src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2019 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  = [
  86                 "APosterioriCorrelations",
  87                 "APosterioriCovariance",
  88                 "APosterioriStandardDeviations",
  89                 "APosterioriVariances",
  90                 "BMA",
  91                 "CurrentState",
  92                 "CostFunctionJ",
  93                 "CostFunctionJb",
  94                 "CostFunctionJo",
  95                 "Innovation",
  96                 ]
  97             )
  98         self.defineRequiredParameter( # Pas de type
  99             name     = "Bounds",
 100             message  = "Liste des valeurs de bornes",
 101             )
 102         self.requireInputArguments(
 103             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 104             optional = ("U", "EM", "CM", "Q"),
 105             )
 106
 107     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 108         self._pre_run(Parameters, Xb, Y, R, B, Q)
 109         #
 110         if self._parameters["EstimationOf"] == "Parameters":
 111             self._parameters["StoreInternalVariables"] = True
 112         #
 113         L     = Xb.size
 114         Alpha = self._parameters["Alpha"]
 115         Beta  = self._parameters["Beta"]
 116         if self._parameters["Kappa"] == 0:
 117             if self._parameters["EstimationOf"] == "State":
 118                 Kappa = 0
 119             elif self._parameters["EstimationOf"] == "Parameters":
 120                 Kappa = 3 - L
 121         else:
 122             Kappa = self._parameters["Kappa"]
 123         Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
 124         Gamma  = math.sqrt( L + Lambda )
 125         #
 126         Ww = []
 127         Ww.append( 0. )
 128         for i in range(2*L):
 129             Ww.append( 1. / (2.*(L + Lambda)) )
 130         #
 131         Wm = numpy.array( Ww )
 132         Wm[0] = Lambda / (L + Lambda)
 133         Wc = numpy.array( Ww )
 134         Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
 135         #
 136         # Opérateurs
 137         # ----------
 138         Hm = HO["Direct"].appliedControledFormTo
 139         #
 140         if self._parameters["EstimationOf"] == "State":
 141             Mm = EM["Direct"].appliedControledFormTo
 142         #
 143         if CM is not None and "Tangent" in CM and U is not None:
 144             Cm = CM["Tangent"].asMatrix(Xb)
 145         else:
 146             Cm = None
 147         #
 148         # Nombre de pas identique au nombre de pas d'observations
 149         # -------------------------------------------------------
 150         if hasattr(Y,"stepnumber"):
 151             duration = Y.stepnumber()
 152         else:
 153             duration = 2
 154         #
 155         # Précalcul des inversions de B et R
 156         # ----------------------------------
 157         if self._parameters["StoreInternalVariables"] \
 158             or self._toStore("CostFunctionJ") \
 159             or self._toStore("CostFunctionJb") \
 160             or self._toStore("CostFunctionJo"):
 161             BI = B.getI()
 162             RI = R.getI()
 163         #
 164         # Initialisation
 165         # --------------
 166         Xn = Xb
 167         if hasattr(B,"asfullmatrix"):
 168             Pn = B.asfullmatrix(Xn.size)
 169         else:
 170             Pn = B
 171         #
 172         self.StoredVariables["Analysis"].store( Xn.A1 )
 173         if self._toStore("APosterioriCovariance"):
 174             self.StoredVariables["APosterioriCovariance"].store( Pn )
 175             covarianceXa = Pn
 176         Xa               = Xn
 177         previousJMinimum = numpy.finfo(float).max
 178         #
 179         for step in range(duration-1):
 180             if hasattr(Y,"store"):
 181                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 182             else:
 183                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 184             #
 185             if U is not None:
 186                 if hasattr(U,"store") and len(U)>1:
 187                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 188                 elif hasattr(U,"store") and len(U)==1:
 189                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 190                 else:
 191                     Un = numpy.asmatrix(numpy.ravel( U )).T
 192             else:
 193                 Un = None
 194             #
 195             Pndemi = numpy.linalg.cholesky(Pn)
 196             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 197             nbSpts = 2*Xn.size+1
 198             #
 199             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 200                 for point in range(nbSpts):
 201                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 202                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 203             #
 204             XEtnnp = []
 205             for point in range(nbSpts):
 206                 if self._parameters["EstimationOf"] == "State":
 207                     XEtnnpi = numpy.asmatrix(numpy.ravel( Mm( (Xnp[:,point], Un) ) )).T
 208                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 209                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 210                         XEtnnpi = XEtnnpi + Cm * Un
 211                     if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 212                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 213                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 214                 elif self._parameters["EstimationOf"] == "Parameters":
 215                     # --- > Par principe, M = Id, Q = 0
 216                     XEtnnpi = Xnp[:,point]
 217                 XEtnnp.append( XEtnnpi )
 218             XEtnnp = numpy.hstack( XEtnnp )
 219             #
 220             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 221             #
 222             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 223                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 224                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 225             #
 226             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 227             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 228             for point in range(nbSpts):
 229                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 230             #
 231             if self._parameters["EstimationOf"] == "Parameters" and self._parameters["Bounds"] is not None:
 232                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 233             else:
 234                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 235             #
 236             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 237             #
 238             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 239                 for point in range(nbSpts):
 240                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 241                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 242             #
 243             Ynnp = []
 244             for point in range(nbSpts):
 245                 if self._parameters["EstimationOf"] == "State":
 246                     Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], None) ) )).T
 247                 elif self._parameters["EstimationOf"] == "Parameters":
 248                     Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], Un) ) )).T
 249                 Ynnp.append( Ynnpi )
 250             Ynnp = numpy.hstack( Ynnp )
 251             #
 252             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 253             #
 254             Pyyn = R
 255             Pxyn = 0.
 256             for point in range(nbSpts):
 257                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 258                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 259             #
 260             d  = Ynpu - Yncm
 261             if self._parameters["EstimationOf"] == "Parameters":
 262                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 263                     d = d - Cm * Un
 264             #
 265             Kn = Pxyn * Pyyn.I
 266             Xn = Xncm + Kn * d
 267             Pn = Pnm - Kn * Pyyn * Kn.T
 268             #
 269             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 270                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 271                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 272             #
 273             self.StoredVariables["Analysis"].store( Xn.A1 )
 274             if self._toStore("APosterioriCovariance"):
 275                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 276             if self._toStore("Innovation"):
 277                 self.StoredVariables["Innovation"].store( numpy.ravel( d.A1 ) )
 278             if self._parameters["StoreInternalVariables"] \
 279                 or self._toStore("CurrentState"):
 280                 self.StoredVariables["CurrentState"].store( Xn )
 281             if self._parameters["StoreInternalVariables"] \
 282                 or self._toStore("CostFunctionJ") \
 283                 or self._toStore("CostFunctionJb") \
 284                 or self._toStore("CostFunctionJo"):
 285                 Jb  = 0.5 * (Xn - Xb).T * BI * (Xn - Xb)
 286                 Jo  = 0.5 * d.T * RI * d
 287                 J   = float( Jb ) + float( Jo )
 288                 self.StoredVariables["CostFunctionJb"].store( Jb )
 289                 self.StoredVariables["CostFunctionJo"].store( Jo )
 290                 self.StoredVariables["CostFunctionJ" ].store( J )
 291                 if J < previousJMinimum:
 292                     previousJMinimum  = J
 293                     Xa                = Xn
 294                     if self._toStore("APosterioriCovariance"):
 295                         covarianceXa  = Pn
 296             else:
 297                 Xa = Xn
 298             #
 299         #
 300         # Stockage supplementaire de l'optimum en estimation de parametres
 301         # ----------------------------------------------------------------
 302         if self._parameters["EstimationOf"] == "Parameters":
 303             self.StoredVariables["Analysis"].store( Xa.A1 )
 304             if self._toStore("APosterioriCovariance"):
 305                 self.StoredVariables["APosterioriCovariance"].store( covarianceXa )
 306         #
 307         if self._toStore("BMA"):
 308             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 309         #
 310         self._post_run(HO)
 311         return 0
 312
 313 # ==============================================================================
 314 if __name__ == "__main__":
 315     print('\n AUTODIAGNOSTIC \n')