2_FD001_updated_RUL_assumption_and_SVR.ipynb

{
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  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro\n",
    "In the previous notebook we explored the FD001 dataset and created a baseline model to predict the RUL. The baseline had an RMSE of 31.95. In this notebook we'll re-examine our assumption of RUL and fit an SVR to get a better score.  \n",
    "Check out my [blog post](https://towardsdatascience.com/the-importance-of-problem-framing-for-supervised-predictive-maintenance-solutions-cc8646826093?source=friends_link&sk=ec51cbfa29f084ed94fe59d0daf51df0) for the full explanation.  \n",
    "  \n",
    "<disclaimer: I aim to showcase the effect of different methods and choices made during model development. These effects are often shown using the test set, something which is considered (very) bad practice but helps for educational purposes.>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.svm import SVR\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data and compute RUL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>unit_nr</th>\n",
       "      <th>time_cycles</th>\n",
       "      <th>setting_1</th>\n",
       "      <th>setting_2</th>\n",
       "      <th>setting_3</th>\n",
       "      <th>s_1</th>\n",
       "      <th>s_2</th>\n",
       "      <th>s_3</th>\n",
       "      <th>s_4</th>\n",
       "      <th>s_5</th>\n",
       "      <th>...</th>\n",
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       "      <td>1400.60</td>\n",
       "      <td>14.62</td>\n",
       "      <td>...</td>\n",
       "      <td>521.66</td>\n",
       "      <td>2388.02</td>\n",
       "      <td>8138.62</td>\n",
       "      <td>8.4195</td>\n",
       "      <td>0.03</td>\n",
       "      <td>392</td>\n",
       "      <td>2388</td>\n",
       "      <td>100.0</td>\n",
       "      <td>39.06</td>\n",
       "      <td>23.4190</td>\n",
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       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0019</td>\n",
       "      <td>-0.0003</td>\n",
       "      <td>100.0</td>\n",
       "      <td>518.67</td>\n",
       "      <td>642.15</td>\n",
       "      <td>1591.82</td>\n",
       "      <td>1403.14</td>\n",
       "      <td>14.62</td>\n",
       "      <td>...</td>\n",
       "      <td>522.28</td>\n",
       "      <td>2388.07</td>\n",
       "      <td>8131.49</td>\n",
       "      <td>8.4318</td>\n",
       "      <td>0.03</td>\n",
       "      <td>392</td>\n",
       "      <td>2388</td>\n",
       "      <td>100.0</td>\n",
       "      <td>39.00</td>\n",
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       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.0043</td>\n",
       "      <td>0.0003</td>\n",
       "      <td>100.0</td>\n",
       "      <td>518.67</td>\n",
       "      <td>642.35</td>\n",
       "      <td>1587.99</td>\n",
       "      <td>1404.20</td>\n",
       "      <td>14.62</td>\n",
       "      <td>...</td>\n",
       "      <td>522.42</td>\n",
       "      <td>2388.03</td>\n",
       "      <td>8133.23</td>\n",
       "      <td>8.4178</td>\n",
       "      <td>0.03</td>\n",
       "      <td>390</td>\n",
       "      <td>2388</td>\n",
       "      <td>100.0</td>\n",
       "      <td>38.95</td>\n",
       "      <td>23.3442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0.0007</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>100.0</td>\n",
       "      <td>518.67</td>\n",
       "      <td>642.35</td>\n",
       "      <td>1582.79</td>\n",
       "      <td>1401.87</td>\n",
       "      <td>14.62</td>\n",
       "      <td>...</td>\n",
       "      <td>522.86</td>\n",
       "      <td>2388.08</td>\n",
       "      <td>8133.83</td>\n",
       "      <td>8.3682</td>\n",
       "      <td>0.03</td>\n",
       "      <td>392</td>\n",
       "      <td>2388</td>\n",
       "      <td>100.0</td>\n",
       "      <td>38.88</td>\n",
       "      <td>23.3739</td>\n",
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       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>-0.0019</td>\n",
       "      <td>-0.0002</td>\n",
       "      <td>100.0</td>\n",
       "      <td>518.67</td>\n",
       "      <td>642.37</td>\n",
       "      <td>1582.85</td>\n",
       "      <td>1406.22</td>\n",
       "      <td>14.62</td>\n",
       "      <td>...</td>\n",
       "      <td>522.19</td>\n",
       "      <td>2388.04</td>\n",
       "      <td>8133.80</td>\n",
       "      <td>8.4294</td>\n",
       "      <td>0.03</td>\n",
       "      <td>393</td>\n",
       "      <td>2388</td>\n",
       "      <td>100.0</td>\n",
       "      <td>38.90</td>\n",
       "      <td>23.4044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   unit_nr  time_cycles  setting_1  setting_2  setting_3     s_1     s_2  \\\n",
       "0        1            1    -0.0007    -0.0004      100.0  518.67  641.82   \n",
       "1        1            2     0.0019    -0.0003      100.0  518.67  642.15   \n",
       "2        1            3    -0.0043     0.0003      100.0  518.67  642.35   \n",
       "3        1            4     0.0007     0.0000      100.0  518.67  642.35   \n",
       "4        1            5    -0.0019    -0.0002      100.0  518.67  642.37   \n",
       "\n",
       "       s_3      s_4    s_5  ...    s_12     s_13     s_14    s_15  s_16  s_17  \\\n",
       "0  1589.70  1400.60  14.62  ...  521.66  2388.02  8138.62  8.4195  0.03   392   \n",
       "1  1591.82  1403.14  14.62  ...  522.28  2388.07  8131.49  8.4318  0.03   392   \n",
       "2  1587.99  1404.20  14.62  ...  522.42  2388.03  8133.23  8.4178  0.03   390   \n",
       "3  1582.79  1401.87  14.62  ...  522.86  2388.08  8133.83  8.3682  0.03   392   \n",
       "4  1582.85  1406.22  14.62  ...  522.19  2388.04  8133.80  8.4294  0.03   393   \n",
       "\n",
       "   s_18   s_19   s_20     s_21  \n",
       "0  2388  100.0  39.06  23.4190  \n",
       "1  2388  100.0  39.00  23.4236  \n",
       "2  2388  100.0  38.95  23.3442  \n",
       "3  2388  100.0  38.88  23.3739  \n",
       "4  2388  100.0  38.90  23.4044  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define filepath to read data\n",
    "dir_path = '../data/unzipped/CMAPSSData/'\n",
    "\n",
    "# define column names for easy indexing\n",
    "index_names = ['unit_nr', 'time_cycles']\n",
    "setting_names = ['setting_1', 'setting_2', 'setting_3']\n",
    "sensor_names = ['s_{}'.format(i) for i in range(1,22)] \n",
    "col_names = index_names + setting_names + sensor_names\n",
    "\n",
    "# read data\n",
    "train = pd.read_csv((dir_path+'train_FD001.txt'), sep='\\s+', header=None, names=col_names)\n",
    "test = pd.read_csv((dir_path+'test_FD001.txt'), sep='\\s+', header=None, names=col_names)\n",
    "y_test = pd.read_csv((dir_path+'RUL_FD001.txt'), sep='\\s+', header=None, names=['RUL'])\n",
    "\n",
    "train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>unit_nr</th>\n",
       "      <th>time_cycles</th>\n",
       "      <th>RUL</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <td>0</td>\n",
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      ],
      "text/plain": [
       "   unit_nr  time_cycles  RUL\n",
       "0        1            1  191\n",
       "1        1            2  190\n",
       "2        1            3  189\n",
       "3        1            4  188\n",
       "4        1            5  187"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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    }
   ],
   "source": [
    "def add_remaining_useful_life(df):\n",
    "    # Get the total number of cycles for each unit\n",
    "    grouped_by_unit = df.groupby(by=\"unit_nr\")\n",
    "    max_cycle = grouped_by_unit[\"time_cycles\"].max()\n",
    "    \n",
    "    # Merge the max cycle back into the original frame\n",
    "    result_frame = df.merge(max_cycle.to_frame(name='max_cycle'), left_on='unit_nr', right_index=True)\n",
    "    \n",
    "    # Calculate remaining useful life for each row\n",
    "    remaining_useful_life = result_frame[\"max_cycle\"] - result_frame[\"time_cycles\"]\n",
    "    result_frame[\"RUL\"] = remaining_useful_life\n",
    "    \n",
    "    # drop max_cycle as it's no longer needed\n",
    "    result_frame = result_frame.drop(\"max_cycle\", axis=1)\n",
    "    return result_frame\n",
    "\n",
    "train = add_remaining_useful_life(train)\n",
    "train[index_names+['RUL']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Re-examine RUL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our current assumption of RUL for the train set is that it declines linearly to zero. However, when we inspect the sensor signals they often show a 'bend' in their curve indicating degradation has started. Based on the information given to us we can't really say anything about RUL before this point, as we don't have any information on initial wear and tear of the engines.[Heimes 2008]  \n",
    "Therefore, we assume RUL to start out constant and only decline linearly after some time. The aim is to get a similar 'bend' in the curve (see image below).   \n",
    "Starting out with a constant RUL achieves two things:  \n",
    "1) Initially constant RUL correlates better with the stable mean sensor signal  \n",
    "2) Lower peak values of RUL results in lower spread of our target variable, making it easier to fit a line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "clipped_rul = train.loc[train['unit_nr']==20].copy()\n",
    "clipped_rul['RUL'].clip(upper=125, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1,1, figsize=(13,5))\n",
    "\n",
    "signal = ax1.plot('RUL', 's_12', 'b',\n",
    "                 data=train.loc[train['unit_nr']==20])\n",
    "plt.xlim(250, 0)  # reverse the x-axis so RUL counts down to zero\n",
    "plt.xticks(np.arange(0, 275, 25))\n",
    "ax1.set_ylabel('s_12', labelpad=20)\n",
    "ax1.set_xlabel('RUL', labelpad=20)\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "rul_line = ax2.plot('RUL', 'RUL', 'k', linewidth=4,\n",
    "                   data=train.loc[train['unit_nr']==20])\n",
    "rul = train.loc[train['unit_nr']==20, 'RUL']\n",
    "rul_line2 = ax2.plot(rul, rul.where(rul <= 125, 125), '--g', linewidth=4, label='clipped_rul')  # SET LABEL MANUALLY?\n",
    "ax2.set_ylabel('RUL', labelpad=20)\n",
    "\n",
    "# code to have equal spacing of y ticks for both axes, so the gridlines allign\n",
    "# from https://stackoverflow.com/questions/20243683/matplotlib-align-twinx-tick-marks?rq=1\n",
    "ax2.set_ylim(0, 250)  # set limits of axis you want to display neatly\n",
    "ax2.set_yticks(\n",
    "    np.linspace(ax2.get_ybound()[0], ax2.get_ybound()[1], 6))  # choose integer to neatly divide your axis, in our case 6\n",
    "ax1.set_yticks(\n",
    "    np.linspace(ax1.get_ybound()[0], ax1.get_ybound()[1], 6))  # apply same spacing to other axis\n",
    "\n",
    "\n",
    "# code to have a unified legend\n",
    "# from https://stackoverflow.com/questions/5484922/secondary-axis-with-twinx-how-to-add-to-legend\n",
    "lines = signal+rul_line+rul_line2\n",
    "labels = [line.get_label() for line in lines]\n",
    "ax1.legend(lines, labels, loc=0)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try this out with our baseline model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prep data\n",
    "# drop unwanted columns and split target variable from training set\n",
    "drop_sensors = ['s_1','s_5','s_6','s_10','s_16','s_18','s_19']\n",
    "drop_labels = index_names+setting_names+drop_sensors\n",
    "\n",
    "X_train = train.drop(drop_labels, axis=1)\n",
    "y_train = X_train.pop('RUL')\n",
    "\n",
    "# Since the true RUL values for the test set are only provided for the last time cycle of each enginge, \n",
    "# the test set is subsetted to represent the same\n",
    "X_test = test.groupby('unit_nr').last().reset_index().drop(drop_labels, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate(y_true, y_hat, label='test'):\n",
    "    mse = mean_squared_error(y_true, y_hat)\n",
    "    rmse = np.sqrt(mse)\n",
    "    variance = r2_score(y_true, y_hat)\n",
    "    print('{} set RMSE:{}, R2:{}'.format(label, rmse, variance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train set RMSE:44.66819159545453, R2:0.5794486527796716\n",
      "test set RMSE:31.952633027741815, R2:0.40877368076574083\n"
     ]
    }
   ],
   "source": [
    "## Linear declining RUL\n",
    "# create and fit model\n",
    "lm = LinearRegression()\n",
    "lm.fit(X_train, y_train)\n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = lm.predict(X_train)\n",
    "evaluate(y_train, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = lm.predict(X_test)\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_clipped = y_train.clip(upper=125)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I previously used the where method, but .clip seems more intuitive\n",
    "all(y_train.where(y_train <= 125, 125) == y_train_clipped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train set RMSE:21.491018701515415, R2:0.7340432868050447\n",
      "test set RMSE:21.900213406890515, R2:0.7222608196546241\n"
     ]
    }
   ],
   "source": [
    "## Clipped RUL\n",
    "# create and fit model\n",
    "lm = LinearRegression()\n",
    "lm.fit(X_train, y_train_clipped)  \n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = lm.predict(X_train)\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = lm.predict(X_test)\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we've updated our assumption of RUL, I feel this should also be reflected in the train evaluation. The True RUL of the test set remains untouched.  \n",
    "The train RMSE has more than halved. Of course we've set those targets ourselves, but it still shows how much impact the high 'assumed' RUL values had on overall model performance. Much more imporant tough, is the improvement on the test set (almost one third!). Which informs us the updated assumption is beneficial for modeling true RUL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train set RMSE:29.57783070266026, R2:0.49623314435506494\n",
      "test set RMSE:29.675150117440094, R2:0.49005151605390174\n"
     ]
    }
   ],
   "source": [
    "# SVM initial regression + clipped RUL\n",
    "svr = SVR(kernel='linear')\n",
    "svr.fit(X_train, y_train_clipped)  \n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = svr.predict(X_train)\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = svr.predict(X_test)\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results are quite a bit worse, let's try scaling our features to improve model performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scaling\n",
    "from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
    "scaler = MinMaxScaler()\n",
    "# scaler = StandardScaler()  # for this specific dataset, the type of scaler does not have any effect\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train set RMSE:21.578263975067888, R2:0.7318795396979632\n",
      "test set RMSE:21.580480163289597, R2:0.730311354095216\n"
     ]
    }
   ],
   "source": [
    "# SVM regression + clipped RUL + scaled\n",
    "svr = SVR(kernel='linear')\n",
    "svr.fit(X_train_scaled, y_train_clipped)  \n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = svr.predict(X_train_scaled)\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = svr.predict(X_test_scaled)\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great, the current RMSE is already an improvement over the baseline regression with clipped RUL. Let's see if we can improve it even further with some feature engineering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20631, 14)\n",
      "(20631, 120)\n"
     ]
    }
   ],
   "source": [
    "# Feature engineering\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "# 2nd degree polynomialFeatures of [a, b] becomes [1, a, b, a^2, ab, b^2]\n",
    "poly = PolynomialFeatures(2)\n",
    "X_train_transformed = poly.fit_transform(X_train_scaled)\n",
    "X_test_transformed = poly.fit_transform(X_test_scaled)\n",
    "\n",
    "print(X_train_scaled.shape)\n",
    "print(X_train_transformed.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train set RMSE:19.716789731130874, R2:0.7761436785704136\n",
      "test set RMSE:20.585402508370592, R2:0.75460868821153\n"
     ]
    }
   ],
   "source": [
    "# SVM regression + clipped RUL + engineered features\n",
    "svr_f = SVR(kernel='linear')\n",
    "svr_f.fit(X_train_transformed, y_train_clipped)  \n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = svr_f.predict(X_train_transformed)\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = svr_f.predict(X_test_transformed)\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original features:\n",
      " Index(['s_2', 's_3', 's_4', 's_7', 's_8', 's_9', 's_11', 's_12', 's_13',\n",
      "       's_14', 's_15', 's_17', 's_20', 's_21'],\n",
      "      dtype='object')\n",
      "Best features:\n",
      " ['x0' 'x1' 'x2' 'x3' 'x5' 'x6' 'x7' 'x9' 'x10' 'x11' 'x12' 'x13' 'x2 x5'\n",
      " 'x2 x8' 'x2 x9' 'x3 x5' 'x3 x8' 'x3 x9' 'x4^2' 'x4 x6' 'x4 x7' 'x4 x8'\n",
      " 'x5^2' 'x5 x6' 'x5 x7' 'x5 x9' 'x5 x12' 'x5 x13' 'x6^2' 'x6 x8' 'x6 x9'\n",
      " 'x7 x8' 'x7 x9' 'x8^2' 'x9^2' 'x9 x12' 'x9 x13']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(37,)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Feature engineering + selection\n",
    "from sklearn.feature_selection import SelectFromModel\n",
    "select_features = SelectFromModel(svr_f, threshold='mean', prefit=True)\n",
    "select_features.get_support()\n",
    "feature_names = poly.get_feature_names()\n",
    "\n",
    "print('Original features:\\n', X_train.columns)\n",
    "print('Best features:\\n', np.array(feature_names)[select_features.get_support()])\n",
    "np.array(feature_names)[select_features.get_support()].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test set RMSE:19.746789101481127, R2:0.775461959316527\n",
      "test set RMSE:20.55613819605483, R2:0.7553058913450649\n"
     ]
    }
   ],
   "source": [
    "# SVM regression + clipped RUL + engineered features + selection\n",
    "svr = SVR(kernel='linear')\n",
    "svr.fit(X_train_transformed[:, select_features.get_support()], y_train_clipped) \n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = svr.predict(X_train_transformed[:, select_features.get_support()])\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = svr.predict(X_test_transformed[:, select_features.get_support()])\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our feature space went from 14 to 120, after feature selection we're back down to 37 features. These features improved out model yet again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple hyper parameter tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epsilon: 0.4 RMSE: 19.74772556660336 R2: 0.7754406619776462\n",
      "epsilon: 0.3 RMSE: 19.747580761069848 R2: 0.7754439552496148\n",
      "epsilon: 0.2 RMSE: 19.74660007817171 R2: 0.7754662580123992\n",
      "epsilon: 0.1 RMSE: 19.746789101481127 R2: 0.775461959316527\n",
      "epsilon: 0.05 RMSE: 19.746532456984006 R2: 0.7754677958176168\n"
     ]
    }
   ],
   "source": [
    "epsilon = [0.4, 0.3, 0.2, 0.1, 0.05]\n",
    "\n",
    "for e in epsilon:\n",
    "    svr = SVR(kernel='linear', epsilon=e)\n",
    "    svr.fit(X_train_transformed[:, select_features.get_support()], y_train_clipped)\n",
    "\n",
    "    # predict and evaluate\n",
    "    y_hat = svr.predict(X_train_transformed[:, select_features.get_support()])\n",
    "    mse = mean_squared_error(y_train_clipped, y_hat)\n",
    "    rmse = np.sqrt(mse)\n",
    "    variance = r2_score(y_train_clipped, y_hat)\n",
    "    print(\"epsilon:\", e, \"RMSE:\", rmse, \"R2:\", variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An epsilon of 0.2 seems best for our current model, let's train it again and evaluate on the test set for our final RMSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test set RMSE:19.74660007817171, R2:0.7754662580123992\n",
      "test set RMSE:20.54412482077374, R2:0.7555918150093489\n"
     ]
    }
   ],
   "source": [
    "svr = SVR(kernel='linear', epsilon=0.2)\n",
    "svr.fit(X_train_transformed[:, select_features.get_support()], y_train_clipped)\n",
    "\n",
    "# predict and evaluate\n",
    "y_hat_train = svr.predict(X_train_transformed[:, select_features.get_support()])\n",
    "evaluate(y_train_clipped, y_hat_train, 'train')\n",
    "\n",
    "y_hat_test = svr.predict(X_test_transformed[:, select_features.get_support()])\n",
    "evaluate(y_test, y_hat_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final SVR has a test RMSE of 20.54. The combination of updating our assumption of RUL and fitting an SVR with tuned boundaries, feature scaling and polynomial features provides a 35.7 % improvement over our baseline model (RMSE = 31.95).  \n",
    "\n",
    "Most of this improvement is attributed to changing our assumption of RUL, which shows the importance of framing your data science problem correctly.\n",
    "\n",
    "In the next analysis we'll delve into timeseries, see you there!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "## sources used\n",
    "\n",
    "# F. O. Heimes, \"Recurrent neural networks for remaining useful life estimation,\" 2008 International Conference on Prognostics and Health Management, Denver, CO, 2008, pp. 1-6, doi: 10.1109/PHM.2008.4711422.\n",
    "\n",
    "# https://towardsdatascience.com/support-vector-machine-simply-explained-fee28eba5496\n",
    "# https://www.researchgate.net/publication/320916953_Predicting_Top-of-Atmosphere_Thermal_Radiance_Using_MERRA-2_Atmospheric_Data_with_Deep_Learning\n",
    "# https://www.researchgate.net/post/When_should_the_support_vector_regression_rather_than_conventional_least_squared_errors_minimization_be_applied\n",
    "# https://cs.adelaide.edu.au/~chhshen/teaching/ML_SVR.pdf\n",
    "# https://stats.stackexchange.com/a/287855\n",
    "# https://towardsdatascience.com/an-introduction-to-support-vector-regression-svr-a3ebc1672c2"
   ]
  }
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