geneticOptimizationSliderCrank.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Slider crank model with verification in MATLAB for machine dynamics course
5# optionally, the slider crank is mounted on a floating frame, leading to vibrations
6# if the system is unbalanced
7# Use this example in combination with cmd: 'python resultsMonitor.py solution/geneticSliderCrank.txt'
8#
9# Author: Johannes Gerstmayr
10# Date: 2019-12-07 (created)
11# 2021-01-10 (adapted for genetic optimization)
12#
13# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
14#
15#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
16
17import exudyn as exu
18from exudyn.itemInterface import *
19from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
20import exudyn.graphics as graphics #only import if it does not conflict
21from exudyn.processing import GeneticOptimization, ParameterVariation, PlotOptimizationResults2D
22
23import numpy as np #for postprocessing
24import os
25from time import sleep
26
27useGraphics = False
28L1=0.1
29L2=0.3
30m1=0.4
31m2=0.2
32m3=0.1
33s1opt = -L1*(m2+m3)/m1 #-0.075
34s2opt = -m3/m2*L2 #-0.15
35
36#this is the function which is repeatedly called from ParameterVariation
37#parameterSet contains dictinary with varied parameters
38def ParameterFunction(parameterSet):
39 SC = exu.SystemContainer()
40 mbs = SC.AddSystem()
41
42 #++++++++++++++++++++++++++++++++++++++++++++++
43 #++++++++++++++++++++++++++++++++++++++++++++++
44 #store default parameters in structure (all these parameters can be varied!)
45 class P: pass #create emtpy structure for parameters; simplifies way to update parameters
46 P.s1=L1*0.5
47 P.s2=L2*0.5
48 P.h=0.002
49 P.computationIndex = ''
50
51 # #now update parameters with parameterSet (will work with any parameters in structure P)
52 for key,value in parameterSet.items():
53 setattr(P,key,value)
54
55 #++++++++++++++++++++++++++++++++++++++++++++++
56 #++++++++++++++++++++++++++++++++++++++++++++++
57 #START HERE: create parameterized model
58
59 testCases = 1 #floating body
60 nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
61 mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGround, coordinate=0)) #Ground node ==> no action
62
63
64 #++++++++++++++++++++++++++++++++
65 #floating body to mount slider-crank mechanism
66 constrainGroundBody = (testCases == 0) #use this flag to fix ground body
67
68 #graphics for floating frame:
69 gFloating = graphics.BrickXYZ(-0.25, -0.25, -0.1, 0.8, 0.25, -0.05, color=[0.3,0.3,0.3,1.])
70
71 if constrainGroundBody:
72 floatingRB = mbs.AddObject(ObjectGround(referencePosition=[0,0,0], visualization=VObjectGround(graphicsData=[gFloating])))
73 mFloatingN = mbs.AddMarker(MarkerBodyPosition(bodyNumber = floatingRB, localPosition=[0,0,0]))
74 else:
75 nFloating = mbs.AddNode(Rigid2D(referenceCoordinates=[0,0,0], initialVelocities=[0,0,0]));
76 mFloatingN = mbs.AddMarker(MarkerNodePosition(nodeNumber=nFloating))
77 floatingRB = mbs.AddObject(RigidBody2D(physicsMass=2, physicsInertia=1, nodeNumber=nFloating, visualization=VObjectRigidBody2D(graphicsData=[gFloating])))
78 mRB0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=0))
79 mRB1 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=1))
80 mRB2 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=2))
81
82 #add spring dampers for reference frame:
83 k=5000 #stiffness of floating body
84 d=k*0.01
85 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB0], stiffness=k, damping=d))
86 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB1], stiffness=k, damping=d))
87 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB2], stiffness=k, damping=d))
88 mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mRB2]))
89
90
91
92 #++++++++++++++++++++++++++++++++
93 #nodes and bodies
94 omega=2*pi/60*300 #3000 rpm
95 M=0.1 #torque (default: 0.1)
96
97 s1L=-P.s1
98 s1R=L1-P.s1
99 s2L=-P.s2
100 s2R=L2-P.s2
101
102 #lambda=L1/L2
103 J1=(m1/12.)*L1**2 #inertia w.r.t. center of mass
104 J2=(m2/12.)*L2**2 #inertia w.r.t. center of mass
105
106 ty = 0.05 #thickness
107 tz = 0.05 #thickness
108
109 graphics1 = graphics.RigidLink(p0=[s1L,0,-0.5*tz],p1=[s1R,0,-0.5*tz],
110 axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
111 thickness=0.8*ty, width=[tz,tz], color=graphics.color.steelblue,nTiles=16)
112
113 graphics2 = graphics.RigidLink(p0=[s2L,0,0.5*tz],p1=[s2R,0,0.5*tz],
114 axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
115 thickness=0.8*ty, width=[tz,tz], color=graphics.color.lightred,nTiles=16)
116
117 #crank:
118 nRigid1 = mbs.AddNode(Rigid2D(referenceCoordinates=[P.s1,0,0],
119 initialVelocities=[0,0,0]));
120 oRigid1 = mbs.AddObject(RigidBody2D(physicsMass=m1,
121 physicsInertia=J1,
122 nodeNumber=nRigid1,
123 visualization=VObjectRigidBody2D(graphicsData= [graphics1])))
124
125 #connecting rod:
126 nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+P.s2,0,0],
127 initialVelocities=[0,0,0]));
128 oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=m2,
129 physicsInertia=J2,
130 nodeNumber=nRigid2,
131 visualization=VObjectRigidBody2D(graphicsData= [graphics2])))
132
133
134 #++++++++++++++++++++++++++++++++
135 #slider:
136 c=0.025 #dimension of mass
137 graphics3 = graphics.BrickXYZ(-c,-c,-c*2,c,c,0,graphics.color.grey)
138
139 #nMass = mbs.AddNode(Point2D(referenceCoordinates=[L1+L2,0]))
140 #oMass = mbs.AddObject(MassPoint2D(physicsMass=m3, nodeNumber=nMass,visualization=VObjectMassPoint2D(graphicsData= [graphics3])))
141 nMass = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+L2,0,0]))
142 oMass = mbs.AddObject(RigidBody2D(physicsMass=m3, physicsInertia=0.001*m3, nodeNumber=nMass,visualization=VObjectRigidBody2D(graphicsData= [graphics3])))
143
144 #++++++++++++++++++++++++++++++++
145 #markers for joints:
146 mR1Left = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid1, localPosition= [s1L,0.,0.])) #support point # MUST be a rigidBodyMarker, because a torque is applied
147 mR1Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=[s1R,0.,0.])) #end point; connection to connecting rod
148
149 mR2Left = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition= [s2L,0.,0.])) #connection to crank
150 mR2Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[s2R,0.,0.])) #end point; connection to slider
151
152 mMass = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oMass, localPosition=[ 0.,0.,0.]))
153 mG0 = mFloatingN
154
155 #++++++++++++++++++++++++++++++++
156 #joints:
157 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mG0,mR1Left]))
158 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR1Right,mR2Left]))
159 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR2Right,mMass]))
160
161
162 #prismatic joint:
163 mRigidGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber = floatingRB, localPosition = [L1+L2,0,0]))
164 mRigidSlider = mbs.AddMarker(MarkerBodyRigid(bodyNumber = oMass, localPosition = [0,0,0]))
165
166 mbs.AddObject(PrismaticJoint2D(markerNumbers=[mRigidGround,mRigidSlider], constrainRotation=True))
167
168
169 #user function for load; switch off load after 1 second
170 userLoadOn = True
171 def userLoad(mbs, t, load):
172 setLoad = 0
173 if userLoadOn:
174 setLoad = load
175 omega = mbs.GetNodeOutput(nRigid1,variableType = exu.OutputVariableType.AngularVelocity)[2]
176 if omega > 2*pi*2:
177 #print("t=",t)
178 userLoadOn = False
179 return setLoad
180
181 #loads and driving forces:
182 mRigid1CoordinateTheta = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nRigid1, coordinate=2)) #angle coordinate is constrained
183 #mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M, loadUserFunction=userLoad)) #torque at crank
184 mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M)) #torque at crank
185
186 #write motion of support frame:
187 sFloating = mbs.AddSensor(SensorNode(nodeNumber=nFloating,
188 storeInternal=True,
189 outputVariableType=exu.OutputVariableType.Position))
190
191 #++++++++++++++++++++++++++++++++
192 #assemble, adjust settings and start time integration
193 mbs.Assemble()
194
195 simulationSettings = exu.SimulationSettings() #takes currently set values or default values
196 tEnd = 3
197
198 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/P.h)
199 simulationSettings.timeIntegration.endTime = tEnd
200
201
202 simulationSettings.solutionSettings.solutionWritePeriod = 2e-3
203 simulationSettings.solutionSettings.writeSolutionToFile = useGraphics
204
205 simulationSettings.timeIntegration.newton.useModifiedNewton = True
206 simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8
207 simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-8
208
209 #++++++++++++++++++++++++++++++++++++++++++
210 #solve index 2 / trapezoidal rule:
211 simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
212 simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
213
214 dSize = 0.02
215 SC.visualizationSettings.nodes.defaultSize = dSize
216 SC.visualizationSettings.markers.defaultSize = dSize
217 SC.visualizationSettings.bodies.defaultSize = [dSize, dSize, dSize]
218 SC.visualizationSettings.connectors.defaultSize = dSize
219
220 #data obtained from SC.GetRenderState(); use np.round(d['modelRotation'],4)
221 SC.visualizationSettings.openGL.initialModelRotation = [[ 0.87758, 0.04786, -0.47703],
222 [ 0. , 0.995 , 0.09983],
223 [ 0.47943, -0.08761, 0.8732]]
224 SC.visualizationSettings.openGL.initialZoom = 0.47
225 SC.visualizationSettings.openGL.initialCenterPoint = [0.192, -0.0039,-0.075]
226 SC.visualizationSettings.openGL.initialMaxSceneSize = 0.4
227 SC.visualizationSettings.general.autoFitScene = False
228 #mbs.WaitForUserToContinue()
229
230 if useGraphics:
231 exu.StartRenderer()
232
233 mbs.SolveDynamic(simulationSettings)
234
235 if useGraphics:
236 SC.WaitForRenderEngineStopFlag()
237 exu.StopRenderer() #safely close rendering window!
238
239 #++++++++++++++++++++++++++++++++++++++++++
240 #evaluate error:
241 #data = np.loadtxt(sensorFileName, comments='#', delimiter=',')
242 data = mbs.GetSensorStoredData(sFloating)
243
244 errorNorm = max(abs(data[:,1])) + max(abs(data[:,2])) #max displacement in x and y direction
245
246 if useGraphics:
247 print("max. oszillation=", errorNorm)
248
249 mbs.PlotSensor(sensorNumbers=[sFloating,sFloating], components=[0,1])
250
251 del mbs
252 del SC
253
254 return errorNorm
255 #++++++++++++++++++++++++++++++++++++++++++
256
257import matplotlib.pyplot as plt
258import matplotlib.ticker as ticker
259
260doOptimize = True
261#now perform parameter variation
262if __name__ == '__main__': #include this to enable parallel processing
263 if doOptimize:
264 import time
265
266 #%%++++++++++++++++++++++++++++++++++++++++++++++++++++
267 #GeneticOptimization
268 start_time = time.time()
269 [pOpt, vOpt, pList, values] = GeneticOptimization(objectiveFunction = ParameterFunction,
270 parameters = {'s1':(-L1,L1), 's2':(-L2,L2)}, #parameters provide search range
271 numberOfGenerations = 30,
272 populationSize = 50,
273 elitistRatio = 0.1,
274 crossoverProbability = 0.1,
275 rangeReductionFactor = 0.5,
276 addComputationIndex=True,
277 randomizerInitialization=0, #for reproducible results
278 #distanceFactor = 0.1, #for this example only one significant minimum
279 debugMode=False,
280 useMultiProcessing=True, #may be problematic for test
281 showProgress=True,
282 resultsFile = 'solution/geneticSliderCrank.txt',
283 )
284 #exu.Print("--- %s seconds ---" % (time.time() - start_time))
285
286 exu.Print("[pOpt, vOpt]=", [pOpt, vOpt])
287 u = vOpt
288 exu.Print("optimum=",u)
289 # using files:
290 # [pOpt, vOpt]= [{'s1': -0.07497827333782427, 's2': -0.14943029494085874}, 3.4312580948e-05]
291 # optimum= 3.4312580948e-05
292
293 # using internal storage:
294 # [pOpt, vOpt]= [{'s1': -0.07497827333782427, 's2': -0.14943029494085874}, 3.431258094752888e-05]
295 # optimum= 3.431258094752888e-05
296
297 if False:
298 # from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
299 import matplotlib.pyplot as plt
300
301 plt.close('all')
302 [figList, axList] = PlotOptimizationResults2D(pList, values, yLogScale=True)
303 else:
304 useGraphics = True
305 parameterSet = {'s1':L1*0.5, 's2':L2*0.5, 'h':1e-5}
306 #parameterSet = {'s1':-0.075, 's2':-0.15, 'h':1e-5}
307 ParameterFunction(parameterSet)