Resonance analysis of a high-speed railway bridge using a stochastic finite element method

There is always some randomness in the material properties of a structure due to several circumstances and ignoring it increases the threat of inadequate structural safety reserves.A numerical approach is used in this study to consider the spatial variability of structural parameters.Statistical moments of the train and bridge responses were computed using the point estimation method(PEM),and the material characteristics of the bridge were set as random fields following Gaussian random distribution,which were discretized using Karhunen-Loève expansion(KLE).The following steps were carried out and the results are discussed herein.First,using the stochastic finite element method(SFEM),the mean value and standard deviation of dynamic responses of the train-bridge system(TBS)were examined.The effectiveness and accuracy of the computation were then confirmed by comparing the results to the Monte-Carlo simulation(MCS).Next,the influence of the train running speed,bridge vibration frequency,and span of the bridge on dynamic coefficient and dynamic response characteristics of resonance were discussed by using the SFEM.Finally,the lowest limit value of the vibration frequency of the simple supported bridges(SSB)with spans of 24 m,32 m,and 40 m are presented.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Quadrature Kalman Filter(QKF) and Reduced Quadrature Kalman Filter(R-QKF)in Ballistic Target Tracking

Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.

The numerical method of Fourier eigen transform and its application in seismicity analysis

This paper′s aim is to study the numerical method of Fourier eigen transform. The characteristics of eigen bases, the Hermite function are analyzed. And a valuable result of eigen coefficients a n by means of Gauss Hermite integral is gotten. Through talking about amplitude frequency peculiarities of basic signals, we prove that the method applied in this paper possesses higher precision and smaller computation quantity. Finally, we conducted quasi real time FET analysis in seismicity, tentatively probed into the feasibility of FET in seismic prediction, obtained something of practical value.

Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

In this paper,we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equalorder element pair P_(1)−P_(1)which do not satisfy the inf-sup condition.The two-scale method consist of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh.Convergence of the optimal order in the H1-norm for velocity and the L^(2)-norm for pressure are obtained.The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relation h=O(H^(2)).Numerical experiments completely confirm theoretic results.Therefore,this method presented in this paper is of practical importance in scientific computation.