{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### Universidade Federal do Rio Grande do Sul (UFRGS) \n", "Programa de Pós-Graduação em Engenharia Civil (PPGEC) \n", "\n", "# PEC00025: Introduction to Vibration Theory\n", "\n", "\n", "### Class 06 - Numerical integration: finite differences and Duhamel techniques\n", "\n", "[1. Introduction](#section_1) \n", "[2. The finite differences technique](#section_2) \n", "[2.1. Formulation](#section_21) \n", "[2.2. Example](#section_22) \n", "[3. The Duhamel's integral technique](#section_3) \n", "[3.1. Formulation](#section_31) \n", "[3.2. Example](#section_32) \n", "[4. Example: excitation recorded as file](#section_4) \n", "[5. Finite differences for nonlinear equations](#section_5) \n", "[6. Assignment](#section_6) \n", "\n", "---\n", "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020) \n", "_Porto Alegre, RS, Brazil_ \n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# Importing Python modules required for this notebook\n", "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from MRPy import MRPy\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Introduction <a name=\"section_1\"></a> \n", "\n", "Besides the basic conceptual solutions presented in the previous class, in practical cases\n", "where the external force $F(t)$ is arbitrarily defined, the dynamic equilibrium equation must \n", "be numerically solved. \n", "\n", "In this class we present two of the most important integration techniques: \n", "* the central finite differences scheme and \n", "* the Duhamel integral method. \n", "\n", "There is also another useful technique that will be presented after we introduce the\n", "Fourier transform and the frequency domain analysis of linear systems, in the next classes.\n", "For the moment we can state that time domain techniques are mainly used for transient loads,\n", "while frequency domain techniques are maily used for periodic or stationary random loads.\n" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[<matplotlib.lines.Line2D at 0x179110309a0>]]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 1200x800 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = MRPy(np.random.randn(8192) + 0.5*np.sin(2*np.pi*0.5*np.linspace(0,8,8192)), fs=1024)\n", "#x.plot_time()\n", "x.integrate().integrate().plot_time()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. The finite differences technique <a name=\"section_2\"></a> \n", "\n", "### 2.1. Formulation <a name=\"section_21\"></a> \n", "\n", "Although the central finite differences technique may be used to solve the dynamic \n", "equilibrium equation of linear systems, its most important application is in the \n", "solution of _nonlinear systems_. \n", "For linear systems it allows the integration scheme to be _explicit_, what means that the system\n", "state (displacement) in future can be _explicitly_ stated as a function of system state in the past.\n", "To understand this concept, let us discretize the time domain as $t_i = i \\Delta t$, where $\\Delta t$\n", "is the so-called _time step_. \n", "This is depicted in the figure below:\n", "\n", "<img src=\"images/finite_differences.jpg\" alt=\"SDOF system\" width=\"480px\"/>\n", "\n", "Consequently, both the sistem response, $u(t)$, as well as the external load, $F(t)$, can be \n", "now expressed at the discrete time instants, $t_i$, as:\n", "\n", "\\begin{align*}\n", " u_i &= u(t_i) \\\\\n", " F_i &= F(t_i)\n", "\\end{align*}\n", "\n", "From this definitions, the system velocity, $\\dot{u}(t)$, and acceleration, $\\ddot{u}(t)$, can be\n", "approximated through a central finite differences scheme as:\n", "\n", "\\begin{align*}\n", "\\dot{ u}_i &= \\frac{1}{2\\Delta t} \\left( u_{i+1} - u_{i-1} \\right) \\\\\n", "\\ddot{u}_i &= \\frac{1}{ \\Delta t^2} \\left( u_{i+1} - 2u_ {i} + u_{i-1} \\right) \n", "\\end{align*}\n", "\n", "Considering that the dynamic equilibrium equation holds also for a generic time instant $t_i$:\n", "\n", "$$ \\ddot{u}_i + 2 \\zeta \\omega_{\\rm n} \\dot{u}_i + \\omega_{\\rm n}^2 u_i = \\frac{F_i}{m} $$\n", "\n", "the discrete kinematic parameters $\\dot{ u}_i$ and $\\ddot{ u}_i$ can be replaced to give:\n", "\n", "$$ \\frac{1}{ \\Delta t^2} \\left( u_{i+1} - 2u_ {i} + u_{i-1} \\right) +\n", " \\frac{2 \\zeta \\omega_{\\rm n}}{2 \\Delta t} \\left( u_{i+1} - u_{i-1} \\right) + \n", " \\omega_{\\rm n}^2 u_i = \\frac{F_i}{m} $$\n", "\n", "By isolating the future system displacement, $u_{i+1}$, it results:\n", "\n", "$$ u_{i+i} = \\frac{1}{\\beta_1} \\left( \\frac{F_i}{m} + \\beta_2 u_{i-1} - \\beta_3 u_{i} \\right) $$\n", "\n", "with:\n", "\n", "\\begin{align*}\n", "\\beta_1 &= \\frac{1}{\\Delta t} \\left( \\zeta\\omega_{\\rm n} + \\frac{1}{\\Delta t}\\right) \\\\\n", "\\beta_2 &= \\frac{1}{\\Delta t} \\left( \\zeta\\omega_{\\rm n} - \\frac{1}{\\Delta t}\\right) \\\\\n", "\\beta_3 &= \\frac{1}{\\Delta t} \\left( \\Delta t \\omega_{\\rm n}^2 - \\frac{2}{\\Delta t}\\right) \n", "\\end{align*}\n", "\n", "which is an _explicit_ expression of the system response at time $t_{i+1}$ as a function \n", "of system responses at times $t_{i-1}$ and $t_i$.\n", "The initial position, $u_0$, and initial velocity, $v_0 = \\dot{u}_0$, must be provided for \n", "the calculation of system responses at instants $t_0$ and $t_1$. \n", "The position at $t_0$ is the provided value $u_0$ itself, while the position at $t_1$\n", "can be calculated with:\n", "\n", "$$ u_1 = u_0 + v_0 \\Delta t + \\frac{F_0 \\Delta t^2}{2}$$\n", "\n", "The finite differences technique presents a severe restriction for the (arbitrarily chosen)\n", "time step, $\\Delta t$:\n", "\n", "$$ \\Delta t \\leq \\frac{T_{\\rm n}}{4} $$ ou $$ f_{\\rm S} \\geq \\frac{4}{T_{\\rm n}} $$\n", "\n", "Whenever this restriction is not respected, the integration scheme will diverge and become\n", "unstable, leading to increasingly large response. \n", "Furthermore, as one tries to increase $\\Delta t$ to reduce computational time, the technique \n", "loose accuracy quite fast.\n", "For these reasons, Duhamel's technique presented in the next section is usually preferable \n", "for solving linear systems.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2. Example of application with ``MRPy``\n", "\n", "The formulation above is implemented as a method for the ``MRPy`` class, as exemplified\n", "in the following example with a unit step loading.\n", "\n", "Firstly, it is necessary to define the mechanical properties of the sdof system.\n", "Let us assume that:\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "m = 1.0 # system mass in kg\n", "fn = 1.0 # natural frequency in Hz\n", "zt = 0.02 # damping as ratio of critical\n", "\n", "u0 = 0. # initial displacement (m)\n", "v0 = 0. # initial velocity (m/s)\n", "\n", "F0 = 2. # external force magnitude (N)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once the system properties are specified, the unit step loading can be created as a ```MRPy```\n", "instance by calling the appropriate constructor:\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fs = 5.0Hz\n", " Td = 102.4s\n", "\n", " NX = 1\n", " N = 512\n", " M = 257\n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x400 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = F0*MRPy.Heaviside(NX=1, N=512, t0=2.5, fs=1/0.2)\n", "t = H.t_axis()\n", "\n", "plt.figure(1, figsize=(10, 4), clear=True)\n", "plt.plot(t, H[0])\n", "\n", "plt.xlim(0, H.Td); plt.xlabel('time (s)') \n", "plt.ylim(-1., 3.); plt.ylabel('Force (N)') \n", "\n", "plt.grid(True) \n", "\n", "H.printAttrib()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe that the number of time steps ```N``` and the total duration ```Td``` will define the \n", "sampling frequency ```fs``` and the time step will be $\\Delta t = 1/f_{\\rm s}$.\n", "Smaller values of ```N``` will then worse the integration accuracy for a given ```Td```.\n", "\n", "The solution by finite differences is then available through the ```sdof_fdiff``` method:\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x400 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u_FD = H.sdof_fdiff(fn, zt, u0, v0)/m\n", "t = u_FD.t_axis()\n", "\n", "plt.figure(2, figsize=(10, 4), clear=True)\n", "plt.plot(t, u_FD[0])\n", "\n", "#plt.xlim(0., u_FD.Td); plt.xlabel('time (s)') \n", "#plt.ylim(-0.1, 0.2); plt.ylabel('displacement (m)') \n", "\n", "plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be clearly observed that, after the step onset, the system will oscillate\n", "with decreasing amplitude around the static response. \n", "This static displacement can be calculated directly from system stiffness:\n" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Static displacement = 0.051m\n" ] } ], "source": [ "k = m*(2*np.pi*fn)**2 # system stiffness from frequency formula (w^2 = k/m)\n", "u_st = F0/k # displacement for maximum applied force (u = F/k)\n", "\n", "print('Static displacement = {0:0.3f}m'.format(u_st))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us see now what happens whenever the time step is too long in comparison to the system\n", "natural period of vibration. \n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x432 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Tn = 1/fn # natural period in seconds\n", "dt = Tn/10 # very coarse time step (explore this!!!)\n", "N = int(H.Td/dt) # new length for the Heaviside's excitation\n", "\n", "H2 = MRPy.Heaviside(NX=1, N=N, t0=2.5, Td=20)\n", "u2 = H2.sdof_fdiff(fn, zt, u0, v0)/m\n", "t2 = H2.t_axis()\n", "\n", "plt.figure(3, figsize=(10, 6), clear=True)\n", "\n", "plt.subplot(2,1,1)\n", "plt.plot(t2, H2[0]); \n", "plt.xlim(0, H2.Td); plt.xlabel('time (s)') \n", "plt.ylim(-0.5, 1.5); plt.ylabel('Force (N)') \n", "plt.grid(True) \n", "\n", "plt.subplot(2,1,2)\n", "plt.plot(t2, -u2[0]); \n", "plt.xlim( 0.0, u2.Td); plt.xlabel('time (s)') \n", "plt.ylim(-0.05, 0.01); plt.ylabel('displacement (m)') \n", "plt.grid(True) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we choose $\\Delta t < T_{\\rm n}$, the solution has diverged!\n", "\n", "To make full use of the Jupyter notebook concept, try now changing the fraction of \n", "$T_{\\rm n}$ used to define the time step in the example above. \n", "What is the worst acceptable accuracy?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. The Duhamel's integral technique <a name=\"section_3\"></a> \n", "\n", "\n", "### 3.1. Formulation <a name=\"section_31\"></a> \n", "\n", "The numerical solution by the Duhamel's integral technique is restricted to linear systems.\n", "It relies on the superposition of system responses to a sequence on impulses $F(\\tau) \\, d\\tau$.\n", "It has been seen that the general solution of the equilibrium equation of a sdof system\n", "subjected to a general load $F(t)$ is given by the convolution of this load with the \n", "impulse response:\n", "\n", "$$ u(t) = u_0(t) + \\frac{1}{m \\omega_{\\rm D}} \n", " \\int_0^t \\exp \\left[ -\\zeta\\omega_{\\rm n}(t - \\tau) \\right] \\;\n", " \\sin \\omega_{\\rm D} (t - \\tau) \\; F(\\tau) \\; d\\tau $$\n", "\n", "where $u_0(t)$ is the system response to the initial conditions.\n", "Considering now the trigonometric identity:\n", "\n", "$$ \\sin \\omega_{\\rm D} (t - \\tau) = \\sin \\omega_{\\rm D}t \\; \\sin \\omega_{\\rm D}\\tau -\n", " \\cos \\omega_{\\rm D}t \\; \\cos \\omega_{\\rm D}\\tau $$\n", "\n", "and disregarding for a moment the initial conditions leads to:\n", "\n", "$$ u(t) = \\frac{1}{m \\omega_{\\rm D}} \\; \\left[\n", " \\frac{A(t) \\sin \\omega_{\\rm D}t - B(t) \\cos \\omega_{\\rm D}t}\n", " {\\exp ( -\\zeta\\omega_{\\rm n}t )} \\right] $$\n", "\n", "with:\n", "\n", "\\begin{align*}\n", "A(t) &= \\int_0^t \\exp ( -\\zeta\\omega_{\\rm n}\\tau ) \\;\n", " \\cos \\omega_{\\rm D} \\tau \\; F(\\tau) \\; d\\tau \\\\\n", "B(t) &= \\int_0^t \\exp ( -\\zeta\\omega_{\\rm n}\\tau ) \\;\n", " \\sin \\omega_{\\rm D} \\tau \\; F(\\tau) \\; d\\tau\n", "\\end{align*}\n", "\n", "The reformulations above suggest that a recursive scheme can be used to spare computational\n", "time spent in the calculations of trigonometric functions. \n", "By using the discretized time $\\tau_i = i \\Delta \\tau$ gives the following discrete evaluations:\n", "\n", "\\begin{align*}\n", "e_i &= \\exp ( -\\zeta\\omega_{\\rm n} \\tau_i ) \\\\\n", "s_i &= \\sin \\omega_{\\rm D} \\tau_i \\\\\n", "c_i &= \\cos \\omega_{\\rm D} \\tau_i \\\\\n", "F_i &= F(\\tau_i)\n", "\\end{align*}\n", "\n", "The functions $A_i = A(t_i)$ and $B_i = B(t_i)$ can be readily calculated as\n", "cumulative summations:\n", "\n", "\\begin{align*}\n", "A_i &= \\Delta \\tau \\; \\sum_{j=0}^i e_j c_j F_j \\\\\n", "B_i &= \\Delta \\tau \\; \\sum_{j=0}^i e_j s_j F_j\n", "\\end{align*}\n", "\n", "and the solution is finally obtained as:\n", "\n", "$$ u_i = u_{0i} + \\frac{1}{m \\omega_{\\rm D} } \\left( \\frac{A_i s_i - B_i c_i}{e_i} \\right)$$\n", "\n", "with the response to the initial conditions (displacement $u_0$ and velocity $v_0$) from:\n", "\n", "$$ u_{0i} = \\frac{1}{e_i} \n", " \\left[ u_0 c_i + \n", " \\left( \\frac{v_0 + u_0 \\zeta \\omega_{\\rm n}}{\\omega_{\\rm D}} \\right) s_i \\right]$$\n", "\n", "This is a quite fast computational scheme, for Python can build de time vector and\n", "evaluate de functions through built-in ```numpy``` commands, including the cumulative summation.\n", "Furthermore, the Duhamel technique does not become unstable no matter how coarse the\n", "chosen time step is, although its accuracy may not be ensured in this case.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2. Example of application with ```MRPy```\n", "\n", "The formulation above is also implemented as a method for the ```MRPy``` class, as exemplified\n", "in the following.\n", "The same system properties and unit step loading from previous example are used.\n", "The class method is:\n", "\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x400 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = F0*MRPy.Heaviside(NX=1, N=512, t0=2.5, fs=1/0.4)\n", "t = H.t_axis()\n", "\n", "u_DH = H.sdof_Duhamel(fn, zt, u0, v0)/m\n", "t = u_DH.t_axis()\n", "\n", "plt.figure(4, figsize=(10, 4), clear=True)\n", "plt.plot(t, u_DH[0])\n", "\n", "#plt.xlim(0, u_DH.Td); plt.xlabel('time (s)') \n", "#plt.ylim(-0.5, 0.1); plt.ylabel('displacement (m)') \n", "\n", "plt.grid(True) \n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x432 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Tn = 1/fn # natural period in seconds\n", "dt = Tn/3 # very coarse time step on the verge of instability (explore this!!!)\n", "N = int(H.Td/dt) # new length for the Heaviside's excitation\n", "\n", "H2 = MRPy.Heaviside(NX=1, N=N, t0=2, Td=10)\n", "u2 = H2.sdof_Duhamel(fn, zt, u0, v0)/m\n", "t2 = H2.t_axis()\n", "\n", "plt.figure(5, figsize=(8, 6), clear=True)\n", "\n", "plt.subplot(2,1,1)\n", "plt.plot(t2, H2[0]); \n", "plt.xlim(0, H2.Td); plt.xlabel('time (s)') \n", "plt.ylim(-0.5, 1.5); plt.ylabel('Force (N)') \n", "plt.grid(True) \n", "\n", "plt.subplot(2,1,2)\n", "plt.plot(t2, -u2[0]); \n", "plt.xlim(0, u2.Td); plt.xlabel('time (s)') \n", "plt.ylim(-0.02, 0.08); plt.ylabel('displacement (m)') \n", "plt.grid(True) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the contrary of the diverged solution by finite differences, even by choosing \n", "$\\Delta t < T_{\\rm n}$ does not cause the solution to diverge.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Example: excitation recorded as file <a name=\"section_4\"></a> \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ```MRPy``` class provides a constructor that reads a time series from file. \n", "There are some formatting options and others can be included as needed.\n", "In this example we will read a file recorded with the cell phone app ```iNVH``` by Bosch.\n", "The file has a _.csv_ format with four columns, the first being the sampling time and\n", "the next three being the accelerations along the three measurement axes ($x$, $y$ and $z$).\n", "\n", "Reading the file is a straighforward calling to the ```from_file``` constructor:\n" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 3 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data = MRPy.from_file('resources/data/iNVH001', form='invh').zero_mean()\n", "t = data.t_axis()\n", "\n", "plt.figure(6, figsize=(8, 8), clear=True)\n", "\n", "for kX, acc in enumerate(data):\n", " \n", " plt.subplot(3, 1 ,kX+1)\n", " plt.plot(t, acc)\n", "\n", " plt.xlim(0, data.Td); \n", " plt.ylim(-15, 15);\n", " plt.ylabel('acc{0} (m/s^2)'.format(kX+1)) \n", "\n", " plt.grid(True) \n", "\n", "plt.xlabel('time (s)');\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This data was obtained at the center of a metallic beam subjected to multiple impacts.\n", "We are interested in the acceleration along the $z$ axis, so it can be isolated from the \n", "complete set with:\n" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "az = MRPy(data[2], data.fs).double()\n", "t = az.t_axis()\n", "\n", "plt.figure(7, figsize=(8, 4), clear=True)\n", "plt.plot(t, az[0])\n", "\n", "plt.xlim(0, az.Td); plt.xlabel('time (s)') \n", "plt.ylim(-10, 10); plt.ylabel('a_z (m/s^2)') \n", "\n", "plt.grid(True) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now this acceleration will be applied as a basis excitation to a sdof system with\n", "the same properties as defined in the previous sections.\n", "The solutions by finite differences and Duhamel are compared:\n" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "u_FD = az.sdof_fdiff (fn, zt, u0, v0)\n", "u_DH = az.sdof_Duhamel(fn, zt, u0, v0)\n", "\n", "plt.figure(8, figsize=(10, 4), clear=True)\n", "plt.plot(t, u_FD[0], 'r', t, u_DH[0], 'b')\n", "\n", "#plt.xlim(0, az.Td); plt.xlabel('time (s)') \n", "#plt.ylim(-0.015, 0.015); plt.ylabel('displacement (m)') \n", "\n", "plt.grid(True) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that both techniques yield almos the same results, so let us take a look at the error:" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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zZmajovMfmdkpNZU1s9Zm9rqZLY6+too5d2uUv8DMLo5J72lmH0fnRqUSOGVt3w4XXghmcMkl8PbbYW9ErPnzwzLIgAEhT/Pm8Pzze1b2/PPhD/7NN8Mdd8Ds2TB58p75Hn0USktDvSecAHfdFT/ouPFGaNAAfvUreOMNePzxPfNUVsLll8Nrr8H06SHo2LJlz3zuoZ0OHaBbtxDoxFNeDj/7GXTsCFdfDRs3xs/nHq73V7+CadPi56kyd26Y1RERka82d0/4IAQbZyXLs68PIAv4FDgCyAHmAt2r5ekPvEp498gZwIyaygK/A0ZEz0cA90bPu0f5GgFdo/JZ0bn3gTOjdl4F+tXU/57g/vrr7u7ur77qDu6TJvlu/vd/Q/rKleH46qvd27Rx37lz93wXXOB+9NHulZXu27e7N2/u/sMf7p5n5073jh3d+/YNx3/7W6h7ypTd8338cUi/++5QX69e7p06ue/YsXu+p58O+caNc3/77fD89tt9D7ffHs5997vu3/9+eP7ii3vmu+mmcO6ii9wbNgztlpTsnqey0v0nPwn5wN3M/Y9/3LOu8nL3a6/dle+SS3a9hjGmTp0arqNXL/djjnG/8073TZv2rG/nTvfx48Nr+p//GcapsnLPfJWV7tOnu48a5f7Xv7ovWrRnniobNoS2X3wxbt++tHq1+7//HR7LlyfOV1zs/uab7q+9ljzftm3uU6e6T5jgPm9e4nyLF7s/9pj7b34T6iwvj59v7lz3e+5xv+OOUG/1780qS5e6/+Uv4Xv6zTe/fP2mTp26e74NG9yffdb9/vvdP/gg/uvs7v7552FMnnnGfcWKxNexdav75Mnub73lvmVL4nwbN4Y+Vv8+j1VZ6f7JJ+7LliXul3uo46OP3NeuTZzH3X3NmvDztm1b8n59+KF7YWHyNouK3GfPDt8HiZSXh/4vWuReWvpl8h5jUFLiXlDgvmpV8jaLi90//TS8xolUVobrXLXKvaIicb6KipBv8+bEedzdy8rCz2ii77MqpaXhd2FNysuTX+N+sscYHKSAWZ7gb6J5vP9sY5jZNHc/M52AJUG9ZwJ3uvvF0fGtAO7+25g8fwXy3f2p6LgA6A10SVS2Ko+7rzazDlH5vOr1m9kk4E5gGTDV3Y+J0gdH5a9N1v9TGzTwWVu3QpMmYUaiVSu46Sa4775dmc48M/zHPnNmOH7uObjySpg6FXr3Dmmffx7+m7/tNvjNb0LakCHw8svhXKNGIe1f/4LLLgv/1X/rW7BjB3TuDGefDS+8sKvNYcPgqafCkkibNmFZpW/fMKsxbFjIU14Oxx8P2dnhv/+srLBc89JLYbmjU6eQ7+OP4eSTw0zD44+Hcj16hNmRBQsgJyfke/HF0Kebb4Y//jEcX3FFmPl49tkwSwLw+9+HvSE33gh33w3XXBOu569/heHDQ56yMvje90K5a6+Fww6DkSOhcWP4+9/DDA/Ahg2sueoq2k2ZEmZp2raFKVOgSxcYNw7OOSfkW7gw1Pfhh2GMKith06aw7+T22+HSS0O+V14JfZoxY/eB7tcPfvlLOPfcENq8/TY89lhYYtqxY1e+k04K13X++dC0KcybB2PGhOWv2GWmnj3hu9+F73wHtm4Ns1BPPhnar6zcle+cc2DQoF0zWq+9Fl6T116D7dt35Tv55DAjNHgwVFSE63z4YRg7dvdZq65d4brr4Ic/hEMPDeP+u9+FtiHMsLmH1+8Xvwhj07gxfPBBGNOqfFX69IGhQ5m1bRunDh8evm9+/evwulTEvJP82GPD6zJkSKjvrbfgD38I1xvbv969w0bmPn3C6zB1aqjrlVd2zfhlZ8NFF4XX7sgjYdmyMKv2zjvw0UehvsaNw1hdeCF84xuh3OzZ8Oab4bF2bUhr3z78XPTrB927w+rV8N57Ic+0abvG9pRTws/dN78JLVqE7/s334T8/PAcQpsXXhi+l846K4xPVf+rfvYBcnNDvosvhlNPhaKiMAM5ceKuuqpesz59wuOII0L/J00Kj+LikCcnB844A84/nzktWtDjtNPC9+akSeE6du7c1eZZZ4VHr15hxnDyZHj9dVi0KORp0CD8Pjj33PDo0CH83Lz9drjOFStCvmbNQh1nnw2nnx6+Z2bPhnffDY+q2cguXcL5M88MS8DFxeF1mDYt5C8rC7/Xjj8eTjstPA49NCwDz5wJs2aFvrmHn+sePcI4nHhiaHPhwrDUO2cOLF8efn8dfXTId+KJcPjhUFISfn/NmxcexcXh5+i440K7xx4bxnPt2nB+4cLwPVxWFto8/vjQ9yOPDK/PihUhX2FhmC3Nzg597tQJOnXis4oKvn7iieF78tNPw9e1a8Pvgtzc8Jp26BB+nzVoEPJ89lmod8eO8Nq2axe+L9u3D33YsCHkWbkyfH82aBD63LZtyNuuHRxySFiuXrkS1qyB9evD36RWrXbly80Nv7PXrNn1KCkJbbZuHc7n5obXZ+PGsKRd9di5E1q2DH9L2rfHRo/+wN1PJY5Ugom7gI+A572mzHvBzK4E+rr7j6Lj7xNujnVDTJ5/ASPd/Z3oeApwCyGYiFvWzDa6e8uYOja4eyszux+Y7u7/iNIfI8xCLIvauDBKPwe4xd0vjdPn4cBwgO45OT0fiNn/cNJPf0rDTZuY9Vh412zD4mK+ceWVLPvBD/hsyBAgLI2cNXAgqwYMoPCGcJkdX3iBbqNG8f6YMWzr2hWAVu+/z0m33ML8O+9k7XnnAXD8bbfRfOFCpo0fj2eHe411feQRDn/6aaY/8QSl7dvTsLiYMwcNYnW/fiz+yU9Cx9zpee21ZG3fzvuPPw5ZWbR77TWOvfde5t11F+vOPReAxp9/Tq8hQ1jTpw8Ft9wC7vS4+WaaLlvGjHHjKG/RAoDW77/PibfcwpIf/YjlV19NTnExp11zDTvatePD++/HowCj07PPctSDD/LZ977H0mHDOPSddzj+jjv4ondvFtxxBzRogO3cyfF33EHr99/nk5tvZt1553HMb39LmxkzKPzxjyn6zncAaLJiBd1/8xuaFRay4sor2dmiBR1feomGxcV8NnQoy6++Gs/Kovm8eRz729/SZNUqNh9zDFu7dKFtfj4VjRqx+KabWHveeVhFBe0nTeLwJ5+kyeefs61jR8ydJqtWsb1DB1YMGsS6s86iwY4dtJ06lU7PPUdOtSWb8qZNWdOnD2suugjcab5gAe0nTeKQJUv2yLe6Xz/WnX02uNPsk09oN2UKzartTylr1YrP+/ZlQ48eVDZpQouPPqLd66/T9LPd71pf2qYN6845h/Wnn87OFi1otmgRh738MocsXUpZy5Zkbd9OVmkplQ0bsvJb32L1JZewo21b2kybRseXXqLl3LlUNmxIWevWNF6zhsqGDVnxH//BiiuvxHNyaD19Op2ee44W8+dT3rQp5V/7Go3XrqUiJ4eVV1zBqssuY2fz5rSfNImujz5KdhTUlLVsScPNm6nMyWHVgAGsO/tsdrRtS6tZszjs5ZdpXlCAN2iAZ2XRYOdOylq0YNWAAaz/xjfwBg1oM2MG7SdOpEm1t0+XtWrF2nPOYf1ZZ4E7LWfPpm1+Po3XrPkyT0Xjxmw67jg2nXACpYceStNly2g9c+Yer92Odu3Y2KMHm044ASoqaDVnDq1mzaJhzNKem1Fy5JFsOukkNufl0XjtWtq89x7NFyzAYn71VTRuzMYTT2Rjjx6UtmtH8/nzOfTdd3frF8DmvDzWn3kmW7t2peGmTbT4+GNaz5pFTsw7vyqzs9l40kkU9+rFjnbt+FpRES3nzqXFxx+TFROslrVqRfFpp7GxRw88K4tDCgtpOXcuhxQWYjFB6JajjmLDqaey9YgjyN6yhWYFBbSYN48mq1bt6n+jRl++FmVt2tB49WqaL1hAi3nzdm+zZUs2nnQSm487jsqGDWm6bBnN58/nkCVLdmtz6+GHs+mEE9h6xBFkbdvGIYWFNF+4kMZffLGrzZwctuTlsbl7d8patyanuJhmixfTrKAg7D+r+h5v3ZotxxxDyZFHUpmTQ5OVKzmksJCmS5fSIApS3YxtnTtTctRRbO/UCSsvp+myZRzy6ad7fG9s7dqVkiOOYGerVmRv3kzTpUtpumzZbuNeeuihbO3She2dOlGZk0POunU0XbaMJkVFZEUb2CuzstjeuTPbO3ZkR9u2WEUFDTdtotG6dTRau5acdetoUFlJedOmbO/Yke0dOrCzZUsalJaSs2EDOevX02j9ehpGv0tKc3PZ0b49pbm5VDZqRNa2bTTcuJGc4mJyiotpWFJCRU4Ope3aUZqbS2mbNgBkl5SE+jZsoOGGDWSVlVHWsiWlhx7Kzlat2NmiBQ1KS8nesiXk2biRhps349nZlLVsyc5WrShr1YqKr32NrG3bQr6NG2m4aRNZ27ZRfsgh7GzenJ0tW7KzeXM8O5vskhIabtpEzoYNNNqwIWEwkcpyxBagEtgJbI6ON9dULoV6rwIejTn+PvCXanleAc6OOZ4C9ExWFthYrY4N0dcHgO/FpD8GXAGcBkyOST8HeLmm/h999NG7z//ce+/uSxqPPRaOZ8/ePd+ll7p//eu7pubOPtv9uON2z1NeHpY0+vcPx8uXuzdo4D5ixO75li93z8py/+Uvw/Fdd4U2q0/PP/tsSH/mmTB1ePjh7j177jk9+LOfhaWHGTPcH3kklHnkEd/Dt7/t3rix++OPu59zjnujRu4LFuyep7LS/Uc/CnWcd17oZ69ee05dbt/u/s1v7lrSyM52Hz16zza3bXO/5ppd+c45x2c99NCe+bZscf/tb927dw99HDw4TCFXV1bmPnZseI0vuyxcS1lZ/HbHjQvLPbff7v73v8efFq6sdH/vvbD8dP/9YRki0fTxokXu990X8n7wQfx2KyvdFy4MSwsjR4Zp/njTzBUV7v/4R/i++slPwhivWRO/3Xnz3G+80f2KK0If162L325+vvvw4WFp66GHwtJFdWVl7osW+YJbbgnjMmJE/HYrK93fecf9ttvcf/7z0L94r0t5ufsbb7j//vfuf/pTWEqJtzRTWRmWDSZNCteTaLp85Ur3V14Jj88+i59n5073adNCn954I/51uofXacIE96eecp85M/F4zZsXlr5eeCEspcRTURF+Jzz5ZFi+qb4UWKW0NLwGzz7rPmdO4iWGDRt87siR7hMnhqWIRFavDq/Fu+8mXj4oKws/+//+d1gmSbR8sGlT6NvbbydflikqCmP/0UfxXzP3cF0FBe6zZoX8idrcsSMsKc2bl/g1cw9juGBBeP0TvWaVlWGZbcmS5P2vqAiv6apVuy0rxTN18uSwpFXTkktZWfKluCo7dtRcV2Vl4tc1VqpLQSnkIckyR1oBQToPwh6FSTHHtwK3VsvzV2BwzHEB0CFZ2ao80fMOQEG8+oFJUT0dgEUx6YOBv9bU/z2Ciblzw8s5Zkw4vuwy986d9xygRx/dFWQsXepf7m+o7le/CgFEUZH7LbeE5/F+QV1xhXvr1uEXZps2uwKQWOXlYU9Bly7ugwaFNqv2e8QqLg59bto0/PHv3Tv+D+Tnn4c/1lV//J96as887uEH8IYb3I84wv366+P/8arq35NPhrX7uXPj56myfv2XwUGN65SJ9glIrakva8VfZRqDzKsvY5BWMEHYlPg94I7ouDPQq6ZyKdSbDSwhbIas2kR5XLU8l7D7Bsz3ayoL3MfuGzB/Fz0/jt03YC5h1wbMmVH9VRsw+9fU/z2CicpK9w4d3K+6KkSoOTnuN9+852isWRMCg5/+1P3Xvw5DsHTpnvkWLw6zBJdc4t6yZQga4nnnnVBHo0bhD/tHH8XPN2OGe7NmIW/VTEY8n3wSAo7rr0/8n5p7CBTy85NvFqxj9eUH+KtMY5B5GoPMqy9jkCyYSOWDvh4kLHNcAPw/oISwZHBaCmUTcvdyM7uBMEOQBYxx9/lmdl10/mFgIuEdHYXANsKdOBOWjaoeCYw3s2HAcsKSCFHd44EFQDlwvbtX7RT7MfA40IQQTLy61xdkFjYdjh4dNu+UlYWNYtW1bRs2y40aFTbUDBgQNixVd9RR4V4SI0eGjTF33x2/3bPOCpsjx44NG+xOOCF+vl69wttU16wJG84S6dYtbOCsSU4ORPs5RESkfktlA+aH7n6Kmc1295OjtLnuftJ+6eFXVF5enhcUFOyeWFAQdgtXVISd1u+9F4KM6oqKwo7unTvD3S7jBRMQdrW//XbYVdy+fa1fw4EuPz+f3lXvipGM0BhknsYg8+rLGJhZwg2YqcxM7DSzLMCjynIJMxVSXV5eeAvdv/4V3uaZ6N5XnTqFG0/VpEED/fcvIiJfeakEE6OAF4C2ZnYPcCVwe5326kD2ne/EX94QERE5SNUYTLj7E2b2AdCHsEHxcndfWOc9ExERkQNCKjMTuPsiYFEd90VEREQOQKl80JeIiIhIQgomREREJC0KJkRERCQt+xRMmNno2u6IiIiIHJj2dWbir7XaCxERETlg7VMw4e4f1HZHRERE5MCU8K2hZvYy0V0v43H3AXXSIxERETmgJLvPxO/3Wy9ERETkgJUwmHD3N6uem1kOcAxhpqLA3cv2Q99ERETkAFDjHTDN7BLgYeBTwu20u5rZte6+9x/TLSIiIgedVG6n/X/A+e5eCGBmRwKvAAomREREJKV3c3xRFUhElgBf1FF/RERE5ACTyszEfDObCIwn7Jm4CphpZt8GcPfn67B/IiIi8hWXSjDRGFgDnBcdrwVaA5cRggsFEyIiIvVYjcGEu19T242aWWvgGaALsAz4jrtviJOvL/BnIAt41N1H1lTezG4FhgEVwE3uPsnMvgY8CxwZpb/s7iOi/D8A7gNWRs3e7+6P1vY1i4iIHKxq3DNhZr8zs+Zm1tDMppjZOjP7XprtjgCmuHs3YEp0XL3dLOABoB/QHRhsZt2TlY/ODwKOA/oCD0b1APze3Y8BTgbOMrN+Mc094+49oocCCRERkb2QygbMi9x9M3ApUAQcDfwizXYHAmOj52OBy+Pk6QUUuvuS6L4WT0flkpUfCDzt7qXuvhQoBHq5+zZ3nwoQ1fUh0CnNaxARERFS2zPRMPraH3jK3YvNLN1227n7agB3X21mbePk6QisiDkuAk6voXxHYHq1Mh1jKzWzloT9Hn+OSb7CzM4FPgF+4u6x7caWHQ4MB8jNzSU/P7+Gy5S6VFJSojHIMI1B5mkMMk9jkFow8bKZLQK2A/9lZrnAjpoKmdlkoH2cU7el2Ld4EUvCzwpJpYyZZQNPAaPcfUmU/DIhSCo1s+sIMx0XxKvc3UcDowHy8vK8d+/eNXRH6lJ+fj4ag8zSGGSexiDzNAapbcAcYWb3ApvdvcLMtrJruSFZuQsTnTOzNWbWIZpV6ED8+1YUAZ1jjjsBq6LniconKwMhEFjs7n+K6ef6mPOPAPcmvzIRERGJlXDPhJldEH39NnA+MDB63hf4RprtTgCGRs+HAi/FyTMT6GZmXaPPBhkUlUtWfgIwyMwamVlXoBvwfnQddwMtgJtjG4mCkSoDgIX7flkiIiL1T7KZifOANwj7C6pL9/4SI4HxZjYMWE64ERZmdhjhLaD93b3czG4AJhHeGjrG3ecnK+/u881sPLAAKAeuj2ZTOhGWVxYBH0Z7PqreAnqTmQ2I8hcDP0jjukREROqdZJ8a+uvoa63fZyJaWugTJ30VYaNn1fFEYGKq5aNz9wD3VEsrIv5+Ctz9VuDWvei+iIiIxEgYTJjZT5MVdPc/1H53RERE5ECTbJmjWfQ1DziNXfsVLgPeqstOiYiIyIEj2TLHXQBm9m/gFHffEh3fSbg1tYiIiEhKd8A8HCiLOS4jfCaGiIiISEo3rfo78L6ZvUB4F8e32HUraxEREannUrlp1T1m9ipwTpR0jbvPrttuiYiIyIEilZkJ3P1DwodjiYiIiOwmlT0TIiIiIgkpmBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0ZCSYMLPWZva6mS2OvrZKkK+vmRWYWaGZjUilvJndGuUvMLOLY9Lzo7Q50aNtlN7IzJ6Jyswwsy51eOkiIiIHnUzNTIwAprh7N2BKdLwbM8sCHgD6Ad2BwWbWPVn56Pwg4DigL/BgVE+Vq929R/T4IkobBmxw96OAPwL31u6lioiIHNwyFUwMBMZGz8cCl8fJ0wsodPcl7l4GPB2VS1Z+IPC0u5e6+1KgMKon1b78E+hjZrZXVyMiIlKPpfQR5HWgnbuvBnD31VVLDtV0BFbEHBcBp9dQviMwvVqZjjHHfzOzCuA54G5399h23L3czDYBbYB11TtkZsOB4QC5ubnk5+enfsVS60pKSjQGGaYxyDyNQeZpDOowmDCzyUD7OKduS7WKOGmeRpmr3X2lmTUjBBPfB8btTTvuPhoYDZCXl+e9e/euoTtSl/Lz89EYZJbGIPM0BpmnMajDYMLdL0x0zszWmFmHaFahA/BFnGxFQOeY407Aquh5ovIJy7j7yujrFjN7krD8MS6mTJGZZQMtgOK9u1oREZH6K1N7JiYAQ6PnQ4GX4uSZCXQzs65mlkPYWDmhhvITgEHROzS6At2A980s28wOBTCzhsClwLw4dV0JvBEtf4iIiEgKMrVnYiQw3syGAcuBqwDM7DDgUXfvH+1fuAGYBGQBY9x9frLy7j7fzMYDC4By4Hp3rzCzpsCkKJDIAiYDj0R1PQb83cwKCTMSg+r64kVERA4mGQkm3H090CdO+iqgf8zxRGBiquWjc/cA91RL2wr0TJB/B1EwIiIiIntPd8AUERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0KJgQERGRtCiYEBERkbQomBAREZG0ZCSYMLPWZva6mS2OvrZKkK+vmRWYWaGZjUilvJndGuUvMLOLo7RmZjYn5rHOzP4UnfuBma2NOfejOr58ERGRg0qmZiZGAFPcvRswJTrejZllAQ8A/YDuwGAz656sfHR+EHAc0Bd40Myy3H2Lu/eoegCfAc/HNPdMzPlH6+B6RUREDlqZCiYGAmOj52OBy+Pk6QUUuvsSdy8Dno7KJSs/EHja3UvdfSlQGNXzJTPrBrQF3q6VKxEREannMhVMtHP31QDR17Zx8nQEVsQcF0VpyconK1NlMGEmwmPSrjCzj8zsn2bWeV8uSEREpL7KrquKzWwy0D7OqdtSrSJOmsdJ29syg4Dvxxy/DDzl7qVmdh1hpuOCuJWbDQeGA+Tm5pKfn19Dd6QulZSUaAwyTGOQeRqDzNMY1GEw4e4XJjpnZmvMrIO7rzazDsAXcbIVAbGzBJ2AVdHzROWTlcHMTgKy3f2DmH6uj8n/CHBvkmsaDYwGyMvL8969eyfKKvtBfn4+GoPM0hhknsYg8zQGmVvmmAAMjZ4PBV6Kk2cm0M3MuppZDmFGYUIN5ScAg8yskZl1BboB78fUORh4KraRKBipMgBYuE9XJCIiUk/V2cxEDUYC481sGLAcuArAzA4DHnX3/u5ebmY3AJOALGCMu89PVt7d55vZeGABUA5c7+4VMe1+B+hfrS83mdmAKH8x8INav1oREZGDWEaCiWhpoU+c9FXE/LF394nAxFTLR+fuAe5JcO6IOGm3Arem2ncRERHZne6AKSIiImlRMCEiIiJpUTAhIiIiaVEwISIiImlRMCEiIiJpUTAhIiIiaVEwISIiImlRMCEiIiJpUTAhIiIiaVEwISIiImlRMCEiIiJpUTAhIiIiaVEwISIiImlRMCEiIiJpUTAhIiIiaVEwISIiImlRMCEiIiJpUTAhIiIiaVEwISIiImnJSDBhZq3N7HUzWxx9bZUgX18zKzCzQjMbUVN5M2tjZlPNrMTM7q9WV08z+ziqa5SZWZTeyMyeidJnmFmXOrx0ERGRg06mZiZGAFPcvRswJTrejZllAQ8A/YDuwGAz615D+R3AHcDP47T5EDAc6BY9+kbpw4AN7n4U8Efg3rSvTkREpB7JVDAxEBgbPR8LXB4nTy+g0N2XuHsZ8HRULmF5d9/q7u8QgoovmVkHoLm7T3N3B8bFtBlb1z+BPlWzFiIiIlKz7Ay1287dVwO4+2ozaxsnT0dgRcxxEXD6XpSvXldRtbo6Vm/H3cvNbBPQBlhXvRIzG06Y3QAoNbN5NbQrdetQ4oyT7Fcag8zTGGRefRmDryc6UWfBhJlNBtrHOXVbqlXESfN97U6SulJux91HA6MBzGyWu5+6j/2RWqAxyDyNQeZpDDJPY1CHwYS7X5jonJmtMbMO0axCB+CLONmKgM4xx52AVdHzVMpXr6tTgrqq2ikys2ygBVBcQ30iIiISydSeiQnA0Oj5UOClOHlmAt3MrKuZ5QCDonKplv9StCSyxczOiPZDDIkpE1vXlcAb0b4KERERSUGm9kyMBMab2TBgOXAVgJkdBjzq7v2j/Qs3AJOALGCMu89PVj6qYxnQHMgxs8uBi9x9AfBj4HGgCfBq9AB4DPi7mRUSZiQGpXgNo/fhuqV2aQwyT2OQeRqDzKv3Y2D6J1xERETSoTtgioiISFoUTIiIiEhaFEzsg0S3+Za6Y2ZjzOyL2Ht7pHpbdkmfmXWOblW/0Mzmm9l/R+kag/3EzBqb2ftmNjcag7uidI3BfmZmWWY228z+FR3X+zFQMLGXarjNt9Sdx9l1C/QqNd6WXWpNOfAzdz8WOAO4Pvq+1xjsP6XABe5+EtAD6GtmZ6AxyIT/BhbGHNf7MVAwsfeS3eZb6oi7v8We9/9I5bbsUgvcfbW7fxg930L4RdoRjcF+40FJdNgwejgag/3KzDoBlwCPxiTX+zFQMLH34t3mu2OCvFK3drutOlDTbdWlFkSfrHsyMAONwX4VTa/PIdyo73V31xjsf38CfglUxqTV+zFQMLH3avM23yIHFDM7BHgOuNndN2e6P/WNu1e4ew/CXXx7mdnxGe5SvWJmlwJfuPsHme7LV42Cib2X7Dbfsn+tiW6nXvXJsDXdVl3SYGYNCYHEE+7+fJSsMcgAd98I5BP2EWkM9p+zgAHRzRGfBi4ws3+gMVAwsQ+S3eZb9q+9uq267LvoNvSPAQvd/Q8xpzQG+4mZ5ZpZy+h5E+BCYBEag/3G3W91907u3oXwu/8Nd/8eGgPdAXNfmFl/wrpZ1W2+78lsjw5+ZvYU0JvwUb9rgF8DLwLjgcOJbqvu7vqQtjpgZmcDbwMfs2ut+FeEfRMag/3AzE4kbO7LIvwjON7df2NmbdAY7Hdm1hv4ubtfqjFQMCEiIiJp0jKHiIiIpEXBhIiIiKRFwYSIiIikRcGEiIiIpEXBhIiIiKRFwYSI1Dkza2lm/xVzfJiZ/bOO2rrczP4nyfkTzOzxumhbpL7SW0NFpM5Fn+fxL3ev89s/m9l7wAB3X5ckz2Tgh+6+vK77I1IfaGZCRPaHkcCRZjbHzO4zsy5mNg/AzH5gZi+a2ctmttTMbjCzn5rZbDObbmato3xHmtlrZvaBmb1tZsdUb8TMjgZKqwIJM7vKzOaZ2Vwzeysm68uEOxiKSC1QMCEi+8MI4FN37+Huv4hz/njgu0Av4B5gm7ufDEwDhkR5RgM3untP4OfAg3HqOQv4MOb4f4CL3f0kYEBM+izgnDSuR0RiZGe6AyIiwFR33wJsMbNNhJkDCLfvPjH6tNJvAM+GjwkBoFGcejoAa2OO3wUeN7PxwPMx6V8Ah9Vi/0XqNQUTIvJVUBrzvDLmuJLwe6oBsDH6+O1ktgMtqg7c/TozOx24BJhjZj3cfT3QOMorIrVAyxwisj9sAZrta2F33wwsNbOrIHyKqZmdFCfrQuCoqgMzO9LdZ7j7/wDrgM7RqaOBefvaHxHZnYIJEalz0WzAu9FmyPv2sZqrgWFmNheYDwyMk+ct4GTbtRZyn5l9HG32fAuYG6WfD7yyj/0QkWr01lAROaiY2Z+Bl919coLzjYA3gbPdvXy/dk7kIKWZCRE52Pwv8LUk5w8HRiiQEKk9mpkQERGRtGhmQkRERNKiYEJERETSomBCRERE0qJgQkRERNKiYEJERETS8v8B0gdne2caWGIAAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 576x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "err = u_FD - u_DH\n", "\n", "plt.figure(9, figsize=(8, 4), clear=True)\n", "plt.plot(t, err[0], 'r')\n", "\n", "plt.xlim(0, az.Td); plt.xlabel('time (s)') \n", "plt.ylim(-0.001, 0.001); plt.ylabel('displ. error (m)') \n", "\n", "plt.grid(True) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This means that, for the provided sampling rate, the integration error is very small." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Assignments <a name=\"section_5\"></a> \n", "\n", "1. Utilizar as propriedades (frequência e amortecimento) do trabalho anterior.\n", "2. Utilizar como entrada o registro de aceleração sísmica fornecido abaixo.\n", "3. Calcular a resposta com ``MRPy.sdof_FDiff()`` e ``MRPy.sdof_Duhamel()``.\n", "4. Relatório com descrição do objeto, gráficos e resultados.\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fs = 33.3Hz\n", " Td = 64.0s\n", "\n", " NX = 1\n", " N = 2132\n", " M = 1067\n", "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import interp1d\n", "\n", "a = MRPy.from_file('resources/data/earthquake', form='columns')\n", "func = interp1d(a.t_axis(), a[0])\n", "\n", "Td = a.Td # duração do sinal é a mesma\n", "dt = 0.03 # passo de tempo proposto\n", "ti = np.linspace(0, Td, int(Td/dt)) # reduz resolução, aumenta dt\n", "fsi = len(ti)/Td # nova taxa de aquisição\n", "ai = MRPy(func(ti), fsi) # aceleração interpolada\n", "ai = ai.double()\n", "\n", "f10 = a.plot_time(10, figsize=(8,4)) # aceleração original\n", "f11 = ai.plot_time(11, figsize=(8,4)) # resolução alterada\n", "\n", "ai.printAttrib()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 }