WAT_analysis.ipynb

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    "#### Example of analysis of data obtained from experiment of Wax Appearance Temperature determination. \n",
    "Log file contains experimental data. During the experiment, the laser was passed through an oil sample with an isobaric temperature decrease. \n",
    "The inflection point indicates the formation of paraffin crystals.\n",
    "\n",
    "##### Folowing steps were taken:\n",
    "- Reading data from log file\n",
    "- Data visualisation\n",
    "- Finding inflection point\n",
    "- Fitting data to the trend lines\n",
    "- Calculating cross-point of trend lines\n",
    "\n",
    "##### [Ramer-Douglas-Peucker algorithm](https://pypi.python.org/pypi/rdp/)  was used to find inflection point "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "df = pd.read_csv('WAT_log_file.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time(min)</th>\n",
       "      <th>Power(W)</th>\n",
       "      <th>Temperature</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Concentration(%)</th>\n",
       "      <th>Cyl(1)</th>\n",
       "      <th>Cyl(2)</th>\n",
       "      <th>Bath</th>\n",
       "      <th>Comments</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>88.3</td>\n",
       "      <td>4177</td>\n",
       "      <td>0.000</td>\n",
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       "      <th>1</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>88.4</td>\n",
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       "      <th>2</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>88.4</td>\n",
       "      <td>4177</td>\n",
       "      <td>-0.003</td>\n",
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       "      <th>3</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>88.4</td>\n",
       "      <td>4177</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>#NAME?</td>\n",
       "      <td>-32768</td>\n",
       "      <td>-32768</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>88.4</td>\n",
       "      <td>4177</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>#NAME?</td>\n",
       "      <td>-32768</td>\n",
       "      <td>-32768</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
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      "text/plain": [
       "   Time(min)  Power(W)  Temperature  Pressure  Volume Concentration(%)  \\\n",
       "0       0.10  0.000241         88.3      4177   0.000              NaN   \n",
       "1       0.20  0.000241         88.4      4177  -0.001           #NAME?   \n",
       "2       0.30  0.000241         88.4      4177  -0.003           #NAME?   \n",
       "3       0.40  0.000241         88.4      4177  -0.003           #NAME?   \n",
       "4       0.51  0.000241         88.4      4177  -0.003           #NAME?   \n",
       "\n",
       "   Cyl(1)  Cyl(2)  Bath  Comments  \n",
       "0  -32768  -32768     0       NaN  \n",
       "1  -32768  -32768     0       NaN  \n",
       "2  -32768  -32768     0       NaN  \n",
       "3  -32768  -32768     0       NaN  \n",
       "4  -32768  -32768     0       NaN  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#1. Look at the data\n",
    "# relevant columns: Temperature, Power(W)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time(min)</th>\n",
       "      <th>Power(W)</th>\n",
       "      <th>Temperature</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Cyl(1)</th>\n",
       "      <th>Cyl(2)</th>\n",
       "      <th>Bath</th>\n",
       "      <th>Comments</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10542.000000</td>\n",
       "      <td>1.054200e+04</td>\n",
       "      <td>10542.000000</td>\n",
       "      <td>10542.000000</td>\n",
       "      <td>10542.000000</td>\n",
       "      <td>10542.0</td>\n",
       "      <td>10542.0</td>\n",
       "      <td>10542.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>531.920597</td>\n",
       "      <td>2.159878e-04</td>\n",
       "      <td>48.650275</td>\n",
       "      <td>4177.305635</td>\n",
       "      <td>8.057862</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>306.696100</td>\n",
       "      <td>8.722547e-05</td>\n",
       "      <td>25.279945</td>\n",
       "      <td>0.839408</td>\n",
       "      <td>5.309835</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.100000</td>\n",
       "      <td>1.220000e-08</td>\n",
       "      <td>8.400000</td>\n",
       "      <td>4174.000000</td>\n",
       "      <td>-0.009000</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>266.705000</td>\n",
       "      <td>2.440000e-04</td>\n",
       "      <td>26.100000</td>\n",
       "      <td>4177.000000</td>\n",
       "      <td>3.198750</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>532.040000</td>\n",
       "      <td>2.510000e-04</td>\n",
       "      <td>48.500000</td>\n",
       "      <td>4177.000000</td>\n",
       "      <td>7.916000</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>797.565000</td>\n",
       "      <td>2.560000e-04</td>\n",
       "      <td>72.000000</td>\n",
       "      <td>4178.000000</td>\n",
       "      <td>12.706000</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1062.540000</td>\n",
       "      <td>2.630000e-04</td>\n",
       "      <td>88.400000</td>\n",
       "      <td>4180.000000</td>\n",
       "      <td>16.871000</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>-32768.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "          Time(min)      Power(W)   Temperature      Pressure        Volume  \\\n",
       "count  10542.000000  1.054200e+04  10542.000000  10542.000000  10542.000000   \n",
       "mean     531.920597  2.159878e-04     48.650275   4177.305635      8.057862   \n",
       "std      306.696100  8.722547e-05     25.279945      0.839408      5.309835   \n",
       "min        0.100000  1.220000e-08      8.400000   4174.000000     -0.009000   \n",
       "25%      266.705000  2.440000e-04     26.100000   4177.000000      3.198750   \n",
       "50%      532.040000  2.510000e-04     48.500000   4177.000000      7.916000   \n",
       "75%      797.565000  2.560000e-04     72.000000   4178.000000     12.706000   \n",
       "max     1062.540000  2.630000e-04     88.400000   4180.000000     16.871000   \n",
       "\n",
       "        Cyl(1)   Cyl(2)     Bath  Comments  \n",
       "count  10542.0  10542.0  10542.0       0.0  \n",
       "mean  -32768.0 -32768.0      0.0       NaN  \n",
       "std        0.0      0.0      0.0       NaN  \n",
       "min   -32768.0 -32768.0      0.0       NaN  \n",
       "25%   -32768.0 -32768.0      0.0       NaN  \n",
       "50%   -32768.0 -32768.0      0.0       NaN  \n",
       "75%   -32768.0 -32768.0      0.0       NaN  \n",
       "max   -32768.0 -32768.0      0.0       NaN  "
      ]
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   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0.0003)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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    {
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YEX8EnpS0byo6imz2kdK/+8kpvNbNBuXH9QQwVdIO6f9mz+dV6vcLQNJb0r97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\n8ZiZWaGceMzMrFD/H/pyU7uwhz3MAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6e07770>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#2. Plot data\n",
    "plt.scatter(df['Temperature'], df['Power(W)'])\n",
    "plt.xlabel('Tempature, degC')\n",
    "plt.ylabel('Power (W)')\n",
    "plt.ylim(0, 0.0003)\n",
    "#y limit - some arbitrary number\n",
    "\n",
    "#Inflection point somewhere in area 20 degC indicates Wax Appearance Temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inflection point 18.8 deg C\n"
     ]
    }
   ],
   "source": [
    "#3. Find Inflection point with Ramer-Douglas-Peucker algorithm \n",
    "from rdp import rdp\n",
    "points = list(zip(df['Temperature'],df['Power(W)']))\n",
    "\n",
    "#find index of inflection point\n",
    "Inflection_point = df['Temperature'][df['Temperature']==rdp(points, 0.0002)[1][0]].index[-1]\n",
    "print ('Inflection point {0} deg C'.format(rdp(points, 0.0002)[1][0]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0.0003)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SOmbWFDgR2FXLtum0WYW7/61iNG13fw5oltj5QERE4pVu4unp7v8DHAZw9/1AqpspK4Be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\nDB48mAsvvJDevXt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oKC1aEc2fAnDA3V8I79cAe9y93MzWEM2/VGGBu+8GMLN5RMMVrQJu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\n/j8P2shiK/14SAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6e33ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visually check if inflection point was find correctly\n",
    "plt.scatter(df['Temperature'][:Inflection_point], df['Power(W)'][:Inflection_point], label = 'Signal before WAT')\n",
    "plt.scatter(df['Temperature'][Inflection_point:], df['Power(W)'][Inflection_point:],label = 'Signal after WAT', color='r')\n",
    "plt.xlabel('Tempature, degC')\n",
    "plt.ylabel('Power (W)')\n",
    "plt.legend()\n",
    "plt.ylim(0, 0.0003)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "equations:  [ -2.83857930e-07   2.68204717e-04] [  8.99834327e-05  -1.37654737e-03]\n",
      "Cross point =  18.2209090469\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 0.0003)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcab30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#4 Make trend lines\n",
    "#9200 - arbitrary number to cut irrelevant tail\n",
    "Eq1 = np.polyfit(df['Temperature'][:Inflection_point], df['Power(W)'][:Inflection_point], 1)\n",
    "Y1 = [i*Eq1[0]+Eq1[1] for i in df['Temperature']]\n",
    "Eq2 = np.polyfit(df['Temperature'][Inflection_point:9200], df['Power(W)'][Inflection_point:9200], 1)\n",
    "Y2 = [i*Eq2[0]+Eq2[1] for i in df['Temperature']]\n",
    "\n",
    "#5 Find cross points of trendlines\n",
    "print ('equations: ',Eq1,Eq2)\n",
    "a,b=list(Eq1)\n",
    "c,d=list(Eq2)\n",
    "x0=(d-b)/(a-c)\n",
    "print ('Cross point = ',x0)\n",
    "\n",
    "\n",
    "#Plot all together\n",
    "plt.plot(df['Temperature'],Y1,'-', label = 'Signal before WAT', color = 'black')\n",
    "plt.plot(df['Temperature'],Y2,'.-', label = 'Signal after WAT', color ='green')\n",
    "plt.scatter(x0,Eq1[0]*x0+Eq1[1], color = 'red', s = 200, \n",
    "            label = 'Intersection point')\n",
    "plt.legend()\n",
    "plt.ylim(0, 0.0003)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### As result inflection point 18.8 degc with RDP altorith, and trend lines cross-point 18.2 degC "
   ]
  }
 ],
 "metadata": {
  "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}