{ "metadata": { "name": "WiiBoard data analysis" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "rcParams[\"figure.figsize\"] = (10, 6)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Load data, format it and visualize it" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all, we're going to load the test data and compute the information we want. The .npy file contains the following columns:\n", "\n", "- time\n", "- top left sensor (mass in kg)\n", "- top righ sensor (mass in kg)\n", "- bottom left sensor (mass in kg)\n", "- bottom right sensor (mass in kg)\n", "\n", "Once this information is extracted, we compute a mean mass and the $x, y$ coordinates of the center of mass using the fact that we know the distance between the left-right (215 * 2 mm) and top-down (117.5 * 2 mm) extremities of the board." ] }, { "cell_type": "code", "collapsed": false, "input": [ "raw_data = np.load('files/WiiBoard_data.npy')\n", "t = raw_data[:, 0]*1e-6 #t in seconds\n", "tl = raw_data[:, 1]\n", "tr = raw_data[:, 2]\n", "bl = raw_data[:, 3]\n", "br = raw_data[:, 4]\n", "m = raw_data[:, 5]\n", "reference_mass = m.mean()\n", "R = tr + br\n", "L = tl + bl\n", "T = tr + tl\n", "B = br + bl\n", "x, y = (215 * (R - L) / reference_mass,\n", " 117.5 * (T - B) / reference_mass) # in mm" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's take a look at the mass curve." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t, m, label='mass')\n", "plot(t, ones(m.shape) * reference_mass, label='mean mass')\n", "legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 24, "text": [ "" ] }, { "output_type": "display_data", "png": 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g6Pr95z+ZeDeT+EYbz15QGVF4JkQzPE348kvzMojoCOwWtm3bhuHDh6Nr167o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\n" } ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "(m > reference_mass + 1).nonzero()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 25, "text": [ "(array([], dtype=int32),)" ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "(m < reference_mass - 1).nonzero()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 26, "text": [ "(array([], dtype=int32),)" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mass is always comprised between + and - 1 kilograms of the average mass. So here, the measurements seem very coherent.\n", "\n", "Let's now take a look at the displacement as a function of time." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t, x, label=\"x\")\n", "plot(t, y, label=\"y\")\n", "xlabel(\"time (s)\")\n", "ylabel(\"coordinate of center of gravity (mm)\")\n", "legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 27, "text": [ "" ] }, { "output_type": "display_data", "png": 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ftRpmgL5ypIefn1jvTusYnMxM4LPP7N2oSvhN12htsLvvFmv4aVXzN+Jy52U2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\nrkJggg==\n" } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the coordinates are not centered. Let's see what it looks like if we center them." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t, x - x.mean(), label=\"x\")\n", "plot(t, y - y.mean(), label=\"y\")\n", "xlabel(\"time (s)\")\n", "ylabel(\"coordinate of center of gravity (mm)\")\n", "legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 28, "text": [ "" ] }, { "output_type": "display_data", "png": 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2wOr7V/PPCST9WvbDZd1l0b5yQznClGEIYoLcWgMyOz8bN70tXeKBNEwVhgrZ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\n" } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the things we see is that the amplitude of $x$ and $y$ displacement is not the same. In fact, the ratio between the two is almost 4!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print x.max() - x.min()\n", "print y.max() - y.min()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.46394312903\n", "17.906250965\n" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what the trajectory looks like in the $(x, y)$ plane." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x - x.mean(), y - y.mean())\n", "xlabel(\"horizontal direction (mm)\")\n", "ylabel(\"vertical direction (mm)\")\n", "title(\"Center of gravity path in the x-y plane\")\n", "axis('equal')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 35, "text": [ "(-3.0, 3.0, -10.0, 15.0)" ] }, { "output_type": "display_data", "png": 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hISFo3bp1/IycSZMmwd7eHiNHjrRUk4iIiIgyjcV6xIyZN28efvzxR9SsWRMzZ86Ek5OT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\n" } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Frequency analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now work with centered data, so that we can use the classical Fourier transform tools." ] }, { "cell_type": "code", "collapsed": false, "input": [ "x_centered = x - x.mean()\n", "y_centered = y - y.mean()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start with the $y$ axis data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "sample_freq = 1 / (t[1] - t[0])\n", "print sample_freq\n", "y_fft = fft.fft(y_centered)\n", "freqs = linspace(0, 1, num=y.shape[0], endpoint=False) * sample_freq / 2\n", "plot(freqs, abs(y_fft))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "90.991810737\n" ] }, { "output_type": "pyout", "prompt_number": 52, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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} ], "prompt_number": 52 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, there are some low frequency components and no high frequencies. Let's focus on the low frequencies." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(freqs, abs(y_fft))\n", "xlim((0, 0.5))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 44, "text": [ "(0, 0.5)" ] }, { "output_type": "display_data", "png": 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pzby8PE2ZMkU1NTUaO3asxowZE/AY2qqUSbtD2eGHB/f1+UPZ559LWVnBPRYAACBYPuPf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\nKmXwQpcutsKTkWGn3MrKvD3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} ], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then output the frequency content of each band of frequencies." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def print_freq_content(y_fft, freqs):\n", " EX1 = sum(abs(y_fft[(freqs > 0.01) & (freqs <0.5)] ** 2))\n", " EX2 = sum(abs(y_fft[(freqs > 0.5) & (freqs < 2)] ** 2))\n", " EX3 = sum(abs(y_fft[ freqs > 2] ** 2))\n", " print \"frequency band 1 = %s\" % (EX1/(EX1+EX2+EX3)*100)\n", " print \"frequency band 2 = %s\" % (EX2/(EX1+EX2+EX3)*100)\n", " print \"frequency band 3 = %s\" % (EX3/(EX1+EX2+EX3)*100)\n", " \n", "print_freq_content(y_fft, freqs)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "frequency band 1 = 34.4120533146\n", "frequency band 2 = 0.484694114847\n", "frequency band 3 = 65.1032525706\n" ] } ], "prompt_number": 51 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, what about the $x$ axis?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x_fft = fft.fft(x_centered)\n", "plot(freqs, abs(x_fft))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 53, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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} ], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(freqs, abs(x_fft))\n", "xlim((0, 0.5))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 54, "text": [ "(0, 0.5)" ] }, { "output_type": "display_data", "png": 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lqvAVqvIFRD7vi+GLiIiIos014Stc2xGIfK8vrdtMAAxfREREZIxrwpdVbcdLL9V2X4Yv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\nlJbK9/LNN9f9GMMXkXGODF9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} ], "prompt_number": 54 }, { "cell_type": "code", "collapsed": false, "input": [ "print_freq_content(x_fft, freqs)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "frequency band 1 = 41.6957576723\n", "frequency band 2 = 1.86334135102\n", "frequency band 3 = 56.4409009767\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Other indicators" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Distance travelled by the center of mass" ] }, { "cell_type": "code", "collapsed": false, "input": [ "dx = x[1:] - x[:-1]\n", "dy = y[1:] - y[:-1]\n", "dx2 = dx * dx\n", "dy2 = dy * dy\n", "L = np.sqrt(dx2 + dy2).sum()\n", "L" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 57, "text": [ "935.87185703233376" ] } ], "prompt_number": 57 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The center of mass travelled 936 mm during the 51 s of the recorded data." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Speed" ] }, { "cell_type": "code", "collapsed": false, "input": [ "dt = t[1:] - t[:-1]\n", "vitesse_inst = np.sqrt((dx2 + dy2) / dt)\n", "vitesse_inst.mean()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 59, "text": [ "1.9325976879295166" ] } ], "prompt_number": 59 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean speed of the $x y$ trajectory of the center of mass was 1.93 mm/s." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Covariance ellipse" ] }, { "cell_type": "code", "collapsed": false, "input": [ "points=np.vstack((x,y)).transpose()\n", "cov = np.cov(points, rowvar=False)\n", "\n", "def eigsorted(cov):\n", " vals, vecs = np.linalg.eigh(cov)\n", " order = vals.argsort()[::-1]\n", " return vals[order], vecs[:,order]\n", " \n", "vals, vecs = eigsorted(cov)\n", "theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))\n", "\n", "nstd = 2\n", "width, height = 2 * nstd * np.sqrt(vals)\n", "ellip = mpl.patches.Ellipse(xy=pos, width=width, height=height, angle=theta)\n", "ellip.set_alpha(0.2)\n", "gca().add_artist(ellip)\n", "scatter(x, y)\n", "axis('equal')\n", "xlabel('x position (mm)')\n", "ylabel('y position (mm)')\n", "title('Covariance ellipse of point cloud during balance state')\n", "annotate(\"width = %.2f, height = %.2f, theta = %.2f\" % (width, height, theta), (x.min(), y.max()))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 82, "text": [ "" ] }, { "output_type": "display_data", "png": 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7zTl8ePf1zfbpp5+yevXqPM83b978nknxoIbRAgICOHnyZL4B144dO5g2bRp7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