Enhancing Cooperative Coevolution for Large Scale Optimization by Adaptively Constructing Surrogate Models

It has been shown that cooperative coevolution (CC) can effectively deal with large scale optimization problems (LSOPs) through a divide-and-conquer strategy. However, its performance is severely restricted by the current context-vector-based sub-solution evaluation method since this method needs to access the original high dimensional simulation model when evaluating each sub-solution and thus requires many computation resources. To alleviate this issue, this study proposes an adaptive surrogate model assisted CC framework. This framework adaptively constructs surrogate models for different sub-problems by fully considering their characteristics. For the single dimensional sub-problems obtained through decomposition, accurate enough surrogate models can be obtained and used to find out the optimal solutions of the corresponding sub-problems directly. As for the nonseparable sub-problems, the surrogate models are employed to evaluate the corresponding sub-solutions, and the original simulation model is only adopted to reevaluate some good sub-solutions selected by surrogate models. By these means, the computation cost could be greatly reduced without significantly sacrificing evaluation quality. Empirical studies on IEEE CEC 2010 benchmark functions show that the concrete algorithm based on this framework is able to find much better solutions than the conventional CC algorithms and a non-CC algorithm even with much fewer computation resources.Comment: arXiv admin note: text overlap with arXiv:1802.0974

Large Amplitude Flexural Vibration of the Orthotropic Composite Plate Embedded with Shape Memory Alloy Fibers

AbstractThe free and forced vibration of large deformation composite plate embedded with shape memory alloy (SMA) fibers is investigated. A thermo-mechanical constitutive equation of SMA proposed by Brinson et al. is employed and the constitutive equations for evaluation of the properties of a hybrid SMA composite laminate are obtained. Based on the nonlinear theory of symmetrically laminated anisotropic plates, the governing equations of flexural vibration in terms of displacement and stress functions are derived. The Galerkin method has been used to convert the original partial differential equation into a nonlinear ordinary differential equation, which is then solved with harmonic balance method. The numerical results show that the relationship between nonlinear natural frequency ratio and temperature for the nonlinear plate has similar characteristics compared with that of the linear one, and the effects of temperature on forced response behavior during phase transformation from Martensite to Austenite are significant. The effects of the volume fraction of the SMA fiber, aspect ratio and free vibration amplitude on the dynamical behavior of the plate are also discussed

Modeling and dynamic analysis of rotating composite shaft

Structural modeling and dynamical analysis of rotating composite shaft are conducted in this paper. A thin-walled composite shaft structure model, which includes the transverse shear deformation of the shaft, rigid disks and the flexible bearings, is presented and then used to predict natural frequencies and dynamical stability. Based on the thin-walled composite beam theory referred to as variational asymptotically method (VAM), the displacement and strain fields of the shaft are described. Hamilton’s principle is employed to derive the equations of motion of the shaft system. Galerkin’s method is used to discretize and solve the governing equations. The validity of the model is proved by comparing the results with those in literatures and convergence examination. The effects of fiber orientation, ratios of length over radius, ratios of radius over thickness and shear deformation on natural frequency and critical speeds are investigated. Finally the unbalance transient responses of the composite shaft system are also given by using the time-integration method

Vibration and stability of internally damped rotating composite Timoshenko shaft

The mechanical model for the dynamic behavior of an internally damped rotating composite shaft is derived using a refined variational asymptotic method and the principle of virtual work. The composite shaft is considered as an anisotropic thin-walled Timoshenko beam. The internal damping of composite shaft is modelled by adopting the multi-scale damping analysis method. Galerkin’s method is employed to discretize and solve the equations of motion. The effect of design parameters including fiber orientation, length aspect ratio, stacking sequences and boundary conditions on the free vibration and stability of composite shaft is investigated

An analytical model for dynamic simulation of the composite rotor with internal damping

A theoretical model for the dynamics of composite rotor is presented. The composite shaft that includes rigid disks and is supported on rigid bearings is considered as a thin-walled Euler-Bernoulli beam. Internal damping of the composite shaft is taken into account. The equations of motion are derived using the thin-walled composite beam theory based on variational asymptotic method and Hamilton’s principle. The internal damping of shaft is introduced by adopting the multi-scale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. To demonstrate the validity of the present model, the convergence of the method is examined and the results are compared with those available in the literature. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds and instability thresholds of composite shaft. In addition, the free vibration responses due to the initial perturbations and the forced responses to unbalance for composite shaft are also presented

Free vibration analysis for wind turbine structure by component mode synthesis method

Based on free interface component modal synthesis method, the free vibration behavior of wind turbine structures is investigated. The wind turbine structure is divided into three parts including tower, wheel hub-cabin and rotor. The tower is modeled as an isotropic metal cantilever beam, the blade as thin-walled composite beam and the wheel hub-cabin as a rigid body due to its large extensional stiffness, bending stiffness and torsion stiffness compared with tower and blades. The displacements of the blades are described by thin-walled composite beam theory. Galerkin’s method is used to discretize blades and tower. Employing Lagrange method, the motion equations of blades are derived and then stiffness and mass matrices are obtained. The natural frequencies and mode shapes of the wind turbine structure are predicted by numerical simulations. Numerical results using the present model are validated by ANSYS software results

Primary resonance of a rotating composite shaft with geometrical nonlineary

The primary resonance of a simply supported rotating composite shafts with geometrical nonlineary is studied. The composite shaft is modeled as a thin-walled Euler-Bernoulli beam. A variational-asymptotical method (VAM) applied to anisotropic thin-walled closed-cross-sectional beams is used to describe the displacement and strain fields of the composite shafts. The geometrical nonlineary is considered in the relationships of strain and displacement of the shaft. The nonlinear extensional-bending-torsional equations of motion for the composite shaft are derived by using the Hamilton principle. In order to emphatically study nonlinear transverse bending vibration, the effects of extensional and torsional deformations are ignored. By means of the method of multiple scales the approximation solution of primary resonance of transverse bending vibration is obtained. The Galerkin method is employed to reduce the governing equations to the ordinary differential equations. By using fourth-order Runge-Kutta method the time histories, phase diagrams and power spectrums are plotted. The study shows the effect of the external damping, ply angle, eccentricity, ratios of length over radius, ratios of radius over thickness and rotating speed on nonlinear dynamic behavior of the shaft. Specifically, the numerical simulation results show that the shaft exhibits the complex dynamic behavior including periodic, quasi-periodic and chaotic motion