< 23pt; LINE-HEIGHT: 15.65pt; TEXT-ALIGN: left; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-char-indent-count: 2.0; mso-pagination: widow-orphan; mso-layout-grid-align: none" align=left>设根据水质评价标准表产生的某次水样的标准水质等级及其水质指标分别为y(i)及{x<SUP>*</SUP>(i,j)|j=1~m},i=1~n。其中,n、m分别为样本容量和水质指标数目。污染越严重,水质等级就越高,最低水质等级设为1、最高水质等级设为N。为消除各水质指标的量纲效应,使建模具有一般性,对水质指标进行标准化处理
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< center; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-pagination: widow-orphan" align=center>x(i,j)=[x<SUP>*</SUP>(i,j)-Ex(j)]/Sx(j)
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<P 23pt; LINE-HEIGHT: 15.65pt; TEXT-ALIGN: left; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-char-indent-count: 2.0; mso-pagination: widow-orphan; mso-layout-grid-align: none" align=left>式中:Ex(j)、Sx(j)分别为原第j个水质指标{x<SUP>*</SUP>(i,j)|i=1~n}的均值和标准差。Shepard插值的基本思想是<SUP>[6]</SUP>,当得到研究水体的水质指标值{x(n+1,j)|j=1~m}后,利用上述n个样本内插研究水体的水质等级yc(n+1),使下式:
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<P center; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-pagination: widow-orphan" align=center><SUB><V:SHAPETYPE><V:STROKE joinstyle="miter"></V:STROKE><V:FORMULAS><V:F eqn="if lineDrawn pixelLineWidth 0"></V:F><V:F eqn="sum @0 1 0"></V:F><V:F eqn="sum 0 0 @1"></V:F><V:F eqn="prod @2 1 2"></V:F><V:F eqn="prod @3 21600 pixelWidth"></V:F><V:F eqn="prod @3 21600 pixelHeight"></V:F><V:F eqn="sum @0 0 1"></V:F><V:F eqn="prod @6 1 2"></V:F><V:F eqn="prod @7 21600 pixelWidth"></V:F><V:F eqn="sum @8 21600 0"></V:F><V:F eqn="prod @7 21600 pixelHeight"></V:F><V:F eqn="sum @10 21600 0"></V:F></V:FORMULAS><VATH connecttype="rect" extrusionok="f" gradientshapeok="t"></VATH><LOCK v:ext="edit" aspectratio="t"></LOCK></V:SHAPETYPE><V:SHAPE><V:IMAGEDATA></V:IMAGEDATA></V:SHAPE></SUB>
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<P 23pt; LINE-HEIGHT: 15.65pt; TEXT-ALIGN: left; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-char-indent-count: 2.0; mso-pagination: widow-orphan; mso-layout-grid-align: none" align=left>达到最小。式(2)中:
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<P 23pt; LINE-HEIGHT: 15.65pt; TEXT-ALIGN: left; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-char-indent-count: 2.0; mso-pagination: widow-orphan; mso-layout-grid-align: none" align=left>式中:d<SUB>i</SUB>为第i个样本的水质指标与研究水体水质指标之间的距离:w<SUB>i</SUB>为权重,表示第i个样本对内插研究水体的水质等级yc(n+1)的贡献大小;b为待定参数,一般为大于1的常数,b取得越大,则在点{x(n+1,j)|j=1~m}附近的拟合曲面将变得越平坦,而使远离点{x(n+1,j)|j=1~m}处的拟合曲面将变得越陡峻。对式(2)求导数并令其为0,可解得式(2)的最小值为:
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<P 23pt; LINE-HEIGHT: 15.65pt; TEXT-ALIGN: left; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-char-indent-count: 2.0; mso-pagination: widow-orphan; mso-layout-grid-align: none" align=left>这就是所求的对应点{x(n+1,j)|j=1~m}的水质等级值。建立SP模型的步骤可归纳为如下3步:(1)根据水质评价标准表随机生成水质等级样本系列x(i,j)及y(i),i=1~n,j=1~m。(2) 根据样本系列对参数b进行优化估计。在样本系列中任取某样本i,由其它n-1个样本进行Shepard插值,得到相应于水质等级y(i)的插值记为yc(i)。可通过求解如下优化问题来优化估计参数b
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<P center; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-pagination: widow-orphan" align=center>s.t 1≤b≤5
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<p></TD></TR></TABLE></DIV>式(6)的区间是根据笔者的经验确定的。这是一个一维非线性优化问题,模拟生物进化过程中优胜劣汰规则与群体内部染色体信息交换机制的加速遗传算法?(Accelerating Genetic Algorithm,简称AGA)<SUP>[7]</SUP>是一种通用的全局性优化方法,用它来求解该问题显得十分简便而有效。AGA的详细算法可参见文献[7]。(3)进行水质综合评价。当得到研究水体各水质指标值{x(n+1,j)|j=1~m}后,与样本系列一起代入式(3)、式(4),即可由n个样本内插出研究水体的水质等级yc(n+1),作为该次水质综合评价的结果。 |