示例：Thiele 插值和回归

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示例：Thiele 插值和回归

可以将使用 ThielecoeffThiele 函数视为一种回归法，因为 Thiele 系数已被提取。

1. 输入一组代表沸水饱和温度的测量数据 (单位：°C)。

2. 使用 Thiele 方法通过数据集进行曲线插值。

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        <id label="Function" xml:space="preserve" label-is-contextual="true">Thiele</id>
        <sequence>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">P</id>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">coeff</id>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">x</id>
        </sequence>
      </apply>
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    <resultFormat>
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3. 使用多项式回归法通过数据集进行曲线拟合。

4. 绘制数据集和两条插值曲线。

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      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="220">
          <axisLine position="bottom" positionticmark="-1" legendWidth="92.1466666666667" />
          <axisGrid>
            <gridFrequency>12</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math resultRef="47">
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">P</id>
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                <id label="Unit" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">bar</id>
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            </plotEquation>
            <plotEquation>
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                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">range</id>
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              <math resultRef="50">
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="290" end="675">
          <axisLine position="origin" positionticmark="0" legendWidth="97.29" />
          <axisGrid>
            <gridFrequency>12</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
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        </yAxis>
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5. 对 Thiele 方法返回的计算结果和蒸汽表中的两个中点进行比较。

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        <str xml:space="preserve"> mid-points </str>
        <apply>
          <scale />
          <real>290.52</real>
          <id label="Unit" xml:space="preserve" label-is-contextual="true">°C</id>
        </apply>
        <apply>
          <scale />
          <real>327.78</real>
          <id label="Unit" xml:space="preserve" label-is-contextual="true">°C</id>
        </apply>
        <str xml:space="preserve">calculated</str>
        <apply>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">TI</id>
          <apply>
            <scale />
            <real>75</real>
            <id label="Unit" xml:space="preserve">bar</id>
          </apply>
        </apply>
        <apply>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">TI</id>
          <apply>
            <scale />
            <real>125</real>
            <id label="Unit" xml:space="preserve">bar</id>
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      <unitOverride>
        <placeholder />
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计算得出的数据点和发布的数据非常接近。

6. 使用 Thiele 插值曲线，计算位于海平面以上 2250 米的墨西哥城中水的沸腾温度。

参考文献

国际水和水蒸汽性质协会，网址为：http://www.iapws.org