added description of optimisation

optimierung_pymoo.ipynb

+{
+ "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
+}