{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "46ea4f25",
   "metadata": {},
   "source": [
    "# Spatial upscaling (length-effect)\n",
    "\n",
    "### Spatial upscaling of failure probability of flood defence\n",
    "\n",
    "In this example, we will demonstrate how to apply the concept of spatial upscaling to the failure probabilities of flood defenses. The random variables are subject to spatial correlation, which affects the failure probability of a flood defense. The upscaling involves translating the failure probability per cross-section (length = 0 meters) to the failure probability per section (length > 0 meters).\n",
    "\n",
    "Spatial upscaling is influenced by a concept known as the length-effect. The length-effect refers to the increase in failure probability when moving from a cross-section to a longitudinal segment, and from a single segment to an entire flood defense system. In other words, it captures how an increase in length affects the probability of failure.\n",
    "\n",
    "The spatial upscaling technique is applied over homogeneous reaches of the flood defense, where \"homogeneous\" means the statistical characteristics remain constant.\n",
    "\n",
    "First, let's import the necessary packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c0d851fb",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from probabilistic_library import ReliabilityProject, DistributionType, ReliabilityMethod, LengthEffectProject\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00bceae",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Next, we define a simple limit state function. In this example, we assume that this limit state function describes a failure mechanism of a flood defence.\n",
    "\n",
    "$Z = 1.9 - (a+b)$\n",
    "\n",
    "This is a linear model involving two variables, $a$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ea8b7c51",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from utils.models import linear_a_b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bf8bb1c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "To perform a reliability analysis, we create a `ReliabilityProject()` and specify the limit state function (model). In this example, we assume that the variables `a` and `b` are normally distributed. We use the `form` calculation technique to derive the failure probability $P(Z<0)$, which corresponds to the failure probability for a cross-section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "42d26675",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reliability results for a cross-section:\n",
      "Reliability (FORM)\n",
      " Reliability index = 2.051\n",
      " Probability of failure = 0.02015\n",
      " Convergence = 0.00801 (converged)\n",
      " Model runs = 15\n",
      "Alpha values:\n",
      " a: alpha = -0.7071, x = 1.45\n",
      " b: alpha = -0.7071, x = 0.45\n",
      "\n"
     ]
    }
   ],
   "source": [
    "project = ReliabilityProject()\n",
    "project.model = linear_a_b\n",
    "\n",
    "project.variables[\"a\"].distribution = DistributionType.normal\n",
    "project.variables[\"a\"].mean = 0.0\n",
    "project.variables[\"a\"].deviation = 1.0\n",
    "project.variables[\"b\"].distribution = DistributionType.normal\n",
    "project.variables[\"b\"].mean = -1.0\n",
    "project.variables[\"b\"].deviation = 1.0\n",
    "\n",
    "project.settings.reliability_method = ReliabilityMethod.form\n",
    "project.settings.relaxation_factor = 0.75\n",
    "project.settings.maximum_iterations = 50\n",
    "project.settings.epsilon_beta = 0.01\n",
    "\n",
    "project.run()\n",
    "dp_cross_section = project.design_point\n",
    "pf_cross_section = dp_cross_section.probability_failure\n",
    "\n",
    "print(\"Reliability results for a cross-section:\")\n",
    "project.design_point.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85f07274",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "In the probabilistic library, the spatial correlation of a random variable is described by the following autocorrelation function:\n",
    "\n",
    "$\\rho_x + (1-\\rho_x)\\cdot\\exp(-x^2/d_x^2)$\n",
    "\n",
    "where: <br>\n",
    "$x$ - distance from the cross-section (m) <br>\n",
    "$d_x$ - spatial correlation length (m) <br>\n",
    "$\\rho_x$ - minimum correlation of the variable between two locations of the same (homogeneous) segment (-) <br>\n",
    "\n",
    "The parameter $d_x$ determines how quickly the correlation of the variable decreases over distance. Both parameters, $d_x$ and $\\rho_x$, need to be determined for each variable based on a combination of measurements and expert judgment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cc97b62d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def autocorrelation(x, d_x, rho_x):\n",
    "    return rho_x + (1-rho_x)*np.exp(-x**2/d_x**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b1c61ae",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Let's assume that $d_x$ is $100$ and $200$ meters, respectively, for `a` and `b`, while $\\rho_x$ is $0.45$ and $0.55$, respectively. Then the corresponding autocorrelation functions are as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "32db3c8e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "gallery",
     "reliability"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_x = [100.0, 200.0]\n",
    "rho_x = [0.45, 0.55]\n",
    "x = np.arange(0.0, 1000.0, 10.0)\n",
    "\n",
    "autocorr_a = [autocorrelation(val, d_x[0], rho_x[0]) for val in x]\n",
    "autocorr_b = [autocorrelation(val, d_x[1], rho_x[1]) for val in x]\n",
    "\n",
    "plt.plot(x, autocorr_a, label='variable a')\n",
    "plt.plot(x, autocorr_b, label='variable b')\n",
    "plt.ylim([0, 1])\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.ylabel('auto-correlation [-]')\n",
    "plt.xlabel('distance from the cross-section [m]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36b00f34",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "The goal is to derive the failure probability for a section with a length greater than $0$ meters. To account for the spatial correlation, we define a `LengthEffectProject()`. We specify the cross-sectional results and the spatial correlation parameters $d_x$ and $\\rho_x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d8e303a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "length_effect = LengthEffectProject()\n",
    "\n",
    "length_effect.design_point_cross_section = dp_cross_section\n",
    "length_effect.correlation_lengths = d_x\n",
    "length_effect.correlation_matrix[\"a\"] = rho_x[0]\n",
    "length_effect.correlation_matrix[\"b\"] = rho_x[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2c7a00e",
   "metadata": {},
   "source": [
    "We run the reliability calculations for different section lengths using `length_effect.run()`. The results are stored in `length_effect.design_point`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "809367cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'section length [m]')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "section_length = np.arange(1.0, 2000.0, 10.0)\n",
    "beta_section = []\n",
    "pf_section = []\n",
    "\n",
    "for val in section_length:\n",
    "\n",
    "    length_effect.length = val\n",
    "    length_effect.run()\n",
    "    dp_section = length_effect.design_point\n",
    "    beta_section.append(dp_section.reliability_index)\n",
    "    pf_section.append(dp_section.probability_failure)\n",
    "\n",
    "plt.plot(section_length, beta_section)\n",
    "plt.grid()\n",
    "plt.ylabel('reliability index [-]')\n",
    "plt.xlabel('section length [m]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01a842fc",
   "metadata": {},
   "source": [
    "The length effect is defined as the ratio of the failure probability of a section to the failure probability of a cross-section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "53cc9de6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'section length [m]')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length_effect = [val/pf_cross_section for val in pf_section]\n",
    "\n",
    "plt.plot(section_length, length_effect)\n",
    "plt.grid()\n",
    "plt.ylabel('length-effect [-]')\n",
    "plt.xlabel('section length [m]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dce2e372",
   "metadata": {},
   "source": [
    "It is also possible to gain insight into the intermediate results of the length-effect calculations. These include:\n",
    "* $\\Delta L$ - length of equal components in the considered section (m)\n",
    "* $\\rho_Z$ - residual correlation length of the limit state function (-)\n",
    "* $d_Z$ - correlation length of the limit state function (m)\n",
    "\n",
    "These intermediate results are stored in the `messages` attribute of a `design_point`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "62fcd112",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intermediate results: Delta L = 150.180655; rhoZ = 0.500000; dZ = 122.859023\n"
     ]
    }
   ],
   "source": [
    "if (len(dp_section.messages)> 0):\n",
    "    print(dp_section.messages[0].text)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}