{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Linear regressions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "During preliminary design and, above all, when optimising solutions, it is useful to have simple equations for calculating the main characteristics of the component. We will now look at how to transform data, coming from catalogs, into algebraic equations using regression.\n",
    " \n",
    "![Simulation Models](./assets/images/RegressionNeeds.png)\n",
    "\n",
    "For interested readers, more information can be found in the following document (Chapter 4 – Metamodels for model-based-design of mechatronic systems):  \n",
    "> Budinger, M. (2014). Preliminary design and sizing of actuation systems (HDR dissertation, UPS Toulouse). [Link](https://hal.science/tel-01112448v1/document)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical data analysis: main steps \n",
    "\n",
    "The main steps to follow in order to obtain an estimation model using data are:  \n",
    "1– **Obtaining data**: components’ data can be provided by catalogues or design models on which we will have simulated a set of well chosen design parameters (using design of experiments for instance).  \n",
    "2– **Choosing parameters** representating primary characteristics: the objective here is to reduce the number of inputs for the model. In order to do that, we can detect and choose the most important parameters using a correlation analysis. A dimensional analysis  can also help to reduce the number of coefficients to be considered.  \n",
    "3– **Choosing the mathematical model type**: this means to choose the mathematical form of the equation on which the regression will be applied (polynoms, linear sum of functions, power products,…).  \n",
    "4– **Apply the regression**: the objective is to minimize the disparity between data and the mathematical equation of the model.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gearbox Data\n",
    "\n",
    "Examples of this notebook will be given using gear reducers data coming from manufacturers.\n",
    "\n",
    "![Simulation Models](./assets/images/GearBoxData.png)\n",
    "\n",
    "These data are stored in excel files, which can be read here using the `pandas` package in `dataframe` format.  The database contains a wide range of information: mass, torsional stiffness, efficiency, dimensions, etc.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Constructor</th>\n",
       "      <th>size</th>\n",
       "      <th>number stage</th>\n",
       "      <th>ratio</th>\n",
       "      <th>torque output</th>\n",
       "      <th>rate input</th>\n",
       "      <th>efficiency</th>\n",
       "      <th>torsional stiffness</th>\n",
       "      <th>backlash</th>\n",
       "      <th>inertia input</th>\n",
       "      <th>mass</th>\n",
       "      <th>Power</th>\n",
       "      <th>Diameter</th>\n",
       "      <th>Length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(-)</td>\n",
       "      <td>(-)</td>\n",
       "      <td>(-)</td>\n",
       "      <td>(-)</td>\n",
       "      <td>(Nm)</td>\n",
       "      <td>(tr/min)</td>\n",
       "      <td>(%)</td>\n",
       "      <td>(Nm/arcmin)</td>\n",
       "      <td>(arcmin)</td>\n",
       "      <td>(kg cm2)</td>\n",
       "      <td>(kg)</td>\n",
       "      <td>(W)</td>\n",
       "      <td>(mm)</td>\n",
       "      <td>(mm)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Constructor</td>\n",
       "      <td>size</td>\n",
       "      <td>Ns</td>\n",
       "      <td>N</td>\n",
       "      <td>Tout</td>\n",
       "      <td>Win</td>\n",
       "      <td>Eta</td>\n",
       "      <td>K</td>\n",
       "      <td>Dteta</td>\n",
       "      <td>J</td>\n",
       "      <td>M</td>\n",
       "      <td>P</td>\n",
       "      <td>D</td>\n",
       "      <td>L</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Constructor  size number stage ratio torque output rate input efficiency  \\\n",
       "0          (-)   (-)          (-)   (-)          (Nm)   (tr/min)        (%)   \n",
       "1  Constructor  size           Ns     N          Tout        Win        Eta   \n",
       "\n",
       "  torsional stiffness  backlash inertia input  mass Power Diameter Length  \n",
       "0         (Nm/arcmin)  (arcmin)      (kg cm2)  (kg)   (W)     (mm)   (mm)  \n",
       "1                   K     Dteta             J     M     P        D      L  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Read the meaning of the different parameters\n",
    "df_head = pd.read_excel(\"GearBoxHead.xlsx\")\n",
    "df_head"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Constructor</th>\n",
       "      <th>size</th>\n",
       "      <th>Ns</th>\n",
       "      <th>N</th>\n",
       "      <th>Tout</th>\n",
       "      <th>Win</th>\n",
       "      <th>Eta</th>\n",
       "      <th>K</th>\n",
       "      <th>Dteta</th>\n",
       "      <th>J</th>\n",
       "      <th>M</th>\n",
       "      <th>P</th>\n",
       "      <th>D</th>\n",
       "      <th>L</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NEUGART</td>\n",
       "      <td>PLS 70 HP-4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>110.0</td>\n",
       "      <td>1700</td>\n",
       "      <td>98</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.42</td>\n",
       "      <td>2.6</td>\n",
       "      <td>4895.648552</td>\n",
       "      <td>75</td>\n",
       "      <td>122.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NEUGART</td>\n",
       "      <td>PLS 70 HP-5</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>110.0</td>\n",
       "      <td>2000</td>\n",
       "      <td>98</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.37</td>\n",
       "      <td>2.6</td>\n",
       "      <td>4607.669225</td>\n",
       "      <td>75</td>\n",
       "      <td>122.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NEUGART</td>\n",
       "      <td>PLS 90 HP-4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>220.0</td>\n",
       "      <td>1350</td>\n",
       "      <td>98</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.05</td>\n",
       "      <td>4.0</td>\n",
       "      <td>7775.441818</td>\n",
       "      <td>100</td>\n",
       "      <td>138.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NEUGART</td>\n",
       "      <td>PLS 90 HP-5</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>220.0</td>\n",
       "      <td>1600</td>\n",
       "      <td>98</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.85</td>\n",
       "      <td>4.0</td>\n",
       "      <td>7372.270760</td>\n",
       "      <td>100</td>\n",
       "      <td>138.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NEUGART</td>\n",
       "      <td>PLS 115 HP-4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>520.0</td>\n",
       "      <td>800</td>\n",
       "      <td>98</td>\n",
       "      <td>22.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.30</td>\n",
       "      <td>7.5</td>\n",
       "      <td>10890.854532</td>\n",
       "      <td>130</td>\n",
       "      <td>189.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Constructor          size  Ns  N   Tout   Win  Eta     K  Dteta     J    M  \\\n",
       "0     NEUGART   PLS 70 HP-4   1  4  110.0  1700   98   7.0    3.0  0.42  2.6   \n",
       "1     NEUGART   PLS 70 HP-5   1  5  110.0  2000   98   7.0    3.0  0.37  2.6   \n",
       "2     NEUGART   PLS 90 HP-4   1  4  220.0  1350   98  10.0    3.0  1.05  4.0   \n",
       "3     NEUGART   PLS 90 HP-5   1  5  220.0  1600   98  10.0    3.0  0.85  4.0   \n",
       "4     NEUGART  PLS 115 HP-4   1  4  520.0   800   98  22.0    3.0  2.30  7.5   \n",
       "\n",
       "              P    D      L  \n",
       "0   4895.648552   75  122.0  \n",
       "1   4607.669225   75  122.0  \n",
       "2   7775.441818  100  138.5  \n",
       "3   7372.270760  100  138.5  \n",
       "4  10890.854532  130  189.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the data\n",
    "df = pd.read_excel(\"GearBoxData.xlsx\")\n",
    "\n",
    "# Print the 5 first lines of the database\n",
    "df.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing parameters\n",
    "\n",
    "We will assume that we want to construct a gearbox mass estimation model. We therefore first need to determine which parameters are most important in estimating this. Using the catalogue data, we can apply a correlation analysis and display it in the form of a table showing the correlation between each parameter. This table is symmetrical."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Statistics Basic:**\n",
    "Classical statistic tools can be used to characterize a data serie and the links that exist between two data series:  \n",
    "-The **mean** of each data series.  \n",
    "$\\bar{x}=\\frac{1}{n}\\sum_{i=1}^{n} x_i$  \n",
    "-The **standard deviation** which gives the dispersion of a series of values, around their mean value.  \n",
    "$\\sigma=\\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n} (x_i-\\bar{x})^2}$  \n",
    "-The **covariance** which is a number that gives the possibility to evaluate the variation way of two variables and , that way, define if these variables are independant or not. That way, if 2 quantities vary the same way, or in opposite ways, the covariance value will be higher.  \n",
    "$cov(x,y)=\\frac{1}{n-1}\\sum_{i=1}^{n} (x_i-\\bar{x})(y_i-\\bar{y})$    \n",
    "-The **correlation**, also related to the link between two variables. It’s actually the Covariance, normalized on a scale from -1 to 1.   \n",
    "$cor(x,y)=\\frac{1}{n-1}\\frac{\\sum_{i=1}^{n} (x_i-\\bar{x})(y_i-\\bar{y})}{s_xs_y}$    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dataframes can be used to calculate the correlation matrix directly and simply. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ns</th>\n",
       "      <th>N</th>\n",
       "      <th>Tout</th>\n",
       "      <th>Win</th>\n",
       "      <th>Eta</th>\n",
       "      <th>K</th>\n",
       "      <th>Dteta</th>\n",
       "      <th>J</th>\n",
       "      <th>M</th>\n",
       "      <th>P</th>\n",
       "      <th>D</th>\n",
       "      <th>L</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ns</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.354501</td>\n",
       "      <td>-0.204966</td>\n",
       "      <td>0.530513</td>\n",
       "      <td>-0.734179</td>\n",
       "      <td>-0.236948</td>\n",
       "      <td>0.680305</td>\n",
       "      <td>-0.238785</td>\n",
       "      <td>-0.103814</td>\n",
       "      <td>-0.203182</td>\n",
       "      <td>-0.263935</td>\n",
       "      <td>0.293952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>N</th>\n",
       "      <td>0.354501</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.063755</td>\n",
       "      <td>0.040779</td>\n",
       "      <td>-0.608730</td>\n",
       "      <td>0.079991</td>\n",
       "      <td>0.182424</td>\n",
       "      <td>0.057529</td>\n",
       "      <td>-0.000207</td>\n",
       "      <td>-0.244010</td>\n",
       "      <td>0.043081</td>\n",
       "      <td>-0.098758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tout</th>\n",
       "      <td>-0.204966</td>\n",
       "      <td>0.063755</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.436716</td>\n",
       "      <td>0.088456</td>\n",
       "      <td>0.916671</td>\n",
       "      <td>-0.320480</td>\n",
       "      <td>0.885686</td>\n",
       "      <td>0.800741</td>\n",
       "      <td>0.290815</td>\n",
       "      <td>0.798191</td>\n",
       "      <td>0.350260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Win</th>\n",
       "      <td>0.530513</td>\n",
       "      <td>0.040779</td>\n",
       "      <td>-0.436716</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.272927</td>\n",
       "      <td>-0.437381</td>\n",
       "      <td>0.639898</td>\n",
       "      <td>-0.301804</td>\n",
       "      <td>-0.442977</td>\n",
       "      <td>-0.127484</td>\n",
       "      <td>-0.652336</td>\n",
       "      <td>-0.139995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Eta</th>\n",
       "      <td>-0.734179</td>\n",
       "      <td>-0.608730</td>\n",
       "      <td>0.088456</td>\n",
       "      <td>-0.272927</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.063514</td>\n",
       "      <td>-0.505211</td>\n",
       "      <td>0.082149</td>\n",
       "      <td>0.073080</td>\n",
       "      <td>0.357831</td>\n",
       "      <td>0.156639</td>\n",
       "      <td>0.000155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K</th>\n",
       "      <td>-0.236948</td>\n",
       "      <td>0.079991</td>\n",
       "      <td>0.916671</td>\n",
       "      <td>-0.437381</td>\n",
       "      <td>0.063514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.332987</td>\n",
       "      <td>0.775942</td>\n",
       "      <td>0.853291</td>\n",
       "      <td>0.219011</td>\n",
       "      <td>0.820234</td>\n",
       "      <td>0.280267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dteta</th>\n",
       "      <td>0.680305</td>\n",
       "      <td>0.182424</td>\n",
       "      <td>-0.320480</td>\n",
       "      <td>0.639898</td>\n",
       "      <td>-0.505211</td>\n",
       "      <td>-0.332987</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.256920</td>\n",
       "      <td>-0.288968</td>\n",
       "      <td>-0.167897</td>\n",
       "      <td>-0.465782</td>\n",
       "      <td>-0.023637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>J</th>\n",
       "      <td>-0.238785</td>\n",
       "      <td>0.057529</td>\n",
       "      <td>0.885686</td>\n",
       "      <td>-0.301804</td>\n",
       "      <td>0.082149</td>\n",
       "      <td>0.775942</td>\n",
       "      <td>-0.256920</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.587566</td>\n",
       "      <td>0.347930</td>\n",
       "      <td>0.640275</td>\n",
       "      <td>0.176444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>-0.103814</td>\n",
       "      <td>-0.000207</td>\n",
       "      <td>0.800741</td>\n",
       "      <td>-0.442977</td>\n",
       "      <td>0.073080</td>\n",
       "      <td>0.853291</td>\n",
       "      <td>-0.288968</td>\n",
       "      <td>0.587566</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.295261</td>\n",
       "      <td>0.791580</td>\n",
       "      <td>0.592270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P</th>\n",
       "      <td>-0.203182</td>\n",
       "      <td>-0.244010</td>\n",
       "      <td>0.290815</td>\n",
       "      <td>-0.127484</td>\n",
       "      <td>0.357831</td>\n",
       "      <td>0.219011</td>\n",
       "      <td>-0.167897</td>\n",
       "      <td>0.347930</td>\n",
       "      <td>0.295261</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.245700</td>\n",
       "      <td>0.355627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>-0.263935</td>\n",
       "      <td>0.043081</td>\n",
       "      <td>0.798191</td>\n",
       "      <td>-0.652336</td>\n",
       "      <td>0.156639</td>\n",
       "      <td>0.820234</td>\n",
       "      <td>-0.465782</td>\n",
       "      <td>0.640275</td>\n",
       "      <td>0.791580</td>\n",
       "      <td>0.245700</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.428592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L</th>\n",
       "      <td>0.293952</td>\n",
       "      <td>-0.098758</td>\n",
       "      <td>0.350260</td>\n",
       "      <td>-0.139995</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.280267</td>\n",
       "      <td>-0.023637</td>\n",
       "      <td>0.176444</td>\n",
       "      <td>0.592270</td>\n",
       "      <td>0.355627</td>\n",
       "      <td>0.428592</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Ns         N      Tout       Win       Eta         K     Dteta  \\\n",
       "Ns     1.000000  0.354501 -0.204966  0.530513 -0.734179 -0.236948  0.680305   \n",
       "N      0.354501  1.000000  0.063755  0.040779 -0.608730  0.079991  0.182424   \n",
       "Tout  -0.204966  0.063755  1.000000 -0.436716  0.088456  0.916671 -0.320480   \n",
       "Win    0.530513  0.040779 -0.436716  1.000000 -0.272927 -0.437381  0.639898   \n",
       "Eta   -0.734179 -0.608730  0.088456 -0.272927  1.000000  0.063514 -0.505211   \n",
       "K     -0.236948  0.079991  0.916671 -0.437381  0.063514  1.000000 -0.332987   \n",
       "Dteta  0.680305  0.182424 -0.320480  0.639898 -0.505211 -0.332987  1.000000   \n",
       "J     -0.238785  0.057529  0.885686 -0.301804  0.082149  0.775942 -0.256920   \n",
       "M     -0.103814 -0.000207  0.800741 -0.442977  0.073080  0.853291 -0.288968   \n",
       "P     -0.203182 -0.244010  0.290815 -0.127484  0.357831  0.219011 -0.167897   \n",
       "D     -0.263935  0.043081  0.798191 -0.652336  0.156639  0.820234 -0.465782   \n",
       "L      0.293952 -0.098758  0.350260 -0.139995  0.000155  0.280267 -0.023637   \n",
       "\n",
       "              J         M         P         D         L  \n",
       "Ns    -0.238785 -0.103814 -0.203182 -0.263935  0.293952  \n",
       "N      0.057529 -0.000207 -0.244010  0.043081 -0.098758  \n",
       "Tout   0.885686  0.800741  0.290815  0.798191  0.350260  \n",
       "Win   -0.301804 -0.442977 -0.127484 -0.652336 -0.139995  \n",
       "Eta    0.082149  0.073080  0.357831  0.156639  0.000155  \n",
       "K      0.775942  0.853291  0.219011  0.820234  0.280267  \n",
       "Dteta -0.256920 -0.288968 -0.167897 -0.465782 -0.023637  \n",
       "J      1.000000  0.587566  0.347930  0.640275  0.176444  \n",
       "M      0.587566  1.000000  0.295261  0.791580  0.592270  \n",
       "P      0.347930  0.295261  1.000000  0.245700  0.355627  \n",
       "D      0.640275  0.791580  0.245700  1.000000  0.428592  \n",
       "L      0.176444  0.592270  0.355627  0.428592  1.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This matrix can then be [graphically formatted](https://medium.com/@szabo.bibor/how-to-create-a-seaborn-correlation-heatmap-in-python-834c0686b88e) for easier analysis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(16, 6)) \n",
    "\n",
    "# define the mask to set the values in the upper triangle to Truemask \n",
    "mask = np.triu(np.ones_like(df.corr(), dtype=bool)) # one_like = 1 matrix with df.corr size + triu = Upper triangle of an array.\n",
    "\n",
    "heatmap = sns.heatmap(df.corr(), mask=mask, vmin=-1, vmax=1, annot=True, cmap='BrBG')\n",
    "heatmap.set_title('Triangle Correlation Heatmap', fontdict={'fontsize':18}, pad=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that :\n",
    "- the reduction ratio and the number of stages have little influence on the mass\n",
    "- the most important and primary parameter is the output torque."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** the [correlation matrix](https://www.ablebits.com/office-addins-blog/correlation-excel-coefficient-matrix-graph/) can also be produced in Excel using the [analysis toolpack](https://support.microsoft.com/fr-fr/office/charger-l-analysis-toolpak-dans-excel-6a63e598-cd6d-42e3-9317-6b40ba1a66b4)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear regression \n",
    "Parametric regressions are based on models requiring the estimation of a finite number of parameters $\\theta$ that express the effects of basis functions on the response surface. With polynomial interpolation or regression, the basis functions are ${1, x, x^2, …, x^p}$. The idea is to obtain a surface that is differentiable and continuous. For a polynomial development of order 2 (p = 2), the expression is:\n",
    "\n",
    "$y=f(\\underline{x}, \\underline{\\theta})=\\theta_0 + \\sum_{i=1}^{k} \\theta_0 x_i + \\sum_{i=1, j=1}^{k} \\theta_{ij} x_i x_j $  \n",
    "\n",
    "with $\\underline{x}=\\begin{pmatrix}\n",
    "           x_{1} \\\\\n",
    "           x_{2} \\\\\n",
    "           \\vdots \\\\\n",
    "           x_{k}\n",
    "         \\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which, for the $n$ experiments, can be written with a matrix representation:\n",
    "$\\underline{Y}=\\underline{X}.\\underline{\\theta}+\\underline{\\varepsilon}$ \n",
    "\n",
    "with $\\underline{Y}=\\begin{pmatrix}\n",
    "           y^{(1)} \\\\\n",
    "           \\vdots \\\\\n",
    "           y^{(n)}\n",
    "         \\end{pmatrix}$ ,\n",
    "         $\\underline{x}=\\begin{pmatrix}\n",
    "           1, x_{1}^{(1)}, ..., x_{k}^{2(1)}   \\\\\n",
    "           \\vdots \\\\\n",
    "           1, x_{1}^{(n)}, ..., x_{k}^{2(n)}   \n",
    "         \\end{pmatrix}$,\n",
    "         $\\underline{x}=\\begin{pmatrix}\n",
    "           \\theta_0 \\\\\n",
    "           \\vdots \\\\\n",
    "           \\theta_{k_{theta}}\n",
    "         \\end{pmatrix}$,\n",
    "         $\\underline{x}=\\begin{pmatrix}\n",
    "           \\varepsilon^{(1)} \\\\\n",
    "           \\vdots \\\\\n",
    "           y^{(n)}\n",
    "         \\end{pmatrix}$\n",
    "\n",
    "where :\n",
    "- $k_x$ is the number of design parameters;\n",
    "- $n$ is the number of experiments of the DoE;\n",
    "- $p$ is the order of the polynomial function;\n",
    "- $k_\\theta$ is the size of vector θ.\n",
    "\n",
    "If $n=k_\\theta$, the matrix $X$ is square and the interpolation is possible. In the most common case, where $k_\\theta$ is lower than $n$, interpolation is impossible. The objective of regression is to find an approximation showing an error of zero mean and a minimum standard deviation. The errors are expressed by:  \n",
    "$\\underline{\\varepsilon}=\\underline{Y}-\\underline{X}.\\underline{\\theta}$   \n",
    "\n",
    "The standard deviation is a function of the sum of the quadratic error $\\underline{\\varepsilon}^t\\underline{\\varepsilon}$ and is minimum for:  \n",
    "\n",
    " $\\underline{\\theta}=(\\underline{X}^t\\underline{X})^{-1} \\underline{X}^t\\underline{Y}$  \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mass and inertia regression \n",
    "\n",
    "The aim is to perform regression on part of the data: the [Sumitomo cyclo-reducers](https://us.sumitomodrive.com/sites/default/files/2023-07/precision-gearbox-catalog-07-2021.pdf). First, only the Sumitomo are selected:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Constructor</th>\n",
       "      <th>size</th>\n",
       "      <th>Ns</th>\n",
       "      <th>N</th>\n",
       "      <th>Tout</th>\n",
       "      <th>Win</th>\n",
       "      <th>Eta</th>\n",
       "      <th>K</th>\n",
       "      <th>Dteta</th>\n",
       "      <th>J</th>\n",
       "      <th>M</th>\n",
       "      <th>P</th>\n",
       "      <th>D</th>\n",
       "      <th>L</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>613</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>106</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>25.0</td>\n",
       "      <td>500</td>\n",
       "      <td>95</td>\n",
       "      <td>1.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>1.2</td>\n",
       "      <td>118.999722</td>\n",
       "      <td>85</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>614</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>106</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>25.0</td>\n",
       "      <td>500</td>\n",
       "      <td>95</td>\n",
       "      <td>1.6</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.2</td>\n",
       "      <td>76.999820</td>\n",
       "      <td>85</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>615</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>106</td>\n",
       "      <td>1</td>\n",
       "      <td>29</td>\n",
       "      <td>25.0</td>\n",
       "      <td>500</td>\n",
       "      <td>95</td>\n",
       "      <td>2.6</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.2</td>\n",
       "      <td>45.137825</td>\n",
       "      <td>85</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>616</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>106</td>\n",
       "      <td>1</td>\n",
       "      <td>43</td>\n",
       "      <td>25.0</td>\n",
       "      <td>500</td>\n",
       "      <td>95</td>\n",
       "      <td>2.8</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.2</td>\n",
       "      <td>30.441789</td>\n",
       "      <td>85</td>\n",
       "      <td>130.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>617</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>108</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>75.0</td>\n",
       "      <td>500</td>\n",
       "      <td>95</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.30</td>\n",
       "      <td>4.3</td>\n",
       "      <td>356.999165</td>\n",
       "      <td>118</td>\n",
       "      <td>180.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Constructor size  Ns   N  Tout  Win  Eta    K  Dteta     J    M  \\\n",
       "613    SUMITOMO  106   1  11  25.0  500   95  1.5    3.0  0.15  1.2   \n",
       "614    SUMITOMO  106   1  17  25.0  500   95  1.6    3.0  0.14  1.2   \n",
       "615    SUMITOMO  106   1  29  25.0  500   95  2.6    3.0  0.14  1.2   \n",
       "616    SUMITOMO  106   1  43  25.0  500   95  2.8    3.0  0.14  1.2   \n",
       "617    SUMITOMO  108   1  11  75.0  500   95  5.0    3.0  1.30  4.3   \n",
       "\n",
       "              P    D      L  \n",
       "613  118.999722   85  130.0  \n",
       "614   76.999820   85  130.0  \n",
       "615   45.137825   85  130.0  \n",
       "616   30.441789   85  130.0  \n",
       "617  356.999165  118  180.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Data Filtering\n",
    "# Keeping only SUMITOMO type\n",
    "df_S = df[df[\"Constructor\"] == \"SUMITOMO\"]\n",
    "df_S.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data shows a dispersion due to several types of reducers. They differ in the type of output shaft. We will now only included the lightest ones here, i.e. the FC range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data\n",
    "plt.plot(df_S[\"Tout\"], df_S[\"M\"], \"bo\")\n",
    "plt.xlabel(\"Low speed torque (N.m)\")\n",
    "plt.ylabel(\"Mass (kg)\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Constructor</th>\n",
       "      <th>size</th>\n",
       "      <th>Ns</th>\n",
       "      <th>N</th>\n",
       "      <th>Tout</th>\n",
       "      <th>Win</th>\n",
       "      <th>Eta</th>\n",
       "      <th>K</th>\n",
       "      <th>Dteta</th>\n",
       "      <th>J</th>\n",
       "      <th>M</th>\n",
       "      <th>P</th>\n",
       "      <th>D</th>\n",
       "      <th>L</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>634</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>FC-A15(G)</td>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "      <td>149.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>95</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.313</td>\n",
       "      <td>2.7</td>\n",
       "      <td>396.692632</td>\n",
       "      <td>120</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>635</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>FC-A15(G)</td>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>149.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>95</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.310</td>\n",
       "      <td>2.7</td>\n",
       "      <td>262.976014</td>\n",
       "      <td>120</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>636</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>FC-A25(G)</td>\n",
       "      <td>1</td>\n",
       "      <td>29</td>\n",
       "      <td>349.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>95</td>\n",
       "      <td>53.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.380</td>\n",
       "      <td>5.2</td>\n",
       "      <td>1890.372131</td>\n",
       "      <td>150</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>637</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>FC-A25(G)</td>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "      <td>349.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>95</td>\n",
       "      <td>70.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.340</td>\n",
       "      <td>5.2</td>\n",
       "      <td>929.165963</td>\n",
       "      <td>150</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>638</th>\n",
       "      <td>SUMITOMO</td>\n",
       "      <td>FC-A25(G)</td>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>349.0</td>\n",
       "      <td>1500</td>\n",
       "      <td>95</td>\n",
       "      <td>70.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.330</td>\n",
       "      <td>5.2</td>\n",
       "      <td>615.963953</td>\n",
       "      <td>150</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Constructor       size  Ns   N   Tout   Win  Eta     K  Dteta      J    M  \\\n",
       "634    SUMITOMO  FC-A15(G)   1  59  149.0  1500   95  20.0    2.0  0.313  2.7   \n",
       "635    SUMITOMO  FC-A15(G)   1  89  149.0  1500   95  20.0    2.0  0.310  2.7   \n",
       "636    SUMITOMO  FC-A25(G)   1  29  349.0  1500   95  53.0    2.0  1.380  5.2   \n",
       "637    SUMITOMO  FC-A25(G)   1  59  349.0  1500   95  70.0    2.0  1.340  5.2   \n",
       "638    SUMITOMO  FC-A25(G)   1  89  349.0  1500   95  70.0    2.0  1.330  5.2   \n",
       "\n",
       "               P    D     L  \n",
       "634   396.692632  120  60.0  \n",
       "635   262.976014  120  60.0  \n",
       "636  1890.372131  150  75.0  \n",
       "637   929.165963  150  75.0  \n",
       "638   615.963953  150  75.0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Data Filtering\n",
    "# Keeping only FC range type\n",
    "df_S = df_S[df_S[\"size\"].astype(str).str[0:2] == \"FC\"]\n",
    "df_S.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data\n",
    "plt.plot(df_S[\"Tout\"], df_S[\"M\"], \"bo\")\n",
    "plt.xlabel(\"Low speed torque (N.m)\")\n",
    "plt.ylabel(\"Mass (kg)\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Scikit-learn](https://scikit-learn.org)  is a free machine learning package and can be used for linear regression.  It features also various classification, regression and clustering algorithms including support-vector machines, random forests, gradient boosting, k-means, ... Below an example of use of this package for [linear regression](https://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html) of the gear reducers data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mass estimation model : M = 1.54 + 0.01 * Tout with R2=0.999\n"
     ]
    }
   ],
   "source": [
    "# Import packages\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.metrics import r2_score\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Data\n",
    "x = df_S[\"Tout\"].values # Torque input\n",
    "y = df_S[\"M\"].values # Mass output\n",
    "\n",
    "# Matrix X and Y\n",
    "n=1 # order of polynomial regression\n",
    "\n",
    "poly = PolynomialFeatures(degree=2, include_bias=False) # 1 vector is nt necessary with sklearn\n",
    "X =poly.fit_transform(x.reshape(-1, 1)) #  reshape(-1,1) transforms our numpy array x from a 1D array to a 2D array\n",
    "\n",
    "Y = y.reshape(-1, 1) \n",
    "      \n",
    "# Create a new object for the linear regression\n",
    "reg_M = linear_model.LinearRegression()\n",
    "\n",
    "reg_M.fit(X, Y)\n",
    "\n",
    "# Y vector prediction\n",
    "M_est = reg_M.predict(X)\n",
    "\n",
    "# M regression Parameters\n",
    "# ----\n",
    "coef = reg_M.coef_\n",
    "intercept = float(reg_M.intercept_)\n",
    "r2 = r2_score(Y, M_est)\n",
    "\n",
    "\n",
    "# Plot the data\n",
    "plt.plot(x, Y, \"o\", label=\"Reference data\")\n",
    "plt.plot(x, M_est, \"-g\", label=\"Data prediction\")\n",
    "plt.xlabel(\"Torque (N.m)\")\n",
    "plt.ylabel(\"Mass (kg)\")\n",
    "plt.title(\"Comparison of reference data and regression\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "print(f\"Mass estimation model : M = {intercept:.2f} + {coef[0,0]:.2f} * Tout with R2={r2:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** the [linear regression](https://www.ablebits.com/office-addins-blog/linear-regression-analysis-excel/) can also be produced in Excel using the [analysis toolpack](https://support.microsoft.com/fr-fr/office/charger-l-analysis-toolpak-dans-excel-6a63e598-cd6d-42e3-9317-6b40ba1a66b4) or with trendline option on excel graphs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Homework**: Adapt previous code to set up an inertia estimation model. Two types of models can be used and compared: an order 2 polynom and a power law. \n",
    "\n",
    "**Note:** A product of power laws, can be linearized by a logarithmic transformation.  \n",
    "$y=a_0 \\prod_i x_i^{a_i} \\longrightarrow log(y)=log(a_0) + \\sum_i a_i log(x_i) $ \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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   "overlay": "<div class='myheader'><h2>Sizing and optimization of mechatronic systems</h2></div><div class='myfooter'><h2>24/10/2022</h2></div><div class='logo'><img src='../../images/logo.png' width=200px height= auto></div>"
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