モデルのパラメータを変えたシミュレーションを行う¶
JModelica User Guild - Version 2.10の5.4.2 を行います。
5.2 のVDPモデルについて、パラメータである初期値 (x1(0),x2(0)) を(−3,0) から (3,0) まで等間隔に変えた11ケースのシミュレーションを行い、各ケースの結果を１個の図にプロットします。横軸 x1、縦軸 x2 の図にすると、各ケースの結果はそれぞれ始点の異なる軌跡となります。
必要となるモジュールをインポートします。
In [1]:
%matplotlib notebook
import numpy as N
import pylab as P
from pymodelica import compile_fmu
from pyfmi import load_fmu
VDP モデルをコンパイルし FMU を作成します。
In [2]:
# Define model file name and class name
model_name = 'VDP'
mofile = 'VDP.mo'
# Compile model
fmu_name = compile_fmu(model_name,mofile)
初期値 (x1(0),x2(0)) の配列を作ります。
In [3]:
# Define initial conditions
N_points = 11
x1_0 = N.linspace(-3.,3.,N_points)
x2_0 = N.zeros(N_points)
シミュレーションを実行します。 for ループ内が各ケースについての処理を表し、モデルのロード、初期値の設定、シミュレーションの実行、結果の取得、プロットを行っています。
In [4]:
fig = P.figure()
P.clf()
# P.hold(True)
P.xlabel('x1')
P.ylabel('x2')
for i in range(N_points):
# Load model
vdp = load_fmu(fmu_name)
# Set initial conditions in model
vdp.set('x1_0',x1_0[i])
vdp.set('x2_0',x2_0[i])
# Simulate
res = vdp.simulate(final_time=20)
# Get simulation result
x1=res['x1']
x2=res['x2']
# Plot simulation result in phase plane plot
P.plot(x1, x2,'b')
P.grid()
P.show()
Final Run Statistics: --- Number of steps : 286 Number of function evaluations : 432 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 32 Number of nonlinear iterations : 428 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0162968635559 seconds. Final Run Statistics: --- Number of steps : 299 Number of function evaluations : 428 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 25 Number of nonlinear iterations : 424 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0186381340027 seconds. Final Run Statistics: --- Number of steps : 288 Number of function evaluations : 403 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 24 Number of nonlinear iterations : 399 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0163948535919 seconds. Final Run Statistics: --- Number of steps : 322 Number of function evaluations : 445 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 25 Number of nonlinear iterations : 441 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0183138847351 seconds. Final Run Statistics: --- Number of steps : 297 Number of function evaluations : 432 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 29 Number of nonlinear iterations : 428 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0169498920441 seconds. Final Run Statistics: --- Number of steps : 3 Number of function evaluations : 7 Number of Jacobian evaluations : 1 Number of function eval. due to Jacobian eval. : 2 Number of error test failures : 0 Number of nonlinear iterations : 3 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.00062108039856 seconds. Final Run Statistics: --- Number of steps : 308 Number of function evaluations : 425 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 23 Number of nonlinear iterations : 421 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0177299976349 seconds. Final Run Statistics: --- Number of steps : 321 Number of function evaluations : 443 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 25 Number of nonlinear iterations : 439 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0185670852661 seconds. Final Run Statistics: --- Number of steps : 288 Number of function evaluations : 403 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 24 Number of nonlinear iterations : 399 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0167670249939 seconds. Final Run Statistics: --- Number of steps : 301 Number of function evaluations : 424 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 24 Number of nonlinear iterations : 420 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0201840400696 seconds. Final Run Statistics: --- Number of steps : 289 Number of function evaluations : 427 Number of Jacobian evaluations : 6 Number of function eval. due to Jacobian eval. : 12 Number of error test failures : 30 Number of nonlinear iterations : 423 Number of nonlinear convergence failures : 0 Solver options: Solver : CVode Linear multistep method : BDF Nonlinear solver : Newton Linear solver type : DENSE Maximal order : 5 Tolerances (absolute) : 1e-06 Tolerances (relative) : 0.0001 Simulation interval : 0.0 - 20.0 seconds. Elapsed simulation time: 0.0179991722107 seconds.
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