作　　者： ; ; ; ;

机构地区： 华南理工大学化学与化工学院

出　　处： 《计算机与应用化学》 2003年第5期643-648,共6页

摘　　要： 化工过程中存在多种状态,多变量过程可以在多维的状态空间中描述。在主元分析中,通过相关矩阵变换可以获得一组主元,选取其中分布占优的部分主元可以代表过程的原始变量,用来描述系统。PCA可以很好地实现过程降维,但是目前没有一种直接有效的方法来确定主元数目的选取。用以描述过程的原始变量间通常都是相关的。用以描述化工过程的变量有六大类:温度(T)、压力(P)、流量(F)、液位或者物料位(L)、组分种类(k)和物性(P_k)。可以用一个目标函数描述状态:State=f(T_(kj),P_(kj),F_(kj),L_(kj),P_k)。对此函数进行量纲分析,普通化工过程对应4个基本因次:长度(L)、物质量(N)、时间(t)和热力学温度(T),因此目标函数可以表示为:State=F(L_(i,j),N_(i,j),t_(i,j),T_(i,j))。时间对于任何系统都是独立的,占一维;温度在集中参数流股中一致,占一维;系统物料可以用i个独立组分描述,占i维;系统存在于三维长度空间,L占j维(j≤3)。这样,状态空间的维数DN=2+i+j。在单相稳态体系中,不考虑系统的几何长度和时间因素,那么,DN=i+1,此结果就是相律在单相体系中的自由度;在线性流股中,j=1,稳态时不考虑时间,DN=i+2,此结果是Duhem定律的自由度。在理想流动的化工过程中,此准则可以用来确定PCA中主元数目的上限。选取了一个典型? There is usually variety of states of chemical processes. A multi-variable process may be imaged to a multidimensional state space. In Principal Component Analysis (PCA) , a set of Principal Components (PCs) is directly obtained via a covariance matrix transformation and some PCs are selected to stand for the original variables. PCA are used successfully in state space reduction, but there are not direct decision methods on the number of PCs at present. A chemical process is usually described by six main categories of variables, temperature ( T ) , pressure ( P ) , flow ( F ) , liquid or matter level ( L ) , component ( k ) and physical property ( pk ). An objective function (State) expresses this. State = f(Tk., Ptj, Fki, Lkj, pt)- Dimensional analysis is done in variables of the function. A general chemical process is mapped by four fundamental dimensions, length ( L ) , amount of substance ( N ) , time ( t ) and temperature ( T ). The objective function is expressed as; State = F (L. ., Ntj, tt , TV .) . Time is always independent to any system and represented in one dimension. Temperature is uniform in stream of lumped parameter system and represented in one dimension. Amount of substance is used to describe the independent component ( i kinds). System consists in three-dimensional-space, the number of dimension is j(j<3) . Asa result, the dimension number of state space is DS = z + i + j . If the phase number of a static system is one, the length and time are not taken into account and DS = i + 1 , the conclusion is consistent with the Gibbs' s Phase Rule. In the linear static stream, time is not studied and DS = i + 2, the result is consistent with Duhem' s theorem. In ideal chemical processes, the criterion for dimensionality of data space can be used to determine the upper limit of the number of PCs in PCA. A typical chemical reaction flow is selected as a study case; the flow consists of a reaction unit and a separation unit. In reaction unit, there are six variables. There are two independent components

关 键 词： 化工过程 状态空间 维数 判定准则 多变量统计分析 主元分析

领　　域： [化学工程]