Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.

Importance Sampling Method in V-Space

Based on the observation of importance sampling and second order information about the failure surface of a structure, an importance sampling region is defined in V-space which is obtained by rotating a U-space at the point of maximum likelihood. The sampling region is a hyper-ellipsoid that consists of the sampling ellipse on each plane of main curvature in V-space. Thus, the sampling probability density function can be constructed by the sampling region center and ellipsoid axes. Several examples have shown the efficiency and generality of this method.

Subinterval Decomposition-Based Interval Importance Analysis Method

The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty.When an input variable is described by a specific interval rather than a certain probability distribution,the interval importance measure of input interval variable can be calculated by the traditional non-probabilistic importance analysis methods.Generally,the non-probabilistic importance analysis methods involve the Monte Carlo simulation(MCS)and the optimization-based methods,which both have high computational cost.In order to overcome this problem,this study proposes an interval important analytical method avoids the time-consuming optimization process.First,the original performance function is decomposed into a combination of a series of one-dimensional subsystems.Next,the interval of each variable is divided into several subintervals,and the response value of each one-dimensional subsystem at a specific input point is calculated.Then,the obtained responses are taken as specific values of the new input variable,and the interval importance is calculated by the approximated performance function.Compared with the traditional non-probabilistic importance analysis method,the proposed method significantly reduces the computational cost caused by the MCS and optimization process.In the proposed method,the number of function evaluations is equal to one plus the sum of the subintervals of all of the variables.The efficiency and accuracy of the proposed method are verified by five examples.The results show that the proposed method is not only efficient but also accurate.

Time-Dependent Reliability Analysis of Offshore Structures

During the life of an offshore structure, its structural strength declines due to various kinds of damages related to the time factor. In this paper, four major kinds of damages, including damages caused by fatigue, dent, corrosion and marine life, are discussed. Based on these analyses, formulas for the evaluation of the damaged structure reliability are derived. Furthermore the computer program ISM for the analysis of structural reliability is developed by the use of Advanced First Order Second Moment method and Monte-Carlo Importance Sampling method. The reliability of a turbular joint and a beam are studied as numerical examples. The results show that the theory and the analysis method given in this paper are reasonable and effective.

Numerical Study of φ^4 Model by Potential Importance Sampling Method

We investigate the phenomena of spontaneous symmetry breaking for φ^4 model on a square lattice in the parameter space by using the potential importance samplingmethod, which was proposed by Milchev, Heermann, and Binder [J. Star. Phys. 44 （1986） 749]. The critical values of the parameters allow us to determine the phase diagram of the model. At the same time, some relevant quantifies such as susceptibility and specific heat are also obtained.

Estimation of an Important Constant in Sieve Method

ζk is one of the most important constant in the siève methods.Tlus paper gives the relatively accurate lower bound and upper bound on it,that is,3-1/kck,where c=1.22... and k】16.

Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

Combining the advantages of the stratified sampling and the importance sampling, a stratified importance sampling method （SISM） is presented to analyze the reliability sensitivity for structure with multiple failure modes. In the presented method, the variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec- tor, and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean point and augmenting the standard deviation by a factor of 2. The sample size generated from the importance sampling function in each subspace is determined by the contribution of the subspace to the reliability sensitivity, which can be estimated by iterative simulation in the sampling process. The formulae of the reliability sensitivity estimation, the variance and the coefficient of variation are derived for the presented SISM. Comparing with the Monte Carlo method, the stratified sampling method and the importance sampling method, the presented SISM has wider applicability and higher calculation efficiency, which is demonstrated by numerical examples. Finally, the reliability sensitivity analysis of flap structure is illustrated that the SISM can be applied to engineering structure.

An enhanced hybrid and adaptive meta-model based global optimization algorithm for engineering optimization problems

Due to the good balance between high efficiency and accuracy, meta-model based optimization algorithm is an important global optimization category and has been widely applied. To better solve the highly nonlinear and computation intensive en- gineering optimization problems, an enhanced hybrid and adaptive meta-model based global optimization （E-HAM） is first proposed in this work. Important region update method （IRU） and different sampling size strategies are proposed in the opti- mization method to enhance the performance. By applying self-moving and scaling strategy, the important region will be up- dated adaptively according to the search results to improve the resulting precision and convergence rate. Rough sampling strategy and intensive sampling strategy are applied at different stages of the optimization to improve the search efficiently and avoid results prematurely gathering in a small design space. The effectiveness of the new optimization algorithm is verified by comparing to six optimization methods with different variables bench mark optimization problems. The E-HAM optimization method is then applied to optimize the design parameters of the practical negative Poisson＇s ratio （NPR） crash box in this work. The results indicate that the proposed E-HAM has high accuracy and efficiency in optimizing the computation intensive prob- lems and can be widely used in engineering industry.