求解化工中非线性方程组的一种改进拟牛顿方法

在求解非线性方程组的拟牛顿法的基础上(本文选用BFGS秩2算法),本文使用部分一维搜索,得到了一种能扩大收敛域,提高数值稳定性的改进拟Newton法——BZ法。并用四个化学工程中的非线性问题和换热网络的模拟对BFGS算法和BZ算法进行了比较。结果表明,BZ算法优于BFGS算法。     

联立方程法模拟多循环流程的新解算策略

<正>化工过程的模拟算法有三类:序贯模块法、联立方程法和联立模块法.序贯模块法已很成熟,应用颇广,国内外通用软件多用此法.但它也有局限性,如难以用于多循环复杂流程的模拟,难以处理设计型、控制型模拟问题等.为克服这些不足,展开了联立方程法等的研究.如进行了SPEEDUP、ASCEND、QUASILIN等软件的开发.由于涉及大型非线性方程组,其求解算法的优劣是此类算法成败的关键.目前人们已对一些典型问题考察了牛顿法及各种拟牛顿法的适用性,在算法取舍和改进方面取得了一些进展,但要获得有效而通用的算法还有许多工作要做.目前,用联立方程法进行实际过程模拟的例子较少,在微机上进行有关研究未见报道.作者从我国微机较为普及这一实情出发,在微机上进行了联立方程法的研究.针对一个具体的多循环复杂流程的模拟与分析问题,提出了一个新的联立方程法解算策略:部分解耦加速牛顿法.     

计算非线性方程组所有解的同伦连续法

在化工领域中，数学模拟导致非线性方程组的求解问题。介绍了一种同伦连续算法，可以不依赖于初值，求出非线性方程组的所有解。特别是经过映射变换，数学计算更为方便。     

分区流化床床面粒子抛撒对床内传热传质的影响

本文从试验和数模计算两个方面研究了床面粒子抛撒对床内传热传质的影响.床面粒子抛撒量随着流化速度的增加而增加,同时也随床层高度的增高而增加.区间床面粒子抛撒量约占区间总传质量的50%～65%,因而对床内过程有较大影响.本文利用戎-范的浅床数模,并考虑区间床面粒子的抛撒,引出了一个动态数模,采用Sincover和Madson提出的“在线法”解非线性偏微分方程组,提高了精度.计算结果与试验结果吻合较好.     

分区流化床床面粒子抛撒对床内传热传质的影响

本文从试验和数模计算两个方面研究了床面粒子抛撒对床内传热传质的影响.床面粒子抛撒量随着流化速度的增加而增加,同时也随床层高度的增高而增加.区间床面粒子抛撒量约占区间总传质量的50%～65%,因而对床内过程有较大影响.本文利用戎-范的浅床数模,并考虑区间床面粒子的抛撒,引出了一个动态数模,采用Sincover和Madson提出的“在线法”解非线性偏微分方程组,提高了精度.计算结果与试验结果吻合较好.     

模拟多组分吸收过程的新算法

该文提出了一种多组分吸收过程的新算法,用高斯—约当法进行矩阵求逆,用牛顿—同伦法扩大了整体牛顿法的收敛范围,对6理论级6组分的吸收问题进行了验算。经11次迭代后收敛,全部运算是在微帆Altos—986上进行的。     

基于非线性PLS小波基神经网络的动态过程监测

引言对于化工动态过程,当某些过程参数,由于人为的误操作、设备性能的下降、仪表故障以及外部环境的干扰等因素的影响,而偏离最优操作区域较远时,则认为是发生了故障．如果在过程刚偏离正常操作区域时,能够有效地监测出过程异常,就能最大限度地保证过程在优良状态下运行．动态过程监测可以理解为对数据窗内采集到的数据x（t）进行实时分类．本文利用小波变换以及非线性PLS（PartialLeastSquares）算法,提出一种新的基于非线性PLS小波基神经网络的动态过程监测方法,并将其用于动态过程监测．1基于非线性PLS小波基神经网络的动态…     

复杂换热网络双层法通用软件的研制

提出了双层模拟法模拟计算复杂换热网络。整个换热网络方程组求解过程分层，内层将模型线性化，线性模型的参数为迭代变量。外层用内层的结果严格计算物性和传热系数，修正线性模型的模型参数。分析指出，操作工况的稳定性及物性对温度的敏感度是影响收敛性的主要因素。提出了模型线必化的方法并实现了矩阵的压缩存储以及方程组的自动生成。工业实例的计算证明了本算法提高了运行速度并实现了通用性。     

等温CMSMPR结晶器定态及瞬态特性分析(Ⅱ)分岔行为及瞬态特性

应用非线性方程组的延拓解法 ,对同时发生初级成核和二次成核的等温连续混合悬浮混合排料(CMSMPR)结晶器的定态方程组进行了求解 ,考察了结晶过程的定态在不同参数区域之间的分岔行为 ,确定了各参数区域内结晶过程的定态数目 ,并应用Routh -Hurwitz准则对各定态的稳定性进行了分析 .采用四阶Runge -Kutta法求解CMSMPR结晶器的动态方程组 ,分析了在多定态区域以及持续振荡区域中结晶过程的瞬态特性     

多级多组分分离过程通用算法

<正> 在石油化工、天然气分离及炼油等工业生产装置中,多级多组分分离过程得到极其广泛的应用。该分离过程的设计、计算问题相应也获得极大的重视,成为化学工程领域的一个重要研究课题。多级多组分分离过程的计算,通常都由物料平衡、能量平衡、相平衡及分子分数总和四组模型方程组来描述。这些方程组数量庞大,且是非线性的,必须     

基于两步矩阵投影的数据分类算法

提出了一种数据分类的两步矩阵投影算法.指出Crowe提出的矩阵投影算法在数据分类中存在由于投影矩阵不惟一,导致已测可校正数据分类不彻底的缺点.采用已测数据预分类的方法,对其进行了修正.在此基础上,将矩阵投影算法引入到了未测数据分类中,提出了基于矩阵投影算法的未测数据分类算法.新算法只需求解两个投影矩阵就可以实现所有数据分类.从而避免了常规方法在未测数据分类时,求解未测数据关联矩阵绝对线性无关列的计算,提高了计算效率.数学推导和算例验证了新算法的有效性.     

基于小生境遗传算法的多峰函数全局优化研究

针对基本遗传算法在求解多峰函数时很难找到全部最优解的问题,研究了基于淘汰相似结构机制的小生境遗传算法。用该算法对两个典型多峰函数求解的测试结果表明,该算法较之基本遗传算法有更强的全局搜索能力和更快的收敛速度。     

An alternate computational architecture for advanced process engineering

An algorithm for equation-oriented (EO) flowsheeting to which the interfacing of external modular procedures is readily allowed is presented. In the algorithm, all the process units in a flowsheet are solved simultaneously in an EO environment while taking advantage of the external software as it is. The algorithm is the basis for the process simulator MIKAN. The simulator consists of two parts, namely EO main, which is the simulator's executive, and add-on blocks to incorporate external procedures. EO main also serves to solve separation processes. The PBM (Pseudo-Binary-Mixture)-based algorithm for separation processes (Ishii & Otto, 2008) is fully exploited in EO main. The equations of the entire system are composed of a set of equations for separation processes and sets of equations representing the input-output relation of each add-on block. The input-output relation is obtained by numerical perturbation where all the component flow rates are perturbed collectively. Although the proposed perturbation is simple and significantly less expensive, it is very reliable since the interactions among the input variables affecting the output are fully accounted for.Robustness, flexibility and efficiency of the new algorithm have been confirmed by its implementation. A serious drawback with the EO approach is the difficult accessibility to the user when incorporating new or external process models. Easy accessibility is an important attribute of the new algorithm, even though the simulator's executive is highly integrated and complex. It is significant that the derivative information at various levels of a flowsheet is easily obtained in the algorithm. The novel algorithmic capabilities of the algorithm provide a robust platform for the next stage of advanced process engineering.     

Kramers-Kronig transforms calculation with a fast convolution algorithm

Kramers-Kronig transforms (KKT) constitute a powerful tool to validate experimental impedance data. A new algorithm, containing a Fast Fourier Transform (FFT) sub-routine, for the numerical calculus of the KKT has been developed. This algorithm is based in the convolution theorem and it uses only two FFT calculi. It was finally tested in the validation of an experimental transfer function for hydrogen permeation into an iron membrane. Unlike common algorithms for numerical integration, this algorithm allows the calculation of all frequencies at the same time at a high speed using a regular frequency interval for the whole calculation with the same or even higher precision. The FFT sub-routine is accessible in all languages so that the use of this code is very simple.     

Computational complexity of a problem in molecular structure prediction

The computational task of protein structure prediction is believedto require exponential time, but previous arguments as to itsintractability have taken into account only the size of a protein'sconformational space. Such arguments do not rule out the possibleexistence of an algorithm, more selective than exhaustive search,that is efficient and exact. (An efficient algorithm is onethat is guaranteed, for all possible inputs, to run in timebounded by a function polynomial in the problem size. An intractableproblem is one for which no efficient algorithm exists.) Questionsregarding the possible intractability of problems are oftenbest answered using the theory of NP-completeness. In this treatmentwe show the NPhardness of two typical mathematical statementsof empirical potential energy function minimization of macromolecules.Unless all NP-compiete problems can be solved efficiently, theseresults imply that a function minimization algorithm can beefficient for protein structure prediction only if it exploitsprotein-specific properties that prohibit the simple geometricconstructions that we use in our proofs. Analysis of furthermathematical statements of molecular structure prediction couldconstitute a systematic methodology for identifying sourcesof complexity in protein folding, and for guiding developmentof predictive algorithms.     

Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor

In this paper, a novel algorithm is proposed for solving multiobjective optimization problems. The proposed algorithm, multiobjective differential evolution (MODE), is applied to optimize industrial adiabatic styrene reactor considering productivity, selectivity and yield as the main objectives. Five combinations of the objectives are considered. Pareto set (a set of equally good solutions) obtained for all the cases is compared with results reported using non-dominated sorting genetic algorithm (NSGA). The results show that all objectives besides profit can be improved compared to those reported using NSGA and current operating conditions. The Pareto optimal front provides wide-ranging optimal operating conditions and an appropriate operating point can be selected based on the requirements of the user.     

Computerized generation of technological structures

This paper introduces an algorithm which can determine the technology structure containing given chemical technological steps and producing given final products from given initial inlet materials.

With the aid of the algorithm all solutions of the problem or the solution with minimal sum of weights can be obtained. In the latter the user assigns weight factors to the different technological steps. It is also possible to determine all solutions haveing a sum of weights not greater than a limit given by the user. The algorithm and the datastructure introduced provide grounds for designing technologies with multi-component materials and recirculations.     

Evaluation of the use of the Chebyshev algorithm with the quadrature method of moments for simulating aerosol dynamics

The quadrature method of moments (QMOM) has been widely used for the simulation of the evolution of moments of the aerosol general dynamic equations. However, there are several shortcomings in a crucial component of the method, the product-difference (P-D) algorithm. The P-D algorithm is used to compute the quadrature points and weights from the moments of an unknown distribution. The algorithm does not work for all types of distributions or for even reasonably high-order quadrature. In this work, we investigate the use of the Chebyshev algorithm and show that it is more robust than the P-D algorithm and can be used for a wider class of problems. The algorithm can also be used in a number of applications, where accurate computations of weighted integrals are required. We also illustrate the use of QMOM with the Chebyshev algorithm to solve several problems in aerosol science that could not be solved using the P-D algorithm.     

填料塔载点算法

讨论了逆流填料塔的流体力学计算方法 ,对泛点算法作了简要的回顾。主要介绍以载点气速为基础的算法 ,列出了全部公式 ,并给出 30种不同的填料品种和规格 ,按同样工艺条件进行计算的结果。认为载点算法是填料塔工艺设计的新工具     

带约束输入的多变量广义预测解耦控制及其在化工过程中的应用

A constrained decoupling （generalized predictive control） GPC algorithm is proposed for MIMO （malti-input multi-output） system. This algorithm takes account of all constraints of inputs and their increments. By solving matrix equations, the multi-step predictive decoupling controllers are realized. This algorithm need not solve Diophantine functions, and weakens the cross-coupling of the variables. At last the simulation results demonstrate the effectiveness of this proposed strategy.