scholarly journals Alternated Superior Chaotic Biogeography Based Algorithm for Optimization Problems

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Dynamical Systems ◽  
Dynamic Behaviour ◽  
Optimization Problems ◽  
Bifurcation Diagrams ◽  
Switching Strategy ◽  
Alternate Version ◽  
Parrondo’S Paradox ◽  
Stable Periodic ◽  
Parameter Values ◽  
Superior Orbit

In this study, we consider a switching strategy that yields a stable desirable dynamic behaviour when it is applied alternatively between two undesirable dynamical systems. From the last few years, dynamical systems employed “chaos1 + chaos2 = order” and “order1 + order2 = chaos” (vice-versa) to control and anti control of chaotic situations. To find parameter values for these kind of alternating situations, comparison is being made between bifurcation diagrams of a map and its alternate version, which, on their own, means independent of one another, yield chaotic orbits. However, the parameter values yield a stable periodic orbit, when alternating strategy is employed upon them. It is interesting to note that we look for stabilization of chaotic trajectories in nonlinear dynamics, with the assumption that such chaotic behaviour is not desirable for a particular situation. The method described in this paper is based on the Parrondo’s paradox, where two losing games can be alternated, yielding a winning game, in a superior orbit.

scholarly journals Controlling the Chaos of Logistic Map using Switching Strategy

2019 ◽  
Vol 9 (2) ◽  
pp. 515-518
Keyword(s):  
Dynamical Systems ◽  
Recent Work ◽  
Periodic Orbits ◽  
Logistic Map ◽  
Switching Strategy ◽  
Stability Performance ◽  
Chaotic Orbits ◽  
Parrondo’S Paradox ◽  
Engineering Problems ◽  
The Stability

In our very recent work (2019), we extended the stability performance of logistic map up to a higher value of r using SP orbit. In this article, we further extend this range of stability by adopting switching strategy (Parrondo’s Paradox) of controlling the chaos of dynamical systems. We observe that even the earlier chaotic orbits of four step feedback procedure can be converted into periodic orbits. Our approach can be used to solve a wider circle of engineering problems.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

Open-loop stable running

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Katja D. Mombaur ◽  
Richard W. Longman ◽  
Hans Georg Bock ◽  
Johannes P. Schlöder
Keyword(s):  
Optimization Methods ◽  
Open Loop ◽  
Bipedal Robots ◽  
Model Parameter ◽  
Stable Periodic ◽  
Parameter Values ◽  
Difficult Issue ◽  
Loop Stability

We present simulated monopedal and bipedal robots that are capable of open-loop stable periodic running motions without any feedback even though they have no statically stable standing positions. Running as opposed to walking involves flight phases which makes stability a particularly difficult issue. The concept of open-loop stability implies that the actuators receive purely periodic torque or force inputs that are never altered by any feedback in order to prevent the robot from falling. The design of these robots and the choice of model parameter values leading to stable motions is a difficult task that has been accomplished using newly developed stability optimization methods.

scholarly journals Comparative Study of Optimization Algorithms for The Optimal Reservoir Operation

2018 ◽  
Vol 246 ◽  
pp. 01003
Author(s):  
Xinyuan Liu ◽  
Yonghui Zhu ◽  
Lingyun Li ◽  
Lu Chen
Keyword(s):  
Reservoir Operation ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Complex Problem ◽  
Optimization Techniques ◽  
Decision Variables ◽  
Handling Methods ◽  
Optimality Algorithm ◽  
Parameter Values

Apart from traditional optimization techniques, e.g. progressive optimality algorithm (POA), modern intelligence algorithms, like genetic algorithms, differential evolution have been widely used to solve optimization problems. This paper deals with comparative analysis of POA, GA and DE and their applications in a reservoir operation problem. The results show that both GA and DES are feasible to reservoir operation optimization, but they display different features. GA and DE have many parameters and are difficult in determination of these parameter values. For simple problems with mall number of decision variables, GA and DE are better than POA when adopting appropriate parameter values and constraint handling methods. But for complex problem with large number of variables, POA combined with simplex method are much superior to GA and DE in time-assuming and quality of optimal solutions. This study helps to select proper optimization algorithms and parameter values in reservoir operation.

scholarly journals Modelling chronic hepatitis B using the Marchuk-Petrov model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012036
Author(s):  
M Yu Khristichenko ◽  
Yu M Nechepurenko ◽  
D S Grebennikov ◽  
G A Bocharov
Keyword(s):  
Time Delay ◽  
Hepatitis B ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stable Periodic ◽  
Delay Differential ◽  
Parameter Values

Abstract Systems of time-delay differential equations are widely used to study the dynamics of infectious diseases and immune responses. The Marchuk-Petrov model is one of them. Stable non-trivial steady states and stable periodic solutions to this model can be interpreted as chronic viral diseases. In this work we briefly describe our technology developed for computing steady and periodic solutions of time-delay systems and present and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values corresponding to the hepatitis B infection.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

Effect of a Planetary Gearbox on the Dynamics of a Rotor System

2018 ◽  
Author(s):  
Ali Tatar ◽  
Christoph W. Schwingshackl
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Rotor System ◽  
Mode Shapes ◽  
Rotating System ◽  
Planetary Gearbox ◽  
Finite Element Software ◽  
Gyroscopic Effects ◽  
The Masses ◽  
Parameter Values

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

Neural Network-Based Metaheuristic Parameterization with Application to the Vehicle Matching Problem in Ride-Hailing Services

2019 ◽  
Vol 2673 (10) ◽  
pp. 311-320
Author(s):  
Arslan Ali Syed ◽  
Irina Gaponova ◽  
Klaus Bogenberger
Keyword(s):  
Neural Network ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Computation Time ◽  
Problem Instance ◽  
Neighborhood Search ◽  
Matching Problem ◽  
Solution Quality ◽  
Actual Problem ◽  
Parameter Values

The majority of transportation problems include optimizing some sort of cost function. These optimization problems are often NP-hard and have an exponential increase in computation time with the increase in the model size. The problem of matching vehicles to passenger requests in ride hailing (RH) contexts typically falls into this category.Metaheuristics are often utilized for such problems with the aim of finding a global optimal solution. However, such algorithms usually include lots of parameters that need to be tuned to obtain a good performance. Typically multiple simulations are run on diverse small size problems and the parameters values that perform the best on average are chosen for subsequent larger simulations.In contrast to the above approach, we propose training a neural network to predict the parameter values that work the best for an instance of the given problem. We show that various features, based on the problem instance and shareability graph statistics, can be used to predict the solution quality of a matching problem in RH services. Consequently, the values corresponding to the best predicted solution can be selected for the actual problem. We study the effectiveness of above described approach for the static assignment of vehicles to passengers in RH services. We utilized the DriveNow data from Bavarian Motor Works (BMW) for generating passenger requests inside Munich, and for the metaheuristic, we used a large neighborhood search (LNS) algorithm combined with a shareability graph.

Remarks on the nonlinear dynamics of a typical aerofoil section in dynamic stall

2007 ◽  
Vol 111 (1125) ◽  
pp. 731-739 ◽  
Author(s):  
U. Galvanetto ◽  
J. Peirò ◽  
C. Chantharasenawong
Keyword(s):  
Mach Number ◽  
Event Detection ◽  
Structural Model ◽  
Dynamic Behaviour ◽  
Equation Of Motion ◽  
Basins Of Attraction ◽  
Dynamic Stall ◽  
Bifurcation Diagrams ◽  
Aerodynamic Loading ◽  
Semi Empirical

Abstract We use standard tools of the theory of dynamical systems such as phase plots, bifurcation diagrams and basins of attraction to analyse and understand the dynamic behaviour of a typical aerofoil section under dynamic stall conditions. The structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model are nonlinear and non-smooth, therefore we have integrated the equation of motion using a Runge-Kutta-Fehlberg (RKF45) algorithm equipped with event detection. We perform simulations of the motion for a range of Mach numbers and show that the model is very sensitive to small variations. This is evidenced by the presence in the bifurcation diagram of co-existing attractors or, in other words, by the existence of more than one steady-state motion for a given Mach number. The mechanisms for the appearance and disappearance of the co-existing attractors are elucidated by analysing the evolution of their basins of attraction as the Mach number changes.

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