diff --git a/optimierung_pymoo.ipynb b/optimierung_pymoo.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..ac9c4407405ceb9e996dd69ace859be1595ad2a1 --- /dev/null +++ b/optimierung_pymoo.ipynb @@ -0,0 +1,57 @@ +{ + "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 +}