template/book/notebooks/contamination/Exercise_Contamination_Render.ipynb

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   "source": [
    "# Contaminant Transport"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ab31a602",
   "metadata": {},
   "source": [
    "````{note}\n",
    "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n",
    "```{eval-rst}\n",
    ":download:`Download zip file for this exercise.<exercise_contamination.zip>`\n",
    "```\n",
    "````"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "06fa7af4",
   "metadata": {},
   "source": [
    "The purpose of this exercise is to:\n",
    "- evaluate component reliability\n",
    "- illustrate functions of random variables\n",
    "- see the effect of random variable distributions on reliability\n",
    "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n",
    "\n",
    "You should accomplish this by playing with the code that is provided with the notebook and trying to answer the following questions:\n",
    "1. Which random variables have the biggest influence on reliability?\n",
    "2. How does the assumption of probability distribution influence reliability?\n",
    "3. Do the random variables act as loads or resistances?\n",
    "\n",
    "## Introduction of Case Study\n",
    "\n",
    "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n",
    "\n",
    "```{figure} ./figures/sketch.png\n",
    "---\n",
    "width: 600px\n",
    "name: sketch_contaminant\n",
    "---\n",
    "\n",
    "```\n",
    "\n",
    "### Contaminant Transport\n",
    "\n",
    "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n",
    "\n",
    "$$\n",
    "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n",
    "$$\n",
    "\n",
    "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n",
    "\n",
    "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n",
    "- $n$ is the soil porosity [$-$]\n",
    "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n",
    "\n",
    "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n",
    "\n",
    "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n",
    "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n",
    "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n",
    "\n",
    "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n",
    "\n",
    "### Definition of Limit States\n",
    "\n",
    "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n",
    "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n",
    "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n",
    "\n",
    "Relating these descriptions to our variables of interest:\n",
    "1. find the probability that $C/C_0$ > threshold \n",
    "2. find the probability that $C/C_0$ < threshold\n",
    "\n",
    "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n",
    "\n",
    "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n",
    "\n",
    "1. $Z=C/C_0 - \\mathrm{threshold}$\n",
    "2. $Z=\\mathrm{threshold} - C/C_0$\n",
    "\n",
    "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n",
    "\n",
    "### Analysis Approach\n",
    "\n",
    "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n",
    "\n",
    "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n",
    "\n",
    "### References\n",
    "\n",
    "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8287dbcf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import erfc\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "\n",
    "from exercise_setup import process_negative_values\n",
    "from exercise_setup import RandomVariableDistribution\n",
    "from exercise_setup import pdf_of_function_of_RV\n",
    "from exercise_setup import monte_carlo"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f",
   "metadata": {},
   "source": [
    "## Defining the Limit States\n",
    "\n",
    "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "64c24956",
   "metadata": {},
   "outputs": [],
   "source": [
    "def C_C0(q, n, a, x, t):\n",
    "    \"\"\"Contaminant concentration ratio.\"\"\"\n",
    "    q, n, a = process_negative_values(q, n, a)\n",
    "    return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n",
    "\n",
    "def limit_state_fun(q, n, a, x, t, threshold):\n",
    "    \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n",
    "    return threshold - C_C0(q, n, a, x, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7410d16-14d4-45c6-9f93-81ae08de0594",
   "metadata": {},
   "source": [
    "## Class `RandomVariableDistribution`\n",
    "\n",
    "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n",
    "\n",
    "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Define a N or LN probability to use in MUDE week 2.7 exercise.\n",
      "    \n",
      "    Usage:\n",
      "    -----\n",
      "    Create an instance of the class\n",
      "        by default, the random variable is ~N(0,1)\n",
      "    Specify distribution using 1st and 2nd moments for N or LN:\n",
      "        --> use method define_distribution to change it!\n",
      "             (the method prints a summary of the change)\n",
      "        for example, copy/paste the following:\n",
      "            test = RandomVariableDistribution()\n",
      "            test.print_status()\n",
      "            test.define_distribution(mean=5, stddev=1, dist_type='LN')\n",
      "    An instance will include the following attributes:\n",
      "        - distribution moment and (scipy) parameters shape, location, scale\n",
      "        - dist_object: distribution object (scipy.stats)\n",
      "        - get_sample: method for getting random samples from the distribution\n",
      "        - plot_pdf_or_cdf:\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(RandomVariableDistribution.__doc__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 5.000e+00\n",
      "The standard deviation is 1.000e+00\n",
      "The distribution is Lognormal\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example_random_variable = RandomVariableDistribution()\n",
    "example_random_variable.define_distribution(mean=5,\n",
    "                                            dist_type='LN',\n",
    "                                            print_new_dist=True)\n",
    "example_random_variable.plot_pdf_or_cdf()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62617026-f251-462b-a93c-b7305cfd3fa4",
   "metadata": {},
   "source": [
    "## Setting up the problem\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4641ae3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10000\n",
    "\n",
    "t = 7\n",
    "x = 100\n",
    "threshold = 1e-4\n",
    "\n",
    "flip_LSF = -1\n",
    "\n",
    "q_rv = RandomVariableDistribution()\n",
    "q_rv.define_distribution(mean=1., stddev=.1)\n",
    "n_rv = RandomVariableDistribution()\n",
    "n_rv.define_distribution(mean=0.2, stddev=.02)\n",
    "a_rv = RandomVariableDistribution()\n",
    "a_rv.define_distribution(mean=10., stddev=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946",
   "metadata": {},
   "source": [
    "## Monte Carlo analysis\n",
    "\n",
    "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n",
    "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n",
    "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n",
    "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n",
    "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n",
    "\n",
    "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n",
    "\n",
    "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n",
    "\n",
    "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n",
    "\n",
    "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n",
    "\n",
    "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n",
    "\n",
    "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ec7883de-544e-48d5-85f2-dfc7856e9028",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MONTE CARLO RESULTS\n",
      "--------------------------------------------------\n",
      "    N = 10000, number of samples\n",
      "   Nf = 18, number of failed realizations\n",
      "   pf = 1.800e-03, estimated failure probability\n",
      "    V = 0.236, c.o.v. of estimated pf\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_q = q_rv.get_sample(N)\n",
    "sample_n = n_rv.get_sample(N)\n",
    "sample_a = a_rv.get_sample(N)\n",
    "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n",
    "sample_Z = flip_LSF*limit_state_fun(sample_q,\n",
    "                                    sample_n,\n",
    "                                    sample_a,\n",
    "                                    x, t, threshold)\n",
    "\n",
    "monte_carlo(sample_Z);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc",
   "metadata": {},
   "source": [
    "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a has 61 negative values that have been set to 1.0e-03.\n",
      "a has 54 negative values that have been set to 1.0e-03.\n",
      "The mean is 1.000e+01\n",
      "The standard deviation is 1.000e+00\n",
      "The distribution is Normal\n",
      "The mean is 1.000e+01\n",
      "The standard deviation is 4.000e+00\n",
      "The distribution is Normal\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C_C0_cases = []\n",
    "Z_cases = []\n",
    "C_C0_cases.append(sample_C_C0)\n",
    "Z_cases.append(sample_Z)\n",
    "\n",
    "a_2 = RandomVariableDistribution()\n",
    "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n",
    "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n",
    "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n",
    "                                        sample_n,\n",
    "                                        a_2.get_sample(N),\n",
    "                                        x, t, threshold))\n",
    "\n",
    "a_rv.print_status()\n",
    "a_2.print_status()\n",
    "\n",
    "pdf_of_function_of_RV(C_C0_cases)\n",
    "pdf_of_function_of_RV(Z_cases, case_C=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "695f1336-8d3e-4503-9196-9969d181ae10",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac",
   "metadata": {},
   "source": [
    "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "53273645-453b-48b9-85c0-e69eb1ac579e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Joint density of 2 RVs with failure realizations\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values_of_RV_1 = sample_q\n",
    "values_of_RV_2 = sample_a\n",
    "\n",
    "g = sns.JointGrid()\n",
    "sns.kdeplot(x=values_of_RV_1,\n",
    "            y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n",
    "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n",
    "                y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n",
    "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n",
    "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n",
    "print('Joint density of 2 RVs with failure realizations')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2",
   "metadata": {},
   "source": [
    "## Case 2: exceeding the health threshold\n",
    "\n",
    "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MONTE CARLO RESULTS\n",
      "--------------------------------------------------\n",
      "    N = 100000, number of samples\n",
      "   Nf = 65, number of failed realizations\n",
      "   pf = 6.500e-04, estimated failure probability\n",
      "    V = 0.124, c.o.v. of estimated pf\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000\n",
    "\n",
    "t = 30\n",
    "x = 500\n",
    "threshold = 1e-4\n",
    "\n",
    "flip_LSF = 1\n",
    "\n",
    "sample_q = q_rv.get_sample(N)\n",
    "sample_n = n_rv.get_sample(N)\n",
    "sample_a = a_rv.get_sample(N)\n",
    "\n",
    "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n",
    "sample_Z = flip_LSF*limit_state_fun(sample_q,\n",
    "                                    sample_n,\n",
    "                                    sample_a,\n",
    "                                    x, t, threshold)\n",
    "\n",
    "monte_carlo(sample_Z);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1d693c6-df03-442f-a100-a065355b2c12",
   "metadata": {},
   "source": [
    "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91",
   "metadata": {},
   "outputs": [],
   "source": [
    "# values_of_RV_1 = sample_q\n",
    "# values_of_RV_2 = sample_a\n",
    "\n",
    "# g = sns.JointGrid()\n",
    "# sns.kdeplot(x=values_of_RV_1,\n",
    "#             y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n",
    "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n",
    "#                 y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n",
    "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n",
    "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n",
    "# print('Joint density of 2 RVs with failure realizations')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e7d0cc4",
   "metadata": {},
   "source": [
    "### Gradient Vector\n",
    "\n",
    "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n",
    "\n",
    "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n",
    "\n",
    "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n",
    "\n",
    "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n",
    "\n",
    "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2}  $, the derivatives are:\n",
    "\n",
    "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n",
    "\n",
    "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n",
    "\n",
    "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n",
    "\n",
    "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n",
    "\n",
    "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a761d424",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(q, n, a, x, t):\n",
    "    Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n",
    "    dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n",
    "    dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n",
    "    dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n",
    "    dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n",
    "    da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n",
    "    return np.array([dq,dn,da,dx,dt])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d6492f20",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.84464056e-01 -3.55580070e+00  1.01594306e-02 -1.62550889e-03\n",
      "  2.37053380e-02]\n"
     ]
    }
   ],
   "source": [
    "print(gradient(2.5, 0.2, 10, x, t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd",
   "metadata": {},
   "source": [
    "## Your turn!\n",
    "\n",
    "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n",
    "1. Which random variables have the biggest influence on reliability?\n",
    "2. How does the assumption of probability distribution influence reliability?\n",
    "3. Do the random variables act as loads or resistances?\n",
    "\n",
    "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n",
    "1. What is the functional influence of the random variables and x and t on the limit-state function?\n",
    "2. What is the stochastic influence of the random variables, \n",
    "3. What is the combined influence of the two aspects above?\n",
    "\n",
    "<!--  \n",
    "Hint: note the striking similarity of these terms to the material you have already seen in the variance propagation part of MUDE, where the variance of a function of random variables is proportional to $\\sigma_x\\cdot \\frac{\\partial Z}{\\partial x}$. The variable with the biggest influence on reliability will have the highest value of this term. Also, the sign of the partial derivative will indicate whether a variable acts as a load or resistance. -->"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
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