src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2018 EDF R&D
   4 #
   5 # This library is free software; you can redistribute it and/or
   6 # modify it under the terms of the GNU Lesser General Public
   7 # License as published by the Free Software Foundation; either
   8 # version 2.1 of the License.
   9 #
  10 # This library is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13 # Lesser General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU Lesser General Public
  16 # License along with this library; if not, write to the Free Software
  17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  18 #
  19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects
  25 import numpy, math
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "UNSCENTEDKALMANFILTER")
  31         self.defineRequiredParameter(
  32             name     = "ConstrainedBy",
  33             default  = "EstimateProjection",
  34             typecast = str,
  35             message  = "Prise en compte des contraintes",
  36             listval  = ["EstimateProjection"],
  37             )
  38         self.defineRequiredParameter(
  39             name     = "EstimationOf",
  40             default  = "State",
  41             typecast = str,
  42             message  = "Estimation d'etat ou de parametres",
  43             listval  = ["State", "Parameters"],
  44             )
  45         self.defineRequiredParameter(
  46             name     = "Alpha",
  47             default  = 1.,
  48             typecast = float,
  49             message  = "",
  50             minval   = 1.e-4,
  51             maxval   = 1.,
  52             )
  53         self.defineRequiredParameter(
  54             name     = "Beta",
  55             default  = 2,
  56             typecast = float,
  57             message  = "",
  58             )
  59         self.defineRequiredParameter(
  60             name     = "Kappa",
  61             default  = 0,
  62             typecast = int,
  63             message  = "",
  64             maxval   = 2,
  65             )
  66         self.defineRequiredParameter(
  67             name     = "Reconditioner",
  68             default  = 1.,
  69             typecast = float,
  70             message  = "",
  71             minval   = 1.e-3,
  72             maxval   = 1.e+1,
  73             )
  74         self.defineRequiredParameter(
  75             name     = "StoreInternalVariables",
  76             default  = False,
  77             typecast = bool,
  78             message  = "Stockage des variables internes ou intermédiaires du calcul",
  79             )
  80         self.defineRequiredParameter(
  81             name     = "StoreSupplementaryCalculations",
  82             default  = [],
  83             typecast = tuple,
  84             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  85             listval  = ["APosterioriCorrelations", "APosterioriCovariance", "APosterioriStandardDeviations", "APosterioriVariances", "BMA", "CurrentState", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "Innovation"]
  86             )
  87         self.defineRequiredParameter( # Pas de type
  88             name     = "Bounds",
  89             message  = "Liste des valeurs de bornes",
  90             )
  91         self.requireInputArguments(
  92             mandatory= ("Xb", "Y", "HO", "R", "B" ),
  93             optional = ("U", "EM", "CM", "Q"),
  94             )
  95
  96     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  97         self._pre_run(Parameters, Xb, Y, R, B, Q)
  98         #
  99         if self._parameters["EstimationOf"] == "Parameters":
 100             self._parameters["StoreInternalVariables"] = True
 101         #
 102         L     = Xb.size
 103         Alpha = self._parameters["Alpha"]
 104         Beta  = self._parameters["Beta"]
 105         if self._parameters["Kappa"] == 0:
 106             if self._parameters["EstimationOf"] == "State":
 107                 Kappa = 0
 108             elif self._parameters["EstimationOf"] == "Parameters":
 109                 Kappa = 3 - L
 110         else:
 111             Kappa = self._parameters["Kappa"]
 112         Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
 113         Gamma  = math.sqrt( L + Lambda )
 114         #
 115         Ww = []
 116         Ww.append( 0. )
 117         for i in range(2*L):
 118             Ww.append( 1. / (2.*(L + Lambda)) )
 119         #
 120         Wm = numpy.array( Ww )
 121         Wm[0] = Lambda / (L + Lambda)
 122         Wc = numpy.array( Ww )
 123         Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
 124         #
 125         # Opérateurs
 126         # ----------
 127         H = HO["Direct"].appliedControledFormTo
 128         #
 129         if self._parameters["EstimationOf"] == "State":
 130             M = EM["Direct"].appliedControledFormTo
 131         #
 132         if CM is not None and "Tangent" in CM and U is not None:
 133             Cm = CM["Tangent"].asMatrix(Xb)
 134         else:
 135             Cm = None
 136         #
 137         # Nombre de pas identique au nombre de pas d'observations
 138         # -------------------------------------------------------
 139         if hasattr(Y,"stepnumber"):
 140             duration = Y.stepnumber()
 141         else:
 142             duration = 2
 143         #
 144         # Précalcul des inversions de B et R
 145         # ----------------------------------
 146         if self._parameters["StoreInternalVariables"]:
 147             BI = B.getI()
 148             RI = R.getI()
 149         #
 150         # Initialisation
 151         # --------------
 152         Xn = Xb
 153         if hasattr(B,"asfullmatrix"):
 154             Pn = B.asfullmatrix(Xn.size)
 155         else:
 156             Pn = B
 157         #
 158         self.StoredVariables["Analysis"].store( Xn.A1 )
 159         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 160             self.StoredVariables["APosterioriCovariance"].store( Pn )
 161             covarianceXa = Pn
 162         Xa               = Xn
 163         previousJMinimum = numpy.finfo(float).max
 164         #
 165         for step in range(duration-1):
 166             if hasattr(Y,"store"):
 167                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 168             else:
 169                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 170             #
 171             if U is not None:
 172                 if hasattr(U,"store") and len(U)>1:
 173                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 174                 elif hasattr(U,"store") and len(U)==1:
 175                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 176                 else:
 177                     Un = numpy.asmatrix(numpy.ravel( U )).T
 178             else:
 179                 Un = None
 180             #
 181             Pndemi = numpy.linalg.cholesky(Pn)
 182             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 183             nbSpts = 2*Xn.size+1
 184             #
 185             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 186                 for point in range(nbSpts):
 187                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 188                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 189             #
 190             XEtnnp = []
 191             for point in range(nbSpts):
 192                 if self._parameters["EstimationOf"] == "State":
 193                     XEtnnpi = numpy.asmatrix(numpy.ravel( M( (Xnp[:,point], Un) ) )).T
 194                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 195                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 196                         XEtnnpi = XEtnnpi + Cm * Un
 197                     if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 198                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 199                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 200                 elif self._parameters["EstimationOf"] == "Parameters":
 201                     # --- > Par principe, M = Id, Q = 0
 202                     XEtnnpi = Xnp[:,point]
 203                 XEtnnp.append( XEtnnpi )
 204             XEtnnp = numpy.hstack( XEtnnp )
 205             #
 206             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 207             #
 208             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 209                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 210                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 211             #
 212             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 213             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 214             for point in range(nbSpts):
 215                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 216             #
 217             if self._parameters["EstimationOf"] == "Parameters" and self._parameters["Bounds"] is not None:
 218                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 219             else:
 220                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 221             #
 222             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 223             #
 224             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 225                 for point in range(nbSpts):
 226                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 227                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 228             #
 229             Ynnp = []
 230             for point in range(nbSpts):
 231                 if self._parameters["EstimationOf"] == "State":
 232                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], None) ) )).T
 233                 elif self._parameters["EstimationOf"] == "Parameters":
 234                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], Un) ) )).T
 235                 Ynnp.append( Ynnpi )
 236             Ynnp = numpy.hstack( Ynnp )
 237             #
 238             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 239             #
 240             Pyyn = R
 241             Pxyn = 0.
 242             for point in range(nbSpts):
 243                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 244                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 245             #
 246             d  = Ynpu - Yncm
 247             if self._parameters["EstimationOf"] == "Parameters":
 248                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 249                     d = d - Cm * Un
 250             #
 251             Kn = Pxyn * Pyyn.I
 252             Xn = Xncm + Kn * d
 253             Pn = Pnm - Kn * Pyyn * Kn.T
 254             #
 255             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 256                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 257                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 258             #
 259             self.StoredVariables["Analysis"].store( Xn.A1 )
 260             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 261                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 262             if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 263                 self.StoredVariables["Innovation"].store( numpy.ravel( d.A1 ) )
 264             if self._parameters["StoreInternalVariables"]:
 265                 Jb  = 0.5 * (Xn - Xb).T * BI * (Xn - Xb)
 266                 Jo  = 0.5 * d.T * RI * d
 267                 J   = float( Jb ) + float( Jo )
 268                 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 269                     self.StoredVariables["CurrentState"].store( Xn )
 270                 self.StoredVariables["CostFunctionJb"].store( Jb )
 271                 self.StoredVariables["CostFunctionJo"].store( Jo )
 272                 self.StoredVariables["CostFunctionJ" ].store( J )
 273                 if J < previousJMinimum:
 274                     previousJMinimum  = J
 275                     Xa                = Xn
 276                     if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 277                         covarianceXa  = Pn
 278             else:
 279                 Xa = Xn
 280             #
 281         #
 282         # Stockage supplementaire de l'optimum en estimation de parametres
 283         # ----------------------------------------------------------------
 284         if self._parameters["EstimationOf"] == "Parameters":
 285             self.StoredVariables["Analysis"].store( Xa.A1 )
 286             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 287                 self.StoredVariables["APosterioriCovariance"].store( covarianceXa )
 288         #
 289         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 290             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 291         #
 292         self._post_run(HO)
 293         return 0
 294
 295 # ==============================================================================
 296 if __name__ == "__main__":
 297     print('\n AUTODIAGNOSTIC \n')