Evaluation of Covariance Matrix Adaptation Evolution Strategy,Shuffled Complex Evolution and Firefly Algorithms for phase stability,phase equilibrium and chemical equilibrium problems

Phase equilibrium calculations and phase stability analysis of reactive and non-reactive systems play a significant role in the simulation, design and optimization of reaction and separation processes in chemical engineering. These challenging problems, which are often multivariable and non-convex, require global optimization methods for solving them. Stochastic global optimization algorithms have shown promise in providing reliable and efficient solutions for these thermodynamic problems. In this study, we evaluate three alternative global optimization algorithms for phase and chemical equilibrium calculations, namely, Covariant Matrix Adaptation-Evolution Strategy (CMA-ES), Shuffled Complex Evolution (SCE) and Firefly Algorithm (FA). The performance of these three stochastic algorithms was tested and compared to identify their relative strengths for phase equilibrium and phase stability problems. The phase equilibrium problems include both multi-component systems with and without chemical reactions. FA was found to be the most reliable among the three techniques, whereas CMA-ES can find the global minimum reliably and accurately even with a smaller number of iterations.     

Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli

Two real-domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency are investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher-order and higher floating-point precision numerical approximation, the latter being novel in this context. A general formula for higher-order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating-point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher-order approximations in standard double precision and increased quadruple precision. It is found that, as the order of the approximation increases, the elasticity moduli tend toward the analytical solution. Using higher floating-point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.     

浮点LMS算法的FPGA实现

LMS(最小均方)算法因其优良的收敛特性及算法简单等特点在自适应滤波器等领域得到了广泛的应用。浮点运算因其运算步骤繁琐及硬件资源消耗大等缺点使得浮点LMS算法的硬件实现十分困难。文中根据多输入高效浮点加法器结构在FPGA(现场可编程门阵列)上实现了浮点LMS算法。测试结果表明,实现后的LMS算法硬件资源消耗较少且收敛性能与理论值接近。     

一种深度流水线的浮点加法器

随着数字信号处理技术的发展,FPGA正越来越频繁地用于实现基于高速硬件的高性能的科学计算.本文通过增加浮点加法器的流水线级数来提高其单位时间的吞吐量,探讨了充分利用FPGA内部丰富的触发器来提高系统主频的可行性.提出了一种指数和尾数操作、加法和减法操作均分离的多路径浮点加法器结构,对于单精度(32位)的操作数,采用Altera公司的StratixⅡ系列芯片,8级流水线可以达到356 MHz以上的速度.     

Floating-point scaling technique for sources separation automatic gain control

Based on the floating-point representation and taking advantage of scaling factor indetermination in blind source separation (BSS) processing, we propose a scaling technique applied to the separation matrix, to avoid the saturation or the weakness in the recovered source signals. This technique performs an automatic gain control in an on-line BSS environment. We demonstrate the effectiveness of this technique by using the implementation of a division-free BSS algorithm with two inputs, two outputs. The proposed technique is computationally cheaper and efficient for a hardware implementation compared to the Euclidean normalisation.     

A Low Power Approach to Floating Point Adder Design for DSP Applications

The demand for high performance, low power floating point adder cores has been on the rise during the recent years particularly for DSP applications. In this paper, we present a new architecture for a low power, IEEE compatible, floating point adder, that is fast and has low latency. The functional partitioning of the adder into three distinct, clock gated data paths allows activity reduction. The switching activity function of the proposed adder is represented as a three state FSM. During any given operation cycle, only one of the data paths is active, during which time, the logic assertion status of the circuit nodes of the other data paths are held at their previous states. Critical path delay and latency are reduced by incorporating speculative rounding and pseudo leading zero anticipatory logic as well as data path simplifications. In contrast to conventional high speed floating point adders that use leading zero anticipatory logic, the proposed scheme offers a worst case power reduction of 50%.     

A Multiple-Precision Study on the Modified Collocation Trefftz Method

Recently, Liu (CMES 21(2007), 53) developed the modified collocation Trefftz method (MCTM) by setting a characteristic length slightly larger than the maximum radius of the computational domain. In this study, we find that the range of admissible characteristic length can be significantly enlarged if the LU decomposition is applied for solving the resulted dense unsymmetric matrix. Furthermore, we discover a range formula for admissible characteristic length, in which the number of the T-complete functions, the shape of the computation domain, and the exponent bits of the involved floating-point arithmetic have been taken into consideration. In order to validate the prescribed formula for different exponent bits, the multiple precision floating-point reliable (MPFR) library is used. In addition, we find that the MCTM is a numerical method of exponential convergence. In other words, increasing the numbers of the T-complete functions can reduce the logarithmic error proportionally till the precision limit, which can be set up for the MPFR library. Numerical experiments are carried out to demonstrate that the proposed MCTM with the LU decomposition can solve the Laplace equation stably and accurately, even for a Cauchy problem. A multiple-precision comparison between the MCTM and the method of fundamental solution is also preformed.     

波束控制算法在FPGA中的实现

从工程实践角度出发,提出了一种对某雷达波束控制算法进行优化改进的方法。利用定点乘加器完成浮点运算,并在FPGA中进行了仿真及实现。在保证精度的前提下,提高了算法运行效率,缩短了系统配相时间,完成了硬件平台的更新。     

浮点协处理器设计及其在电力电子数字控制平台中的应用

由于定点数字信号处理器(digital signal processor,DSP)存在字长效应和运算能力不足的问题,在一些电力电子应用场合不得不采用浮点DSP。为了解决定点DSP的电力电子数字控制平台的计算瓶颈问题,该文提出了用现场可编程逻辑阵列配置浮点协处理器的方法来提升平台的计算能力。该文给出了浮点运算单元的详细设计过程,并提出了一种更为简单的浮点除法算法实现方法,该算法的误差分析表明：最大绝对值误差不超过2个最小位。仿真和实验验证该浮点协处理器的运算速度可达2.5千万次浮点运算。用快速傅里叶变换算法测试运算效率的实验表明：浮点协处理器的运算效率比DSP算法运算效率快5倍之多。     

基于FPGA的浮点向量协处理器设计

为满足现代数字信号处理中大量数据的运算需求,利用ARM946和Xilinx公司的现场可编程门阵列芯片逻辑资源和IP库,设计专门用于浮点复数向量运算的64位协处理器,对相关浮点运算进行优化,并在硬件仿真平台上进行测试。结果表明,该协处理器可使浮点复数向量运算性能得到大幅提高。