diff --git a/Applications/Equilibrium Points.ipynb b/Applications/Equilibrium Points.ipynb new file mode 100644 index 00000000..4604f1bf --- /dev/null +++ b/Applications/Equilibrium Points.ipynb @@ -0,0 +1,464 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "629d62ed", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "Finding and analyzing equilibrium points of ODE systems is a key part of stability analysis. However, finding equilibriums get increasingly difficult the more complex a system gets. Thankfully, any high order system of ODEs can be turned into a first order system of N equations with N unknowns. \n", + "\n", + "Since this system is square, Yroots can be used to search for equilibrium points within a region. Yroots prove to be especially useful in this area as Yroots can also handle non-polynomial equations, provided each equation is smooth." + ] + }, + { + "cell_type": "markdown", + "id": "46c53c36", + "metadata": {}, + "source": [ + "Here is an example taken from the paper *Nonlinear analysis and control strategy evaluation of vehicle three degrees of freedom planar motion stability.* from 2010. In the paper, we are given a 2 Degree of Freedom (DOF) vehicle model described by the equations\n", + "\n", + "
\n", + "\n", + "$\\LARGE \\dot v_y = -v_{x_{0}} \\omega + \\frac{F_{sf}\\cos\\delta_f+F_{sr}}{m}$\n", + "\n", + "$\\LARGE \\dot \\omega = \\frac{F_{sf} \\cos\\delta_f \\cdot l_f - F_{sr} \\cdot l_r}{I_z}$\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "7180da7d", + "metadata": {}, + "source": [ + "where $v_y$ is lateral velocity, $\\omega$ is yaw velocity, $\\delta_f$/$\\delta_r$ is front/rear wheel steering angle, $m$ is mass of vehicle, $I_z$ is moment of inertia, $l_f$/$l_r$ is the distance from front/rear wheel to center of mass, and $F_s$ is the lateral tire force as described by the figure below.\n" + ] + }, + { + "attachments": { + "vehicle dynamics.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "id": "2eea2410", + "metadata": {}, + "source": [ + "![vehicle dynamics.png]()" + ] + }, + { + "cell_type": "markdown", + "id": "0c78a12b", + "metadata": {}, + "source": [ + "The respective force $F$ on the tires are calculated using the Pacejka's Magic Tire Formula\n", + "\n", + "
\n", + "\n", + "$F=D*sin(C*arctan(B\\alpha-E(B\\alpha-arctan(B\\alpha))))$\n", + "\n", + "
\n", + "\n", + "and tire slip angle $\\alpha$ is given by\n", + "\n", + "
\n", + "\n", + "$\\large \\alpha_f = \\delta_f - arctan(v_y + \\frac{\\omega l_f}{v_x})$\n", + "\n", + "$\\large \\alpha_r = \\delta_r - arctan(v_y - \\frac{\\omega l_r}{v_x})$\n", + "\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "7779ecdf", + "metadata": {}, + "source": [ + "This model is especially meaningful in that both equations utilize arctan, which cannot be solved by algorithms such as Bertini. The aforementioned paper describes a method of finding the equilibrium points of this system by utilizing a hybrid method of Genetic Algorithm and Newton’s Method. \n", + "\n", + "Below, we compare the average solve time and max residual of YRoots and a naive implementation of the hybrid method proposed by the paper." + ] + }, + { + "cell_type": "markdown", + "id": "9a7e84de", + "metadata": {}, + "source": [ + "## Setting Up the System" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2f26a90f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import yroots as yr\n", + "from time import time\n", + "import matplotlib.pyplot as plt\n", + "import pygad" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1a2550b8", + "metadata": {}, + "outputs": [], + "source": [ + "# Vehicle Control Parameters\n", + "vx = 20 # longitudinal velocity\n", + "df = 0.008 # front wheel sterring angle\n", + "\n", + "# Vehicle Sturcture Parameters\n", + "d_r = 0 # rear wheel steering angle\n", + "m = 1500 # mass\n", + "I_z = 3000 # moment of inertia\n", + "l_f = 1.2 # distance from front wheel to center of mass\n", + "l_r = 1.3 # distance from rear wheel to center of mass\n", + "\n", + "# Tire Force Parameter ([B, C, D, E])\n", + "lf_val = [11.275, 1.56, 2576.8, 0.4109]\n", + "sf_val = [11.275, 1.56, 2574.7, -1.999]\n", + "lr_val = [18.631, 1.56, 1749.6, 0.4108]\n", + "sr_val = [18.631, 1.56, 1749.7, -1.7908]\n", + "\n", + "# Tire slip angle\n", + "alpha_f = lambda vy, w: df - np.arctan2((vy + w*l_f) / vx)\n", + "alpha_r = lambda vy, w: - np.arctan2((vy - w*l_r) / vx)\n", + "\n", + "# Magic Formula\n", + "F = lambda B, C, D, E, alpha: D*np.sin(C*np.arctan2((1 - E)*B*alpha + E*np.arctan2(B*alpha)))\n", + "\n", + "F_lf = lambda vy, w: F(*lf_val, alpha_f(vy, w)) # longitudinal tire force of the front wheels\n", + "F_sf = lambda vy, w: F(*sf_val, alpha_f(vy, w)) # lateral tire force of the front wheels\n", + "F_lr = lambda vy, w: F(*lr_val, alpha_r(vy, w)) # longitudinal tire force of the rear wheels\n", + "F_sr = lambda vy, w: F(*sr_val, alpha_r(vy, w)) # lateral tire force of the rear wheels\n", + "\n", + "\n", + "# Equilibrium System\n", + "f_v_y = lambda vy, w: - vx*w + (F_sf(vy, w)*np.cos(df) + F_sr(vy, w)) / m\n", + "f_w = lambda vy, w: (F_sf(vy, w) * l_f * np.cos(df) - F_sr(vy, w) * l_r) / I_z" + ] + }, + { + "cell_type": "markdown", + "id": "09f59bcb", + "metadata": {}, + "source": [ + "## Using Yroots" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "58ba3eec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Avg time to solve: 0.29134779930114746\n", + "Max residual of solutions: 6.252776074688882e-13\n", + "Roots:\n", + "[[-0.87868266 0.12041469]\n", + " [-0.19185052 0.04338104]\n", + " [ 1.20053088 -0.12052591]]\n" + ] + } + ], + "source": [ + "a = [-5, -1] # Lower boundaries of v_y, omega\n", + "b = [5, 1] # Upper boundaries of v_y, omega\n", + "funcs = [f_v_y, f_w]\n", + "\n", + "yr.solve(funcs, a, b)\n", + "\n", + "avg_time = 0\n", + "for _ in range(50):\n", + " start = time()\n", + " roots = yr.solve(funcs, a, b)\n", + " avg_time += time() - start\n", + "\n", + "print(\"Avg time to solve:\", avg_time / 50)\n", + "\n", + "residue = []\n", + "for func in funcs:\n", + " for root in roots:\n", + " residue.append(func(*root))\n", + "\n", + "print(\"Max residual of solutions:\", max(residue))\n", + "print(\"Roots:\")\n", + "print(roots)" + ] + }, + { + "cell_type": "markdown", + "id": "d4203c19", + "metadata": {}, + "source": [ + "## Using the hybrid method" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "d5346f57", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/yroots/.local/lib/python3.11/site-packages/pygad/pygad.py:733: UserWarning: The percentage of genes to mutate (mutation_percent_genes=10) resulted in selecting (0) genes. The number of genes to mutate is set to 1 (mutation_num_genes=1).\n", + "If you do not want to mutate any gene, please set mutation_type=None.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average time = 1.01166841506958\n", + "Max residual of solutions: 3.8763214860182416e-11\n", + "Roots:\n", + "[[ 1.20053088 -0.12052591]\n", + " [-0.87868266 0.12041469]\n", + " [-0.19185052 0.04338104]]\n" + ] + } + ], + "source": [ + "funcs2 = [f_v_y, f_w]\n", + "\n", + "def F_vec(x):\n", + " vy, w = x\n", + " return np.array([f(vy, w) for f in funcs2], dtype=float)\n", + "\n", + "def numerical_jacobian(F, x, h=1e-6):\n", + " x = np.asarray(x, dtype=float)\n", + " n = len(x)\n", + " J = np.zeros((n, n))\n", + " for j in range(n):\n", + " e = np.zeros(n); e[j] = 1.0\n", + " J[:, j] = (F(x + h*e) - F(x - h*e)) / (2*h)\n", + " return J\n", + "\n", + "def damped_newton(F, x0, tol=1e-10, max_iter=50):\n", + " x = np.array(x0, dtype=float)\n", + "\n", + " def merit(r): return 0.5 * float(r @ r)\n", + "\n", + " r = F(x); phi = merit(r)\n", + " for k in range(max_iter):\n", + " if np.linalg.norm(r) < tol:\n", + " return x, True\n", + "\n", + " J = numerical_jacobian(F, x)\n", + " dx, *_ = np.linalg.lstsq(J, -r, rcond=None)\n", + "\n", + " # backtracking\n", + " alpha = 1.0\n", + " for _ in range(20):\n", + " x_new = x + alpha*dx\n", + " r_new = F(x_new)\n", + " if merit(r_new) < phi:\n", + " x, r, phi = x_new, r_new, merit(r_new)\n", + " break\n", + " alpha *= 0.5\n", + " else:\n", + " return x, False\n", + "\n", + " return x, False\n", + "\n", + "def unique_roots(cands, eps=1e-5):\n", + " roots = []\n", + " for x in cands:\n", + " if not any(np.linalg.norm(x - r) < eps for r in roots):\n", + " roots.append(x)\n", + " return np.array(roots)\n", + "\n", + "def objective(x):\n", + " r = F_vec(x)\n", + " return float(r @ r)\n", + "\n", + "def fitness_func(ga_instance, solution, solution_idx):\n", + " return 1.0 / (1.0 + objective(solution))\n", + "\n", + "timer = 0\n", + "for _ in range(50):\n", + " start = time()\n", + " ga = pygad.GA(\n", + " num_generations=300,\n", + " sol_per_pop=80,\n", + " num_parents_mating=20,\n", + " num_genes=2,\n", + " gene_space=[{\"low\": -5, \"high\": 5}, # vy bounds\n", + " {\"low\": -1, \"high\": 1}], # w bounds\n", + " fitness_func=fitness_func,\n", + " random_seed=0\n", + " )\n", + "\n", + " ga.run()\n", + "\n", + " x0, _, _ = ga.best_solution()\n", + " timer += time() - start\n", + "\n", + " x0 = np.array(x0, dtype=float)\n", + "\n", + " start = time()\n", + " # ---- after you run ga.run() ----\n", + " pop = np.array(ga.population, dtype=float) # (sol_per_pop, 2)\n", + "\n", + " # score population by residual norm (smaller = better)\n", + " scores = np.array([np.linalg.norm(F_vec(ind)) for ind in pop])\n", + " idx = np.argsort(scores)\n", + "\n", + " # take top K candidates and polish\n", + " K = min(30, len(pop))\n", + " polished = []\n", + " for i in idx[:K]:\n", + " x_star, ok = damped_newton(F_vec, pop[i])\n", + " if ok and np.linalg.norm(F_vec(x_star)) < 1e-8:\n", + " polished.append(x_star)\n", + "\n", + " polished = np.array(polished)\n", + " roots = unique_roots(polished, eps=1e-5)\n", + "\n", + " timer += time() - start \n", + "\n", + "print(f\"Average time = {timer / 50}\")\n", + "\n", + "residue = []\n", + "for func in funcs2:\n", + " for root in roots:\n", + " residue.append(func(*root))\n", + "\n", + "print(\"Max residual of solutions:\", max(residue))\n", + "print(\"Roots:\")\n", + "print(roots)" + ] + }, + { + "cell_type": "markdown", + "id": "ff0ba54b", + "metadata": {}, + "source": [ + "## Graph of EQ Solutions" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "7037adcf", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def numerical_jacobian(funcs, x, h=1e-6):\n", + " x = np.asarray(x, dtype=float)\n", + " n = x.size\n", + " m = len(funcs)\n", + " J = np.zeros((m, n))\n", + " for j in range(n):\n", + " e = np.zeros(n); e[j] = 1.0\n", + " xp = x + h*e\n", + " xm = x - h*e\n", + " fp = np.array([f(*xp) for f in funcs], dtype=float)\n", + " fm = np.array([f(*xm) for f in funcs], dtype=float)\n", + " J[:, j] = (fp - fm) / (2*h)\n", + " return J\n", + "\n", + "def classify_equilibria(funcs, roots, h=1e-6, tol=1e-8):\n", + " stable = []\n", + " unstable = []\n", + " inconclusive = []\n", + "\n", + " for r in roots:\n", + " J = numerical_jacobian(funcs, r, h=h)\n", + " eig = np.linalg.eigvals(J)\n", + " re = np.real(eig)\n", + "\n", + " if np.any(re > tol):\n", + " unstable.append(r)\n", + " elif np.all(re < -tol):\n", + " stable.append(r)\n", + " else:\n", + " inconclusive.append(r)\n", + "\n", + " return np.array(stable), np.array(unstable), np.array(inconclusive)\n", + "\n", + "stable, unstable, inconclusive = classify_equilibria(funcs, roots)\n", + "\n", + "y = np.linspace(a[0], b[0], 50) \n", + "w = np.linspace(a[1], b[1], 50)\n", + "Y, W = np.meshgrid(y, w)\n", + "\n", + "dy = np.zeros_like(Y)\n", + "dw = np.zeros_like(W)\n", + "\n", + "for i in range(Y.shape[0]):\n", + " for j in range(W.shape[1]):\n", + " # Evaluate the ODEs at each grid point (X[i, j], Y[i, j])\n", + " y_ij = Y[i, j]\n", + " w_ij = W[i, j]\n", + "\n", + " dy[i, j] = f_v_y(y_ij, w_ij)\n", + " dw[i, j] = f_w(y_ij, w_ij)\n", + "\n", + "# Plot the phase portrait\n", + "plt.figure(figsize=(8, 6))\n", + "plt.streamplot(Y, W, dy, dw, density=1.5, color='b', linewidth=1.5)\n", + "\n", + "if stable.ndim > 1:\n", + " plt.scatter(stable[:, 0], stable[:, 1], label=\"Stable\")\n", + "if unstable.ndim > 1:\n", + " plt.scatter(unstable[:, 0], unstable[:, 1], label=\"Unstable\")\n", + "if inconclusive.ndim > 1:\n", + " plt.scatter(inconclusive[:, 0], inconclusive[:, 1], label=\"Inconclusive\")\n", + "plt.legend()\n", + "plt.xlabel('$v_y$')\n", + "plt.ylabel('$\\omega$')\n", + "plt.title(\"Equilibrium solutions of System\")\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/README.md b/README.md index 474a69d1..184d8c4f 100644 --- a/README.md +++ b/README.md @@ -54,7 +54,12 @@ b = np.array([0,1]) #upper bounds on x and y yr.solve([f,g],a,b) ``` -If the system includes polynomials, there are specialized `Polynomial` objects which may be allow for faster solving. See [YRoots Tutorial](https://github.com/tylerjarvis/RootFinding/blob/main/YRootsTutorial.ipynb) and [YRoots Demo](https://github.com/tylerjarvis/RootFinding/blob/main/YRootsDemo.ipynb) for more details. +If the system includes polynomials, there are specialized `Polynomial` objects which may be allow for faster solving. See [Combined Notebook](https://github.com/tylerjarvis/RootFinding/blob/main/CombinedNotebook.ipynb) for more details. + + +## Examples of Applications +Below is a list of Jupyter notebooks in which YRoots has been used to solve real-world problems: +- [Solving Equilibrium Points of First Order ODE Systems] (https://github.com/tylerjarvis/RootFinding/blob/main/Applications/Equilibrium Points.ipynb) ## Contributing Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.