twenty_fitting_pier_compressive_failure_probability_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#https://stackoverflow.com/questions/73071058/fit-data-with-a-lognormal-function-via-maximum-likelihood-estimators/73112103#73112103\n",
    "#https://towardsdatascience.com/log-normal-distribution-a-simple-explanation-7605864fb67c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "import numpy as np\n",
    "from scipy import optimize, stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stored variables and their in-db values:\n",
      "arch_capacity_geometry_variables                   -> {'b': 1, 't': 0.5, 'e': 0.08333333333333333}\n",
      "arch_compressive_demand_thrust                     -> array([525.16363953, 492.96620384, 530.32649903, .\n",
      "arch_compressive_failure_points_number             -> [69, 69, 69, 69, 259, 1880, 15286, 74760, 99995, 1\n",
      "compressive_demand_from_arch                       -> {'H_a': array([40.52707914, 33.18183373, 41.704889\n",
      "compressive_demand_from_backfill                   -> {'H_a': array([246.2211967, 246.2211967, 246.22119\n",
      "compressive_demand_from_parapet                    -> {'H_a': array([11.18458987,  9.15746235, 11.509639\n",
      "compressive_demand_from_spandrel_walls             -> {'H_a': array([56.10087926, 45.93299314, 57.731300\n",
      "compressive_resistance_realisations                -> array([6.07743858, 4.41155859, 6.34456247, ..., 6.\n",
      "compressive_resistances                            -> [4.691352777703492, 6.2279668592488475]\n",
      "condition_factor                                   -> [[0.7200000000000001, 0.7200000000000001, 0.720000\n",
      "convergence_simulation_number                      -> 100000\n",
      "df_arch_compressive_capacity                       ->    scour depth  condition factor           0      \n",
      "masonry_unit_weight_realisations                   -> array([21.64551063, 17.72241548, 22.27457902, ...,\n",
      "pier_local_scour_depth                             -> [[0.0, 0.2888888888888889, 0.5777777777777778, 0.8\n"
     ]
    }
   ],
   "source": [
    "%store"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "%store -r pier_local_scour_depth\n",
    "%store -r arch_compressive_failure_points_number\n",
    "%store -r convergence_simulation_number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Failure probability data from Baker (2015), https://doi.org/10.1193/021113EQS025M\n",
    "# im = np.array([0.2, 0.3, 0.4, 0.6, 0.7, 0.8, 0.9, 1])\n",
    "# number_of_analyses = np.array([40, 40, 40, 40, 40, 40, 40, 40])\n",
    "# number_of_collapses = np.array([0, 0, 0, 4, 6, 13, 12, 16])\n",
    "\n",
    "#Failure probability data from Qeshta et al., 2021, https://doi.org/10.1080/15732479.2021.1892774\n",
    "# im = np.array([4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.46])\n",
    "# number_of_analyses = np.array([10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) \n",
    "# number_of_collapses = np.array([0, 0, 0, 0, 0, 0, 1, 3, 7, 9, 10])\n",
    "\n",
    "#Failure probability data from \"twelve_arch_compressive_limit_state_equation.ipynb\"\n",
    "# im = np.array([0.289, 0.578, 0.867, 1.156, 1.444, 1.733, 2.022, 2.311, 2.6])\n",
    "# number_of_analyses = np.array([100_000, 100_000, 100_000, 100_000, 100_000, 100_000, 100_000, 100_000, 100_000])\n",
    "# number_of_collapses = np.array([69, 69, 69, 259, 1880, 15286, 74760, 99995, 100_000])\n",
    "\n",
    "#Failure probability data from \"twelve_arch_compressive_limit_state_equation.ipynb\" and other stored values\n",
    "im = np.array(pier_local_scour_depth[0])\n",
    "number_of_analyses = np.ones(len(pier_local_scour_depth[0]))*convergence_simulation_number\n",
    "number_of_collapses = np.array(arch_compressive_failure_points_number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "teta                beta                log_likelihood_sum  \n"
     ]
    }
   ],
   "source": [
    "np.seterr(divide = 'ignore') #equal to IFERROR function of EXCEL\n",
    "im_log = np.log(im)\n",
    "\n",
    "FORMAT_STRING = \"{:<20}{:<20}{:<20}\"\n",
    "print(FORMAT_STRING.format(\"teta\", \"beta\", \"log_likelihood_sum\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def neg_log_likelihood_sum(params, im_l, no_a, no_c):\n",
    "    \n",
    "    teta, beta = params\n",
    "    theoretical_fragility_function = stats.norm(np.log(teta), beta).cdf(im_l)\n",
    "    likelihood = stats.binom.pmf(no_c, no_a, theoretical_fragility_function)\n",
    "    #https://stackoverflow.com/questions/21610198/runtimewarning-divide-by-zero-encountered-in-log\n",
    "    log_likelihood = np.log(likelihood)\n",
    "    log_likelihood_sum = np.sum(log_likelihood)\n",
    "\n",
    "    print(FORMAT_STRING.format(teta, beta, log_likelihood_sum))\n",
    "    \n",
    "    return -log_likelihood_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_optimize.py:790: RuntimeWarning: invalid value encountered in subtract\n",
      "  np.max(np.abs(fsim[0] - fsim[1:])) <= fatol):\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "0.5                 0.1                 -inf                \n",
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      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      "0.5                 0.1                 -inf                \n",
      " final_simplex: (array([[0.5, 0.1],\n",
      "       [0.5, 0.1],\n",
      "       [0.5, 0.1]]), array([inf, inf, inf]))\n",
      "           fun: inf\n",
      "       message: 'Maximum number of iterations has been exceeded.'\n",
      "          nfev: 3999\n",
      "           nit: 1000\n",
      "        status: 2\n",
      "       success: False\n",
      "             x: array([0.5, 0.1])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\fn20944\\AppData\\Local\\Temp\\ipykernel_9080\\3676437843.py:9: RuntimeWarning: Maximum number of iterations has been exceeded.\n",
      "  res = optimize.minimize(neg_log_likelihood_sum_partial, x0 = guess_values,\n"
     ]
    }
   ],
   "source": [
    "guess_values = (0.5, 0.1) #guess_values = (1.6, 0.1) for Baker and my data, while guess_values = (8, 0.1) for Qeshta et al. (2021) data. \n",
    "params_bounds = ((0.01, None), (0.01, None)) #teta and beta must be positive because of the problem physics\n",
    "desired_tolerance = 1e-6\n",
    "number_of_iterations = 1000\n",
    "\n",
    "neg_log_likelihood_sum_partial = partial(neg_log_likelihood_sum, im_l=im_log, no_a=number_of_analyses, no_c=number_of_collapses)\n",
    "\n",
    "#https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html\n",
    "res = optimize.minimize(neg_log_likelihood_sum_partial, x0 = guess_values, \n",
    "                method=\"Nelder-Mead\", options={'maxiter':number_of_iterations, \n",
    "                'disp':True}, bounds = params_bounds, tol = desired_tolerance)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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