Exemple : Surface de réponse de deuxième ordre

Fonctions > Plan d'expériences > Analyse de régression > Exemple : Surface de réponse de deuxième ordre

Utilisez les fonctions boxwilson, polyfitc et polyfit pour concevoir une expérience et créer un modèle du traitement étudié. Utilisez un bloc de résolution pour trouver le rendement maximum prévu par le modèle.

1. Définissez une matrice d'expériences boxwilson.

2. Définissez les valeurs réelles de A (temps de réaction en minutes) et B (température en degrés Fahrenheit) qui sont des variables naturelles du traitement chimique étudié.

3. Appelez la fonction doelabel pour convertir les valeurs codées de la matrice d'expériences en valeurs réelles des variables naturelles.

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4. Enregistrez le rendement du traitement chimique pour chaque analyse.

5. Appelez polyfitc pour effectuer une régression de polynôme de deuxième ordre avec les valeurs codées.

6. Extrayez les coefficients de régression du résultat de polyfitc.

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            <real>2</real>
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        </apply>
        <real>1</real>
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7. Créez une fonction de valeurs codées qui modélise la réaction chimique. Utilisez cette fonction pour prévoir le rendement si A=-1 et B=1.

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        <plus />
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                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                  <real>1</real>
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                  <mult />
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                    <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                    <real>2</real>
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                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
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              <apply>
                <mult />
                <apply>
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                  <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>
              </apply>
            </apply>
            <apply>
              <mult />
              <apply>
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                  <indexer />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
                  <real>4</real>
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                <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" />
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8. Appelez polyfit pour créer une fonction de valeurs réelles qui modélise la réaction chimique. Utilisez cette fonction pour prévoir le rendement si t=80 min et T=170F.

Comme prévu, le rendement calculé est identique à celui de l'étape 7.

9. Utilisez un bloc de résolution pour déterminer le rendement maximal.

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          <define xmlns="http://schemas.mathsoft.com/math50">
            <matrix rows="2" cols="1">
              <id labels="VARIABLE" xml:space="preserve">t_max</id>
              <id labels="VARIABLE" xml:space="preserve">T_max</id>
            </matrix>
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              <id labels="KEYWORD" xml:space="preserve">maximize</id>
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10. Un tracé d'isolignes permet de visualiser comment le rendement change aux valeurs t_max et T_max.

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Référence

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

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