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 *
20from exudyn.processing import GeneticOptimization, ParameterVariation, PlotOptimizationResults2D
21
22import numpy as np #for postprocessing
23import os
24from time import sleep
25
26useGraphics = False
27L1=0.1
28L2=0.3
29m1=0.4
30m2=0.2
31m3=0.1
32s1opt = -L1*(m2+m3)/m1 #-0.075
33s2opt = -m3/m2*L2 #-0.15
34
35#this is the function which is repeatedly called from ParameterVariation
36#parameterSet contains dictinary with varied parameters
37def ParameterFunction(parameterSet):
38 SC = exu.SystemContainer()
39 mbs = SC.AddSystem()
40
41 #++++++++++++++++++++++++++++++++++++++++++++++
42 #++++++++++++++++++++++++++++++++++++++++++++++
43 #store default parameters in structure (all these parameters can be varied!)
44 class P: pass #create emtpy structure for parameters; simplifies way to update parameters
45 P.s1=L1*0.5
46 P.s2=L2*0.5
47 P.h=0.002
48 P.computationIndex = ''
49
50 # #now update parameters with parameterSet (will work with any parameters in structure P)
51 for key,value in parameterSet.items():
52 setattr(P,key,value)
53
54 #++++++++++++++++++++++++++++++++++++++++++++++
55 #++++++++++++++++++++++++++++++++++++++++++++++
56 #START HERE: create parameterized model
57
58 testCases = 1 #floating body
59 nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
60 mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGround, coordinate=0)) #Ground node ==> no action
61
62
63 #++++++++++++++++++++++++++++++++
64 #floating body to mount slider-crank mechanism
65 constrainGroundBody = (testCases == 0) #use this flag to fix ground body
66
67 #graphics for floating frame:
68 gFloating = GraphicsDataOrthoCube(-0.25, -0.25, -0.1, 0.8, 0.25, -0.05, color=[0.3,0.3,0.3,1.])
69
70 if constrainGroundBody:
71 floatingRB = mbs.AddObject(ObjectGround(referencePosition=[0,0,0], visualization=VObjectGround(graphicsData=[gFloating])))
72 mFloatingN = mbs.AddMarker(MarkerBodyPosition(bodyNumber = floatingRB, localPosition=[0,0,0]))
73 else:
74 nFloating = mbs.AddNode(Rigid2D(referenceCoordinates=[0,0,0], initialVelocities=[0,0,0]));
75 mFloatingN = mbs.AddMarker(MarkerNodePosition(nodeNumber=nFloating))
76 floatingRB = mbs.AddObject(RigidBody2D(physicsMass=2, physicsInertia=1, nodeNumber=nFloating, visualization=VObjectRigidBody2D(graphicsData=[gFloating])))
77 mRB0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=0))
78 mRB1 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=1))
79 mRB2 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=2))
80
81 #add spring dampers for reference frame:
82 k=5000 #stiffness of floating body
83 d=k*0.01
84 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB0], stiffness=k, damping=d))
85 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB1], stiffness=k, damping=d))
86 mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB2], stiffness=k, damping=d))
87 mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mRB2]))
88
89
90
91 #++++++++++++++++++++++++++++++++
92 #nodes and bodies
93 omega=2*pi/60*300 #3000 rpm
94 M=0.1 #torque (default: 0.1)
95
96 s1L=-P.s1
97 s1R=L1-P.s1
98 s2L=-P.s2
99 s2R=L2-P.s2
100
101 #lambda=L1/L2
102 J1=(m1/12.)*L1**2 #inertia w.r.t. center of mass
103 J2=(m2/12.)*L2**2 #inertia w.r.t. center of mass
104
105 ty = 0.05 #thickness
106 tz = 0.05 #thickness
107
108 graphics1 = GraphicsDataRigidLink(p0=[s1L,0,-0.5*tz],p1=[s1R,0,-0.5*tz],
109 axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
110 thickness=0.8*ty, width=[tz,tz], color=color4steelblue,nTiles=16)
111
112 graphics2 = GraphicsDataRigidLink(p0=[s2L,0,0.5*tz],p1=[s2R,0,0.5*tz],
113 axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
114 thickness=0.8*ty, width=[tz,tz], color=color4lightred,nTiles=16)
115
116 #crank:
117 nRigid1 = mbs.AddNode(Rigid2D(referenceCoordinates=[P.s1,0,0],
118 initialVelocities=[0,0,0]));
119 oRigid1 = mbs.AddObject(RigidBody2D(physicsMass=m1,
120 physicsInertia=J1,
121 nodeNumber=nRigid1,
122 visualization=VObjectRigidBody2D(graphicsData= [graphics1])))
123
124 #connecting rod:
125 nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+P.s2,0,0],
126 initialVelocities=[0,0,0]));
127 oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=m2,
128 physicsInertia=J2,
129 nodeNumber=nRigid2,
130 visualization=VObjectRigidBody2D(graphicsData= [graphics2])))
131
132
133 #++++++++++++++++++++++++++++++++
134 #slider:
135 c=0.025 #dimension of mass
136 graphics3 = GraphicsDataOrthoCube(-c,-c,-c*2,c,c,0,color4grey)
137
138 #nMass = mbs.AddNode(Point2D(referenceCoordinates=[L1+L2,0]))
139 #oMass = mbs.AddObject(MassPoint2D(physicsMass=m3, nodeNumber=nMass,visualization=VObjectMassPoint2D(graphicsData= [graphics3])))
140 nMass = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+L2,0,0]))
141 oMass = mbs.AddObject(RigidBody2D(physicsMass=m3, physicsInertia=0.001*m3, nodeNumber=nMass,visualization=VObjectRigidBody2D(graphicsData= [graphics3])))
142
143 #++++++++++++++++++++++++++++++++
144 #markers for joints:
145 mR1Left = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid1, localPosition= [s1L,0.,0.])) #support point # MUST be a rigidBodyMarker, because a torque is applied
146 mR1Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=[s1R,0.,0.])) #end point; connection to connecting rod
147
148 mR2Left = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition= [s2L,0.,0.])) #connection to crank
149 mR2Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[s2R,0.,0.])) #end point; connection to slider
150
151 mMass = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oMass, localPosition=[ 0.,0.,0.]))
152 mG0 = mFloatingN
153
154 #++++++++++++++++++++++++++++++++
155 #joints:
156 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mG0,mR1Left]))
157 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR1Right,mR2Left]))
158 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR2Right,mMass]))
159
160
161 #prismatic joint:
162 mRigidGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber = floatingRB, localPosition = [L1+L2,0,0]))
163 mRigidSlider = mbs.AddMarker(MarkerBodyRigid(bodyNumber = oMass, localPosition = [0,0,0]))
164
165 mbs.AddObject(PrismaticJoint2D(markerNumbers=[mRigidGround,mRigidSlider], constrainRotation=True))
166
167
168 #user function for load; switch off load after 1 second
169 userLoadOn = True
170 def userLoad(mbs, t, load):
171 setLoad = 0
172 if userLoadOn:
173 setLoad = load
174 omega = mbs.GetNodeOutput(nRigid1,variableType = exu.OutputVariableType.AngularVelocity)[2]
175 if omega > 2*pi*2:
176 #print("t=",t)
177 userLoadOn = False
178 return setLoad
179
180 #loads and driving forces:
181 mRigid1CoordinateTheta = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nRigid1, coordinate=2)) #angle coordinate is constrained
182 #mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M, loadUserFunction=userLoad)) #torque at crank
183 mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M)) #torque at crank
184
185 #write motion of support frame:
186 sFloating = mbs.AddSensor(SensorNode(nodeNumber=nFloating,
187 storeInternal=True,
188 outputVariableType=exu.OutputVariableType.Position))
189
190 #++++++++++++++++++++++++++++++++
191 #assemble, adjust settings and start time integration
192 mbs.Assemble()
193
194 simulationSettings = exu.SimulationSettings() #takes currently set values or default values
195 tEnd = 3
196
197 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/P.h)
198 simulationSettings.timeIntegration.endTime = tEnd
199
200
201 simulationSettings.solutionSettings.solutionWritePeriod = 2e-3
202 simulationSettings.solutionSettings.writeSolutionToFile = useGraphics
203
204 simulationSettings.timeIntegration.newton.useModifiedNewton = True
205 simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8
206 simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-8
207
208 #++++++++++++++++++++++++++++++++++++++++++
209 #solve index 2 / trapezoidal rule:
210 simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
211 simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
212
213 dSize = 0.02
214 SC.visualizationSettings.nodes.defaultSize = dSize
215 SC.visualizationSettings.markers.defaultSize = dSize
216 SC.visualizationSettings.bodies.defaultSize = [dSize, dSize, dSize]
217 SC.visualizationSettings.connectors.defaultSize = dSize
218
219 #data obtained from SC.GetRenderState(); use np.round(d['modelRotation'],4)
220 SC.visualizationSettings.openGL.initialModelRotation = [[ 0.87758, 0.04786, -0.47703],
221 [ 0. , 0.995 , 0.09983],
222 [ 0.47943, -0.08761, 0.8732]]
223 SC.visualizationSettings.openGL.initialZoom = 0.47
224 SC.visualizationSettings.openGL.initialCenterPoint = [0.192, -0.0039,-0.075]
225 SC.visualizationSettings.openGL.initialMaxSceneSize = 0.4
226 SC.visualizationSettings.general.autoFitScene = False
227 #mbs.WaitForUserToContinue()
228
229 if useGraphics:
230 exu.StartRenderer()
231
232 mbs.SolveDynamic(simulationSettings)
233
234 if useGraphics:
235 SC.WaitForRenderEngineStopFlag()
236 exu.StopRenderer() #safely close rendering window!
237
238 #++++++++++++++++++++++++++++++++++++++++++
239 #evaluate error:
240 #data = np.loadtxt(sensorFileName, comments='#', delimiter=',')
241 data = mbs.GetSensorStoredData(sFloating)
242
243 errorNorm = max(abs(data[:,1])) + max(abs(data[:,2])) #max displacement in x and y direction
244
245 if useGraphics:
246 print("max. oszillation=", errorNorm)
247
248 mbs.PlotSensor(sensorNumbers=[sFloating,sFloating], components=[0,1])
249
250 del mbs
251 del SC
252
253 return errorNorm
254 #++++++++++++++++++++++++++++++++++++++++++
255
256import matplotlib.pyplot as plt
257import matplotlib.ticker as ticker
258
259doOptimize = True
260#now perform parameter variation
261if __name__ == '__main__': #include this to enable parallel processing
262 if doOptimize:
263 import time
264
265 #%%++++++++++++++++++++++++++++++++++++++++++++++++++++
266 #GeneticOptimization
267 start_time = time.time()
268 [pOpt, vOpt, pList, values] = GeneticOptimization(objectiveFunction = ParameterFunction,
269 parameters = {'s1':(-L1,L1), 's2':(-L2,L2)}, #parameters provide search range
270 numberOfGenerations = 30,
271 populationSize = 50,
272 elitistRatio = 0.1,
273 crossoverProbability = 0.1,
274 rangeReductionFactor = 0.5,
275 addComputationIndex=True,
276 randomizerInitialization=0, #for reproducible results
277 #distanceFactor = 0.1, #for this example only one significant minimum
278 debugMode=False,
279 useMultiProcessing=True, #may be problematic for test
280 showProgress=True,
281 resultsFile = 'solution/geneticSliderCrank.txt',
282 )
283 #exu.Print("--- %s seconds ---" % (time.time() - start_time))
284
285 exu.Print("[pOpt, vOpt]=", [pOpt, vOpt])
286 u = vOpt
287 exu.Print("optimum=",u)
288 # using files:
289 # [pOpt, vOpt]= [{'s1': -0.07497827333782427, 's2': -0.14943029494085874}, 3.4312580948e-05]
290 # optimum= 3.4312580948e-05
291
292 # using internal storage:
293 # [pOpt, vOpt]= [{'s1': -0.07497827333782427, 's2': -0.14943029494085874}, 3.431258094752888e-05]
294 # optimum= 3.431258094752888e-05
295
296 if False:
297 # from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
298 import matplotlib.pyplot as plt
299
300 plt.close('all')
301 [figList, axList] = PlotOptimizationResults2D(pList, values, yLogScale=True)
302 else:
303 useGraphics = True
304 parameterSet = {'s1':L1*0.5, 's2':L2*0.5, 'h':1e-5}
305 #parameterSet = {'s1':-0.075, 's2':-0.15, 'h':1e-5}
306 ParameterFunction(parameterSet)