fractional_operators.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples of using Variable-Order Fractional Calculus (VO-FC) operators for integration and differentiation of time series signals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Packages import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper functions definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_vector_generator(sample_time, simulation_end_time):\n",
    "    number_of_samples = int(simulation_end_time / sample_time) + 1\n",
    "    print(\"___________________________________\")\n",
    "    print(f\"Simulation time step: {sample_time}\")\n",
    "    print(f\"Simulation end time: {simulation_end_time}\")\n",
    "    print(f\"Number of simulation samples: {number_of_samples}\")\n",
    "    print(\"___________________________________\")\n",
    "    return np.arange(0, number_of_samples, 1) * sample_time\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Class definition of an Variable-Order Fractional Calculus (VO-FC) operator  \n",
    "The class was built based on the modified Grünwald-Letnikov definition given below [[1]](https://ieeexplore.ieee.org/abstract/document/9684478)\n",
    "$$\n",
    "\\mathscr {D}^{\\alpha (t)}_{f} f(t) \\approx h^{-\\alpha (t)} \\sum _{k=0}^{\\infty } w_{k}(t) f(t-kh)\n",
    "$$  \n",
    "where $w_k(t)$ are coefficients that can be expressed recursively as:  \n",
    "$$\n",
    "\\begin{align*} w_{0}(t)=&1, \\\\ w_{j}(t)=&\\left ({1-\\frac {\\alpha (t)+1}{j}}\\right)w_{j-1}, \\quad \\text {for} ~j=1,2,\\ldots\\tag{9}\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fractional_weights(alpha, m):\n",
    "    if m == 0:\n",
    "        w = np.ones(1)\n",
    "        return w\n",
    "    else:\n",
    "        w = np.zeros(m + 1)\n",
    "        w[0] = 1.0\n",
    "        for i in range(1, m + 1):\n",
    "            w[i] = (1 - ((alpha + 1) / i)) * w[i - 1]\n",
    "        return w\n",
    "\n",
    "\n",
    "class VofidGl:\n",
    "    __slots__ = [\"order\", \"input_signal\", \"model\", \"step\", \"input_len\", \"model_state\", \"dx_dt_memory\"]\n",
    "\n",
    "    def __init__(self, order, input_signal, model):\n",
    "        self.order = order\n",
    "        self.step = model.ts\n",
    "        self.input_signal = input_signal\n",
    "        self.input_len = len(input_signal)\n",
    "        self.model = model\n",
    "        self.model_state = np.zeros_like(input_signal)\n",
    "        self.dx_dt_memory = np.zeros_like(input_signal)\n",
    "\n",
    "    def sim(self):\n",
    "        for i in range(self.input_len - 1):\n",
    "            self.dx_dt_memory[i] = self.model.sim_dx(self.input_signal[i], self.model_state[i])\n",
    "            w = fractional_weights(-self.order[i], i)  # Order changes sign due to integration\n",
    "            self.model_state[i + 1] = (self.step ** (self.order[i])) * (\n",
    "                w @ np.flip(self.dx_dt_memory[: i + 1])\n",
    "            )  # Order changes sign due to integration\n",
    "        return self.model_state\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of simple integrator class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Integrator:\n",
    "    __slots__ = [\"k\", \"ts\", \"state_no\"]\n",
    "\n",
    "    def __init__(self, k, ts, state_no):\n",
    "        self.k = k\n",
    "        self.ts = ts\n",
    "        self.state_no = state_no  # for future implementation\n",
    "\n",
    "    def sim_dx(self, u, x):\n",
    "        dx = self.k * u\n",
    "        return dx\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization  \n",
    "Sample time selection and time vector definition "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "___________________________________\n",
      "Simulation time step: 0.01\n",
      "Simulation end time: 10\n",
      "Number of simulation samples: 1001\n",
      "___________________________________\n"
     ]
    }
   ],
   "source": [
    "dt = 0.01\n",
    "time_vector = time_vector_generator(dt, 10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creation of order and input signals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "ord_signal = np.ones_like(time_vector)\n",
    "idx = np.arange(1001)\n",
    "ord_signal[idx <= 500] = 1.0\n",
    "ord_signal[idx > 500] = -1.0\n",
    "input_signal = np.linspace(0, 10, 1001)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creation of integrator and VO-FC operator instances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "integ = Integrator(k=1, ts=dt, state_no=1)\n",
    "deriv = VofidGl(ord_signal, input_signal, integ)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "response = deriv.sim()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot of results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=2, ncols=1, figsize=(12, 9))\n",
    "axs[0].plot(time_vector, input_signal, label=\"Input\")\n",
    "axs[0].plot(time_vector, response, label=\"Response\")\n",
    "axs[1].plot(time_vector, ord_signal, label=\"Order\")\n",
    "[ax.grid() for ax in axs]\n",
    "[ax.set_xlabel(\"Time [s]\") for ax in axs]\n",
    "[ax.legend() for ax in axs]\n",
    "fig.set_tight_layout(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] B. Puchalski, \"Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC),\" in IEEE Access, vol. 10, pp. 7989-8004, 2022, doi: [10.1109/ACCESS.2022.3143893](https://ieeexplore.ieee.org/abstract/document/9684478)"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "b846e335854ab72a3b7be38bb41c563297750067dd573b9dd0b51d0e1a332f45"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 64-bit ('.venv': venv)",
   "language": "python",
   "name": "python3"
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