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