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1st Simulation - Interactive
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Main.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Enhanced STW estimation using the Discrete Linear Kalman Filter - 1st iteration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**WARNING!** Use the button below to toggle on/off the raw code."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
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" code_show = !code_show\n",
"} \n",
"$( document ).ready(code_toggle);\n",
"</script>\n",
"<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>"
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"<IPython.core.display.HTML object>"
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}
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"source": [
"from IPython.display import HTML\n",
"\n",
"HTML('''<script>\n",
"code_show=true; \n",
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"</script>\n",
"<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>''')"
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},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Load Libraries"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
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"\n",
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" index: 0\n",
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" }\n",
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"\n",
" var NB_LOAD_WARNING = {'data': {'text/html':\n",
" \"<div style='background-color: #fdd'>\\n\"+\n",
" \"<p>\\n\"+\n",
" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
" \"</p>\\n\"+\n",
" \"<ul>\\n\"+\n",
" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
" \"</ul>\\n\"+\n",
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"\n",
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" console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.0.1.min.css\");\n",
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" Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.0.1.min.css\");\n",
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"}(window));"
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from simulator_functions import *\n",
"from numpy import dot\n",
"from scipy.linalg import inv\n",
"import pandas as pd\n",
"import numpy as np\n",
"from numpy.random import randn\n",
"import math\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib\n",
"# %matplotlib inline\n",
"from bokeh.plotting import figure,output_notebook,show,ColumnDataSource\n",
"from bokeh.models import Range1d\n",
"from bokeh.layouts import gridplot\n",
"output_notebook()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Create a simulation of a container vessel in 4-DOF"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This implementation is based on [Marine Systems Simulator](https://github.com/cybergalactic/MSS) built by **T. I. Fossen and T. Perez** as a **Matlab** library on Github. The below code is a **Python** implementation (translated from the original Matlab library) of a container ship with the following characteristics: \n",
"* $L_{oa}=175 \\ [m]$ (nonlinear|linear maneuvering model including the roll mode)\n",
"\n",
"The research question of the below implementation is to find out if, in a container vessel that sails **towards North** (in non-linaer surge motion) in constant conditions (**constant propeler revolutions $n$ and constant current speed $U_{curr}$**), we can predict(estimate) its speed-through-water $U_{TW}$ signal, without the use of a doppler velocity log. Additionally, the sensor measuremets in this implementation will be enhanced with the noise intensity claimed by each sensor manufacturer accordingly."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Build the simulator"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first simulation scenario represents a vessel which initiates its surge motion with $U_{OG}=10 \\ [m/s]$, $n = 70 \\ [rpm]$ and positive currents equal to $U_{curr}= 1 \\ [m/s]$. Since currents are positive and based on the fact that $U_{TW}=U_{OG}-U_{curr}$, we initiate the state of the simulation as follows:\n",
"\n",
" > $ u = surge \\ velocity \\ SOG \\quad \\quad \\quad [m/s]$ \n",
" > $ v = sway \\ velocity \\ SOG \\quad \\quad \\quad[m/s]$ \n",
" > $ r = yaw \\ velocity \\quad \\quad \\quad \\quad \\quad[rad/s]$ \n",
" > $ x = position \\ in \\ x-direction \\quad \\quad [m]$ \n",
" > $ y = position \\ in \\ y-direction \\quad \\quad [m]$ \n",
" > $ psi = yaw \\ angle \\quad \\quad \\quad \\quad \\quad \\quad[rad]$ \n",
" > $ p = roll \\ velocity \\quad \\quad \\quad \\quad \\quad \\ [rad/s]$ \n",
" > $ phi = roll \\ angle \\quad \\quad \\quad \\quad \\quad \\quad[rad]$ \n",
" > $ delta = actual \\ rudder \\ angle \\quad \\quad [rad]$ \n",
" > $ n = actual \\ shaft \\ velocity \\quad \\quad \\ \\ \\; [rpm]$ \n",
" > $ ucx = current \\ surge \\ velocity \\quad \\quad[m/s]$ \n",
" > $ ucy = current \\ sway \\ velocity \\quad \\quad[m/s]$ \n",
" \n",
" \n",
"|Initial Simulation State of non-Linear Model| \n",
"|:-------------:|\n",
"$$\\mathbf x_{non-lin} = \n",
"\\begin{bmatrix} 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 70 & 1 & 0 \\end{bmatrix}$$\n",
"\n",
"\n",
"![1st_scenario](1st_scenario_constant_RPM.png)\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Simulating container under PD-control with psi_ref=0 (deg) ...\n"
]
}
],
"source": [
"print('Simulating container under PD-control with psi_ref=0 (deg) ...')\n",
"\n",
"t_f = 1000 # final simulation time (sec)\n",
"h = 1 # sample time (sec)\n",
"\n",
"Kp = 1 # controller P-gain\n",
"Td = 10 # controller derivative time\n",
"\n",
"# initial states (x:non-linear, x2:linear)\n",
"x = np.array([10, 0, 0, 0, 0, 0, 0, 0, 0, 70, 1, 0]) # x = [u, v, r, x, y, psi, p, phi, delta, n, ucx, ucy]'\n",
"x2 = np.array([[10, 0, 0, 0, 0, 0, 0, 0, 0]]).T # x2= [u, v, r, x, y, psi, p, phi, delta]'\n",
"\n",
"# --- MAIN LOOP ---\n",
"N = round(t_f/h) # number of samples\n",
"xout = np.zeros((N+1,len(x)+6)) # memory allocation for non-linear simulation\n",
"xout2= np.zeros((N+1,x2.shape[0]+2)) # memory allocation for linear simulation\n",
"\n",
"for i in range(0,N+1):\n",
" \n",
" time = i*h # simulation time in seconds\n",
"\n",
" r = x[2]\n",
" psi = x[5]\n",
" \n",
" # control system\n",
" psi_ref = 0#5*(math.pi/180) # desired heading\n",
" delta_c = 0#-Kp*((psi-psi_ref)+Td*r) # PD-controller\n",
" n_c = 70\n",
" \n",
" # ship model\n",
" xdot, U, Uog, T, R = container(x,[delta_c, n_c]) # ship model non-linear container parameters\n",
" xdot2,U2= Lcontainer(x2,delta_c,U0=x2[0,0]) # ship model linear container parameters\n",
"\n",
" # store data for presentation\n",
" xout[i,:] = np.hstack((time,x,U,Uog,T,R,xdot[0])) # this should output 18 values [time, x[0], x[1], x[2], ..., R, a]\n",
" xout2[i,:] = np.hstack((time,x2.T[0],U2)) \n",
"\n",
" # numerical integration\n",
" x = euler2(xdot,x,h) # Euler integration\n",
" x2 = euler2(xdot2,x2,h)\n",
" \n",
"# time-series non-linear model\n",
"t = xout[:,0] # time\n",
"u = xout[:,1] # surge velocity (m/s)\n",
"v = xout[:,2] # sway velocity (m/s) \n",
"r = xout[:,3]*180/math.pi # yaw velocity (rad/s)\n",
"x = xout[:,4] # position in x-direction (m)\n",
"y = xout[:,5] # position in y-direction (m)\n",
"psi = xout[:,6]*180/math.pi # yaw angle (rad)\n",
"p = xout[:,7]*180/math.pi # roll velocity (rad/s)\n",
"phi = xout[:,8]*180/math.pi # roll angle (rad)\n",
"delta = xout[:,9]*180/math.pi # actual rudder angle (rad)\n",
"n = xout[:,10] # actual shaft velocity (rpm)\n",
"ucx = xout[:,11] # surge current speed (m/s)\n",
"ucy = xout[:,12] # sway current speed (m/s)\n",
"U = xout[:,13] # service speed STW (m/s)\n",
"Uog = xout[:,14] # satellite speed SOG(m/s)\n",
"T = xout[:,15] # Thrust (kg*m/s^2)\n",
"R = xout[:,16] # Resistance in surge (kg*m/s^2)\n",
"a = xout[:,17] # acceleration in surge\n",
"\n",
"# time-series linear model\n",
"t2 = xout2[:,0] # time\n",
"u2 = xout2[:,1] # surge velocity (m/s)\n",
"v2 = xout2[:,2] # sway velocity (m/s) \n",
"r2 = xout2[:,3]*180/math.pi # yaw velocity (rad/s)\n",
"x2 = xout2[:,4] # position in x-direction (m)\n",
"y2 = xout2[:,5] # position in y-direction (m)\n",
"psi2 = xout2[:,6]*180/math.pi # yaw angle (rad)\n",
"p2 = xout2[:,7]*180/math.pi # roll velocity (rad/s)\n",
"phi2 = xout2[:,8]*180/math.pi # roll angle (rad)\n",
"delta2= xout2[:,9]*180/math.pi # actual rudder angle (rad)\n",
"U2 = xout2[:,10] # service speed (m/s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simulation returns 18 vectors which are the following: \n",
" > $ \\mathbf t = time \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\ \\ \\ [s]$ \n",
" > $ \\mathbf u = surge \\ velocity \\ SOG \\quad \\quad \\quad [m/s]$ \n",
" > $ \\mathbf v = sway \\ velocity \\ SOG \\quad \\quad \\quad[m/s]$ \n",
" > $ \\mathbf r = yaw \\ velocity \\quad \\quad \\quad \\quad \\quad[rad/s]$ \n",
" > $ \\mathbf x = position \\ in \\ x-direction \\quad \\quad [m]$ \n",
" > $ \\mathbf y = position \\ in \\ y-direction \\quad \\quad [m]$ \n",
" > $ \\mathbf{psi} = yaw \\ angle \\quad \\quad \\quad \\quad \\quad \\quad[rad]$ \n",
" > $ \\mathbf{p} = roll \\ velocity \\quad \\quad \\quad \\quad \\quad \\ [rad/s]$ \n",
" > $ \\mathbf{phi} = roll \\ angle \\quad \\quad \\quad \\quad \\quad \\quad[rad]$ \n",
" > $ \\mathbf{delta} = actual \\ rudder \\ angle \\quad \\quad [rad]$ \n",
" > $ \\mathbf n = actual \\ shaft \\ velocity \\quad \\quad \\ \\ \\; [rpm]$ \n",
" > $ \\mathbf{ucx} = current \\ surge \\ velocity \\quad \\quad[m/s]$ \n",
" > $ \\mathbf{ucy} = current \\ sway \\ velocity \\quad \\quad[m/s]$ \n",
" > $ \\mathbf U = service \\ speed \\ STW \\quad \\quad \\quad [m/s]$ \n",
" > $ \\mathbf{U_{og}}= satellite \\ speed \\ SOG \\quad \\quad \\ \\ [m/s]$ \n",
" > $ \\mathbf T = thrust \\quad \\quad \\quad \\quad \\quad \\quad \\ [kg*m/s^2]$ \n",
" > $ \\mathbf R = resistance \\ in \\ surge \\quad \\ \\ [kg*m/s^2]$ \n",
" > $ \\mathbf a = acceleration \\ in \\ surge \\quad \\quad \\ \\ \\ [m/s^2]$"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([70., 70., 70., ..., 70., 70., 70.])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visualize the simulation measurements results (**Motions** and **Forces**)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bellow we are viualizing what happens when a container vessel sails through water, based on the characteristics of the simulation. In this case the total amount of measurements of the simulation have been set to 300 seconds and the frequency to 1 sec."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" > **Motions**"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"1063\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1062\",\"type\":\"UnionRenderers\"}},\"id\":\"1039\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1068\",\"type\":\"Line\"},{\"attributes\":{\"overlay\":{\"id\":\"1032\",\"type\":\"BoxAnnotation\"}},\"id\":\"1026\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1048\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1062\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1025\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1020\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1027\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1092\",\"type\":\"Selection\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1032\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"dimension\":1,\"plot\":{\"id\":\"1004\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"1020\",\"type\":\"BasicTicker\"}},\"id\":\"1023\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"1066\",\"type\":\"ColumnDataSource\"}},\"id\":\"1070\",\"type\":\"CDSView\"},{\"attributes\":{\"data_source\":{\"id\":\"1039\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1040\",\"type\"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"\n",
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" embed_document(root);\n",
" } else {\n",
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" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
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},
"metadata": {
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"id": "1004"
}
},
"output_type": "display_data"
}
],
"source": [
"p1 = figure(plot_width=700, plot_height=300, title = 'Speed vectors representation [m/s]',x_axis_label = 'time [s]',y_axis_label = 'speed [m/s]',toolbar_location='below')\n",
"p1.line(t,U,color=\"blue\",line_width=1,legend='STW true')\n",
"p1.line(t,Uog,color=\"red\",line_width=1,legend='SOG true')\n",
"p1.line(t,ucx,color=\"grey\",line_width=1,legend='Ucurr true')\n",
"#p1.line(t,a,color=\"black\",line_width=1,legend='acceleration')\n",
"show(p1)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
" <div class=\"bk-root\" id=\"80da000a-6051-4143-af33-aca56fd39c34\"></div>\n"
]
},
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"1609\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1608\",\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  $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@      $@\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"1552\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1551\",\"type\":\"UnionRenderers\"}},\"id\":\"1215\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_color\":\"red\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1266\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1372\",\"type\":\"BasicTicker\"},{\"attributes\":{\"source\":{\"id\":\"1202\",\"type\":\"ColumnDataSource\"}},\"id\":\"1206\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1585\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1187\",\"type\":\"PanTool\"},{\"attributes\":{\"dimension\":1,\"plot\":{\"id\":\"1356\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"1372\",\"type\":\"BasicTicker\"}},\"id\":\"1375\",\"type\":\"Grid\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"1598\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1597\",\"type\":\"UnionRenderers\"}},\"id\":\"1467\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1191\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1253\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"1608\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1377\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1439\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"1254\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1192\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1609\",\"type\":\"Selection\"},{\"attributes\":{\"overlay\":{\"id\":\"1384\",\"type\":\"BoxAnnotation\"}},\"id\":\"1378\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"1440\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1255\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1379\",\"type\":\"SaveTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1447\",\"type\":\"BoxAnnotation\"}},\"id\":\"1441\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"toolbar\":{\"id\":\"1614\",\"type\":\"ProxyToolbar\"},\"toolbar_location\":\"above\"},\"id\":\"1615\",\"type\":\"ToolbarBox\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1250\",\"type\":\"PanTool\"},{\"id\":\"1251\",\"type\":\"WheelZoomTool\"},{\"id\":\"1252\",\"type\":\"BoxZoomTool\"},{\"id\":\"1253\",\"type\":\"SaveTool\"},{\"id\":\"1254\",\"type\":\"ResetTool\"},{\"id\":\"1255\",\"type\":\"HelpTool\"}]},\"id\":\"1256\",\"type\":\"Toolbar\"},{\"attributes\":{\"line_color\":\"red\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1203\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1380\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1442\",\"type\":\"SaveTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1187\",\"type\":\"PanTool\"},{\"id\":\"1188\",\"type\":\"WheelZoomTool\"},{\"id\":\"1189\",\"type\":\"BoxZoomTool\"},{\"id\":\"1190\",\"type\":\"SaveTool\"},{\"id\":\"1191\",\"type\":\"ResetTool\"},{\"id\":\"1192\",\"type\":\"HelpTool\"}]},\"id\":\"1193\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1381\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1443\",\"type\":\"ResetTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1258\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1195\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1444\",\"type\":\"HelpTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1376\",\"type\":\"PanTool\"},{\"id\":\"1377\",\"type\":\"WheelZoomTool\"},{\"id\":\"1378\",\"type\":\"BoxZoomTool\"},{\"id\":\"1379\",\"type\":\"SaveTool\"},{\"id\":\"1380\",\"type\":\"ResetTool\"},{\"id\":\"1381\",\"type\":\"HelpTool\"}]},\"id\":\"1382\",\"type\":\"Toolbar\"},{\"attributes\":{\"data_source\":{\"id\":\"1391\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1392\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1393\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1395\",\"type\":\"CDSView\"}},\"id\":\"1394\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1209\",\"type\":\"BasicTickFormatter\"},{\"at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model\"},\"renderers\":[{\"id\":\"1205\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1214\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1398\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"1454\",\"type\":\"ColumnDataSource\"}},\"id\":\"1458\",\"type\":\"CDSView\"},{\"attributes\":{\"below\":[{\"id\":\"1240\",\"type\":\"LinearAxis\"}],\"left\":[{\"id\":\"1245\",\"type\":\"LinearAxis\"}],\"plot_height\":300,\"plot_width\":400,\"renderers\":[{\"id\":\"1240\",\"type\":\"LinearAxis\"},{\"id\":\"1244\",\"type\":\"Grid\"},{\"id\":\"1245\",\"type\":\"LinearAxis\"},{\"id\":\"1249\",\"type\":\"Grid\"},{\"id\":\"1258\",\"type\":\"BoxAnnotation\"},{\"id\":\"1276\",\"type\":\"Legend\"},{\"id\":\"1268\",\"type\":\"GlyphRenderer\"},{\"id\":\"1281\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"1229\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"1256\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"1232\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"1236\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"1234\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"1238\",\"type\":\"LinearScale\"}},\"id\":\"1230\",\"subtype\":\"Figure\",\"type\":\"Plot\"}],\"root_ids\":[\"1616\"]},\"title\":\"Bokeh Application\",\"version\":\"1.0.1\"}};\n",
" var render_items = [{\"docid\":\"95512eeb-af76-4257-9e35-18f842c95583\",\"roots\":{\"1616\":\"80da000a-6051-4143-af33-aca56fd39c34\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "1616"
}
},
"output_type": "display_data"
}
],
"source": [
"# Initiate the multiplot\n",
"p1 = figure(plot_width=400, plot_height=300, title = 'Service Speed - STW [m/s]',x_axis_label = 'time [s]',toolbar_location='below')\n",
"p1.line(t,U,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p1.line(t,U2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"p2 = figure(plot_width=400, plot_height=300, title = 'Ship position',x_axis_label = 'East', y_axis_label = 'North', toolbar_location='below')\n",
"p2.line(y,x,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p2.line(y2,x2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"p3 = figure(plot_width=400, plot_height=300, title = 'Yaw rate r [deg/s]',x_axis_label = 'time [s]', toolbar_location=None)\n",
"p3.line(t,r,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p3.line(t,r2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"p4 = figure(plot_width=400, plot_height=300, title = 'Roll angle \\phi [deg]',x_axis_label = 'time [s]', toolbar_location='below')\n",
"p4.line(t,phi,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p4.line(t,phi2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"p5 = figure(plot_width=400, plot_height=300, title = 'Yaw angle \\psi [deg]',x_axis_label = 'time [s]', toolbar_location='below')\n",
"p5.line(t,psi,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p5.line(t,psi2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"p6 = figure(plot_width=400, plot_height=300, title = 'Rudder angle \\delta [deg]',x_axis_label = 'time [s]', toolbar_location=None)\n",
"p6.line(t,delta,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p6.line(t,delta2,color=\"blue\",line_width=1,legend='linear model')\n",
"\n",
"simu_grid_1 = gridplot([[p1, p2], [p3, p4], [p5, p6]])\n",
"\n",
"show(simu_grid_1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> **Forces**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
" <div class=\"bk-root\" id=\"c60761de-502a-4f68-9f07-3055b2da728e\"></div>\n"
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},
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"2155\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2154\",\"type\":\"UnionRenderers\"}},\"id\":\"2085\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"2125\",\"type\":\"HelpTool\"},{\"attributes\":{\"axis_label\":\"time [s]\",\"formatter\":{\"id\":\"2144\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"2100\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2111\",\"type\":\"BasicTicker\"}},\"id\":\"2110\",\"type\":\"LinearAxis\"},{\"attributes\":{\"use_scientific\":false},\"id\":\"2092\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"2120\",\"type\":\"PanTool\"},{\"id\":\"2121\",\"type\":\"WheelZoomTool\"},{\"id\":\"2122\",\"type\":\"BoxZoomTool\"},{\"id\":\"2123\",\"type\":\"SaveTool\"},{\"id\":\"2124\",\"type\":\"ResetTool\"},{\"id\":\"2125\",\"type\":\"HelpTool\"}]},\"id\":\"2126\",\"type\":\"Toolbar\"},{\"attributes\":{\"source\":{\"id\":\"2085\",\"type\":\"ColumnDataSource\"}},\"id\":\"2089\",\"type\":\"CDSView\"},{\"attributes\":{\"data_source\":{\"id\":\"2135\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"2136\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2137\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"2139\",\"type\":\"CDSView\"}},\"id\":\"2138\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2071\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"2128\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"2070\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"2094\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"2135\",\"type\":\"ColumnDataSource\"}},\"id\":\"2139\",\"type\":\"CDSView\"},{\"attributes\":{\"use_scientific\":false},\"id\":\"2142\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"2108\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2066\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"2144\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"label\":{\"value\":\"nonlinear model\"},\"renderers\":[{\"id\":\"2088\",\"type\":\"GlyphRenderer\"}]},\"id\":\"2097\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"2106\",\"type\":\"LinearScale\"},{\"attributes\":{\"items\":[{\"id\":\"2147\",\"type\":\"LegendItem\"}],\"plot\":{\"id\":\"2100\",\"subtype\":\"Figure\",\"type\":\"Plot\"}},\"id\":\"2146\",\"type\":\"Legend\"},{\"attributes\":{\"below\":[{\"id\":\"2060\",\"type\":\"LinearAxis\"}],\"left\":[{\"id\":\"2065\",\"type\":\"LinearAxis\"}],\"plot_height\":300,\"plot_width\":400,\"renderers\":[{\"id\":\"2060\",\"type\":\"LinearAxis\"},{\"id\":\"2064\",\"type\":\"Grid\"},{\"id\":\"2065\",\"type\":\"LinearAxis\"},{\"id\":\"2069\",\"type\":\"Grid\"},{\"id\":\"2078\",\"type\":\"BoxAnnotation\"},{\"id\":\"2096\",\"type\":\"Legend\"},{\"id\":\"2088\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"2049\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"2076\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"2052\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"2056\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"2054\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"2058\",\"type\":\"LinearScale\"}},\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"dimension\":1,\"plot\":{\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2066\",\"type\":\"BasicTicker\"}},\"id\":\"2069\",\"type\":\"Grid\"},{\"attributes\":{\"items\":[{\"id\":\"2097\",\"type\":\"LegendItem\"}],\"plot\":{\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"}},\"id\":\"2096\",\"type\":\"Legend\"},{\"attributes\":{\"callback\":null},\"id\":\"2104\",\"type\":\"DataRange1d\"},{\"attributes\":{\"plot\":{\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2061\",\"type\":\"BasicTicker\"}},\"id\":\"2064\",\"type\":\"Grid\"},{\"attributes\":{\"line_color\":\"red\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2086\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"2085\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"2086\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2087\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"2089\",\"type\":\"CDSView\"}},\"id\":\"2088\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null},\"id\":\"2102\",\"type\":\"DataRange1d\"},{\"attributes\":{\"label\":{\"value\":\"nonlinear model\"},\"renderers\":[{\"id\":\"2138\",\"type\":\"GlyphRenderer\"}]},\"id\":\"2147\",\"type\":\"LegendItem\"},{\"attributes\":{\"children\":[{\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"id\":\"2100\",\"subtype\":\"Figure\",\"type\":\"Plot\"}]},\"id\":\"2167\",\"type\":\"Row\"},{\"attributes\":{\"children\":[{\"id\":\"2167\",\"type\":\"Row\"}]},\"id\":\"2168\",\"type\":\"Column\"},{\"attributes\":{\"formatter\":{\"id\":\"2092\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"2050\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2066\",\"type\":\"BasicTicker\"}},\"id\":\"2065\",\"type\":\"LinearAxis\"},{\"attributes\":{\"plot\":null,\"text\":\"Thrust in surge [kg*m/s^2]\"},\"id\":\"2049\",\"type\":\"Title\"},{\"attributes\":{\"callback\":null},\"id\":\"2054\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"2111\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"2154\",\"type\":\"UnionRenderers\"}],\"root_ids\":[\"2171\"]},\"title\":\"Bokeh Application\",\"version\":\"1.0.1\"}};\n",
" var render_items = [{\"docid\":\"2f34e49a-2f05-41b5-ba70-a481dc4ff893\",\"roots\":{\"2171\":\"c60761de-502a-4f68-9f07-3055b2da728e\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "2171"
}
},
"output_type": "display_data"
}
],
"source": [
"# Plot the forces\n",
"p7 = figure(plot_width=400, plot_height=300, title = 'Thrust in surge [kg*m/s^2]',x_axis_label = 'time [s]',toolbar_location='below')\n",
"p7.line(t,T,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p7.left[0].formatter.use_scientific = False\n",
"\n",
"p8 = figure(plot_width=400, plot_height=300, title = 'Resistance in surge (drag force) [kg*m/s^2]',x_axis_label = 'time [s]',toolbar_location='below')\n",
"p8.line(t,R,color=\"red\",line_width=1,legend='nonlinear model')\n",
"p8.left[0].formatter.use_scientific = False\n",
"\n",
"simu_grid_2 = gridplot([[p7, p8]])\n",
"\n",
"show(simu_grid_2)\n",
"\n",
"plt.show()"
]
},
{
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"metadata": {},
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{
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"source": [
"Testing the code has been proved a good tactic since finally the visualizations depict the reasonable response of forces. In this case, when we initiate the state the state with $U=10m/s$ and $n=70rpm$, since the shaft revolutions remain always constant, the thrust($T$) force is increasing until the volume of revolutions stabilizes with the adequate constant velocity, and the resistance($R$) almost equals thrust($T$). \n",
" \n",
"It should be noted that the resistance ($R$) and the propeller thrust ($T$) will outbalance each other in steady state if the loss term $T_{loss} = 0$, that is: \n",
" \n",
"$\\dot u= 0 => -X_{|u|u}|u|u = (1 - t)T$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Add controlled noise to the simulation measurements"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since sensor readings are noisy by nature, we should add controlled noise intensity to come as closer to the true conditions of a vessel's sensor readings as possible. Based on the user's manual of a similar container vessel of our fleet, the below noise intesities have been given by the manufacturer of each sensor. In this case we assume that the STW sensor is providing extremely bad signal measurements."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# Define noise intensity\n",
"noise=[2.5,0.065,1,0.2,0] # [0]position, [1]SOG, [2]STW, [3]currents, [4]resistance "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Add noise i surge vectors only\n",
"x_noise = [i+randn()*noise[0] for i in x]\n",
"SOG_noise = [i+randn()*noise[1] for i in Uog]\n",
"STW_noise = [i+randn()*noise[2] for i in U]\n",
"Ucurr_noise = [i+randn()*noise[3] for i in ucx]\n",
"R_noise = [(j/U[i]**2)*STW_noise[i]**2 for i,j in enumerate(R)] # Works only in surge motion heading north. If else, it should be modified accordingly"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visualize the simulation measurements results with added noise (**Motions** and **Forces**)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> **Motions**"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"2515\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2514\",\"type\":\"UnionRenderers\"}},\"id\":\"2405\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Position [m]\",\"formatter\":{\"id\":\"2399\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"2357\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2373\",\"type\":\"BasicTicker\"}},\"id\":\"2372\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"2514\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2377\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"2378\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"axis_label\":\"Time [s]\",\"formatter\":{\"id\":\"2401\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"2357\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2368\",\"type\":\"BasicTicker\"}},\"id\":\"2367\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"2515\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"2363\",\"type\":\"LinearScale\"},{\"attributes\":{\"plot\":{\"id\":\"2357\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"2368\",\"type\":\"BasicTicker\"}},\"id\":\"2371\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2382\",\"type\":\"HelpTool\"},{\"attributes\":{\"callback\":null},\"id\":\"2361\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"2368\",\"type\":\"BasicTicker\"}],\"root_ids\":[\"2357\"]},\"title\":\"Bokeh Application\",\"version\":\"1.0.1\"}};\n",
" var render_items = [{\"docid\":\"c9966c60-cfc9-4a2e-8f13-01276d44018a\",\"roots\":{\"2357\":\"d4e6b3c0-aade-4f75-a71e-da2ea0c5e25b\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "2357"
}
},
"output_type": "display_data"
}
],
"source": [
"# Initiate the plot\n",
"p = figure(plot_width=750, plot_height=300, title = 'Non-linear surge position [m]',y_axis_label = \"Position [m]\",x_axis_label = \"Time [s]\")\n",
"\n",
"# Add line - scatter renderer\n",
"p.line(t,x_noise,color=\"black\",line_width=1,legend='Added noise')\n",
"p.line(t,x,color=\"black\",line_width=1,legend='Real', line_dash=[4, 4])\n",
"show(p)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
" <div class=\"bk-root\" id=\"37c0baf7-022c-4bed-9c1c-2c24f171e7e0\"></div>\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/javascript": [
"(function(root) {\n",
" function embed_document(root) {\n",
" \n",
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"3941\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3940\",\"type\":\"UnionRenderers\"}},\"id\":\"3910\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3928\",\"type\":\"Line\"},{\"attributes\":{\"axis_label\":\"Speed 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"# Initiate the plot\n",
"p = figure(plot_width=800, plot_height=400, title = 'Non-linear velocity vectors with added manufacturer/provider noise [m/s]',y_axis_label = \"Speed [m/s]\",x_axis_label = \"Time [s]\")\n",
"\n",
"# Add line - scatter renderer\n",
"p.line(t,SOG_noise,color=\"red\",line_width=1,legend='SOG log')\n",
"p.line(t,Uog,color=\"red\",line_width=1,legend='SOG real', line_dash=[4, 4])\n",
"#p.line(t,STW_noise,color=\"blue\",line_width=1,legend='STW log')\n",
"p.line(t,U,color=\"blue\",line_width=1,legend='STW real', line_dash=[4, 4])\n",
"p.line(t,Ucurr_noise,color=\"grey\",line_width=1,legend='Ucurr log')\n",
"p.line(t,ucx,color=\"grey\",line_width=1,legend='Ucurr real', line_dash=[4, 4])\n",
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"Resistance's added noise outcome should be quite high, because of its quadratic relationship with STW velocity. For that reason we will use the quadratic random scalar we used for STW noise above. So the two forces look like the following:"
]
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"source": [
"> **Forces**"
]
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{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"3145\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3144\",\"type\":\"UnionRenderers\"}},\"id\":\"3003\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data_source\":{\"id\":\"3003\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3004\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3005\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3007\",\"type\":\"CDSView\"}},\"id\":\"3006\",\"type\":\"GlyphRenderer\"}],\"root_ids\":[\"2941\"]},\"title\":\"Bokeh Application\",\"version\":\"1.0.1\"}};\n",
" var render_items = [{\"docid\":\"b85958d0-eafa-4eb8-abde-5a5d6285dcb5\",\"roots\":{\"2941\":\"81af3d2d-b037-42ea-8992-b19dbc761713\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "2941"
}
},
"output_type": "display_data"
}
],
"source": [
"# Initiate the plot\n",
"p = figure(plot_width=750, plot_height=300, title = 'Non-linear Forces with added noise [kg*m/s^2]',y_axis_label = \"Force [kg*m/s^2]\",x_axis_label = \"Time [s]\")\n",
"\n",
"# Add line - scatter renderer\n",
"p.line(t,R_noise,color=\"black\",line_width=1,legend='R log')\n",
"p.line(t,R,color=\"black\",line_width=1,legend='R real', line_dash=[4, 4])\n",
"p.line(t,T,color=\"brown\",line_width=1,legend='T log', line_dash=[4, 4])\n",
"show(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Resistance's noise intensity will be added to the system as the std of a stationary timeframe of the above signal."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# Define resistance noise intensity\n",
"noise[4]=np.std(R[270:300]) # Only a small stationary timeframe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Create a Linear Kalman Filter (1st version without the use of STW)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Define the available noisy measurements for the filter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We assume that: \n",
"$x=[P_{GPS},U_{OG},a, U_{TW}, U_{curr}]$ and \n",
"$z=[P_{GPS},U_{OG},a,U_{curr}]$ \n",
"\n",
"and the system dynamics are designed as follows:\n",
"\n",
"|System dynamics of non-Linear Model| \n",
"|:-------------:|\n",
"$$ \\begin{cases} P_{GPS(k+1)} &= P_{GPS(k)} + U_{OG(k)} \\Delta t + \\frac{1}{2} a_{(k)} \\Delta t^2 \\\\\n",
"U_{OG(k+1)} &= U_{OG(k)} + a_{(k)} \\Delta t \\\\\n",
"a_{(k+1)} &= a_{(k)} \\\\\n",
"U_{TW(k+1)} &= U_{OG(k)} - U_{curr(k)} \\\\\n",
"U_{curr(k+1)} &= U_{curr(k)} \\end{cases}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# position, SOG, accelaration, currents # STW in later version\n",
"measurements = map(list,zip(x_noise,SOG_noise,a,Ucurr_noise)) #STW in later verison\n",
"\n",
"# No control vector on the first iteration\n",
"# Thrust\n",
"#control = np.asarray(T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Define the system matrices"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\begin{equation}\n",
" \\begin{cases}\n",
" \\begin{aligned}\n",
" \\mathbf{x}_{k+1} &= \\overbrace{\\begin{bmatrix}1 & \\Delta t & \\frac{1}{2} \\Delta t^2 & 0 & 0 \\\\ 0 & 1 & \\Delta t & 0 & 0 \\\\ 0&0&1&0&0 \\\\ 0&1&0&0&-1 \\\\ 0&0&0&0&1 \\end{bmatrix}}^{\\mathbf{F}_{k}}\\mathbf{x}_{k} + \\overbrace{\\begin{bmatrix} 0&0&0&0&0 \\\\ 0&0&0&0&0 \\\\ 0&0&0&0&0 \\\\ 0&0&0&0&0 \\\\ 0&0&0&0&0 \\end{bmatrix}}^{\\mathbf{Q}_{k}} \\\\\n",
" \\mathbf{y}_{k} &= \\overbrace{\\begin{bmatrix} 1&0&0&0&0 \\\\ 0&1&0&0&0 \\\\ 0&0&1&0&0 \\\\ 0&0&0&0&1 \\end{bmatrix}}^{\\mathbf{H}_{k}}\\mathbf{x}_{k} + \\overbrace{\\begin{bmatrix}6.25&0&0&0 \\\\ 0&0.004225&0&0 \\\\ 0&0&0&0 \\\\ 0&0&0&0.004 \\end{bmatrix}}^{\\mathbf{R}_{k}}\n",
" \\end{aligned}\n",
" \\end{cases}\n",
"\\end{equation}$$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# State vector initial conditions\n",
"x = np.array([0, 10, 0, 9, 1]).T\n",
"\n",
"# State covariance matrix\n",
"P = np.array([[500, 0, 0, 0, 0],\n",
" [0, 16, 0, 0, 0],\n",
" [0, 0, 0, 0, 0],\n",
" [0, 0, 0, 16, 0],\n",
" [0, 0, 0, 0, 2]])\n",
"\n",
"# Process noise matrix. Initiate with zero values\n",
"Q = np.array([[0, 0, 0, 0, 0],\n",
" [0, 0, 0, 0, 0],\n",
" [0, 0, 0, 0, 0],\n",
" [0, 0, 0, 0, 0],\n",
" [0, 0, 0, 0, 10**(-4)]]) #10**(-4)\n",
"\n",
"# position, SOG, a, Ucurr noise intensity\n",
"R = np.diag([noise[0]**2, noise[1]**2, 0, noise[3]**2])\n",
"\n",
"# Process function matrix\n",
"F = np.array([[1, h, 0.5*(h**2), 0, 0],\n",
" [0, 1, h, 0, 0],\n",
" [0, 0, 1, 0, 0],\n",
" [0, 1, 0, 0, -1],\n",
" [0, 0, 0, 0, 1]]) \n",
"\n",
"# Measurement matrix\n",
"H = np.array([[1, 0, 0, 0, 0], \n",
" [0, 1, 0, 0, 0],\n",
" [0, 0, 1, 0, 0],\n",
" [0, 0, 0, 0, 1]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Run the filter algorithm"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"### Uncorrelated measurement and process noise\n",
"mu, cov = [], []\n",
"for z in measurements:\n",
" # predict\n",
" x = F @ x # The a priori state prediction equation\n",
" y = H @ x # The a priori measurement prediction equation\n",
" P = F @ P @ F.T + Q # The a priori covariance prediction equation with white noise Q = V_1\n",
"\n",
" # update avoid singularity matrix by adding a bit of noise in S matrix\n",
" S = H @ P @ H.T + R +randn()*0.0000001 # The right half of the Kalman gain equation\n",
" K = P @ H.T @ inv(S) # The Kalman gain\n",
" y = z - y # The right half of the a posteriori state equation (measurement update)\n",
" x += K @ y # The a posteriori state equation (measurement update)\n",
" P = P - K @ H @ P # The a posteriori covariance equation\n",
"\n",
" # Fill the lists above with the updated state and covariance\n",
" mu.append(x)\n",
" cov.append(P)\n",
"\n",
"mu, cov = np.array(mu), np.array(cov)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot the results"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
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\",\"dtype\":\"float64\",\"shape\":[1001]}},\"selected\":{\"id\":\"3618\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3617\",\"type\":\"UnionRenderers\"}},\"id\":\"3591\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"overlay\":{\"id\":\"3571\",\"type\":\"BoxAnnotation\"}},\"id\":\"3565\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"3563\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"3773\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"3564\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"axis_label\":\"Time[s]\",\"formatter\":{\"id\":\"3587\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"3543\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"3554\",\"type\":\"BasicTicker\"}},\"id\":\"3553\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"3554\",\"type\":\"BasicTicker\"}],\"root_ids\":[\"3543\"]},\"title\":\"Bokeh 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" var render_items = [{\"docid\":\"0c9c4522-903f-4161-aace-cbcbb855d132\",\"roots\":{\"3543\":\"f88a92ba-7170-4dc9-909c-8e4f0733e3b0\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" clearInterval(timer);\n",
" }\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" clearInterval(timer);\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "3543"
}
},
"output_type": "display_data"
}
],
"source": [
"# Initiate the plot\n",
"p = figure(plot_width=750, plot_height=300, title = 'Measurement Simulation, Kinetic model v1',y_axis_label = \"Speed [m/s]\",x_axis_label = \"Time[s]\")\n",
"\n",
"# add a line renderer\n",
"p.line(t, SOG_noise, line_color=\"red\", line_width=1,legend=\"SOG log\")\n",
"#p.line(t, STW_noise, line_color=\"blue\", line_width=1,legend=\"STW log\")\n",
"p.line(t, U, line_color=\"blue\", line_width=1,legend=\"STW real\", line_dash=[4, 4])\n",
"p.line(t, mu[:, 3], line_color=\"purple\", line_width=1,legend=\"STW filter\")\n",
"\n",
"show(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It seems like the filter quickly reacted to sensor noise and estimated the STW measurement better than a noisy sensor! Which is great news! At the second itteration, we will use a non-linear Kalman Filter (particularly the Unscented Kalman Filter) which is supposed to give better results in the above non-linear motion of the vessel. Stay tuned!"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:python]",
"language": "python",
"name": "conda-env-python-py"
},
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"name": "ipython",
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},
"file_extension": ".py",
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}
},
"nbformat": 4,
"nbformat_minor": 2
}
Raw
requirements.txt
numpy==1.15.4
scipy==1.1.0
pandas==0.23.4
bokeh==1.0.1
matplotlib==3.0.2
Raw
simulator_functions.py
import numpy as np
import math
from numpy.linalg import inv
def container(x,ui):
'''
container function returns the speed U in m/s (optionally) and the
time derivative of the state vector: x = [ u v r x y psi p phi delta n ] for
a container ship L = 175 m, where
u = surge velocity SOG (m/s)
v = sway velocity SOG (m/s)
r = yaw velocity (rad/s)
x = position in x-direction (m)
y = position in y-direction (m)
psi = yaw angle (rad)
p = roll velocity (rad/s)
phi = roll angle (rad)
delta = actual rudder angle (rad)
n = actual shaft velocity (rpm)
ucx = current surge velocity (m/s) invoke constant current x
ucy = current sway velocity (m/s) invoke constant current y
The input vector is :
ui = [ delta_c n_c ]' where
delta_c = commanded rudder angle (rad)
n_c = commanded shaft velocity (rpm)
Reference: Son og Nomoto (1982). On the Coupled Motion of Steering and
Rolling of a High Speed Container Ship, Naval Architect of Ocean Engineering,
20: 73-83. From J.S.N.A. , Japan, Vol. 150, 1981.
Author: Trygve Lauvdal
Date: 12th May 1994
Revisions: 18th July 2001 (Thor I. Fossen): added output U, changed order of x-vector
20th July 2001 (Thor I. Fossen): changed my = 0.000238 to my = 0.007049
10th January 2019 (Angelos Ikonomakis): translated the whole script in python
'''
assert (len(x) == 12),'x-vector must have dimension 10 !'
assert (len(ui) == 2),'u-vector must have dimension 2 !'
# Normalization variables
L = 175 # length of ship (m)
#U = np.sqrt(x[0]**2 + x[1]**2) # service speed STW (m/s)
U = np.sqrt((x[0]-x[10])**2 + (x[1]-x[11])**2) # service speed STW (m/s)
Uog = np.sqrt(x[0]**2 + x[1]**2) # SOG
# Check service speed
assert (U > 0),'The ship must have speed greater than zero'
assert (x[9] > 0),'The propeller rpm must be greater than zero'
delta_max = 10; # max rudder angle (deg)
Ddelta_max = 5; # max rudder rate (deg/s)
n_max = 160; # max shaft velocity (rpm)
# Non-dimensional states and inputs
delta_c = ui[0];
n_c = ui[1]/60*L/U;
u = (x[0]-x[10])/U; v = (x[1]-x[11])/U;
p = x[6]*L/U; r = x[2]*L/U;
phi = x[7]; psi = x[5];
delta = x[8]; n = x[9]/60*L/U;
# Parameters, hydrodynamic derivatives and main dimensions
m = 0.00792; mx = 0.000238; my = 0.007049;
Ix = 0.0000176; alphay = 0.05; lx = 0.0313;
ly = 0.0313; Ix = 0.0000176; Iz = 0.000456;
Jx = 0.0000034; Jz = 0.000419; xG = 0;
B = 25.40; dF = 8.00; g = 9.81;
dA = 9.00; d = 8.50; nabla = 21222;
KM = 10.39; KB = 4.6154; AR = 33.0376;
Delta = 1.8219; D = 6.533; GM = 0.3/L;
rho = 1025; t = 0.175; T = 0.0005;
W = rho*g*nabla/(rho*L**2*U**2/2);
Xuu = -0.0004226; Xvr = -0.00311; Xrr = 0.00020;
Xphiphi = -0.00020; Xvv = -0.00386;
Kv = 0.0003026; Kr = -0.000063; Kp = -0.0000075;
Kphi = -0.000021; Kvvv = 0.002843; Krrr = -0.0000462;
Kvvr = -0.000588; Kvrr = 0.0010565; Kvvphi = -0.0012012;
Kvphiphi = -0.0000793; Krrphi = -0.000243; Krphiphi = 0.00003569;
Yv = -0.0116; Yr = 0.00242; Yp = 0;
Yphi = -0.000063; Yvvv = -0.109; Yrrr = 0.00177;
Yvvr = 0.0214; Yvrr = -0.0405; Yvvphi = 0.04605;
Yvphiphi = 0.00304; Yrrphi = 0.009325; Yrphiphi = -0.001368;
Nv = -0.0038545; Nr = -0.00222; Np = 0.000213;
Nphi = -0.0001424; Nvvv = 0.001492; Nrrr = -0.00229;
Nvvr = -0.0424; Nvrr = 0.00156; Nvvphi = -0.019058;
Nvphiphi = -0.0053766; Nrrphi = -0.0038592; Nrphiphi = 0.0024195;
kk = 0.631; epsilon = 0.921; xR = -0.5;
wp = 0.184; tau = 1.09; xp = -0.526;
cpv = 0.0; cpr = 0.0; ga = 0.088;
cRr = -0.156; cRrrr = -0.275; cRrrv = 1.96;
cRX = 0.71; aH = 0.237; zR = 0.033;
xH = -0.48;
# Masses and moments of inertia
m11 = (m+mx);
m22 = (m+my);
m32 = -my*ly;
m42 = my*alphay;
m33 = (Ix+Jx);
m44 = (Iz+Jz);
# Rudder saturation and dynamics
if np.abs(delta_c) >= delta_max*math.pi/180:
delta_c = np.sign(delta_c)*delta_max*math.pi/180;
delta_dot = delta_c - delta
if np.abs(delta_dot) >= Ddelta_max*math.pi/180:
delta_dot = np.sign(delta_dot)*Ddelta_max*math.pi/180;
# Shaft velocity saturation and dynamics
n_c = n_c*U/L;
n = n*U/L;
if np.abs(n_c) >= n_max/60:
n_c = np.sign(n_c)*n_max/60;
if n > 0.3:
Tm=5.65/n;
else:
Tm=18.83;
n_dot = 1/Tm*(n_c-n)*60;
# Calculation of state derivatives
vR = ga*v + cRr*r + cRrrr*r**3 + cRrrv*r**2*v;
uP = math.cos(v)*((1 - wp) + tau*((v + xp*r)**2 + cpv*v + cpr*r));
J = uP*U/(n*D);
KT = 0.527 - 0.455*J;
uR = uP*epsilon*np.sqrt(1 + 8*kk*KT/(math.pi*J**2));
alphaR = delta + math.atan(vR/uR);
FN = - ((6.13*Delta)/(Delta + 2.25))*(AR/L**2)*(uR**2 + vR**2)*math.sin(alphaR);
T = 2*rho*D**4/(U**2*L**2*rho)*KT*n*np.abs(n); # Thrust
T_real = rho*D**4*KT*n*np.abs(n); # Denormalized Thrust (surge)
R_real = 0.5*rho*U**2*L**2*Xuu*u**2 # Denormalized Resistance (surge)
# Forces and moments
X = Xuu*u**2 + (1-t)*T + Xvr*v*r + Xvv*v**2 + Xrr*r**2 + Xphiphi*phi**2 + \
cRX*FN*math.sin(delta) + (m + my)*v*r;
Y = Yv*v + Yr*r + Yp*p + Yphi*phi + Yvvv*v**3 + Yrrr*r**3 + Yvvr*v**2*r + \
Yvrr*v*r**2 + Yvvphi*v**2*phi + Yvphiphi*v*phi**2 + Yrrphi*r**2*phi + \
Yrphiphi*r*phi**2 + (1 + aH)*FN*math.cos(delta) - (m + mx)*u*r;
K = Kv*v + Kr*r + Kp*p + Kphi*phi + Kvvv*v**3 + Krrr*r**3 + Kvvr*v**2*r + \
Kvrr*v*r**2 + Kvvphi*v**2*phi + Kvphiphi*v*phi**2 + Krrphi*r**2*phi + \
Krphiphi*r*phi**2 - (1 + aH)*zR*FN*math.cos(delta) + mx*lx*u*r - W*GM*phi;
N = Nv*v + Nr*r + Np*p + Nphi*phi + Nvvv*v**3 + Nrrr*r**3 + Nvvr*v**2*r + \
Nvrr*v*r**2 + Nvvphi*v**2*phi + Nvphiphi*v*phi**2 + Nrrphi*r**2*phi + \
Nrphiphi*r*phi**2 + (xR + aH*xH)*FN*math.cos(delta);
# Dimensional state derivatives xdot = [ u v r x y psi p phi delta n ]'
detM = m22*m33*m44-m32**2*m44-m42**2*m33;
xdot =np.array([ X*(U**2/L)/m11,
-((-m33*m44*Y+m32*m44*K+m42*m33*N)/detM)*(U**2/L),
((-m42*m33*Y+m32*m42*K+N*m22*m33-N*m32**2)/detM)*(U**2/L**2),
(math.cos(psi)*u-math.sin(psi)*math.cos(phi)*v)*U,
(math.sin(psi)*u+math.cos(psi)*math.cos(phi)*v)*U,
math.cos(phi)*r*(U/L),
((-m32*m44*Y+K*m22*m44-K*m42**2+m32*m42*N)/detM)*(U**2/L**2),
p*(U/L),
delta_dot,
n_dot,
0, # hardcode x-current acceleration
0 # hardcode y-current acceleration
]);
return xdot, U, Uog, T_real, R_real
def Lcontainer(x,ui,U0=7.0):
'''Lcontainer(x,ui,U0) returns the speed U in m/s (optionally) and the
time derivative of the state vector: x = [ u v r x y psi p phi delta ]' using the
the LINEARIZED model corresponding to the nonlinear model container.m.
u = surge velocity (m/s)
v = sway velocity (m/s)
r = yaw velocity (rad/s)
x = position in x-direction (m)
y = position in y-direction (m)
psi = yaw angle (rad)
p = roll velocity (rad/s)
phi = roll angle (rad)
delta = actual rudder angle (rad)
The inputs are :
Uo = service speed (optinally. Default speed U0 = 7 m/s
ui = commanded rudder angle (rad)
Reference: Son og Nomoto (1982). On the Coupled Motion of Steering and
Rolling of a High Speed Container Ship, Naval Architect of Ocean Engineering,
20: 73-83. From J.S.N.A. , Japan, Vol. 150, 1981.
Author: Thor I. Fossen
Date: 23rd July 2001
Revisions:
'''
# Check of input and state dimensions
assert (x.shape[0] == 9),'x-vector must have dimension 9 !'
assert (U0 > 0),'The ship must have speed greater than zero'
# Normalization variables
rho = 1025 # water density (kg/m^3)
L = 175 # length of ship (m)
U = np.sqrt(U0**2 + x[1,0]**2) # ship speed (m/s)
# rudder limitations
delta_max = 10 # max rudder angle (deg)
Ddelta_max = 5 # max rudder rate (deg/s)
# States and inputs
delta_c = ui
v = x[1,0]; y = x[4,0];
r = x[2,0]; psi = x[5,0];
p = x[6,0]; phi = x[7,0];
nu = np.array([[v, r, p]]).T
eta = np.array([[y, psi, phi]]).T
delta = x[8,0]
# Linear model using nondimensional matrices and states with dimension (see Fossen 2002):
# TM'inv(T) dv/dt + (U/L) TN'inv(T) v + (U/L)^2 TG'inv(T) eta = (U^2/L) T b' delta
T = np.diag([ 1, 1/L, 1/L]);
Tinv = np.diag([ 1, L, L ]);
M = np.array([[ 0.01497, 0.0003525, -0.0002205],
[ 0.0003525, 0.000875, 0],
[-0.0002205, 0, 0.0000210 ]])
N = np.array([[ 0.012035, 0.00522, 0],
[ 0.0038436, 0.00243, -0.000213],
[-0.000314, 0.0000692, 0.0000075]])
G = np.array([[ 0, 0, 0.0000704],
[ 0, 0, 0.0001468],
[ 0, 0, 0.0004966]])
b = np.array([[-0.002578, 0.00126, 0.0000855]]).T
# Rudder saturation and dynamics
if np.abs(delta_c) >= delta_max*math.pi/180:
delta_c = np.sign(delta_c)*delta_max*math.pi/180
delta_dot = delta_c - delta
if np.abs(delta_dot) >= Ddelta_max*math.pi/180:
delta_dot = np.sign(delta_dot)*Ddelta_max*math.pi/180
# TM'inv(T) dv/dt + (U/L) TN'inv(T) v + (U/L)^2 TG'inv(T) eta = (U^2/L) T b' delta
nudot = inv(T @ M @ Tinv) @ ((U**2/L)*T@b*delta - (U/L)*T@N@Tinv@nu - (U/L)**2*T@G@Tinv@eta)
# Dimensional state derivatives xdot = [ u v r x y psi p phi delta ]'
xdot =np.array([[ 0,
nudot[0,0],
nudot[1,0],
math.cos(psi)*U0-math.sin(psi)*math.cos(phi)*v,
math.sin(psi)*U0+math.cos(psi)*math.cos(phi)*v,
math.cos(phi)*r,
nudot[2,0],
p,
delta_dot ]]).T
return xdot, U
def euler2(xdot,x,h):
'''
EULER2 Integrate a system of ordinary differential equations using
Euler's 2nd-order method.
xnext = euler2(xdot,x,h)
xdot - dx/dt(k) = f(x(k)
x - x(k)
xnext - x(k+1)
h - step size
Author: Thor I. Fossen
Date: 14th June 2001
Revisions:
'''
xnext = x + h*xdot;
return xnext
def zigzag(ship,x,ui,t_final,t_rudderexecute,h,maneuver=[20,20]):
'''
ZIGZAG [t,u,v,r,x,y,psi,U] = zigzag(ship,x,ui,t_final,t_rudderexecute,h,maneuver)
performs the zig-zag maneuver, see ExZigZag.m
Inputs :
'ship' = ship model. Compatible with the models under .../gnc/VesselModels/
x = initial state vector for ship model
ui = [delta,:] where delta=0 and the other values are non-zero if any
t_final = final simulation time
t_rudderexecute = time control input is activated
h = sampling time
maneuver = [rudder angle, heading angle]. Default 20-20 deg that is: maneuver = [20, 20]
rudder is changed to maneuver(1) when heading angle is larger than maneuver(2)
Outputs :
t = time vector
u,v,r,x,y,psi,U = time series
Author: Thor I. Fossen
Date: 22th July 2001
Revisions: 15th July 2002, switching logic has been modified to handle arbitrarily maneuvers
'''
assert (t_final>t_rudderexecute),'t_final must be larger than t_rudderexecute';
N = round(t_final/h) # number of samples
xout = np.zeros((N+1,9)) # memory allocation
print('Simulating...')
u_ship=ui
for i in range(0,N+1):
time = i*h;
psi = x[5]*180/math.pi
r = x[2]
if round(time)==t_rudderexecute:
u_ship[0]=maneuver[0]*math.pi/180
if round(time) > t_rudderexecute:
if (psi>=maneuver[1] and r>0):
u_ship[0] = -maneuver[0]*math.pi/180
elif (psi<=-maneuver[1] and r<0):
u_ship[0] = maneuver[0]*math.pi/180
xdot,U, X, Y, K, N = container(x,ui) # ship model
xout[i,:] = np.hstack((time,x[0:6],U,u_ship[0]))
x = euler2(xdot,x,h) # Euler integration
# time-series
t = xout[:,0];
u = xout[:,1];
v = xout[:,2];
r = xout[:,3]*180/math.pi;
x = xout[:,4];
y = xout[:,5];
psi = xout[:,6]*180/math.pi;
U = xout[:,7];
delta_c = xout[:,8]*180/math.pi;
return t,u,v,r,x,y,psi,U,delta_c
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