2-target-metrics-baseline.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "# Target, Evaluation Metircs and Baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "In this notebook we:\n",
    "\n",
    "* Define our target\n",
    "\n",
    "* Discuss the evaluation metrics\n",
    "\n",
    "* Build a Baseline Model\n",
    "\n",
    "\n",
    "**NOTE:** Before starting exploring this notebook, I recommend checking `1-EDA.ipynb` notebook first - it contains Exploratory Data Analysis of the engines datasets and will help you get some understanding of the datasets. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:26.750035Z",
     "start_time": "2021-11-06T17:21:25.723857Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "First, let's read the data, we start with \"FD001\" dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:26.868934Z",
     "start_time": "2021-11-06T17:21:26.752889Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [],
   "source": [
    "from utils import read_dataset\n",
    "\n",
    "train_data, test_data, test_rul = read_dataset('FD001')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "# The Target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "Our taget will be estimating engines **Remaing Useful Life (RUL):** \n",
    "\n",
    "> RUL - remaining time that a component can function with an acceptable performance before it fails. In our case - it's a number of cycles from a current cycle to the engine's end of useful life (last cycle). \n",
    "\n",
    "Let's see RUL values for a couple of picked engines:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:26.875817Z",
     "start_time": "2021-11-06T17:21:26.871457Z"
    }
   },
   "outputs": [],
   "source": [
    "def calculate_RUL(X, upper_threshold=None):\n",
    "    '''\n",
    "    Calculate Remaining Useful Life per `unit`\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    X : pd.DataFrame, with `unit` and `time_cycles` columns\n",
    "    upper_threshold: int, limit maximum RUL valus, default is None\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    np.array with Remaining Useful Life values\n",
    "    '''\n",
    "    lifetime = X.groupby(['unit'])['time_cycles'].transform(max)\n",
    "    rul = lifetime - X['time_cycles']\n",
    "\n",
    "    if upper_threshold:\n",
    "        rul = np.where(rul > upper_threshold, upper_threshold, rul)\n",
    "\n",
    "    return rul"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.108134Z",
     "start_time": "2021-11-06T17:21:26.879238Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_data['rul'] = calculate_RUL(train_data)\n",
    "\n",
    "for _unit in [1, 2, 5, 10]:\n",
    "    plt.plot(\n",
    "        train_data[train_data['unit'] == _unit]['time_cycles'], \n",
    "        train_data[train_data['unit'] == _unit]['rul'], \n",
    "        label=f'Engine {_unit}'\n",
    "    )\n",
    "plt.legend()\n",
    "plt.xlabel('cycle')\n",
    "plt.ylabel('RUL')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "And the distributions of RUL values in the Train/Test sets are visualized below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.549219Z",
     "start_time": "2021-11-06T17:21:27.110320Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.set_title('Distributions of RUL in Train/Test sets', loc='left', size=14)\n",
    "sns.distplot(test_rul, label='Test set RUL')\n",
    "sns.distplot(train_data['rul'], label='Train set RUL')\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "As you can see from the figure above, the Train set contains samples with RUL way higher than in the Test set and this is because there're engines full lifetime data in the Train set, and in the Test set there's engines data till some period of time before its end of life. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "In most of the papers related to this problem, maximum value of RUL is being **limited to some constant value**. And the motivation is that a degradatation process will be only noticeable in the data after a unit has operated for some time. You can read more about this in this paper - https://www.researchgate.net/publication/224358896_Recurrent_neural_networks_for_remaining_useful_life_estimation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-11-07T21:43:15.175687Z",
     "start_time": "2020-11-07T21:43:15.171373Z"
    },
    "tags": [
     "remove"
    ]
   },
   "source": [
    "So, we are going to **limit a maximum value of RUL with 135** (you can find details about how this specific value was picked in the paper following the link above) - please, see the changed RUL plots below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.554032Z",
     "start_time": "2021-11-06T17:21:27.551188Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [],
   "source": [
    "RUL_UPPER_THRESHOLD = 135"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.762376Z",
     "start_time": "2021-11-06T17:21:27.555795Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_data['rul'] = calculate_RUL(train_data, upper_threshold=RUL_UPPER_THRESHOLD)\n",
    "\n",
    "for _unit in [1, 2, 5, 10]:\n",
    "    plt.plot(\n",
    "        train_data[train_data['unit'] == _unit]['time_cycles'], \n",
    "        train_data[train_data['unit'] == _unit]['rul'], \n",
    "        label=f'Engine {_unit}'\n",
    "    )\n",
    "plt.legend()\n",
    "plt.xlabel('cycle')\n",
    "plt.ylabel('RUL')\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "train_data = train_data.drop(columns=['rul'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "# Evaluation Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "We are solving a Regression problem here and let's list and discuss the metrics we can use to evaluate the models for estimating Remaining Useful Life:\n",
    "\n",
    "1. **RMSE** - Root Mean Squared Error - one of the standard metrics for regression, it's a squared root of averaged squared difference between actual and predicted values. An important characteristic of RMSE is that it penalizes larger errors more. \n",
    "\n",
    "$$ RMSE = \\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}{(y_i - \\hat{y_i})^2}} $$\n",
    "\n",
    "2. **MAE** - Mean Absolute Error - an average of absolute difference between actual and predicted values. MAE uses the same scale as the data and it's more robust to outliers.\n",
    "\n",
    "$$ MAE = \\frac{1}{n} \\sum_{i=1}^{n}{ |y_i - \\hat{y_i}| } $$\n",
    "\n",
    "3. **MAPE** - Mean Absolute Percentage Error - average ratio of error over actual value, it measures the size of error as a percentage. **NOTE that this metric is not defined for $y=0$**. Also, if the actual values are very small, MAPE can be very high because of that. \n",
    "Another interesing characteristic of this metric is that **it's biased towards predictions which are lower than the actual values**. MAPE score will be lower for a prediction lower than the actual value, but it will be higher for a prediction which is higher than the actual value by the same amount, e.g. $ y=1, \\hat{y}=2$, then $ MAPE = 100\\% $, but when $ y=2, \\hat{y}=1 $, then $MAPE=50\\%$. \n",
    "\n",
    "$$ MAPE = 100 * \\frac{1}{n} \\sum_{i=1}^{n}{ |\\frac{y_i - \\hat{y_i}}{y_i}| } $$\n",
    "\n",
    "\n",
    "4. **Custom Score** - this score is being used in most of the papers about estimating Remaining Useful Life for the turbofan data we use here, provided in Saxena et al. [1]. \n",
    "\n",
    "$$ SCORE = \\sum_{i=1}^{n}{(e^{-\\frac{(y_i - \\hat{y_i})}{w}} - 1 ) }, $$\n",
    "\n",
    "where $ w = 10 $, if $\\hat{y} \\geq y $\n",
    "and $ w = 13 $, if $\\hat{y} \\lt y $\n",
    "\n",
    "**NOTE that since this metric is a SUM, it cannot be compared across datasets of a different size!** It will be larger for a higher $n$. \n",
    "\n",
    "This scoring function assigns a **higher penalty when the Predicted RUL is higher than the true RUL** - please, see the figure below. The motivation for this is that late predictions are potentially more costly - predicting end of engine's life after it actually ended can cause much more problems than predicting it too early. \n",
    "\n",
    "\n",
    "[1] A. Saxena, K. Goebel, D. Simon, N. Eklund\n",
    "Damage propagation modeling for aircraft engine run-to-failure simulation\n",
    "2008 International Conference on Prognostics and Health Management, IEEE (2008), pp. 1-9\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-17T09:54:20.016279Z",
     "start_time": "2020-10-17T09:54:19.892571Z"
    },
    "tags": [
     "remove"
    ]
   },
   "source": [
    "Now let's see how the **Custom score** (Item 4 on the list above) function assigns a higher weight to predictions higher than the actual:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.769757Z",
     "start_time": "2021-11-06T17:21:27.765054Z"
    }
   },
   "outputs": [],
   "source": [
    "def rul_score_f(err):\n",
    "    if err >= 0:\n",
    "        return np.exp(err / 10) - 1\n",
    "    else:\n",
    "        return np.exp(- err / 13) - 1\n",
    "\n",
    "\n",
    "# Why this metric is a sum? Why not average?\n",
    "# it means the metric increases with the size of the dataset\n",
    "# and it means that it's not comparable between datasets\n",
    "# of different sizes\n",
    "def rul_score(true_rul, estimated_rul):\n",
    "    err = estimated_rul - true_rul\n",
    "    return np.sum([rul_score_f(x) for x in err])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:27.979853Z",
     "start_time": "2021-11-06T17:21:27.772369Z"
    },
    "scrolled": true,
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(-50, 50), \n",
    "         [rul_score_f(x) for x in np.arange(-50, 50)])\n",
    "plt.xlabel('estimated RUL - true RUL')\n",
    "plt.ylabel('Custom score')\n",
    "plt.grid(linewidth=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.056656Z",
     "start_time": "2021-11-06T17:21:27.985092Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, mean_absolute_percentage_error\n",
    "\n",
    "\n",
    "def rul_metrics_scorer(model, X, true_rul, metrics='all'):\n",
    "    '''\n",
    "    Calculate evaluation metrics:\n",
    "        1. rmse - Root Mean Squared Error\n",
    "        2. mae - Mean Absolute Error\n",
    "        3. mape - Mean Absolute Percentage Error\n",
    "        4. score - Custom metric with higher weight on underestimated RUL\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    dict with metrics\n",
    "    '''\n",
    "    scores_f = {\n",
    "        'rmse': lambda y_true, y_pred: np.sqrt(mean_squared_error(y_true, y_pred)),\n",
    "        'mae': mean_absolute_error,\n",
    "        'mape': mean_absolute_percentage_error,\n",
    "        'score': rul_score\n",
    "    }\n",
    "\n",
    "    pred_rul = model.predict(X)\n",
    "\n",
    "    def calculate_scores(metrics_list):\n",
    "        return {m: scores_f[m](true_rul, pred_rul) for m in metrics_list}\n",
    "\n",
    "    if metrics == 'all':\n",
    "        return calculate_scores(scores_f.keys())\n",
    "    elif isinstance(metrics, list):\n",
    "        return calculate_scores(metrics)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prognostics Performance Evaluation Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prognostics has different performance requirements than general forecasting applications, which translates into differences in metrics. A couple of prognostics metrics are described in [2]: \n",
    "\n",
    "\n",
    "![](figures/prognostics_metrics.png)\n",
    "\n",
    "*Figure source: [2]*\n",
    "\n",
    "[2] Saxena, A.; Celaya, J.; Saha, B.; Saha, S.; Goebel, K. Metrics for Offline Evaluation of Prognostic Performance. Int. J. Progn. Health Manag. 2010\n",
    "\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "\n",
    "1. **Prognostic Horizon** - difference between time index when predictions first meet the specified performance criteria, specified in terms of error bounds $\\alpha$, and the time index for end of life. It answers how much time it allows for any corrective action to be taken. The choice of error margin depends on time required for corrective action. \n",
    "\n",
    "\n",
    "![](figures/prognostic_horizon.png)\n",
    "*Figure source: [2]*\n",
    "\n",
    "See the function below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.065815Z",
     "start_time": "2021-11-06T17:21:28.058630Z"
    }
   },
   "outputs": [],
   "source": [
    "def prognostic_horizon(pred_rul_dists, true_rul, beta=0.75, alphas=[-7, 7]):\n",
    "    '''Calculate Prognostic Horizon \n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    pred_rul_dists : list w predicted distributions with method dist.cdf\n",
    "    true_rul : np.array, ground truth Remaining Useful Life\n",
    "    beta : float, probability threshold\n",
    "    alphas : list, error margins\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    a tuple of prognostic horizon and corresponding probabilities\n",
    "    '''\n",
    "    assert len(alphas) == 2, \"expect `alphas` to be a list of length 2\"\n",
    "    assert len(pred_rul_dists) == len(true_rul), \"expect pred dists and true rul w same len\"\n",
    "    \n",
    "    prog_horizon = 0\n",
    "    prob_within_bounds = np.zeros(len(true_rul))\n",
    "    \n",
    "    horizon_found = False\n",
    "    for i in range(len(true_rul)):\n",
    "        pred_rul_cdfs = []\n",
    "        for alpha in alphas:\n",
    "            pred_rul_cdfs.append(\n",
    "                pred_rul_dists[::-1][i].dist.cdf(np.maximum(true_rul[::-1][i] + alpha, 0)))\n",
    "        beta_proba = pred_rul_cdfs[1] - pred_rul_cdfs[0]\n",
    "        prob_within_bounds[::-1][i] = beta_proba\n",
    "        \n",
    "        if not horizon_found:\n",
    "            if beta_proba >= beta:\n",
    "                prog_horizon = true_rul[::-1][i]\n",
    "            else:\n",
    "                horizon_found = True \n",
    "\n",
    "    return int(prog_horizon), prob_within_bounds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. **$\\alpha-\\lambda$ accuracy** - binary check if prediction at specific time instance $t_{\\lambda}$ (fraction of time beetween time index when the first prediction is made and end of life) falls within error bounds ($\\alpha$ bounds). Time instance $t_{\\lambda}$ can be defined as a fraction of engines lifetime - $\\lambda$:\n",
    "\n",
    "$$t_{\\lambda} = t_{0} + \\lambda * (t_{EOL} - t_{0}),$$\n",
    "\n",
    "where\n",
    "* $t_{EOL}$ engined End Of Life\n",
    "* $t_{0}$ is a time instance of a first prediction made.\n",
    "\n",
    "\n",
    "![](figures/alpha_lambda_performance.png)\n",
    "*Figure source: [2]*\n",
    "\n",
    "See the function below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.074460Z",
     "start_time": "2021-11-06T17:21:28.067716Z"
    }
   },
   "outputs": [],
   "source": [
    "def alpha_lambda_acc(pred_rul_dists, true_rul, time_frac=[0.5, 0.75, 0.9], beta=0.75, alpha=0.1):\n",
    "    '''Calculate Alpha-Lambda Accuracy\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    pred_rul_dists : list w predicted distributions with method dist.cdf\n",
    "    true_rul : np.array, ground truth Remaining Useful Life\n",
    "    time_frac : list of time fractions for predictions\n",
    "    beta : float, probability threshold\n",
    "    alpha : float, error margin around actual RUL\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    a tuple of binary alpha-lambda acc and corresponding probabilities\n",
    "    '''\n",
    "    assert len(pred_rul_dists) == len(true_rul), \"expect pred dists and true rul w same len\"\n",
    "    \n",
    "    n_time_inst = len(true_rul)\n",
    "    \n",
    "    alha_lambda_acc = np.full(len(time_frac), -1)\n",
    "    pred_probas = np.full(len(time_frac), -1.0)\n",
    "    for i, t_frac in enumerate(time_frac):\n",
    "        t_instance = int(np.round(n_time_inst * t_frac))\n",
    "        t_inst_true_rul = true_rul[t_instance]\n",
    "        upper_bound = np.maximum(np.round(t_inst_true_rul * (1 + alpha)), 2)\n",
    "        low_bound = np.round(t_inst_true_rul * (1 - alpha))\n",
    "        \n",
    "        t_inst_pred = pred_rul_dists[t_instance]\n",
    "        \n",
    "        pred_probas[i] = t_inst_pred.dist.cdf(upper_bound) - t_inst_pred.dist.cdf(low_bound)\n",
    "        \n",
    "        if pred_probas[i] >= beta:\n",
    "            alha_lambda_acc[i] = 1\n",
    "        else:\n",
    "            alha_lambda_acc[i] = 0\n",
    "\n",
    "    return alha_lambda_acc, pred_probas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "3. **Relative Accuracy** - error relative to actual RUL at specific time instance $t_{\\lambda}$:\n",
    "\n",
    "$$RA_{\\lambda} = 1 - \\frac{RUL error_{\\lambda}}{true RUL_{\\lambda}}$$\n",
    "\n",
    "Time instance $t_{\\lambda}$ can be defined as a fraction of engines lifetime - $\\lambda$:\n",
    "\n",
    "$$t_{\\lambda} = t_{0} + \\lambda * (t_{EOL} - t_{0}),$$\n",
    "\n",
    "where\n",
    "* $t_{EOL}$ engined End Of Life\n",
    "* $t_{0}$ is a time instance of a first prediction made.\n",
    "\n",
    "<br>\n",
    "See the function below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.081572Z",
     "start_time": "2021-11-06T17:21:28.076351Z"
    }
   },
   "outputs": [],
   "source": [
    "def relative_accuracy(pred_rul, true_rul, time_frac=[0.5, 0.75, 0.9]):\n",
    "    '''Calculate Relative Accuracy\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    pred_rul : np.array, w predicted Remaining Useful Life\n",
    "    true_rul : np.array, ground truth Remaining Useful Life\n",
    "    time_frac : list of time fractions for predictions\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    np.array of relative accuracy at every time instance from `time_frac`\n",
    "    '''\n",
    "    assert len(pred_rul) == len(true_rul), \"expect predicted and true rul w same length\"\n",
    "\n",
    "    n_time_inst = len(true_rul)\n",
    "\n",
    "    rel_acc = np.full(len(time_frac), -1.0)\n",
    "    for i, t_frac in enumerate(time_frac):\n",
    "        t_instance = int(np.round(n_time_inst * t_frac))\n",
    "        t_inst_true_rul = true_rul[t_instance]\n",
    "        t_inst_pred = pred_rul[t_instance]\n",
    "\n",
    "        rel_acc[i] = 1 - np.abs(t_inst_true_rul - t_inst_pred) / t_inst_true_rul\n",
    "\n",
    "    return rel_acc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "# Baseline Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "We start with a Baseline Model which will be our reference point to which compare all the other models. For instance, a baseline model can be even a random guess, and if a model you developed can't beat such baseline - that's your red flag."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "Our Baseline Model will be based on a random sample from engines RUL in the train set. Let's go through the steps it takes:\n",
    "\n",
    "1. for a given test engine, consider only engines in the train set which lifespan was higher than the current cycle for the test engine\n",
    "2. estimate Remaining Useful Life as a difference between AVG lifespan of the sampled engines from the train set and the test engine current cycle\n",
    "3. if there are no engines in the train set with a higher lifespan than the test engine, estimate RUL with a randomly picked integer from [1, 50]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "And here's the Baseline Model implemented:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.090017Z",
     "start_time": "2021-11-06T17:21:28.083479Z"
    }
   },
   "outputs": [],
   "source": [
    "class BaselineModel:\n",
    "    '''\n",
    "    Estimate Remaining Useful Life as an Average RUL of \n",
    "    engines with longer lifetime.\n",
    "    \n",
    "    If there are no older engines in train set, it randomly samples from [0, 50]. \n",
    "    '''\n",
    "    def fit(self, X):\n",
    "        '''\n",
    "        Parameters\n",
    "        ----------\n",
    "        X : pd.DataFrame, engines data\n",
    "        '''\n",
    "        self.lifetime = X.groupby(['unit'])['time_cycles'].max().reset_index(name='last_cycle')\n",
    "        \n",
    "    def predict(self, X):\n",
    "        '''\n",
    "        Parameters\n",
    "        ----------\n",
    "        X : pd.DataFrame, engines data\n",
    "        '''\n",
    "        rul = []\n",
    "        for current_cycle in X['time_cycles'].values:\n",
    "            lifetime_sample = self.lifetime.loc[\n",
    "                (self.lifetime['last_cycle'] > current_cycle),\n",
    "                'last_cycle'\n",
    "            ]\n",
    "\n",
    "            if lifetime_sample.shape[0] == 0:\n",
    "                estimated_rul = np.random.randint(low=1, high=50, size=1)[0]\n",
    "            else:\n",
    "                estimated_rul = np.round(lifetime_sample.mean()) - current_cycle\n",
    "\n",
    "            rul.append(estimated_rul)\n",
    "        return np.array(rul)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.096647Z",
     "start_time": "2021-11-06T17:21:28.092008Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_residuals_vs_actual(actual_rul, predicted_rul,\n",
    "                             title='Test set - Residuals vs Actual RUL',\n",
    "                             xlabel='Actual RUL', ylabel='Residuals',\n",
    "                             ax=None):\n",
    "    '''A scatter plot of residuals vs '''\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(figsize=(10, 6))\n",
    "    residual = predicted_rul - actual_rul\n",
    "    ax.set_title(title)\n",
    "    sns.regplot(x=actual_rul, y=residual, lowess=True, ax=ax)\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "    ax.axhline(y=0, color='red', linestyle='--')\n",
    "    ax.grid()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "<br>\n",
    "\n",
    "Initialize an instance of a BaselineModel and train it with the train dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.104223Z",
     "start_time": "2021-11-06T17:21:28.098949Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [],
   "source": [
    "baseline_model = BaselineModel()\n",
    "baseline_model.fit(train_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "And here we test it on the TEST dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.112157Z",
     "start_time": "2021-11-06T17:21:28.106456Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [],
   "source": [
    "test_last_cycles = test_data.groupby('unit', as_index=False)['time_cycles'].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.165469Z",
     "start_time": "2021-11-06T17:21:28.114402Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'rmse': 36.63836786757838,\n",
       " 'mae': 31.37,\n",
       " 'mape': 0.906682116160513,\n",
       " 'score': 7657.158284814168}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rul_metrics_scorer(baseline_model, test_last_cycles, test_rul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-06T17:21:28.429847Z",
     "start_time": "2021-11-06T17:21:28.168019Z"
    },
    "tags": [
     "remove"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_pred = baseline_model.predict(test_last_cycles)\n",
    "\n",
    "plot_residuals_vs_actual(test_rul, test_pred, \n",
    "                         title='Baseline Model: Test set - Residuals vs Actual RUL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove"
    ]
   },
   "source": [
    "This gives us starting metrics scores (evaluated on the TEST data) that we will try to improve with ML models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
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