Weibull Power Safety-Margin (WSM) for WLTP GearShifting¶

WeibullSafetyMargin.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "extensions": {
     "jupyter_dashboards": {
      "version": 1,
      "views": {
       "grid_default": {
        "hidden": true
       },
       "report_default": {
        "hidden": false
       }
      }
     }
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "#%matplotlib nbagg\n",
    "from matplotlib import pyplot as plt\n",
    "import os, sys\n",
    "from os import path as osp\n",
    "from IPython.display import display, clear_output\n",
    "from ipywidgets import interact, fixed\n",
    "import numpy as np, pandas as pd\n",
    "# plt.style.use('ggplot')\n",
    "# plt.rc('font', size=13)\n",
    "# plt.rc('figure', figsize=(10,6))\n",
    "import seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weibull Power Safety-Margin (WSM) for WLTP GearShifting\n",
    "\n",
    "Let's take this Weibull:\n",
    "\n",
    "$$\n",
    "\\frac{k}{s}\n",
    "\\left(\n",
    "    \\frac{x-c}{s}\n",
    "\\right)^{k-1} \n",
    "\\exp\\left(\n",
    "    - \\left(\\frac{x-c}{s}\\right)^k \n",
    "\\right)\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $x$: is the RPMs;\n",
    "- $k$: the \"shape\", which according to this site[1], it can be:\n",
    "  - $1 < k < 2$: long tail (positive kurtosis)\n",
    "  - $3 < k < 4$: symetric\n",
    "  - $10 < k$: long head (negative kurtosis)\n",
    "- $s$: the \"scale\" param, the X-axis where 63.2% percentile is met (in RPMs);\n",
    "- $c$: a positive/negative \"offset\" param moving right/left the curve.\n",
    "\n",
    "[1] http://blog.minitab.com/blog/understanding-statistics/why-the-weibull-distribution-is-always-welcome\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Top of the curve:\n",
    "We want to identify the \"center position\" (the $x$ position of the top of the curve, in RPMs).\n",
    "For that, we take the $WSM$ derivative(calculated by this Wolfram-alpha[2]), and try to find where it becomes zero:\n",
    "\n",
    "$$\n",
    "\\frac{k\\left(\n",
    "    \\frac{\\hat{x}}{s}\n",
    "\\right)^k\n",
    "\\exp\\left(\n",
    "    - \\left(\n",
    "        \\frac{\\hat{x}}{s}\n",
    "    \\right)^k\n",
    "\\right)}{\\hat{x}^2}\n",
    "\\left(\n",
    "    k\\left(\n",
    "        \\frac{\\hat{x}}{s}\n",
    "    \\right)^k-k+1\n",
    "\\right) \n",
    "$$\n",
    "where:\n",
    "- $\\hat{x} = x - c$\n",
    "\n",
    "So we set its 3rd non-trivial factor to 0, to solve it against $\\hat{x_{center}}$:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "k\\left(\n",
    "    \\frac{\\hat{x_{center}}}{s}\n",
    "\\right)^k-k+1\n",
    "= 0 \\\\\n",
    "\\Rightarrow \\hat{x_{center}} = \\exp\\left(\n",
    "    \\frac\n",
    "        {\\ln \\frac{k-1}{k}}\n",
    "        {k} \n",
    "    + \\ln{s}\n",
    "\\right) \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "So the final formula for the \"top of the curve\", including the \"offset\", is this:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "x_{center} = \\exp\\left(\n",
    "    \\frac\n",
    "        {\\ln \\frac{k-1}{k}}\n",
    "        {k} \n",
    "    + \\ln{s}\n",
    "\\right) \n",
    "+ c\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "and the max-value according to Wolfram-alpha[3] is:\n",
    "\n",
    "$$\n",
    "y_{center} = \\frac{k}{s}\n",
    "\\left(\\frac{x_{center} - c}{s}\\right)^{k-1}\n",
    "exp\\left( \n",
    "    - \\left(\n",
    "        \\frac{x_{center} - c}{s}\n",
    "    \\right)^k\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "So to control its magnitude, we have to divide the *weibull* by the max-value ($y_{center}$) to come up with the final *\"Weibull Safety Margin\"* or *WSM*:\n",
    "\n",
    "$$\n",
    "WSM = \\frac{WSM_0}{y_{center}}\\frac{k}{s}\n",
    "\\left(\n",
    "    \\frac{x-c}{s}\n",
    "\\right)^{k-1} \n",
    "\\exp\\left(\n",
    "    - \\left(\\frac{x-c}{s}\\right)^k \n",
    "\\right)\n",
    "$$\n",
    "Where:\n",
    "- $WSM_0$: is the magnitude.\n",
    "- $x_{center}, k, s, c$: defined above\n",
    "\n",
    "### Notes:\n",
    "- [2] http://www.wolframalpha.com/input/?i=-%28e%5E%28-%28x%2Fs%29%5Ek%29+k+%28x%2Fs%29%5Ek+%281%2Bk+%28-1%2B%28x%2Fs%29%5Ek%29%29%29%2Fx%5E2\n",
    "- [3] http://www.wolframalpha.com/input/?i=k%2Fn+*+%28x%2Fn%29%5E%28k-1%29+*+exp%28-+%28x%2Fn%29%5Ek%29,+x%3Dexp%28log%28%28k-1%29%2Fk%29%2Fk+%2B+log%28n%29%29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_center=908.34\n",
      "Y_center=0.00\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAFVCAYAAAAt79zdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X9wXPV9//vX2V9aSbv6tZL8Q7ZlYxDhpxObNCngxOTi\nlFJ6UwopJklpJ0w60JBkWpIJTmkw0xCRNnOntw3MJE2mzJC5Xyd8oU0u3863iW+IKU5KwImd2IAh\n2GDjH5JWv3e1K2n3nPuH9qxsWfaurF2dPec8HzOZWLtH2rc+SHrt53M+PwzLsiwBAICaFnC6AAAA\nUBqBDQCACxDYAAC4AIENAIALENgAALgAgQ0AgAuUFdj79+/Xn/7pn571+E9+8hPdfvvt2rZtm556\n6qmKFwcAAGaESl3w7W9/Wz/4wQ/U2Nh4xuO5XE6PPvqonnnmGdXV1enOO+/Uhz70ISUSiaoVCwCA\nX5XsYXd3d+uxxx476/E333xT3d3disViCofD2rRpk15++eWqFAkAgN+VDOytW7cqGAye9XgqlVI8\nHi9+3NjYqPHx8cpWBwAAJC1i0lksFlMqlSp+nE6n1dTUVPLz/L4T6vBYVp/8yo/0h/f/QPHWjBqa\nJ/SRz/9AL7/aN3vR2rUz/wMAoKDkPWzb3KBdv3693n77bY2NjSkajeqll17S3XffXfLrGIahgQF/\n9sQty9L/9f39GhjO6P+8bq32P1Wn6ZypYDCgf3jyZX31L96vpsaI2kxLwYB/22mhOjritFUZaKfy\n0VbloZ3K09ERL31RGcruYRuGIUl69tln9dRTTykUCmn79u365Cc/qTvvvFMf/ehH1dnZWZGivOqX\nrw/o4JEhXbGuTR+5fp0kKRwK6PYt6zUxmdPTu990uEIAQK0qq4fd1dWlnTt3SpJuueWW4uNbtmzR\nli1bqlKY11iWpf93z1syDOnjW3uKb4Ak6UMbu/TTXx3Xzw6c0keuX6c2B+sEANQmNk5ZIq+8Nayj\n/Sldc2mnlrc1nPFcMBDQTe9bo7xpadfL7zhUIQCglhHYS+SnvzouSbrpfWvmff53r1iuWH1YPztw\n0vcT8wAAZyOwl0A6O639bybV1dGotcvnn3wQCgb0vsuXaWxiWtM5c4krBADUOgJ7Cew9NKBc3tLv\nXrH8jHvXc1175XJJ0uR0fqlKAwC4BIG9BF58ZWaN9fsuW3be69Yuj6u9OaqpnCkGxQEApyOwqywz\nmdPrx0a0bkVcieboea81DEMbLm6XZVkMiwMAzkBgV9nBI0PKm5auuqi8Q1E2XDxz3eQUw+IAgFkE\ndpX9+vCgJOnq9e1lXX/p6lYZMjTFfWwAwGkI7CqyLEu/eXNQ8Yaw1q4ob2u6cCigcCignGlqJDVZ\n5QoBAG5BYFfR8WRao+kpXbmuTYHzzA6fKxya+c9y6OhItUoDALgMgV1FbxybCdxL17Qu6PNmA3u4\n4jUBANyJwK6iQ4XA7lndsqDPCwUMGYah1+hhAwAKCOwqsSxLrx8bUVNjRMta6xf2yYahSCigU0MT\nGk1PVadAAICrENhVMjCS0UhqSj2rW867u9m52MPih0+MVro0AIALEdhVYg+HX7rA4XBbKBiUJB05\nOVaxmgAA7kVgV8lv35npGV+yqvmCPn+2h01gAwAI7Ko5cnJMkXBAXR2NF/T5AUNa1tagIyfHZXLc\nJgD4HoFdBZPTeR1PprVmWVzBwIU38UUr4spM5tQ3NFHB6gAAbkRgV8HRvnFZlrRuedOivs66FTOf\nz7A4AIDAroIjJ8clSevK3I70XOzAfuvU+KJrAgC4G4FdBW8VZnbbgXuhVnXEZEg61p+qQFUAADcj\nsKvgyMkx1deF1LnQDVPmqIsE1dnWoGP9KVlMPAMAXyOwK2wiO62+4YzWLo9f0IYpc63ujCkzmdPg\nWLYC1QEA3IrArrC3+2aGr8s9TrOU1Z0xSQyLA4DfEdgV9k4hWNd0EtgAgMohsCvs2MBMsK4qBO1i\nrSGwAQAisCvunf6UQkFDy9sWN+HM1hqvU2M0RGADgM8R2BVkmpaOJ9NamWhc1A5npzMMQ6s7YxoY\nzig7lavI1wQAuA+BXUF9wxOazpkVGw63dbXHZEk6xRalAOBbBHYFvTOQljSz4UklrWhvkCSdSKYr\n+nUBAO5BYFeQfZ95dYV72CsSMyd+nRykhw0AfkVgV5C9pKvSQ+Ir22cCmx42APgXgV1B7wyk1NQQ\nVnNjpKJft6khrMZoSCfoYQOAbxHYFZKZzCk5mlVXhe9fSzMzxVe0N2pgOKNc3qz41wcA1D4Cu0Ls\n+8tdheHrSluZaJBpWepjpjgA+BKBXSEnB2fuL6+oUmAz8QwA/I3ArhA7SFcmGqry9Zl4BgD+RmBX\niN3DXp6oVg+7sBZ7kMAGAD8isCvkxOCEGqMhNTWEq/L125qiioQDOsWQOAD4EoFdAbm8qYHhjFYk\nGmUYRlVeI2AY6mxpUN9wRpZlVeU1AAC1i8CugL7hjEzLKg5bV8uytnpNTuc1mp6q6usAAGoPgV0B\nJwsTwVZU6f61bVnrzBsClnYBgP8Q2BVwshCgVe9ht86csd03nKnq6wAAag+BXQHVXoNtW9ZW6GEP\n08MGAL8hsCvgZHJCoWBA7U3Rqr6O3cPuH6KHDQB+Q2AvkmlZOjmU1vK2BgUC1ZkhbmtqjKguEqSH\nDQA+RGAv0vDYpKamTa1sr+79a2nmEJBlrfXqL8xKBwD4B4G9SKcKE86Wt1U/sCWps7VBUzlTI+OT\nS/J6AIDaQGAvkj08vWyJApuZ4gDgTwT2IvUVJoDZa6SrrbgWm/vYAOArBPYi9ReCs7PQ8622ZW3M\nFAcAPyKwF6lvOKPGaEix+uoc+jEXPWwA8CcCexHypqmBkYw6l2g4XJLiDWHVRYIaGKGHDQB+QmAv\nwtDYpPKmVRymXgqGYaijuV4Do1lO7QIAHykZ2JZl6aGHHtK2bdt011136dixY2c8/53vfEd//Md/\nrI9+9KPatWtX1QqtRcUZ4kvYw5akjpaoJqfyGs9ML+nrAgCcEyp1wa5duzQ1NaWdO3dq//796u3t\n1eOPPy5JGh8f13e/+13t2rVL6XRaf/RHf6Qbb7yx6kXXiv7C0qqlmnBm62iZeb3kSFZNDZElfW0A\ngDNK9rD37t2rzZs3S5I2bNigAwcOFJ+rr69XV1eX0um0JiYmFAj4a4R9qZd02dqbZ/Ys5z42APhH\nyR52KpVSPB6f/YRQSKZpFsN52bJluvnmm2VZlv7iL/6irBft6IiXvsgFhtNTkqQrLulQ7AJ6uvb7\nm7Pao7An+bna6eLuNklSJmd6pi0Xi3YoD+1UPtqqPLTT0ikZ2LFYTOl0uvjx6WH9/PPPK5lM6rnn\nnpNlWbr77ru1ceNGXXXVVef9mgMD44ssuza80zeuxmhImfSkMumFbxVqmjPHcQ4MpM94vM20FAwY\n52yncOGMkbeOj3imLRejoyNOO5SBdiofbVUe2qk8lXpTU3IMe+PGjdq9e7ckad++ferp6Sk+19TU\npGg0qnA4rEgkong8rvFxf/zHs5d0LdWWpKebHRLPLvlrAwCcUbKHvXXrVu3Zs0fbtm2TJPX29uqJ\nJ55Qd3e3brjhBv385z/Xn/zJnygQCGjTpk269tprq150LRgsLOla6glnklQXDqq5McI9bADwkZKB\nbRiGHn744TMeW7duXfHfn/nMZ/SZz3ym8pXVuH6HlnTZOlrqdfjEmPKmqaDPJvsBgB/xl/4Czc4Q\nX/oetiS1t0RlWpaGxjhmEwD8gMC+QLNrsB3qYTfba7EZFgcAPyCwL9DsOdjO9bAlaWCUiWcA4AcE\n9gXqL5zS1RhdmlO65uos7HbGxDMA8AcC+wKYlqXkaLa4RagT2psJbADwEwL7Aoylp5TLm8X10E5o\njdfNbK7CWmwA8AUC+wIkCyFp93KdEAgYSjRHlRylhw0AfkBgXwA7JO2JX07paI5qfGJa2amco3UA\nAKqPwL4AyVG7h+1sYCcKrz/IWmwA8DwC+wIUe9gODolLUqKpENgs7QIAzyOwL4Ddw07UTA+bwAYA\nryOwL0ByJKumxojqwkFH66CHDQD+QWAvkGlaGhzLOn7/WqKHDQB+QmAv0Ehq5ljNWgjs1nidAoZB\nDxsAfIDAXqDZGeLOTjiTpGAgoNZ4hB42APgAgb1A9lagTq/BtiWaohoZn1QubzpdCgCgigjsBRqs\nkTXYtkRzVJakoXHWYgOAlxHYCzRQI2uwbfbEsyHuYwOApxHYC2T3sO0lVU4rLu3iPjYAeBqBvUAD\nI1m1xCIKh2qj6YpLu+hhA4Cn1UbquETeNDU8Pql2B8/BnsvuYSfpYQOApxHYCzA8NinTqo012DZ2\nOwMAfyCwF2CghtZg2yLhoJoawtzDBgCPI7AXYPaUrtrpYUsz97GHxrIyLcvpUgAAVUJgL0ByZKYX\n21Frgd0UVS5vaSw95XQpAIAqIbAXoHisZg1NOpOkNu5jA4DnEdgLkBzNyDCktnid06WcgVO7AMD7\nCOwFSI5m1RavUyhYW83WTg8bADyvtpKnhk3nTI2MTypRQzPEbXYPm7XYAOBdBHaZhsazslR7E84k\ndjsDAD8gsMtkzxBP1GBgN9SFFI0EuYcNAB5GYJfJXoPdUWMzxCXJMIziWmwAgDcR2GVK1tg52HMl\nmqLKTOY1kc05XQoAoAoI7DIla3Bb0tPZS82GxullA4AXEdhlSo5mFAwYaq2xNdi21sLSrqGxSYcr\nAQBUA4FdpuRIVm1NdQoEDKdLmVeiiR42AHgZgV2Gqem8RtNTNTscLkltcbuHTWADgBcR2GWwl0vV\n4pIuW5vdw2ZIHAA8icAugz3hrBY3TbG10sMGAE8jsMuQHLHPwa7dIfFwKKCmxgg9bADwKAK7DMUl\nXS2128OWZpZ2DY1PyrIsp0sBAFQYgV2GgRpfg21LNEWVy5san5h2uhQAQIUR2GUYHM0oFDTUHIs4\nXcp5tRYmnrGnOAB4D4FdhoGRrBJNUQWM2lyDbZtd2sV9bADwGgK7hOxUTqnMtNpr8NCPuexlZ2ye\nAgDeQ2CXMFjjh36crrifOEPiAOA5BHYJA24KbPYTBwDPIrBLGHTJDHFJam6MKBgw6GEDgAcR2CUM\nFDdNqf0ediBgqCU2sxYbAOAtBHYJxR62CyadSTOndo2kJpXLm06XAgCoIAK7hIHRjCKhgJoawk6X\nUpa2pqgsSxpJ0csGAC8hsEsYHM0q0RyVUeNrsG2tnNoFAJ5EYJ/HRDandDbniglntkQTa7EBwItC\npS6wLEs7duzQoUOHFIlE9Mgjj2j16tXF53fv3q3HH39chmHo8ssv15e//OWqFryUkqOFCWc1fujH\n6djtDAC8qWQPe9euXZqamtLOnTt1//33q7e3t/hcOp3W17/+dX3zm9/Uzp071dXVpeHh4aoWvJSS\nLlqDbWtrYvMUAPCikoG9d+9ebd68WZK0YcMGHThwoPjcr371K/X09OjRRx/Vxz/+cSUSCbW2tlav\n2iVmB3aHi4bE2TwFALyp5JB4KpVSPB6f/YRQSKZpKhAIaHh4WC+++KJ++MMfKhqN6uMf/7je8573\nqLu7u6pFL5VkYQ12wkU97MZoSJFwgB42AHhMycCOxWJKp9PFj+2wlqSWlhZdddVVamtrkyRdc801\nevXVV0sGdkdH/LzP14rxbE6S9K71HWpqrPzRmoVmPLs9Asb8j5epo6VBw6kp17RzJfjpe10M2ql8\ntFV5aKelUzKwN27cqOeee0433XST9u3bp56enuJzV1xxhd544w2NjIwoFotp//79uuOOO0q+6MDA\n+OKqXiLH+1OqiwSVTWc1OVH5IWbTbJQkDQykz3i8zbQUDBgX3E4tjWEdH0jpnRMjqgsHF11nrevo\niLvmZ8pJtFP5aKvy0E7lqdSbmpKBvXXrVu3Zs0fbtm2TJPX29uqJJ55Qd3e3brjhBv31X/+1PvnJ\nT8owDN188826+OKLK1KY0yzLUnI0o3YXrcG2tRbvY2e1ItHocDUAgEooGdiGYejhhx8+47F169YV\n/33zzTfr5ptvrnxlDktnc8pO5V014cxWPGZzfJLABgCPYOOUc7DXYLtpwpktcVoPGwDgDQT2OSRH\n7CVd7gtslnYBgPcQ2Odgr8FOuHFInM1TAMBzCOxzsIfEO1y0LamtuD0p52IDgGcQ2Ofgxm1JbXWR\noBqjIXrYAOAhBPY5JEezaqgLqSHqjnOw52primpobFKWZTldCgCgAgjseZy+BtutEk1RTU7nNTGZ\nc7oUAEAFENjzGJ+Y1tS06colXbbWwsSzwVGGxQHACwjseRRP6Wpx3wxx2+mbpwAA3I/AnoebN02x\n2ZunDDPxDAA8gcCehxvPwZ7L3jxlkM1TAMATCOx52Odgu3nSWXHzlHF62ADgBQT2PGZ3OXNvYLfE\n6mSI7UkBwCsI7HkMjGYVqw+rvq7kYWY1KxQMqDkWYfMUAPAIAnsO07I0OJp19XC4LdEU1fD4pEyT\nzVMAwO0I7DlGU1PK5U1PBHZrU1R509JoesrpUgAAi0Rgz2FvNNLu4jXYtgQTzwDAMwjsOQZG3T9D\n3Ma52ADgHQT2HG4+pWsue/MUticFAPcjsOeYXYPthSFxu4dNYAOA2xHYc3hhDbbN3jxlkMAGANcj\nsOcYHM2qqTGiunDQ6VIWLVYfViQUILABwAMI7NOYpqXBMW+swZYkwzCUaI4y6QwAPIDAPs1IalJ5\n0/JMYEszM8VTmWlNTuWdLgUAsAgE9mkGPDThzMZabADwBgL7NMUlXS3e6mFLTDwDALcjsE9j97Dd\nfA72XAk2TwEATyCwT+PpHjabpwCAqxHYp0mOZGRotlfqBcV72AyJA4CrEdinGRjNqrWpTqGgd5ql\nNc49bADwAu8k0yJN50yNjE+q3UO9a0kKhwJqbowQ2ADgcgR2wdB4Vpa8cazmXG1NM5unmJbldCkA\ngAtEYBckR7xzStdciaY65U1LY+kpp0sBAFwgArvAPge7w4M9bPsgE4bFAcC9COwCL/ew21iLDQCu\nR2AXJL3cw2YtNgC4HoFdMDCSVTBgqCVW53QpFTe72xmBDQBuRWAXJEczSjRHFQgYTpdScW2FzVO4\nhw0A7kVgS8pO5TQ+Ma0OD96/lqRYfViRUIB72ADgYgS2Zu/tenENtiQZhqG2pig9bABwMQJbM1uS\nSt6cIW5LNNUplZnW5FTe6VIAABeAwNbMoR+S1O6hYzXnKi7tGqeXDQBuRGDLm8dqzlVc2sWwOAC4\nEoEtaaDQw+7wcA/b3u2MiWcA4E4EtmZ62JFwQPGGsNOlVE0bm6cAgKv5PrAty1JyNKOO5noZhvfW\nYNsShbXYbJ4CAO7k+8BOZ3PKTOY9PUNcklrj3MMGADfzfWB7fQ22LRwKqLkxwj1sAHAp3wf27IQz\nb/ewpZn72EPjWZmW5XQpAIAF8n1gJ33Sw5Zm7mPn8pbG0lNOlwIAWCDfB/bAqL1pij962BL3sQHA\njXwf2MkRe1tSP/SwWdoFAG5FYI9m1BgNqSEacrqUqrM3T6GHDQDuUzKwLcvSQw89pG3btumuu+7S\nsWPH5r3mU5/6lL73ve9VpchqMS1LAyNZX9y/lmaH/ZP0sAHAdUoG9q5duzQ1NaWdO3fq/vvvV29v\n71nX/OM//qPGxsaqUmA1jYxPKpc31embwJ75Pu3bAAAA9ygZ2Hv37tXmzZslSRs2bNCBAwfOeP4/\n//M/FQgEite4ib2kq7PVH4HdEA2pMRpSsjDRDgDgHiUDO5VKKR6PFz8OhUIyTVOS9MYbb+jZZ5/V\nZz/72epVWEX9w4U12D7pYUsz97EHR7OyWIsNAK5ScqZVLBZTOp0ufmyapgKBmZz/93//d/X39+uu\nu+7S8ePHFYlE1NXVpeuvv/68X7OjI37e55dKaiovSepZm3CkpkIznv3aAWP+xyugqzOuo30phesj\nxe1KvaBWfqZqHe1UPtqqPLTT0ikZ2Bs3btRzzz2nm266Sfv27VNPT0/xuS984QvFf3/jG99QR0dH\nybCWpIGB8Qsst7LePjEqSYoYliM1mWajJGlgIH3G422mpWDAqEpN8cJs+ENvJrW+q7niX98JHR3x\nmvmZqmW0U/loq/LQTuWp1JuakoG9detW7dmzR9u2bZMk9fb26oknnlB3d7duuOGGihThlP7hjELB\ngFridU6XsmTs4f/kaNYzgQ0AflAysA3D0MMPP3zGY+vWrTvruvvuu69yVS2RgZGMOlqiCnj4WM25\nEsWlXUw8AwA38e3GKenstNLZnK8mnEmzh5ywFhsA3MW3gW3PEPfLGmxbsYc9Qg8bANzEt4FdPFbT\nJ2uwbdFISPGGMD1sAHAZ3wa2X3vY0swWpYNjnIsNAG7i38D22S5np2tvrlcub2k0xbnYAOAWvg3s\ngeGMDPnjWM252pkpDgCu49vA7h/JqLWpTuGQ/5rAPp2MQ0AAwD38l1aSpnN5jYxP+vL+tUQPGwDc\nyJeBPTCSlSV/HfpxOjuwB5gpDgCu4cvA9vOEM2k2sAcJbABwDV8G9oAPj9U8XTgUVHMsUlyLDgCo\nfb4MbL/3sKWZXvbw+KTyhbPNAQC1zZeBbfcs/TrpTJI6muuVNy0Nj086XQoAoAy+DOz+4YwaoyE1\nRMNOl+KY2T3FuY8NAG7gu8DOm6YGRjJa1tbgdCmOskcXuI8NAO7gu8AeHM0qb1pa1urzwC7cv+8n\nsAHAFXwX2H2FGeLL2/x7/1qSOgtvWOz2AADUNt8F9qmhCUny/ZB4cyyicChQXOIGAKhtvgvsPjuw\nfT4kHjAMdbbUq39kQhbHbAJAzfNvYPt8SFyauY+dmcwrlZl2uhQAQAm+C+xTQxm1xCKKRkJOl+I4\ne6e3fobFAaDm+Sqwp3N5DY1ltdzn969ty5gpDgCu4avA7h/OyNLsDGm/62ilhw0AbuGrwD41ZC/p\nIrCl2TcuBDYA1D5fBXbfMBPOTpdoqlMwYKh/ZMLpUgAAJfgqsO012PSwZwQDASWao6zFBgAX8FVg\n9w9NyDD8ew72fDpb6zU2Ma3MZM7pUgAA5+GrwD41nFF7c1ShoK++7fPqZGkXALiCb5JrIpvTWHrK\n91uSzmVPPOPULgCobb4JbHvC2XKWdJ3B7mHb7QMAqE3+CWwO/ZiXfcwmPWwAqG2+CexT7CE+r46W\nqAxJfUMENgDUMt8E9onBmcBemWh0uJLaEg4FlWiOFt/QAABqk28C++RgWnWRoFrjdU6XUnOWJxo0\nmp7SRJalXQBQq3wR2HnTVN/QhFa0NcgwDKfLqTn2RjL0sgGgdvkisJMjWeXyllYwHD6vFcXATjtc\nCQDgXHwR2CcGZ4JoZTszxOezvPBGhh42ANQuXwT2ycKEM3rY87OHxO12AgDUHn8EdnKmh70iQQ97\nPi2xiOoiQXrYAFDDfBHYJwYnFAwYxU1CcCbDMLS8rUF9QxmZpuV0OQCAeXg+sC3L0snBtJa3NSgY\n8Py3e8FWJBqUy5tKjmWdLgUAMA/PJ9jw+KSyU3mGw0soLu3iPjYA1CTPBzYTzsrDWmwAqG2eD2x7\nSdcKlnSd1wqWdgFATfN8YJ9kD/GyLGutlyHp1CCbpwBALfJ+YCfTMjQ75Iv5RcJBtTVFWYsNADXK\n04FtWZaOJ9Nqb4kqEg46XU7NW9neqNH0lNLZaadLAQDM4enAHktPKZWZ1qqOmNOluEJXx8xtg+MD\nDIsDQK3xdGC/UwieLgK7LF3thcBOEtgAUGs8HtgpSdKqDiaclWO2h51yuBIAwFy+COzVnfSwy7Ei\n0ShDDIkDQC3yeGCnFQoG2EO8THXhoDpa63U8mZZlsac4ANQSzwa2aVo6kUxrZTt7iC9EV3ujUplp\njaWnnC4FAHAazyZZ3/CEpnMmM8QXyJ6g9w4TzwCgpoRKXWBZlnbs2KFDhw4pEonokUce0erVq4vP\nP/HEE/qP//gPGYahD3zgA/r0pz9d1YLLZd+HJbAXxp6gd2IgrSvWtjlcDQDAVrKHvWvXLk1NTWnn\nzp26//771dvbW3zu2LFjevbZZ/X9739fO3fu1AsvvKDXX3+9qgWXixniF2Z2aRczxQGglpQM7L17\n92rz5s2SpA0bNujAgQPF51auXKlvf/vbkiTDMJTL5VRXV1elUhfGXoO9ihniC7KsrUHBgMFMcQCo\nMSWHxFOplOLx+OwnhEIyTVOBQEDBYFAtLS2SpK997Wu6/PLL1d3dXfJFOzriJa9ZrJNDE4o3RHTx\n2oQMw6j6610Iey7cWe0RMOZ/fIl0dcZ0YjCtRCKmQKA2224up9rKbWin8tFW5aGdlk7JwI7FYkqn\nZ3tbdljbpqamtH37dsXjce3YsaOsFx0YGF94pQswOZXXqWRal65pUbKGh3ZNc2b4eWBOb7bNtBQM\nGFVvp3NZ3lqvo6fG9eqbA+psqf0lcR0dccfayk1op/LRVuWhncpTqTc1JYfEN27cqN27d0uS9u3b\np56enjOev/fee3XZZZdpx44dNdOTfWcgJUsMh1+o7mUzP1xHT/GLCAC1omQPe+vWrdqzZ4+2bdsm\nSert7dUTTzyh7u5u5fN5vfzyy5qentbu3btlGIbuv/9+bdiwoeqFn89bhaBZu5yhmguxptBub/eN\n65p3dTpcDQBAKiOwDcPQww8/fMZj69atK/57//79la9qkd7umwlsu6eIhSn2sPtq93YCAPiNJzdO\nOXpqXJFQQMsTDU6X4kqx+rDamup0tI8hcQCoFZ4L7OmcqePJtFZ3xtiSdBG6l8U1mp7SSGrS6VIA\nAPJgYB9PppQ3La1hOHxR1hSHxellA0At8Fxgv12YcNbNhLNFWbNsZob929zHBoCa4L3ALgQME84W\nh6VdAFBbvBfYp8YVDBha2c4e4ovRGq9TrD5cnHEPAHCWpwI7lzd1rD+lro5GhUOe+taWnGEYWrs8\nruRoVqnMtNPlAIDveSrVTg5OKJc3GQ6vkItWNkmSDp8YdbgSAICnAtsOlnWFoMHiXLSyWZL05vEx\nhysBAHgqsN88MRMs6wtBg8Whhw0AtcNTgX34xJjqwkF1MeGsImL1YS1ra9Dhk2MyLcvpcgDA1zwT\n2BPZnE4cw50OAAANm0lEQVQm01q3Iu6aM5zdYP3KJmUm8zo5OOF0KQDga54J7COnxmRp9r4rKmM9\nw+IAUBM8E9iHj88EynomnFWU/Qbo8AkmngGAk7wT2IVAuYjArqhVnY2KhAP67XF62ADgJE8EtmVZ\nevPEmBJNUTXH6pwux1OCgYDWr2zW8YE0G6gAgIM8Edj9wxmlMtP0rqvk0jUtkqTXj404XAkA+Jcn\nAvtQIUh6Vrc4XIk3XVpo19eODjtcCQD4lycC2+75XUpgV8VFK5sUDgV06Cg9bABwiicC+9DRETVG\nQ1rZwYYp1RAOBbV+ZZPe6U9xHxsAHOL6wE6OZjQ4llXP6hYFDDZMqZZL17TKkvQG97EBwBGuD2yG\nw5fG7H1sAhsAnOCZwO5ZQ2BX0/quJkXCAR04Muh0KQDgS64P7ENHRxSNBLWmkzOwqykcCuqyNa06\nOTih5EjG6XIAwHdcHdhDY1n1DWdm7l9z4EfVXbU+IUn6zWF62QCw1Fwd2AeODEmSrljX5nAl/nDV\nRXZgDzlcCQD4jycC+0oCe0l0tNRreVuDXn17WNM50+lyAMBXXBvYpmnp1beGlGiq0/K2BqfL8Y2r\nLkpocjrPNqUAsMRcG9hHTo0pnc3pinVtMlh/vWTefUm7JOmXrw84XAkA+ItrA/vgYXs4POFwJf7S\ns7pZ8Yaw9r4+INO0nC4HAHzDtYH9myODMgzpsrWtTpfiK8FAQBt7OjSWntIb7zAsDgBLxZWBPZqa\n1OHjY+pZ1aLGaNjpcnznmnd1SpJeeq3f4UoAwD9cGdi/+m1SlqT39HQ4XYovvWtNi2L1Ye09xLA4\nACwVdwb260lJ0nsKE6CwtIKBgDZd2qHR9JReeYs12QCwFFwX2JnJnF59e0irO2PqaKl3uhzfuv7q\nFZKk//r1SYcrAQB/cF1g/+bwoHJ5SxsZDnfURSuatLK9Ub96Y4AzsgFgCbgusP/7YJ8k6ZpLCWwn\nGYah669aoVze0s8PnnK6HADwPFcFdiozrd8cHtSazpi6OmJOl+N71165XMGAoed+eVymxeQzAKgm\nVwX2S6/1K29aev8Vy50uBZKaGiN6/+XLdGpoQr9+kxO8AKCaXBXYPz94Soak912+zOlSUPDh31kj\nSfrRL446XAkAeJtrAvt4Mq3fvjOqy9a2qjVe53Q5KFjdGdMVa1v12tERHTk55nQ5AOBZrgnsn/7q\nuCRpy7u7HK4Ec938/m5J0r89f9jhSgDAu1wR2NmpnH524KRaYpHiaVGoHZetbdPla1t14MiQXnt7\n2OlyAMCTXBHY/32wT5nJvD747i6Fgq4o2Xdu++B6SdJTP/0tM8YBoApqPv3ypqn//eJRhYKGPrBh\npdPl4BzWrWjS71zWqSMnx4u3LwAAlVPzgf2LV/vVP5LR5qtXMtmsxt35f1yi+rqQnt79pobHJ50u\nBwA8paYD2zQtPfuztxQMGPr9961xuhyU0Byr00dvWK/MZF7ffvYVTvICgAqq6cB+fv8JnRyc0LVX\nLlc7B324wgc3rNS7L27Xq28P64d7jjhdDgB4Rs0G9kR2Ws88f1h1kaD++AMXOV0OymQYhj75B5cp\n0RTVD/e8pf9+hX3GAaASajawn/rpm0plpnXL73arOca9azeJ1Yf12duvVn1dSN959lXt/23S6ZIA\nwPVqMrB//eagdu87oVUdMX34vdy7dqPVnTF99rarFAgY+sYzv9Ge33BuNgAsRs0Fdv9IRt9+9hUF\nA4Y+9YeXKxyquRJRpkvXtOrz296taCSo7/yvV/Xkjw5pajrvdFkA4Eo1lYZj6Sn930/tVyozrU98\nuEerOzlC0+0uWdWi7Z/YpK72Rj33y+N66F9f0r7fJmWxuQoALEjJwLYsSw899JC2bdumu+66S8eO\nHTvj+e9///u67bbbtG3bNv30pz+94EKSIxl97f/5pU4OTujD712tD7JnuGesbG/U3/7ZNbpx0yr1\nD0/on/7nr/XV7+7Vi6/0KZc3nS4PAFwhVOqCXbt2aWpqSjt37tT+/fvV29urxx9/XJKUTCb15JNP\n6t/+7d+UzWZ155136rrrrlM4HC67ANO09LMDp/Q//r83lJnM6cPvXa07PnTxhX9HqEmRcFAf29qj\nD757pZ7efVj7fpvUm8cPqr4uqKsuSuiKdW26aGWzViQaFDAMp8sFgJpTMrD37t2rzZs3S5I2bNig\nAwcOFJ/79a9/rU2bNikUCikWi2nt2rU6dOiQrrzyynN+vTVrTOXzDcpblnI5U5PTeeXNVTK0So31\nYe1/Kqh/qMA35gYnTswE06ZNjWc8HjjxgiRD5pzHvaFR0jLl85ayUzlN5kw9e9oGK4akYMBQIGAo\nGDBkGIYChmQEDBkyZGd58f9lKBA0ZZoNZ70SsX+mQNCSmT+7nXA217WVQz/swYCl/Dy/ezjTO8dK\nX1OOkoGdSqUUj8dnPyEUkmmaCgQCZz3X0NCg8fHx83695Gj2jI8NSXXhoBqiIQUD/In1i2DQUGN9\nWI2ScnlTuZyp6bylXN5U3rSUY5c0AJ5RmTc1JQM7FospnU4XP7bD2n4ulUoVn0un02pqajrv15sY\n5d3Y2ea+UVntSBXOqam5jwBQk0r+pdy4caN2794tSdq3b596enqKz1199dXau3evpqamND4+rsOH\nD+uSSy6pXrUAAPiUYZVYX2NZlnbs2KFDhw5Jknp7e7V79251d3frhhtu0FNPPaXvfe97sixL9957\nr2688cYlKRwAAD8pGdgAAMB53DwEAMAFCGwAAFyAwAYAwAUIbAAAXKDkOuxKOX22eSQS0SOPPKLV\nq/223njW/v379fWvf11PPvmkjh49qgceeECBQECXXHKJHnroIUnSN77xDe3evVuhUEjbt2/X1Vdf\nfc5rvSaXy+lLX/qSjh8/runpad1zzz26+OKLaad5mKapBx98UEeOHFEgENDDDz+sSCRCW53D4OCg\nbrvtNv3rv/6rgsEg7XQOt956a3FjrFWrVumOO+7QI488olAopGuvvVb33XffOf+u79u3T1/96lfP\nuNarvvWtb+knP/mJpqen9bGPfUzvfe97q/czZS2RH/3oR9YDDzxgWZZl7du3z7r33nuX6qVrzr/8\ny79Yt9xyi3XHHXdYlmVZ99xzj/XSSy9ZlmVZX/7yl60f//jH1sGDB60/+7M/syzLsk6cOGHddttt\n57zWi55++mnrq1/9qmVZljUyMmJt2bKFdjqHH//4x9aXvvQly7Is68UXX7Tuvfde2uocpqenrU9/\n+tPW7/3e71mHDx+mnc5hcnLSuvXWW8947CMf+Yh17Ngxy7Is61Of+pT1yiuvnPPv+nzXetGLL75o\n3XPPPZZlWVY6nbb++Z//uao/U0s2JH6+Pcn9pru7W4899ljx44MHD+qaa66RJH3gAx/Qz372M+3d\nu1fXXXedJGnFihUyTVNDQ0NnXfvzn/986b+BJfD7v//7+tznPidppgcZDAb1yiuv0E7zuPHGG/V3\nf/d3kqQTJ06oubmZtjqHr33ta7rzzjvV2dkpy7Jop3N47bXXNDExobvvvlt//ud/rpdfflnT09Na\ntWqVJOn6668vttXpf9cPHjyoVCp11rVebasXXnhBPT09+su//Evde++92rJlS1V/ppYssM+1J7kf\nbd26VcFgsPixddpS+MbGRo2PjyudTp/RXo2NjWdsA3v6tV5UX1+vhoYGpVIpfe5zn9Nf/dVf0U7n\nEQgE9MADD+grX/mKbrnlFtpqHs8884wSiYSuu+66Yvuc/jeIdpoVjUZ199136zvf+Y527Nih7du3\nKxqNFp8/V1sFg0Gl02nFYrGzrvWi4eFhHThwQP/0T/+kHTt26POf/3xVf6aW7B72+fYk97vT2yGd\nTqu5uXnefdrj8fhZ15bau93NTp48qfvuu0+f+MQn9Ad/8Af6h3+YPceNdjrbo48+qsHBQd1+++2a\nnJwsPk5bzXjmmWdkGIb27NmjQ4cO6Ytf/KKGh4eLz9NOs9auXavu7u7iv+PxuEZHR4vP2201OTl5\n1t/1Czljwq1aWlq0fv16hUIhrVu3TnV1derr6ys+X+mfqSVLzPPtSe53l19+uV566SVJ0vPPP69N\nmzbpPe95j/bs2SPLsnTixAmZpqnW1lZddtllZ13rRclkUnfffbe+8IUv6NZbb5Wkeb93v7eTJP3g\nBz/Qt771LUlSXV2dAoGArrzySv3iF7+QRFvZvvvd7+rJJ5/Uk08+qXe96136+7//e23evJmfqXk8\n/fTTevTRRyVJfX19ymQyqq+v17Fjx2RZll544YViW839u97Y2KhIJHLWtV60adMm/dd//Zek2XZ6\n//vfX7XfvSXrYW/dulV79uzRtm3bJM3sSY4ZX/ziF/W3f/u3mp6e1vr163XTTTfJMAxt2rRJd9xx\nhyzLKs4enO9aL/rmN7+psbExPf7443rsscdkGIb+5m/+Rl/5yldopzk+/OEPa/v27frEJz6hXC6n\nBx98UBdddJEefPBB2qoEfvfmd/vtt2v79u362Mc+pkAgoN7eXgUCgeKQ73XXXaerr75aV1111bx/\n108fHrav9aItW7bo5Zdf1u23316cMd/V1VW13z32EgcAwAW4iQwAgAsQ2AAAuACBDQCACxDYAAC4\nAIENAIALENgAALgAgQ0AgAv8/4kIg+VeGIQhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc276ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = np.arange(0, 6000)\n",
    "\n",
    "def weibull(N, shape, scale, offset):\n",
    "    X = (N-offset) / scale\n",
    "    Y = shape/scale * X**(shape-1) * np.exp(-X**shape)\n",
    "    return Y\n",
    "\n",
    "def center(shape, scale, offset):\n",
    "    return np.exp(np.log((shape-1) / shape)/shape + np.log(scale)) + offset\n",
    "\n",
    "def top(x_center, shape, scale, offset):\n",
    "    X = (x_center - offset) / scale\n",
    "    return shape / scale * (X ** (shape - 1) * np.exp(- X ** shape))\n",
    "\n",
    "@interact(\n",
    "    N=fixed(N),\n",
    "    shape=(0.0, 40),\n",
    "    scale=(0, 4000),\n",
    "    offset=(-3000, 3000),\n",
    "    mag=(0.05, 1),\n",
    ")\n",
    "def plot_weibull(N, shape=3.5, scale=1000, offset=500, mag=1):\n",
    "    Y = weibull(N, shape, scale, offset)\n",
    "    x_center = center(shape, scale, offset)\n",
    "    y_center = top(x_center, shape, scale, offset)\n",
    "    Y = mag * Y / y_center\n",
    "    print(\"X_center=%.2f\\nY_center=%.2f\" % (x_center, y_center))\n",
    "\n",
    "    ax = plt.plot(N, Y)\n",
    "    plt.axvline(x_center)\n",
    "    plt.axvline(scale+offset, color='r')\n",
    "    plt.axhline(y_center)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion:\n",
    "It is possible to *coarsly* configure a weibull function by following this empirical procedure:\n",
    "\n",
    "1. Start with a *symmetric* bell-curve by fixing the *shape* (`'k'`) parameter to $3.5$.\n",
    "2. The $n_{start}$ of the curve is always near 0.\n",
    "3. Control very roughly the $n_{end}$ of the curve with the *scale* (`'s'`) parameter;\n",
    "   for instance, $s=1000$, means that the integral of curve from 0 will be 63.2% at 1000 RPMs (red-line above).\n",
    "4. We can validate the position of the $n_{center}$, and shift all RPM params ($n_{start}, n_{center}, n_{end}$) with the *offset* (`'c'`) parameter; for instance $c = +500$ will move the *top-of-the-curve* roughly from $900RPM \\Rightarrow 1400 RPM$ to the right.\n",
    "5. Finally we can fiddle with the *shape* (`'k'`) parameter to *skew* the curve as we like:\n",
    "      - $1 < k < 2$: long tail (positive kurtosis)\n",
    "      - $3 < k < 4$: symetric ($3.5$ is the starting value)\n",
    "      - $10 < k$: long head (negative kurtosis)\n",
    "      - see http://blog.minitab.com/blog/understanding-statistics/why-the-weibull-distribution-is-always-welcome\n"
   ]
  }
 ],
 "metadata": {
  "extensions": {
   "jupyter_dashboards": {
    "activeView": "grid_default",
    "version": 1,
    "views": {
     "grid_default": {
      "cellMargin": 10,
      "defaultCellHeight": 20,
      "maxColumns": 12,
      "name": "grid",
      "type": "grid"
     },
     "report_default": {
      "name": "report",
      "type": "report"
     }
    }
   }
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "widgets": {
   "state": {
    "01ce5a376d364170835cbf4dc4b8ae1f": {
     "views": []
    },
    "02f6a25eada34418a17226362b0481ff": {
     "views": []
    },
    "03209a9fe1614d34925ada8161c137e8": {
     "views": []
    },
    "036b4681f9e44c5d8cdbbb353f8be760": {
     "views": []
    },
    "03b6e789a2094a8c9c15b8dfda0eb73e": {
     "views": []
    },
    "07a6573e092345728d2edabf96fbe0b5": {
     "views": []
    },
    "081c9f63f9dd49f4813b85f2b2d30da9": {
     "views": []
    },
    "0aa30f6544f246ffb4eac57dfca236f4": {
     "views": []
    },
    "0aac99a8b74944d5b80ff1513715c28c": {
     "views": []
    },
    "0acce5c1001749ccaf5a7799c9290495": {
     "views": []
    },
    "0b966257511f43e1b9cddb2196037af3": {
     "views": []
    },
    "0c41ccaf74554673a0dc413de94faa6f": {
     "views": []
    },
    "0d0d6aafc9924a2eb971483da9400518": {
     "views": [
      {
       "cell_index": 3
      }
     ]
    },
    "0f3c9d90c7aa459a874f2ad32a49d8e1": {
     "views": []
    },
    "0f8d3c6c50c2442c9556f564073a92cd": {
     "views": []
    },
    "110c889870a74c72a403304d50383896": {
     "views": []
    },
    "11ff15c00961424584515921d7e76647": {
     "views": []
    },
    "12927bcbda4f4f4cb2faf91374ec741a": {
     "views": []
    },
    "12c0bda55201406dad1529966482b7d9": {
     "views": []
    },
    "13c6de8b56a64958a5559f7280c2fb46": {
     "views": []
    },
    "14006466ef1940158fad434e22a9d60d": {
     "views": []
    },
    "1567fb0707b94eafb1ec9d858273a71d": {
     "views": []
    },
    "15e5fd49a6374247afea49730e645f03": {
     "views": []
    },
    "16ee0a3dd754454db05c8b95861860e2": {
     "views": []
    },
    "170838955a854aba8da9453d3734c877": {
     "views": []
    },
    "172060b3e6344a2894df5c27b8c2f20c": {
     "views": []
    },
    "174a3d32f0f8469d87af6a660d20efa6": {
     "views": []
    },
    "1a8a81b48d704736bff8c9ee209f2af7": {
     "views": []
    },
    "1b332971d5144e64a67f25f8cd76b3da": {
     "views": []
    },
    "1bbfe92478ce4472a865c94c55918d60": {
     "views": []
    },
    "1c3af8c2976a4e258a3bafaa21c4e5ed": {
     "views": []
    },
    "1c82199a4232439084e44240daee112e": {
     "views": []
    },
    "1d1a45a8000d448ea280bc0c91d35cc8": {
     "views": []
    },
    "1d48f7979730444e8eb55bd8d2d88db1": {
     "views": []
    },
    "215a08bd1a0648489259bc293f736ca8": {
     "views": []
    },
    "2170a6cd250f492c9c950c42633123d2": {
     "views": []
    },
    "2237a934576b460e9c2b9052738f8706": {
     "views": []
    },
    "23c90f222f3446ba85fd3aca1097e302": {
     "views": []
    },
    "23d28ea8f41f40babd12b70487f73999": {
     "views": []
    },
    "23ea849257e344619f6b8be8d345f06e": {
     "views": []
    },
    "2451096cfc3046869c3ce49ba2a8fd2b": {
     "views": []
    },
    "286df688417b418ca6df406102486d53": {
     "views": []
    },
    "289ef00582c546bdbfd2f86b441dc4de": {
     "views": []
    },
    "28c697a622ca47629463ceb6a67ea08e": {
     "views": []
    },
    "29471ca27a7e41b6897af58a494dbf86": {
     "views": []
    },
    "2be0fee0b4124732a0d1e74c56769283": {
     "views": []
    },
    "2d80f49d28804d5d82bfa33bf4b8c291": {
     "views": []
    },
    "2e152c9ef1a94c06bbde7d27407f0423": {
     "views": []
    },
    "2f7ffcf407bf4d49adc3ecd0c28b8b93": {
     "views": []
    },
    "30ee07d48eb64f86a278979299052a5f": {
     "views": []
    },
    "310e66f31dfa4b1da69410173daf28f4": {
     "views": []
    },
    "35357721557749f591be959fcec4061e": {
     "views": []
    },
    "357c6ce3e49c4a0fabf1ae60101dbab9": {
     "views": []
    },
    "366b69d296c048e684c08b9b6996400d": {
     "views": []
    },
    "37dc345a9a58439683354146f19032e6": {
     "views": []
    },
    "392101ac7edb4b7d9dda456d149ba4f7": {
     "views": []
    },
    "39f53ca418204c2599833e68295591db": {
     "views": []
    },
    "3a850fba4e974ee0b869f93ea310f675": {
     "views": []
    },
    "3bc5db04b7e94de4bf179c201a393ca5": {
     "views": []
    },
    "3c286e9a7ba54efabf3411b50843190d": {
     "views": []
    },
    "3e25811020c443989cfeb52fb71a81ea": {
     "views": []
    },
    "3e42ea9142d8466f9c5d4368bf6bf475": {
     "views": []
    },
    "3e575bd778b746ad9724bbbb16969e11": {
     "views": []
    },
    "40dfcce2957949ebb1e576f36c0fa085": {
     "views": []
    },
    "40e8fe592b3b4b188952078e47c1a701": {
     "views": []
    },
    "42643a55cb724cbfa6455e85cf4bf6d3": {
     "views": []
    },
    "4298b67a5f254ec796738594e46706d1": {
     "views": []
    },
    "44be8743f1564de48c7e502363828305": {
     "views": []
    },
    "47294d24a94c4a2f8e11ed339292b7c3": {
     "views": []
    },
    "48469400dcc4466b99e31d7bb6c77660": {
     "views": []
    },
    "484cea37c85948d788ba4b18075666d0": {
     "views": []
    },
    "4853a392d28749aeb15aaefa4dcaa3d2": {
     "views": []
    },
    "4a15c1647080452e8cf1b051cd107ffa": {
     "views": []
    },
    "4daf34e45fb6472a8cec8452476153e3": {
     "views": []
    },
    "4ddac734908f464e98fb48e0842f29e8": {
     "views": []
    },
    "4e45e997cff542e19043c091bbec8b3d": {
     "views": []
    },
    "501133f715764a3ea5a61cad0bef4492": {
     "views": []
    },
    "50a7608be56e4639990063058428568d": {
     "views": []
    },
    "5117c795532f4e30af5e0421b7325d4b": {
     "views": []
    },
    "53f8289619d6466b8825cc829df99235": {
     "views": []
    },
    "552dba9ae6214125a05568b19fc08142": {
     "views": []
    },
    "5666a4763d2d486bbce488e29ff524b5": {
     "views": []
    },
    "567de7b818274706b07286b7afaa53ea": {
     "views": []
    },
    "589358651ba34414b11d84703de17bb6": {
     "views": []
    },
    "59046ba2c0e1409ebf47dc6d26984674": {
     "views": []
    },
    "5ab7b41858c14f88a52269702571acd5": {
     "views": []
    },
    "5b7b9b18cf364f88957c555bd96db9a3": {
     "views": []
    },
    "5cb6d5421725483594f31aebc01ca2f3": {
     "views": []
    },
    "5d353c7bcb3a459c89d262b573df34f7": {
     "views": []
    },
    "5f2d1b8824884a749bf5442a5e2a6839": {
     "views": []
    },
    "602281b4cd574603a1030e2054a25bce": {
     "views": []
    },
    "617337c03fe041eb8bc13f55d8f3eb91": {
     "views": []
    },
    "6248f818decd4c469896e12e7e568899": {
     "views": []
    },
    "62dc6bd72b254ce2a4c3fa328383a00b": {
     "views": []
    },
    "6309d054580d452b9059a118bd0b56ec": {
     "views": []
    },
    "6362be0fa35a49e5bb913d9df9e53f60": {
     "views": []
    },
    "6474e4b5c4a64becbe3405594ecb6fb1": {
     "views": []
    },
    "656110ca19c1498c9cb6307f956baf44": {
     "views": []
    },
    "65c53bbb04e34be88b365a5c2301ecf6": {
     "views": []
    },
    "6821c35acecf46a88225287607b4ca89": {
     "views": []
    },
    "68ea8be56baf4deb8f8d656984668c4b": {
     "views": []
    },
    "6b0d8a3df9d34b9aa03a74ca70585f35": {
     "views": []
    },
    "6bb68a0f9c4d4f30baca4fb7ca2b0290": {
     "views": []
    },
    "6c01470a037b492f9e0f72310b61e1a1": {
     "views": []
    },
    "6c18362bc6bb47ee994e1753acfb2877": {
     "views": []
    },
    "6f1e2c8cbeef4e52ae869a239b7d1659": {
     "views": []
    },
    "702c08a28ab44e9fa0c2ecc55866e49f": {
     "views": []
    },
    "70656a993c184623a3d2f4adc0ea670b": {
     "views": []
    },
    "71c216315d7a40fabf1780fd2e74b867": {
     "views": []
    },
    "756b2b9d0b90411381a87a2b5dd48a4c": {
     "views": []
    },
    "76980ac8d2084743b375efdc9b67b6a4": {
     "views": []
    },
    "76e13b6bcbd34f9b935017a96a297db2": {
     "views": []
    },
    "78aac8e7d7f641d89734114b2cdb71c5": {
     "views": []
    },
    "78fc9f809bc24373bab598c2e3566b0d": {
     "views": []
    },
    "7985a7a3b6384d269d6af4a73932403a": {
     "views": []
    },
    "7b2448f2625d4368a42625c2ffd6a7c1": {
     "views": []
    },
    "7b644a3b30b74e04bcfa2a5622714180": {
     "views": []
    },
    "7c4f23d5377e4a6b9c3ed4f31b715790": {
     "views": []
    },
    "7cf45571d69341539d74099f039fdeb1": {
     "views": []
    },
    "7f2d575e4be84e96beed3c9a17139d03": {
     "views": []
    },
    "80382d65ebe945ad845983fb5ed760cd": {
     "views": []
    },
    "8096b13d81604341be534a55283cbb03": {
     "views": []
    },
    "80bc417f06b24286916295254db2b248": {
     "views": []
    },
    "80d1b3d283fb4cdebeb4d248df8bfb07": {
     "views": []
    },
    "813aef6761b64bbb9db9a95167f1954a": {
     "views": []
    },
    "8277ec0d36754d95babff74256f1c6af": {
     "views": []
    },
    "84871d2ca5e148658284ddea993b6f5b": {
     "views": []
    },
    "85067783e2464b8197e10be56f225ec0": {
     "views": []
    },
    "85e21e223c234de18a58d65c70303cf6": {
     "views": []
    },
    "86a20345172d4632b451096fc389f904": {
     "views": []
    },
    "88072bd601c348e689698713168efd21": {
     "views": []
    },
    "8827cd4337f44096a6497a67c56c4772": {
     "views": []
    },
    "88f0c7fe4a834dc79a1155428ce79f63": {
     "views": []
    },
    "89ff178619b34ab2905e747688553201": {
     "views": []
    },
    "8adf7d27c824429ab716b72108a72c1b": {
     "views": []
    },
    "8c1e821a38394379bd526841b060f848": {
     "views": []
    },
    "8c2504525cdb4fe3b73fcbaf1e4ee1c5": {
     "views": []
    },
    "8c2687d44e0d4d7187a7db39636f76bb": {
     "views": []
    },
    "8cc247eb691949f9b2297b55e4149061": {
     "views": []
    },
    "8d1676ee0d8847e5b8b3324226438451": {
     "views": []
    },
    "8d9e805c0c094be3b159347cadf17493": {
     "views": []
    },
    "8dc64a4c345d433891885b5c2c11a782": {
     "views": []
    },
    "8f0e29fb9f2945f18d2de06f9b53a6e8": {
     "views": []
    },
    "8f479f6157fb4dd49077b2010a499e17": {
     "views": []
    },
    "91dc56197f0c4aba84b35eac60a4f4a2": {
     "views": []
    },
    "923a0e1fe3404046b099ff5bee388038": {
     "views": []
    },
    "95647eda464942ef88e0b3f9da957587": {
     "views": []
    },
    "957ba0c5e63d4b848f19b757d746acd0": {
     "views": []
    },
    "96708a3744674bc98d5652c24be2dcfe": {
     "views": []
    },
    "96c479972652443c9ae4723e82127db9": {
     "views": []
    },
    "98030a54cbad4368b269af8f0877ad86": {
     "views": []
    },
    "981d5388ad554cd099b5b2296c228830": {
     "views": []
    },
    "982585b1414f4fcfbff94c29a3edadd4": {
     "views": []
    },
    "99714415a69d472cb3ee9ecacfb638e0": {
     "views": []
    },
    "9d45ff542632420b92c606e2c30e548b": {
     "views": []
    },
    "9d63cd1e26e54b57a43d64b391cb5432": {
     "views": []
    },
    "9ffa083b31cc4f62a2062ba66569c086": {
     "views": []
    },
    "a16fbadc49bc48bdbf2c26be6a046c45": {
     "views": []
    },
    "a29bebee759e43d186632f3cfd13e3ba": {
     "views": []
    },
    "a34d84369445450c99623efe8303eecb": {
     "views": []
    },
    "a431c682bb334ced843e8077c590a9e4": {
     "views": []
    },
    "a5807873843d4eeb902263207ab7656b": {
     "views": []
    },
    "a724d04a780249bf93685ed846413703": {
     "views": []
    },
    "a7a9b2c5583444dfaf665944f5e0d857": {
     "views": []
    },
    "a8413cfb5eb14ad481efe1db490b4646": {
     "views": []
    },
    "a9233cdb3e11406aacc6d62065de805e": {
     "views": []
    },
    "a9df791cdd0145e39bd11304405c0dae": {
     "views": []
    },
    "aa54b9a6c9634195b8011fa2b6e786c6": {
     "views": []
    },
    "aab785bc4ae048c5b2ea0139cff3bade": {
     "views": []
    },
    "aba3b9872e9c4b77b015c4a605c78b67": {
     "views": []
    },
    "abf5730300e74c7cbd402046b22e43d5": {
     "views": []
    },
    "ac91f5b21d944b5996cbfafc852f3dfe": {
     "views": []
    },
    "ad1f4beb1b404a269137577e6eb9e824": {
     "views": []
    },
    "ad3c50993bdd461eb8837cb7d8c0b7fc": {
     "views": []
    },
    "ae353d7449b348768e5e836387b7e89c": {
     "views": []
    },
    "ae4dcdfc493848d8b1bc490b683c923f": {
     "views": []
    },
    "b10c3761f9af4f7a9423ff56dd5da477": {
     "views": []
    },
    "b1f11ca6d8d24ea090a2db868d7f2808": {
     "views": []
    },
    "b5760d9bcdfd426788724829d0b29625": {
     "views": []
    },
    "b627c04a3ce242e4a85abf14610b00b6": {
     "views": []
    },
    "b83822cffebf4e79841a9661f2ec7397": {
     "views": []
    },
    "b8d96b796c064f139fde92d724b17c40": {
     "views": []
    },
    "b9c0ea5565c3403ca920da97b2969277": {
     "views": []
    },
    "bbbf6224a6a34454bd65d674a7534624": {
     "views": []
    },
    "bc2ffa3528784fe2a84d3419068f5ad9": {
     "views": []
    },
    "bc8c9262ce52448eb966b2fc820f0495": {
     "views": []
    },
    "bc902b98a3004e5d84d620c4175092b1": {
     "views": []
    },
    "bd63c8a3ab55499384fd199014eae25e": {
     "views": []
    },
    "be411396d98648f8a3e2b5232d858974": {
     "views": []
    },
    "bfcd01f2cfa14ac287560824a870c614": {
     "views": []
    },
    "c0bc91a256f6495999937ce1a3911a0e": {
     "views": []
    },
    "c2d43c6532304af4b758b0197426490f": {
     "views": []
    },
    "c65ebd103460495eabc6db41e3f68831": {
     "views": []
    },
    "c971ed8b14d048d09da22e03ddf3fe6b": {
     "views": []
    },
    "c985c08069bc432bb32b2f301c5a2cff": {
     "views": []
    },
    "c9e12d6d9e924d55b4aacab2c11771d6": {
     "views": []
    },
    "cad704cda270422abb5d1aa1540cd90a": {
     "views": []
    },
    "cd423298d09a4424a27ee0599eb26db4": {
     "views": []
    },
    "cd926cb491f94a62ad8b1b843a48df1d": {
     "views": []
    },
    "ce1aaee978044847aa2e41098c3771a3": {
     "views": []
    },
    "ce3e5180fdd7444f98c85f85ce834658": {
     "views": []
    },
    "cfd1b0777b2d48f5837c6764a90a53ca": {
     "views": []
    },
    "cff1aa86a77b43c3b49594e68a292cee": {
     "views": []
    },
    "d1175dc13fa0449eb4f9fe1caa15a86e": {
     "views": []
    },
    "d17edcd169c7475db7cfc0f155161ce4": {
     "views": []
    },
    "d2bc1eeaaba5465e8340f10a0fd3344e": {
     "views": []
    },
    "d32d471992d848e4b9cf1e4c9240faf1": {
     "views": []
    },
    "d3965a8974564277abd769bab91c28ef": {
     "views": []
    },
    "d462ce7d18e44c558483724885d11429": {
     "views": []
    },
    "d68008eaaf3f42b788f63056d92649b6": {
     "views": []
    },
    "d865d53248cd41e0bee65f4c77d24608": {
     "views": []
    },
    "de061845f7834d0c93fe4e3dbb9f2898": {
     "views": []
    },
    "deda6e0c10a04837812ef37507ec1899": {
     "views": []
    },
    "df37a15c8917410f9f35f1fa1d1007eb": {
     "views": []
    },
    "df6875e60987421bace701a4944167c8": {
     "views": []
    },
    "df7176745e8b4dc8987fa24a65d36ef6": {
     "views": []
    },
    "e0af754880114e2dbd36d4aca1630fe0": {
     "views": []
    },
    "e117f1172e64476c9b3c2b4cf175a362": {
     "views": []
    },
    "e39f84aa768e42cfbb6988412c8d9479": {
     "views": []
    },
    "e42f466f1ec64b87b7171119c0ae6968": {
     "views": []
    },
    "e74c707026df466ca903f8fc84297b79": {
     "views": []
    },
    "e74d1ea83f774eddbc05e854aed87f73": {
     "views": []
    },
    "e7982070c0ec4c08ab8aad4c3252ff16": {
     "views": []
    },
    "e7d8d4c6db9649c98c372750c471a201": {
     "views": []
    },
    "e91bbc3e0bf94a1db0b76bce18ea1859": {
     "views": []
    },
    "e982ce4a8f7c415aba1a8707b1ad2b7b": {
     "views": []
    },
    "e9b073e0b91742d598705d56b7f62a28": {
     "views": []
    },
    "eb8763d03fa34ecfb14d426b9a2f3722": {
     "views": []
    },
    "eba3603aec0a4705ad45b1742467545d": {
     "views": []
    },
    "ed698f3087774d7b88b76fa4dbb4a86b": {
     "views": []
    },
    "ef5d2f1d573b453e88e647cef9194ad9": {
     "views": []
    },
    "f129c7500ec748f7b8a8d9030075e7e8": {
     "views": []
    },
    "f1aec8e8ab0d4f5292c1133066603a66": {
     "views": []
    },
    "f261636e9e7b4210a64fe533f053b828": {
     "views": []
    },
    "f360f4349b174ce4a19ef7c0b2f91e8b": {
     "views": []
    },
    "f388158d071a486285a89b564b98aa74": {
     "views": []
    },
    "f408d805142946e795b83df88f19bf7c": {
     "views": []
    },
    "f5d82222f0a34f7d9b7f69f998259ef2": {
     "views": []
    },
    "f5f187d2c3d94eedb0fa78742e6ef345": {
     "views": []
    },
    "f656e6e51d414505a31ce837b75d2516": {
     "views": []
    },
    "f6c8c06159a640a993daa376029774d3": {
     "views": []
    },
    "f700140f6d0d45ca9be79edff2f6e841": {
     "views": []
    },
    "f9255407f20146cb946758744fccc53c": {
     "views": []
    },
    "f9f19ffcab6c4e6bbd032f01eb9ab586": {
     "views": []
    },
    "fc35722f76434d768df79183d1d029b8": {
     "views": []
    },
    "fd373cd6f6d44279903565dcdf9b31e3": {
     "views": []
    },
    "fe1e1dbaef884fa4897b2640c9826f32": {
     "views": []
    },
    "fee695aad0454ec3ba2368454d7824b0": {
     "views": []
    }
   },
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}