Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.     

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements,Spectral Elements,and Discontinuous Galerkin

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite differences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods. Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (Meteorol Atmos Phys 82:287–301, 2003), this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.     

A Comparative Study of Non-traditional Methods for Vehicle Crashworthiness and NVH Optimization

In this paper, metamodeling and five well-known metaheuristic optimization algorithms were used to reduce the weight and improve crash and NVH attributes of a vehicle simultaneously. A high-fidelity full vehicle model is used to analyze peak acceleration, intrusion and component’s internal-energy under Full-Frontal, Offset-Frontal, and Side crash scenarios as well as vehicle natural frequencies. The radial basis functions method is used to approximate the structural responses. A nonlinear surrogate-based mass minimization was formulated and solved by five different optimization algorithms under crash-vibration constraints. The performance of these algorithms is investigated and discussed.     

Exponential Stability of Switched Time-varying Delayed Neural Networks with All Modes Being Unstable

This paper aims to design an appropriate switching law to stabilize the switched neural networks with time-varying delays when all subsystems are unstable. By using the discretized Lyapunov function approach and the extended comparison principle for impulsive systems, the stability of switched delayed neural networks composed full of unstable subsystems is analyzed and a computable sufficient condition is derived in the framework of dwell time. The effectiveness of the proposed results is illustrated by a numerical example.     

Dispersion Constraint Based Non-negative Sparse Coding Model

Based on advantages of basic non-negative sparse coding (NNSC) model, and considered the prior class constraint of image features, a novel NNSC model is discussed here. In this NNSC model, the sparseness criteria is selected as a two-parameter density estimation model and the dispersion ratio of within-class and between-class is used as the class constraint. Utilizing this NNSC model, image features can be extracted successfully. Further, the feature recognition task by using different classifiers can be implemented well. Simulation results prove that our NNSC model proposed is indeed effective in extracting image features and recognition task in application.     

A New and Fast Implementation of Orthogonal LDA Algorithm and Its Incremental Extension

Linear discriminant analysis (LDA) is one of the most popular dimension reduction methods and has been widely used in many applications. In the last decades many LDA-based dimension reduction algorithms have been reported. Among these methods, orthogonal LDA (OLDA) is a famous one and several different implementations of OLDA have been proposed. In this paper, we propose a new and fast implementation of OLDA. Compared with the other OLDA implementations, our proposed implementation of OLDA is the fastest one when the dimensionality d is larger than the sample size n. Then, based on our proposed implementation of OLDA, we present an incremental OLDA algorithm which can accurately update the projection matrix of OLDA when new samples are added into the training set. The effectiveness of our proposed new OLDA algorithm and its incremental version are demonstrated by some real-world data sets.     

Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models

By combining of the benefits of high-order network and TSK (Tagaki-Sugeno-Kang) inference system, Pi-Sigma network is capable to dispose with the nonlinear problems much more effectively, which means it has a compacter construction, and quicker computational speed. The aim of this paper is to present a gradient-based learning method for Pi-Sigma network to train TSK fuzzy inference system. Moreover, some strong convergence results are established based on the weak convergence outcomes, which indicates that the sequence of weighted fuzzy parameters gets to a fixed point. Simulation results show the modified learning algorithm is effective to support the theoretical results.     

An SNN-Based Semantic Role Labeling Model with Its Network Parameters Optimized Using an Improved PSO Algorithm

Semantic role labeling (SRL) is a fundamental task in natural language processing to find a sentence-level semantic representation. The semantic role labeling procedure can be viewed as a process of competition between many order parameters, in which the strongest order parameter will win by competition and the desired pattern will be recognized. To realize the above-mentioned integrative SRL, we use synergetic neural network (SNN). Since the network parameters of SNN directly influence the synergetic recognition performance, it is important to optimize the parameters. In this paper, we propose an improved particle swarm optimization (PSO) algorithm based on log-linear model and use it to effectively determine the network parameters. Our contributions are two-folds: firstly, a log-linear model is introduced to PSO algorithm which can effectively make use of the advantages of a variety of different knowledge sources, and enhance the decision making ability of the model. Secondly, we propose an improved SNN model based on the improved PSO and show its effectiveness in the SRL task. The experimental results show that the proposed model has a higher performance for semantic role labeling with more powerful global exploration ability and faster convergence speed, and indicate that the proposed model has a promising future for other natural language processing tasks.     

Neural Networks Based PID Control of Bidirectional Inductive Power Transfer System

Inductive power transfer (IPT) systems facilitate contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. However, IPT systems constitute a high order resonant circuit and, as such, are difficult to design and control. Aiming at the control problems for bidirectional IPT system, a neural networks based proportional-integral-derivative (PID) control strategy is proposed in this paper. In the proposed neural PID method, the PID gains, \(K_{P}\), \(K_{I}\) and \(K_{D}\) are treated as Gaussian potential function networks (GPFN) weights and they are adjusted using online learning algorithm. In this manner, the neural PID controller has more flexibility and capability than conventional PID controller with fixed gains. The convergence of the GPFN weights learning is guaranteed using Lyapunov method. Simulations are used to test the effective performance of the proposed controller.