#!/usr/bin/env python # -*- coding: utf-8 -*- """ *********************************************************************************** tutorial_che_opt_5.py DAE Tools: pyDAE module, www.daetools.com Copyright (C) Dragan Nikolic *********************************************************************************** DAE Tools is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with the DAE Tools software; if not, see <http://www.gnu.org/licenses/>. ************************************************************************************ """ __doc__ = """ COPS test 13: Methanol to Hydrocarbons. Determine the reaction coefficients for the conversion of methanol into various hydrocarbons. Reference: Benchmarking Optimization Software with COPS 3.0, Mathematics and Computer Science Division, Argonne National Laboratory, Technical Report ANL/MCS-273, 2004. `PDF <http://www.mcs.anl.gov/~more/cops/cops3.pdf>`_ Experimental data generated following the procedure described in the COPS test. Run options: - Simulation with optimal parameters: python tutorial_che_opt_5.py simulation - Parameter estimation console run: python tutorial_che_opt_5.py console - Parameter estimation GUI run: python tutorial_che_opt_5.py gui Currently, the parameter estimation results are (solver options/scaling should be tuned): .. code-block:: none Fobj = 1.274997e-2 p1 = 2.641769 p2 = 1.466245 p3 = 1.884254 p4 = 1.023885 p5 = 0.471067 The concentration plots (for optimal 'p' from the literature): .. image:: _static/tutorial_che_opt_5-results.png :width: 500px The concentration plots (for optimal 'p' from this optimisation): .. image:: _static/tutorial_che_opt_5-results2.png :width: 500px """ import sys from time import localtime, strftime from daetools.pyDAE import * from daetools.solvers.trilinos import pyTrilinos from daetools.solvers.nlopt import pyNLOPT from pyUnits import m, kg, s, K, Pa, mol, J, W, kJ, hour, l y_t = daeVariableType("y_t", unit(), -1.0e+20, 1.0e+20, 0.0, 1e-07) L2_t = daeVariableType("L2_t", unit(), -1.0e+20, 1.0e+20, 0.0, 1e-07) ######################################################### # Methanol to Hydrocarbons ######################################################### # Mathematical model class modMethanol2Hydrocarbons(daeModel): def __init__(self, Name, Parent = None, Description = ""): daeModel.__init__(self, Name, Parent, Description) # Reaction coefficients self.p1 = daeVariable("p1", no_t, self, "Reaction coefficient 1") self.p2 = daeVariable("p2", no_t, self, "Reaction coefficient 2") self.p3 = daeVariable("p3", no_t, self, "Reaction coefficient 3") self.p4 = daeVariable("p4", no_t, self, "Reaction coefficient 4") self.p5 = daeVariable("p5", no_t, self, "Reaction coefficient 5") # State variables self.y1 = daeVariable("y1", y_t, self, "1 concentration") self.y2 = daeVariable("y2", y_t, self, "2 concentration") self.y3 = daeVariable("y3", y_t, self, "3 concentration") def DeclareEquations(self): # Create adouble objects to make equations more readable y1 = self.y1() y2 = self.y2() y3 = self.y3() p1 = self.p1() p2 = self.p2() p3 = self.p3() p4 = self.p4() p5 = self.p5() # Derivatives dy1_dt = self.y1.dt() dy2_dt = self.y2.dt() dy3_dt = self.y3.dt() # y1 eq = self.CreateEquation("y1", "") eq.Residual = dy1_dt + (2*p1 - p1*y2/((p2+p5)*y1+y2+1e-10) + p3 + p4)*y1 eq.CheckUnitsConsistency = False # y2 eq = self.CreateEquation("y2", "") eq.Residual = dy2_dt - (p1*y1*(p2*y1-y2)/((p2+p5)*y1+y2+1e-10) + p3*y1) eq.CheckUnitsConsistency = False # y3 eq = self.CreateEquation("y3", "") eq.Residual = dy3_dt - (p1*y1*(y2+p5*y1)/((p2+p5)*y1+y2+1e-10) + p4*y1) eq.CheckUnitsConsistency = False # Simulation (can be run independently from optimisation) class simMethanol2Hydrocarbons(daeSimulation): def __init__(self): daeSimulation.__init__(self) self.m = modMethanol2Hydrocarbons("tutorial_che_opt_5") self.m.Description = __doc__ def SetUpParametersAndDomains(self): pass def SetUpVariables(self): # The reaction coefficients below are used to generate the experimental data. # The noise self.m.p1.AssignValue(2.69) self.m.p2.AssignValue(0.5) self.m.p3.AssignValue(3.02) self.m.p4.AssignValue(0.5) self.m.p5.AssignValue(0.5) self.m.y1.SetInitialCondition(y1_t0) self.m.y2.SetInitialCondition(y2_t0) self.m.y3.SetInitialCondition(y3_t0) ######################################################### # Parameter Estimation Part ######################################################### # We need some additional variables to determine reaction coefficients. # Derive a new class from modMethanol2Hydrocarbons and add extra data. # Nota Bene: # modMethanol2Hydrocarbons_Opt inherits all parameters/variables from the base class. class modMethanol2Hydrocarbons_Opt(modMethanol2Hydrocarbons): def __init__(self, Name, Parent = None, Description = ""): modMethanol2Hydrocarbons.__init__(self, Name, Parent, Description) # Observed values at the specific time interval self.y1_obs = daeVariable("y1_obs", no_t, self, "Observed value 1 at the specified time interval") self.y2_obs = daeVariable("y2_obs", no_t, self, "Observed value 2 at the specified time interval") self.y3_obs = daeVariable("y3_obs", no_t, self, "Observed value 3 at the specified time interval") # This L2 norm sums all L2 norms in the previous time intervals self.L2 = daeVariable("L2", L2_t, self, "Current L2 norm: ||yi(t) - yi_obs(t)||^2") self.L2_prev = daeVariable("L2_prev", L2_t, self, "L2 norm in previous time intrvals") def DeclareEquations(self): modMethanol2Hydrocarbons.DeclareEquations(self) # L2-norm ||yi(t) - yi_obs(t)||^2 # L2 norm is a sum of the L2 norm in the previous time steps (L2_prev) # and the current norm: s1 + s2. # L2_prev will be reset after every time interval where we have observed values. s1 = (self.y1() - self.y1_obs())**2 s2 = (self.y2() - self.y2_obs())**2 s3 = (self.y3() - self.y3_obs())**2 eq = self.CreateEquation("L2", "") eq.Residual = self.L2() - (self.L2_prev() + s1 + s2 + s3) eq.CheckUnitsConsistency = False # Simulation class that will be used by the optimisation. class simMethanol2Hydrocarbons_opt(daeSimulation): def __init__(self): daeSimulation.__init__(self) self.m = modMethanol2Hydrocarbons_Opt("tutorial_che_opt_5") self.m.Description = __doc__ def SetUpParametersAndDomains(self): pass def SetUpVariables(self): # modMethanol2Hydrocarbons part self.m.p1.AssignValue(2.69) self.m.p2.AssignValue(0.5) self.m.p3.AssignValue(3.02) self.m.p4.AssignValue(0.5) self.m.p5.AssignValue(0.5) self.m.y1.SetInitialCondition(y1_t0) self.m.y2.SetInitialCondition(y2_t0) self.m.y3.SetInitialCondition(y3_t0) # Initialise variables required for parameter estimation. # Notate bene: # Observed values should match initial conditions at t = 0 # L2_prev should be 0.0 initially self.m.y1_obs.AssignValue(y1_t0) self.m.y2_obs.AssignValue(y2_t0) self.m.y3_obs.AssignValue(y3_t0) self.m.L2_prev.AssignValue(0.0) def Run(self): for t, tn in enumerate(times): # Reset L2_prev value to the current L2 if t == 0: self.m.L2_prev.ReAssignValue(0.0) else: L2 = self.m.L2.GetValue() self.m.L2_prev.ReAssignValue(L2) # Reset observed values to match the current interval end time self.m.y1_obs.ReAssignValue(y1_obs[t]) self.m.y2_obs.ReAssignValue(y2_obs[t]) self.m.y3_obs.ReAssignValue(y3_obs[t]) # Reinitialise the DAE system after all changes made above self.Reinitialize() # Integrate, report data and set progress self.Log.Message('Integrating from %f to %f ...' % (self.CurrentTime, tn), 0) self.IntegrateUntilTime(tn, eDoNotStopAtDiscontinuity) self.ReportData(self.CurrentTime) self.Log.SetProgress(int(100.0 * self.CurrentTime/self.TimeHorizon)) def SetUpOptimization(self): # Minimise L2-norm ||yi(t) - yi_obs(t)||^2 self.ObjectiveFunction.Residual = self.m.L2() * 1e4 # scale Fobj self.ObjectiveFunction.AbsTolerance = 1e-6 p_lb = 0.0 p_ub = 20.0 p_init = 1.0 p1 = self.SetContinuousOptimizationVariable(self.m.p1, p_lb, p_ub, p_init) p2 = self.SetContinuousOptimizationVariable(self.m.p2, p_lb, p_ub, p_init) p3 = self.SetContinuousOptimizationVariable(self.m.p3, p_lb, p_ub, p_init) p4 = self.SetContinuousOptimizationVariable(self.m.p4, p_lb, p_ub, p_init) p5 = self.SetContinuousOptimizationVariable(self.m.p5, p_lb, p_ub, p_init) # Experimental data (20 measurements, skip t=0) generated by the simulation below times = numpy.array([0.071875, 0.143750, 0.215625, 0.287500, 0.359375, 0.431250, 0.503125, 0.575000, 0.646875, 0.718750, 0.790625, 0.862500, 0.934375, 1.006250, 1.078125, 1.150000]) y1_obs = numpy.array([0.552208, 0.300598, 0.196879, 0.101175, 0.065684, 0.045096, 0.028880, 0.018433, 0.011509, 0.006215, 0.004278, 0.002698, 0.001944, 0.001116, 0.000732, 0.000426]) y2_obs = numpy.array([0.187768, 0.262406, 0.350412, 0.325110, 0.367181, 0.348264, 0.325085, 0.355673, 0.361805, 0.363117, 0.327266, 0.330211, 0.385798, 0.358132, 0.380497, 0.383051]) y3_obs = numpy.array([0.117684, 0.175074, 0.236679, 0.234442, 0.270303, 0.272637, 0.274075, 0.278981, 0.297151, 0.297797, 0.298722, 0.326645, 0.303198, 0.277822, 0.284194, 0.301471]) # Initial conditions y1_t0 = 1.0 y2_t0 = 0.0 y3_t0 = 0.0 def setOptions(nlpsolver): nlpsolver.xtol_rel = 1e-6 nlpsolver.xtol_abs = 1e-6 nlpsolver.ftol_rel = 1e-6 nlpsolver.ftol_abs = 1e-6 def consoleSimulation(): # Create Log, Solver, DataReporter and Simulation object log = daePythonStdOutLog() daesolver = daeIDAS() datareporter = daeDelegateDataReporter() simulation = simMethanol2Hydrocarbons_opt() dr_tcpip = daeTCPIPDataReporter() dr_data = daeNoOpDataReporter() datareporter.AddDataReporter(dr_tcpip) datareporter.AddDataReporter(dr_data) # Enable reporting of all variables simulation.m.SetReportingOn(True) # Set the time horizon and the reporting interval simulation.ReportingInterval = 1.15/16 simulation.TimeHorizon = 1.15 # Connect data reporter simName = simulation.m.Name + strftime(" [%d.%m.%Y %H:%M:%S]", localtime()) if(dr_tcpip.Connect("", simName) == False): sys.exit() # Initialize the simulation simulation.Initialize(daesolver, datareporter, log) # Save the model report and the runtime model report simulation.m.SaveModelReport(simulation.m.Name + ".xml") simulation.m.SaveRuntimeModelReport(simulation.m.Name + "-rt.xml") # Solve at time=0 (initialization) simulation.SolveInitial() # Run simulation.Run() simulation.Finalize() dvars = dr_data.Process.dictVariables # Skip the ts = dvars['tutorial_che_opt_5.y1'].TimeValues[1:] y1 = dvars['tutorial_che_opt_5.y1'].Values[1:] y2 = dvars['tutorial_che_opt_5.y2'].Values[1:] y3 = dvars['tutorial_che_opt_5.y3'].Values[1:] nt = len(ts) y1_exp = numpy.array([y + numpy.random.uniform(-y*0.1, y*0.1) for y in y1]) y2_exp = numpy.array([y + numpy.random.uniform(-y*0.1, y*0.1) for y in y2]) y3_exp = numpy.array([y + numpy.random.uniform(-y*0.1, y*0.1) for y in y3]) float_formatter = lambda x: "%.6f" % x numpy.set_printoptions(formatter={'float_kind':float_formatter}) print('times = numpy.%s' % repr(ts)) print('y1 = numpy.%s' % repr(y1)) print('y1_obs = numpy.%s' % repr(y1_exp)) print('y2 = numpy.%s' % repr(y2)) print('y2_obs = numpy.%s' % repr(y2_exp)) print('y3 = numpy.%s' % repr(y3)) print('y3_obs = numpy.%s' % repr(y3_exp)) def run(**kwargs): simulation = simMethanol2Hydrocarbons_opt() nlpsolver = pyNLOPT.daeNLOPT('NLOPT_LD_SLSQP') lasolver = pyTrilinos.daeCreateTrilinosSolver("Amesos_Klu", "") relativeTolerance = 1e-6 reportingTimes = times.tolist() return daeActivity.optimize(simulation, reportingInterval = 1, timeHorizon = 1, reportingTimes = reportingTimes, lasolver = lasolver, nlpsolver = nlpsolver, nlpsolver_setoptions_fn = setOptions, relativeTolerance = relativeTolerance, reportSensitivities = True, **kwargs) if __name__ == "__main__": if len(sys.argv) > 1 and (sys.argv[1] == 'simulation'): consoleSimulation() else: guiRun = False if (len(sys.argv) > 1 and sys.argv[1] == 'console') else True run(guiRun = guiRun)