{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "expmkveO04pw"
},
"source": [
"## Pouch Cell Model Parameter Identification\n",
"\n",
"In this notebook, we present the single particle model with a two dimensional current collector. This is achieved via the potential-pair models introduced in Marquis et al. [[1]](https://doi.org/10.1149/1945-7111/abbce4) as implemented in PyBaMM. At a high-level this is accomplished as a potential-pair model which is resolved across the discretised spatial locations.\n",
"\n",
"### Setting up the Environment\n",
"\n",
"Before we begin, we need to ensure that we have all the necessary tools. We will install PyBOP and upgrade dependencies:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "X87NUGPW04py",
"outputId": "0d785b07-7cff-4aeb-e60a-4ff5a669afbf"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/Users/engs2510/Documents/Git/Second_PyBOP/.nox/notebooks-overwrite/bin/python3: No module named pip\r\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Note: you may need to restart the kernel to use updated packages.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"/Users/engs2510/Documents/Git/Second_PyBOP/.nox/notebooks-overwrite/bin/python3: No module named pip\r\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Note: you may need to restart the kernel to use updated packages."
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"%pip install --upgrade pip ipywidgets -q\n",
"%pip install pybop -q"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jAvD5fk104p0"
},
"source": [
"### Importing Libraries\n",
"\n",
"With the environment set up, we can now import PyBOP alongside other libraries we will need:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "SQdt4brD04p1"
},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"import pybop\n",
"\n",
"go = pybop.plot.PlotlyManager().go\n",
"pybop.plot.PlotlyManager().pio.renderers.default = \"notebook_connected\""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5XU-dMtU04p2"
},
"source": [
"## Generating Synthetic Data\n",
"\n",
"To demonstrate parameter estimation, we first need some data. We will generate synthetic data using a forward model, which requires defining a parameter set and the model itself.\n",
"\n",
"### Defining Parameters and Model\n",
"\n",
"We start by creating an example parameter set and then instantiate the single-particle model (SPM):"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"parameter_set = pybop.ParameterSet.pybamm(\"Marquis2019\")\n",
"parameter_set.update(\n",
" {\n",
" \"Negative electrode active material volume fraction\": 0.495,\n",
" \"Positive electrode active material volume fraction\": 0.612,\n",
" }\n",
")\n",
"model = pybop.lithium_ion.SPM(\n",
" parameter_set=parameter_set,\n",
" options={\"current collector\": \"potential pair\", \"dimensionality\": 2},\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Updating the Spatial Grid\n",
"\n",
"Next, we update the number of spatial locations to solve the potential-pair model,"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"model.var_pts[\"y\"] = 5\n",
"model.var_pts[\"z\"] = 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulating the Forward Model\n",
"\n",
"We can then simulate the model using the `predict` method, with a default constant current to generate voltage data."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "sBasxv8U04p3"
},
"outputs": [],
"source": [
"t_eval = np.arange(0, 900, 3)\n",
"values = model.predict(t_eval=t_eval)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Adding Noise to Voltage Data\n",
"\n",
"To make the parameter estimation more realistic, we add Gaussian noise to the data."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sigma = 0.001\n",
"corrupt_values = values[\"Voltage [V]\"].data + np.random.normal(0, sigma, len(t_eval))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "X8-tubYY04p_"
},
"source": [
"## Identifying the Parameters"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "PQqhvSZN04p_"
},
"source": [
"We will now set up the parameter estimation process by defining the datasets for optimisation and selecting the model parameters we wish to estimate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Creating a Dataset\n",
"\n",
"The dataset for optimisation is composed of time, current, and the noisy voltage data:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "zuvGHWID04p_"
},
"outputs": [],
"source": [
"dataset = pybop.Dataset(\n",
" {\n",
" \"Time [s]\": t_eval,\n",
" \"Current function [A]\": values[\"Current [A]\"].data,\n",
" \"Voltage [V]\": corrupt_values,\n",
" }\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ffS3CF_704qA"
},
"source": [
"### Defining Parameters to Estimate\n",
"\n",
"We select the parameters for estimation and set up their prior distributions and bounds:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "WPCybXIJ04qA"
},
"outputs": [],
"source": [
"parameters = pybop.Parameters(\n",
" pybop.Parameter(\n",
" \"Negative electrode active material volume fraction\",\n",
" prior=pybop.Gaussian(0.7, 0.05),\n",
" bounds=[0.45, 0.9],\n",
" ),\n",
" pybop.Parameter(\n",
" \"Positive electrode active material volume fraction\",\n",
" prior=pybop.Gaussian(0.58, 0.05),\n",
" bounds=[0.5, 0.8],\n",
" ),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For plotting purposes, we want additional variables to be stored in the problem class. These are defined as,"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"additional_variables = [\n",
" \"Negative current collector potential [V]\",\n",
" \"Positive current collector potential [V]\",\n",
"]"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "n4OHa-aF04qA"
},
"source": [
"### Setting up the Optimisation Problem\n",
"\n",
"With the datasets and parameters defined, we can set up the optimisation problem, its cost function, and the optimiser."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "etMzRtx404qA"
},
"outputs": [],
"source": [
"problem = pybop.FittingProblem(\n",
" model, parameters, dataset, additional_variables=additional_variables\n",
")\n",
"cost = pybop.SumSquaredError(problem)\n",
"optim = pybop.CMAES(cost, max_iterations=30)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "caprp-bV04qB"
},
"source": [
"### Running the Optimisation\n",
"\n",
"We proceed to run the CMA-ES optimisation algorithm to estimate the parameters:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "-9OVt0EQ04qB"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Halt: Maximum number of iterations (30) reached.\n",
"OptimisationResult:\n",
" Initial parameters: [0.65919975 0.65030567]\n",
" Optimised parameters: [0.49949096 0.60907043]\n",
" Final cost: 0.0002845276080247215\n",
" Optimisation time: 36.19517993927002 seconds\n",
" Number of iterations: 30\n",
" SciPy result available: No\n"
]
}
],
"source": [
"results = optim.run()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-4pZsDmS04qC"
},
"source": [
"### Viewing the Estimated Parameters\n",
"\n",
"After the optimisation, we can examine the estimated parameter values:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Hgz8SV4i04qC",
"outputId": "e1e42ae7-5075-4c47-dd68-1b22ecc170f6"
},
"outputs": [
{
"data": {
"text/plain": [
"array([0.49949096, 0.60907043])"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"results.x"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KxKURtH704qC"
},
"source": [
"## Plotting and Visualisation\n",
"\n",
"PyBOP provides various plotting utilities to visualise the results of the optimisation."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-cWCOiqR04qC"
},
"source": [
"### Comparing System Response\n",
"\n",
"We can quickly plot the system's response using the estimated parameters compared to the target:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 467
},
"id": "tJUJ80Ve04qD",
"outputId": "855fbaa2-1e09-4935-eb1a-8caf7f99eb75"
},
"outputs": [
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"text/html": [
" \n",
" "
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"source": [
"pybop.plot.quick(problem, problem_inputs=results.x, title=\"Optimised Comparison\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Spatial Plotting\n",
"\n",
"We can now plot the spatial variables from the solution object. First, the final negative current collector potential can be displayed. In this example, this is just a reference variable, but could be used for fitting or optimisation in the correct workflows."
]
},
{
"cell_type": "code",
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"metadata": {},
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{
"data": {
"text/html": [
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"source": [
"sol = problem.evaluate(parameters.as_dict(results.x))\n",
"\n",
"go.Figure(\n",
" [\n",
" go.Contour(\n",
" x=np.arange(0, model.var_pts[\"y\"] - 1, 1),\n",
" y=np.arange(0, model.var_pts[\"z\"] - 1, 1),\n",
" z=sol[\"Negative current collector potential [V]\"][:, :, -1],\n",
" colorscale=\"Viridis\",\n",
" )\n",
" ],\n",
" layout=dict(\n",
" title=\"Negative current collector potential [V]\",\n",
" xaxis_title=\"x node\",\n",
" yaxis_title=\"y node\",\n",
" width=600,\n",
" height=600,\n",
" ),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We plot can then plot the positive current collector potential,"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
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],
"source": [
"go.Figure(\n",
" [\n",
" go.Contour(\n",
" x=np.arange(0, model.var_pts[\"y\"] - 1, 1),\n",
" y=np.arange(0, model.var_pts[\"z\"] - 1, 1),\n",
" z=sol[\"Positive current collector potential [V]\"][:, :, -1],\n",
" colorscale=\"Viridis\",\n",
" )\n",
" ],\n",
" layout=dict(\n",
" title=\"Positive current collector potential [V]\",\n",
" xaxis_title=\"x node\",\n",
" yaxis_title=\"y node\",\n",
" width=600,\n",
" height=600,\n",
" ),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Convergence and Parameter Trajectories\n",
"\n",
"To assess the optimisation process, we can plot the convergence of the cost function and the trajectories of the parameters:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "N5XYkevi04qD"
},
"outputs": [
{
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],
"source": [
"pybop.plot.convergence(optim)\n",
"pybop.plot.parameters(optim);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cost Landscape\n",
"\n",
"Finally, we can visualise the cost landscape and the path taken by the optimiser:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
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],
"source": [
"pybop.plot.surface(optim);"
]
}
],
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