{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differentiating voltage data\n",
    "\n",
    "Differential Voltage Analysis (DVA) and Incremental Capacity Analysis are popular\n",
    "methods of characterising the degradation state of a cell. PyProBE offers multiple\n",
    "methods to the user which will be explored in this example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First import the package and dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "%pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pyprobe\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "info_dictionary = {\n",
    "    \"Name\": \"Sample cell\",\n",
    "    \"Chemistry\": \"NMC622\",\n",
    "    \"Nominal Capacity [Ah]\": 0.04,\n",
    "    \"Cycler number\": 1,\n",
    "    \"Channel number\": 1,\n",
    "}\n",
    "data_directory = \"../../../tests/sample_data/neware\"\n",
    "\n",
    "# Create a cell object\n",
    "cell = pyprobe.Cell(info=info_dictionary)\n",
    "cell.import_from_cycler(\n",
    "    procedure_name=\"Sample\",\n",
    "    cycler=\"neware\",\n",
    "    input_data_path=data_directory + \"/sample_data_neware.xlsx\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The break-in cycles of this dataset are at C/10, so can be analysed as pseudo-OCV curves. We're going to look at the last cycle:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_cycle = cell.procedure[\"Sample\"].experiment(\"Break-in Cycles\").cycle(-1)\n",
    "\n",
    "final_cycle.discharge(0).plot(x=\"Time [hr]\", y=\"Voltage [V]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to look at using the finite-difference based differentiation method, first \n",
    "on the raw data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyprobe.analysis import differentiation\n",
    "\n",
    "raw_data_dVdQ = differentiation.gradient(\n",
    "    final_cycle.discharge(0),\n",
    "    \"Capacity [Ah]\",\n",
    "    \"Voltage [V]\",\n",
    ")\n",
    "print(raw_data_dVdQ.columns)\n",
    "raw_data_dVdQ.plot(x=\"Capacity [Ah]\", y=\"d(Voltage [V])/d(Capacity [Ah])\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a clearly poor result. This is due to the noise in the experimental data.\n",
    "We can apply a smoothing function to the voltage prior to differentiating to remove this\n",
    "noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyprobe.analysis import smoothing\n",
    "\n",
    "downsampled_data = smoothing.downsample(\n",
    "    input_data=final_cycle.discharge(0),\n",
    "    target_column=\"Voltage [V]\",\n",
    "    sampling_interval=0.002,\n",
    ")\n",
    "fig, ax = plt.subplots()\n",
    "final_cycle.discharge(0).plot(\n",
    "    x=\"Capacity [Ah]\",\n",
    "    y=\"Voltage [V]\",\n",
    "    ax=ax,\n",
    "    label=\"Raw data\",\n",
    ")\n",
    "downsampled_data.plot(\n",
    "    x=\"Capacity [Ah]\",\n",
    "    y=\"Voltage [V]\",\n",
    "    ax=ax,\n",
    "    style=\"--\",\n",
    "    label=\"Downsampled data\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now differentiate the smoothed data object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "downsampled_data_dVdQ = differentiation.gradient(\n",
    "    downsampled_data,\n",
    "    \"Voltage [V]\",\n",
    "    \"Capacity [Ah]\",\n",
    ")\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "downsampled_data_dVdQ.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"Downsampled data\",\n",
    ")\n",
    "ax.set_ylabel(\"d(Capacity [Ah])/d(Voltage [V])\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyProBE has multiple smoothing methods, so you can easily compare their effect on the ICA result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "spline_smoothed_data = smoothing.spline_smoothing(\n",
    "    input_data=final_cycle.discharge(0),\n",
    "    x=\"Capacity [Ah]\",\n",
    "    target_column=\"Voltage [V]\",\n",
    "    smoothing_lambda=1e-10,\n",
    ")\n",
    "spline_smoothed_data_dVdQ = differentiation.gradient(\n",
    "    spline_smoothed_data,\n",
    "    \"Voltage [V]\",\n",
    "    \"Capacity [Ah]\",\n",
    ")\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "downsampled_data_dVdQ.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"Downsampled data\",\n",
    ")\n",
    "spline_smoothed_data_dVdQ.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"Spline smoothed data\",\n",
    ")\n",
    "ax.set_ylabel(\"d(Capacity [Ah])/d(Voltage [V])\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also compare to an alternative differentiation method, the LEAN method described in Feng X, Merla Y, Weng C, Ouyang M, He X, Liaw BY, et al. A reliable approach of differentiating discrete sampled-data for battery diagnosis. eTransportation. 2020;3: 100051. https://doi.org/10.1016/j.etran.2020.100051."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LEAN_dQdV = differentiation.differentiate_LEAN(\n",
    "    input_data=final_cycle.discharge(0),\n",
    "    x=\"Capacity [Ah]\",\n",
    "    y=\"Voltage [V]\",\n",
    "    k=10,\n",
    "    gradient=\"dxdy\",\n",
    ")\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "downsampled_data_dVdQ.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"Downsampled data\",\n",
    ")\n",
    "spline_smoothed_data_dVdQ.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"Spline smoothed data\",\n",
    ")\n",
    "LEAN_dQdV.plot(\n",
    "    x=\"Voltage [V]\",\n",
    "    y=\"d(Capacity [Ah])/d(Voltage [V])\",\n",
    "    ax=ax,\n",
    "    label=\"LEAN smoothed data\",\n",
    ")\n",
    "ax.set_ylabel(\"d(Capacity [Ah])/d(Voltage [V])\")"
   ]
  }
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