示例：二阶响应曲面

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示例：二阶响应曲面

使用 boxwilson、polyfitc 和 polyfit 函数，设计实验并创建正在研究的过程的模型。使用求解命令块求得该模型所预测的最大结果。

1. 定义 boxwilson 设计矩阵。

2. 为 A (以分钟为单位的反应时间) 和 B (华氏温度) 定义实数值，两个量均为所研究的化学过程的自然变量。

3. 调用 doelabel 函数，将设计矩阵的编码值转换为自然变量的实数值。

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        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
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4. 记录每个游程的化学过程的结果。

5. 调用 polyfitc，利用编码值执行二阶多项式回归。

6. 从 polyfitc 的输出中提取回归系数。

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            <real>2</real>
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        <real>1</real>
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7. 创建编码值的函数，对化学反应进行模拟。使用此函数预测 A=-1 和 B=1 时的结果。

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                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                  <real>1</real>
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                  <mult />
                  <apply>
                    <indexer />
                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                    <real>2</real>
                  </apply>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
                </apply>
              </apply>
              <apply>
                <mult />
                <apply>
                  <indexer />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                  <real>3</real>
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                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
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            <apply>
              <mult />
              <apply>
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                  <indexer />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                  <real>4</real>
                </apply>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
              </apply>
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <indexer />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
              <real>5</real>
            </apply>
            <apply>
              <pow />
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
              <real>2</real>
            </apply>
          </apply>
        </apply>
        <apply>
          <mult />
          <apply>
            <indexer />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
            <real>6</real>
          </apply>
          <apply>
            <pow />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
            <real>2</real>
          </apply>
        </apply>
      </apply>
    </define>
    <resultFormat>
      <general precision="3" show-trailing-zeros="false" radix="dec" zero-threshold="15" imaginary-value="i" exponential-threshold="3" />
      <matrix size="14,8" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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8. 调用 polyfit 创建实数值函数，对化学反应进行建模。使用该函数预计在 t=80 min 和 T=170F 的收益。

正如所料，计算所得的收益与步骤 7 的结果一样。

9. 使用求解命令块找出最大收益

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10. 使用等值线图来显示结果如何在 t_max 和 T_max 附近变化。

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参考文献

Montgomery, D.C., Design and Analysis of Experiments, 5th ed., John Wiley & Sons, New York, 2001, pp. 442.