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Steinmann, Victor
Learning Python
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50452ba7
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50452ba7
authored
7 months ago
by
Steinmann
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added description of optimisation
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Formulieren der Optimierungsgleichung in pymoo "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Es gilt die Kontinuitätsgleichung:\n",
"\n",
"$ \\Sigma \\dot{V}_k(t) = O$\n",
"\n",
"und die aus der Topologie resultierende Inzidenzmatrix $A_i$\n",
"\n",
"sowie die aus dem Pumpenkennfeld folgende Beziehung: \n",
"\n",
"$\\Delta p=\\alpha_1 Q^2+\\alpha_2 Q n+\\alpha_3 n^2 : n\\epsilon \\{0\\},[n_{min},n_{max}] $\n",
"\n",
"$P=\\beta_1 Q^3+\\beta_2 Q^2 n+\\beta_3 Q n^2+\\beta_4n^3+\\beta_5$ \n",
"\n",
"und die beziehung für den Druckverlust an den Ventilen:\n",
"\n",
"$\\Delta p_{loss} = - \\frac{1}{2} \\varrho \\zeta \\cdot \\frac{Q^2}{A^{\\prime}} = -l Q^2 :l\\epsilon [l_{min}:\\infty )$\n",
"\n",
"\n",
"nun soll für einen Gegebenen Volumenstrom $Q$ eine Optimale Drehzahl bestimmt werden, welche die Pumpenlesitung minimiert.\n",
"\n",
"$min P(n) , n\\epsilon [n_{min},n_{max}]$\n",
"\n",
"$ \\overrightarrow{n} = (1,n,n^2,n^3)^T$\n",
"\n",
"$min P = A \\overrightarrow{n}$\n",
"\n",
"$-n\\leqq n_{min}$\n",
"\n",
"$n\\leqq n_{max}$\n",
"\n",
"\n",
"\n",
"\n",
"\n"
]
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
%% Cell type:markdown id: tags:
Formulieren der Optimierungsgleichung in pymoo
%% Cell type:markdown id: tags:
Es gilt die Kontinuitätsgleichung:
$
\S
igma
\d
ot{V}_k(t) = O$
und die aus der Topologie resultierende Inzidenzmatrix $A_i$
sowie die aus dem Pumpenkennfeld folgende Beziehung:
$
\D
elta p=
\a
lpha_1 Q^2+
\a
lpha_2 Q n+
\a
lpha_3 n^2 : n
\e
psilon
\{
0
\}
,[n_{min},n_{max}] $
$P=
\b
eta_1 Q^3+
\b
eta_2 Q^2 n+
\b
eta_3 Q n^2+
\b
eta_4n^3+
\b
eta_5$
und die beziehung für den Druckverlust an den Ventilen:
$
\D
elta p_{loss} = -
\f
rac{1}{2}
\v
arrho
\z
eta
\c
dot
\f
rac{Q^2}{A^{
\p
rime}} = -l Q^2 :l
\e
psilon [l_{min}:
\i
nfty )$
nun soll für einen Gegebenen Volumenstrom $Q$ eine Optimale Drehzahl bestimmt werden, welche die Pumpenlesitung minimiert.
$min P(n) , n
\e
psilon [n_{min},n_{max}]$
$
\o
verrightarrow{n} = (1,n,n^2,n^3)^T$
$min P = A
\o
verrightarrow{n}$
$-n
\l
eqq n_{min}$
$n
\l
eqq n_{max}$
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