The grid-shift technique for moiré analysis of strain in solid propellants

Moiré principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moiré data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.     

Random parameters induce chaos in power systems

We study how random parameter (namely, noise-perturbed parameter) effects the dynamical behaviors of power systems using random Melnikov technique and numerical simulation. The studied model is described by the classical single-machine-infinite-bus systems which operate in a stable periodic regime far away from chaotic behavior with deterministic parameter. It is found that when the parameter perturbations are weak, chaos is absent in power systems. With the intensity of random parameter \(\rho \) increasing, power systems become unstable and fall into chaos as \(\rho \) is further increased. These phenomena imply that random parameter can induce and enhance chaos in power systems. Our results may provide a useful tip for understanding power systems’ security operation.     

Chaotic thermal convection of couple-stress fluid layer

In this work we study the pattern of bifurcations and intermittent-chaos of non-Newtonian couple-stress shallow fluid layer subject to heating from below. The couple-stress parameter delays onset of convection, synchronizes chaotic behavior, and decreases the heat transfer . Some global aspects of the dynamics such as homoclinic bifurcations and transition to chaos are explored. The effects of particle size on the intermittent-chaos regime at particular normalized Rayleigh number, say \(r=166.1\), are investigated. With the increase in couple-stress parameter, the present Lorenz-like system synchronizes to a steady state via a series of periodic solutions interspersed with intervals of chaotic behaviors.     

A image encryption scheme based on dynamical perturbation and linear feedback shift register

Because low-dimensional chaotic precision degradation has seriously affected the security of encryption, compound chaotic function is designed. It is based on two new one-dimensional chaotic functions. By the definition of Devaney chaotic, the properties of compound chaotic functions are rigidly proved. Based on the compound chaotic function and linear feedback shift register (LFSR), a new pseudo-random sequence generator is designed to generate a more random sequence and expand the key space. The properties of compound chaotic functions and LFSR are also established. In the scheme, a dynamic block division of the 3D baker and dynamical perturbation are illustrated using the compound chaotic map to derive the confusion image. The new pseudo-random sequence generator expands the key space and improves the security of image encryption scheme. The results of entropy analysis, difference analysis, weak-key analysis, statistical analysis, cipher random analysis, and cipher sensitivity analysis show that the encryption scheme has a better security. Compared with traditional encryption scheme and one-dimensional logistic chaotic map, the new image encryption scheme has a better performance in speed, complexity, and security. This paper illustrates how to solve the problem of short periods and low precision of one-dimensional chaotic function by perturbation and LFSR together.     

On the formation of hidden chaotic attractors and nested invariant tori in the Sprott A system

We consider the well-known Sprott A system, which depends on a single real parameter a and, for \(a=1\), was shown to present a hidden chaotic attractor. We study the formation of hidden chaotic attractors as well as the formation of nested invariant tori in this system, performing a bifurcation analysis by varying the parameter a. We prove that, for \(a=0\), the Sprott A system has a line of equilibria in the z-axis, the phase space is foliated by concentric invariant spheres with two equilibrium points located at the south and north poles, and each one of these spheres is filled by heteroclinic orbits of south pole–north pole type. For \(a\ne 0\), the spheres are no longer invariant algebraic surfaces and the heteroclinic orbits are destroyed. We do a detailed numerical study for \(a>0\) small, showing that small nested invariant tori and a limit set, which encompasses these tori and is the \(\alpha \)- and \(\omega \)-limit set of almost all orbits in the phase space, are formed in a neighborhood of the origin. As the parameter a increases, this limit set evolves into a hidden chaotic attractor, which coexists with the nested invariant tori. In particular, we find hidden chaotic attractors for \(a<1\). Furthermore, we make a global analysis of Sprott A system, including the dynamics at infinity via the Poincaré compactification, showing that for \(a>0\), the only orbit which escapes to infinity is the one contained in the z-axis and all other orbits are either homoclinic to a limit set (or to a hidden chaotic attractor, depending on the value of a), or contained on an invariant torus, depending on the initial condition considered.     

Emergence of chaotic regimes in the generalized Lorenz canonical form: a competitive modes analysis

The recently-developed technique of competitive modes analysis is applied to determine parameter regimes for which the generalized Lorenz canonical form, a system constructed by Celikovsky and Chen, which holds many other chaotic systems (such as the Lorenz system, the Lü system, the Chen system, and the Shimizu?CMorioka system), may exhibit chaotic behavior. We verify that the generalized Lorenz canonical form exhibits interesting behaviors in the many parameter regimes thus obtained, thereby demonstrating the great utility of the competitive modes approach in delineating chaotic regimes in multi-parameter systems, where their identification can otherwise involve tedious numerical searches.     

Erratum to: Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.     

Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.     

Chaos detection and parameter identification in fractional-order chaotic systems with delay

The paper first applies the 0–1 test for chaos to detecting chaos exhibited by fractional-order delayed systems. The results of the test reveal that there exists chaos in some fractional-order delayed systems with specific parameter values, which coincides with previous reports based on the phase portrait. In addition, it is very important to identify exactly the unknown specific parameters of fractional-order chaotic delayed systems in chaos control and synchronization. Thus, a method for parameter identification of fractional-order chaotic delayed systems based on particle swarm optimization (PSO) is presented. By treating the orders as parameters, the parameters and orders are identified through minimizing an objective function. PSO can efficiently find the optimal feasible solution of the objective function. Finally, numerical simulations on fractional-order chaotic logistic delayed system and fractional-order chaotic Chen delayed system show that the proposed method has effective performance of parameter identification.     

Parameter identification of chaotic systems using improved differential evolution algorithm

In this paper, an improved differential evolution algorithm, named the Taguchi-sliding-based differential evolution algorithm (TSBDEA), is proposed to solve the problem of parameter identification for Chen, Lü and Rossler chaotic systems. The TSBDEA, a powerful global numerical optimization method, combines the differential evolution algorithm (DEA) with the Taguchi-sliding-level method (TSLM). The TSLM is used as the crossover operation of the DEA. Then, the systematic reasoning ability of the TSLM is provided to select the better offspring to achieve the crossover, and consequently enhance the DEA. Therefore, the TSBDEA can be more robust, statistically sound, and quickly convergent. Three illustrative examples of parameter identification for Chen, Lü and Rossler chaotic systems are given to demonstrate the applicability of the proposed TSBDEA, and the computational experimental results show that the proposed TSBDEA not only can find optimal or close-to-optimal solutions but also can obtain both better and more robust results than the DEA.     

An analytical approach to determine conventional S−N curves from accelerated-fatigue data

This paper describes an analytical method of obtaining conventional S?N curves from the accelerated-fatigue tests, namely the generalized Prot accelerated-fatigue-testing technique in which the stress amplitude increases linearly with respect to cycle. Miner's cumulative-damage theory was applied and an expression for the sum of a series of natural numbers raised to a certain nonintegral power was developed to achieve this. The agreement between analytical prediction and experimental verification is quite reasonable.     

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

In this paper, the approximate Bayesian computation combines the particle swarm optimization and sequential Monte Carlo methods, which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system. Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed, which verifies the effectiveness of the proposed method. Finally, a partial response sample of the regular and chaotic responses, determined by the maximum Lyapunov exponent, is applied to detect whether chaotic motion occurs in them by a 0–1 test. This paper can provide a reference for data-based parameter identification and chaotic prediction of chaotic vibration energy harvester systems.     

Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised Lorenz system; then using the new system a new complex no equilibrium point hyperchaotic system is reported. Both the new systems have hidden chaotic attractors. Various dynamical behaviours are observed in the new systems like chaotic, periodic, quasi-periodic and hyperchaotic. Both the systems have inverse crisis route to chaos with the variation of parameter a and crisis route to chaos with the variation of parameters \(b,\ c\) and d. These phenomena along with hidden attractors in a complex hyperchaotic system are not seen in the literature. Synchronisation between the identical new hyperchaotic systems is achieved using the contraction theory. Further the synchronisation between the identical new complex hyperchaotic systems is achieved using adaptive contraction theory. The proposed synchronisation strategies are validated using the MATLAB simulation and circuit implementation results. Further, an application of the proposed system is shown by transmitting and receiving an audio signal.     

A photoviscoelastic analysis of time-dependent stresses in a polyphase system

The method of photoviscoelastic stress analysis is used to predict time-dependent stress redistributions in a polyphase-material system having a viscoelastic binder and subjected to applied exteernal-loading conditions. The polyphase-material model studied is composed of a photoviscoelastic matrix material and contains rigid inclusions and voids, thus simulating a threephase composite system. In order to perform the study, a photoviscoelastic model material is developed. An epoxy-resin system consisting primarily of Shell Epon 828 and Epon 871, optimized to display the properties desirable for such application, is utilized. The time-dependent stess distributions obtained by the photoviscoelastic analysis are compared with results obtained by applying the “correspondence rule” to a finite-element solution for the elastic stress field of a mathematical model of the three-phase material system. The comparison of results indicates that the technique of photoviscoelastic stress analysis is extremely applicable to complex models such as the one studied. The feasibility of this application to more complex polyphase models with varying loading conditions is indicated.     

Existence of a Singularly Degenerate Heteroclinic Cycle in the Lorenz System and Its Dynamical Consequences: Part I

We prove that the Lorenz system with appropriate choice of parameter values has a specific type of heteroclinic cycle, called a singularly degenerate heteroclinic cycle, that consists of a line of equilibria together with a heteroclinic orbit connecting two of the equilibria. By an arbitrarily small but carefully chosen perturbation to the Lorenz system, we also show that the geometric model of Lorenz attractors formulated by Guckenheimer will bifurcate from it, among other things. Although not proven, one may also expect various other types of chaotic dynamics such as Hénon-like chaotic attractors, Lorenz attractors with hooks which were recently studied by S. Luzzatto and M. Viana [22], and what were observed in the original Lorenz system with large r and small b in the Sparrows book [34]. Our analysis is all done within a family of three dimensional ODEs that contains, as its subfamilies, the Lorenz system, the Rösslers second system and the Shimizu–Morioka system, which are known to exhibit Lorenz-like chaotic dynamics.     

Thermal radiation effects on MHD-Rayleigh flow with constant surface heat flux

Thermal radiation heat transfer effects on the Rayleigh flow of gray viscous fluids under the effect of a transverse magnetic field are investigated. The free convection heat transfer problem from constant surface heat flux moving plate is selected for study. It is found that the increasing of the magnetic field number M= H₀² / U₀²decreased velocities inside boundary layer, the increasing of the conduction–radiation parameter Rd=k__R/4aT³ decreased both temperatures and heat transfer rates. It is also found that the increasing of the dimensionless surface heat flux parameter q₀^*=q₀ /(kU₀T₎ increased the temperatures inside the boundary layer and increased the heat transfer rates. Comparison with previous works shows excellent agreement. Different transient velocity profiles, temperature profiles and local Nusselt numbers against different dimensionless groups are drawn.     

Second-order sliding-mode controller for autonomous underwater vehicle in the presence of unknown disturbances

We propose the use of a second-order sliding-mode controller (2-SMC) to stabilize an autonomous underwater vehicle (AUV) which is subject to modeling errors and often suffers from unknown environmental disturbances. The 2-SMC is effective in compensating for the uncertainties in the hydrodynamic and hydrostatic parameters of the vehicle and rejecting the unpredictable disturbance effects due to ocean waves, tides, and currents. The 2-SMC is comprised of an equivalent controller and a switching controller to suppress the parameter uncertainties and external disturbances, and its closed-loop system is exponentially stable in the presence of parameter uncertainties and unknown disturbances. We performed numerical simulations to validate the proposed control approach, and experimental tests using Cyclops AUV were conducted to demonstrate its practical feasibility. The proposed controller increased the accuracy of trajectory tracking for an AUV in the presence of uncertain hydrodynamics and unknown disturbances.     

Investigation of the Dynamic Response of Swirling Flows Based on LES and Experiments

The dynamic response of a swirling flow undergoing vortex breakdown is investigated via Large Eddy Simulation (LES) and experiments in a water flow facility. The investigation is carried out following previous work on the link between thermoacoustic combustion instabilities and coherent structures in lean premixed gas turbine combustors. The velocity field transfer function is obtained in LES from the Unit Impulse Response determined via application of a low intensity broadband noise perturbation of the inflow mass flow rate and the Wiener-Hopf filtering method. In the experiments, harmonic fluctuations in the water flow rate through the swirler are generated via a piston mounted on the side wall of the test facility and activated with a low frequency linear motor. The velocity field transfer function is then obtained via phase averaging applied to Particle Image Velocimetry snapshots which are collected at prescribed values of the harmonic phase. The analysis, which is carried out in terms of coherent structures identified via Proper Orthogonal Decomposition, gives numerical transfer functions with amplitude and phase consistent with the experimental ones.