only within certain periods of time determined as situations. In the second stage, based on the generalization (on an ensemble) of the obtained retrospective situational models, inductive “levels” models are built, which reflect the behaviour of a controlled parameter of the system or process (a resulting variable) at several fixed values of a predictor in time. The inductive models are used in extrapolative predicting situational models belonging to future periods (situations).In total, three predictions were made: (1) taking into account the annual maximum flood discharges from 1954 to 1979 (before the flood of 1980); (2) the same from 1954 to 1985 (before the flood of 1986); (3) the same from 1954 to 1997 (before the flood of 1998). The study found that there had been a possibility to predict the confirmed monetary losses inflicted by the flood of 1986 and 1998 (relative predicting errors of 7.2-8.7% and 6.0-12.8% depending on the prediction options).

Gradient flows and randomised thresholding: sparse inversion and classification* *The author thanks the anonymous reviewers for their helpful remarks.

Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an L1/LASSO regulariser. In classification, we consider, e.g., the sum of a data fidelity term and a non-smooth Ginzburg–Landau energy. Standard (sub)gradient descent methods have shown to be inefficient when approaching such problems. Splitting techniques are much more useful: here, the target function is partitioned into a sum of two subtarget functions—each of which can be efficiently optimised. Splitting proceeds by performing optimisation steps alternately with respect to each of the two subtarget functions. In this work, we study splitting from a stochastic continuous-time perspective. Indeed, we define a differential inclusion that follows one of the two subtarget function’s negative subdifferential at each point in time. The choice of the subtarget function is controlled by a binary continuous-time Markov process. The resulting dynamical system is a stochastic approximation of the underlying subgradient flow. We investigate this stochastic approximation for an L1-regularised sparse inversion flow and for a discrete Allen–Cahn equation minimising a Ginzburg–Landau energy. In both cases, we study the longtime behaviour of the stochastic dynamical system and its ability to approximate the underlying subgradient flow at any accuracy. We illustrate our theoretical findings in a simple sparse estimation problem and also in low- and high-dimensional classification problems.

An investigation on optimal outrigger locations for hybrid outrigger system under wind and earthquake excitation

Outriggers are considered as an effective system to alleviate the responses caused due to the lateral loads on high rise buildings. The concept of hybrid outrigger system which has a conventional and a virtual outrigger at different levels has been proposed. This study analyzes the static and dynamic behaviour of hybrid outrigger system based on stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, and height of the building as varying parameters, and investigated on optimal positions of hybrid outrigger system under wind and earthquake loads. The dynamic behaviour was evaluated using nonlinear time history analysis, and the static wind and earthquake response using Indian Standard codes. Analytical models of 40, 60 and 80 storeys having building heights of 140 m, 210 m and 280 m, respectively were considered for the parametric study. The optimal positions for hybrid outrigger system were obtained based on the response from absolute maximum inter storey drift ratio (ISDmax), roof displacement (disproof), roof acceleration (accroof) and base bending moment. A performance index criterion was introduced which was utilized to obtain the optimal position of the hybrid outrigger system considering the combined effect of ISDmax, accroof and disproof under each load. The study concludes with a flowchart giving the preliminary recommendations for choosing the optimal position of hybrid outrigger system.

DEVELOPMENT OF FINITE ELEMENT ANALYSIS PROGRAM FOR ROTORDYNAMIC PREDICTION OF SINGLE AND MULTI DISK ROTOR MODEL

The rotating equipment is a crucial part of system performance reliability. Vibration, as a characteristic of an oscillating body, is a fundamental parameter to determine the dynamic behaviour of the rotor system. The dynamic characteristics include natural frequency, critical speed, mode shape, and vibration response. This paper discussed the application of rotordynamics analysis as a tool to numerically predict the dynamic behaviour of a rotor system. The aim is to determine a rotor system's natural frequency and critical speed by a finite element analysis (FEA) program. The selected method is validated using various analytical methods from other references with small discrepancies in the result. The calculation of FEA using the computational program; they applied the developed program to describe the dynamic characteristic of single and multi-disk rotors. The developed works provided comprehensive results about a rotor system's natural frequency, mode shape, and critical speed and predicted the vibration response due to unbalance. However, other types of rotors, such as coaxial dual rotors, can be further investigated to make the program capable of the general purpose of the rotor. Validation with the real case problem could be an interesting investigation to satisfy the result of developed works.

Bifurcation, chaotic and multistability analysis of the $(2+1)$-dimensional elliptic nonlinear Schrödinger equation with external perturbation

This paper presents a theory of weakly nonlinear wave propagation in superposed fluids in the existence of magnetic fields. The extended direct algebraic approach has been utilized to draw and examine the solitonic wave solutions to the -dimensional elliptic nonlinear Schrödinger equation (ENLSE). These obtained solutions are more novel and valuable to researchers for understanding physical marvels. The graphical representation of some selected exact solutions is reported with different parametric values to show their propagation. Furthermore, the examined equation is changed into the planer dynamical structure by utilizing Galilean transformation. By utilizing the idea of bifurcation, all the possible phase portraits of nonlinear and super nonlinear traveling wave solutions have been explored. Moreover, after adding an external force to the dynamical system, the periodic, quasi-periodic, and chaotic behaviors of the 2D, 3D and time series are also observed. Meantime, for various initial conditions, the sensitivity of the derived solutions is investigated in detail. It is discovered that the considered equation is multistable for the same values of parameters but different initial conditions.