src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2020 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         __n = Xb.size
 168         Xn = Xb
 169         if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
 170         else:                         Pn = B
 171         #
 172         if len(self.StoredVariables["Analysis"])==0 or not self._parameters["nextStep"]:
 173             self.StoredVariables["Analysis"].store( numpy.ravel(Xb) )
 174             if self._toStore("APosterioriCovariance"):
 175                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 176                 covarianceXa = Pn
 177         #
 178         Xa               = Xb
 179         XaMin            = Xb
 180         previousJMinimum = numpy.finfo(float).max
 181         #
 182         for step in range(duration-1):
 183             if hasattr(Y,"store"):
 184                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 185             else:
 186                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 187             #
 188             if U is not None:
 189                 if hasattr(U,"store") and len(U)>1:
 190                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 191                 elif hasattr(U,"store") and len(U)==1:
 192                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 193                 else:
 194                     Un = numpy.asmatrix(numpy.ravel( U )).T
 195             else:
 196                 Un = None
 197             #
 198             Pndemi = numpy.linalg.cholesky(Pn)
 199             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 200             nbSpts = 2*Xn.size+1
 201             #
 202             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 203                 for point in range(nbSpts):
 204                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 205                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 206             #
 207             XEtnnp = []
 208             for point in range(nbSpts):
 209                 if self._parameters["EstimationOf"] == "State":
 210                     XEtnnpi = numpy.asmatrix(numpy.ravel( Mm( (Xnp[:,point], Un) ) )).T
 211                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 212                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 213                         XEtnnpi = XEtnnpi + Cm * Un
 214                     if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 215                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 216                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 217                 elif self._parameters["EstimationOf"] == "Parameters":
 218                     # --- > Par principe, M = Id, Q = 0
 219                     XEtnnpi = Xnp[:,point]
 220                 XEtnnp.append( XEtnnpi )
 221             XEtnnp = numpy.hstack( XEtnnp )
 222             #
 223             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 224             #
 225             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 226                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 227                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 228             #
 229             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 230             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 231             for point in range(nbSpts):
 232                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 233             #
 234             if self._parameters["EstimationOf"] == "Parameters" and self._parameters["Bounds"] is not None:
 235                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 236             else:
 237                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 238             #
 239             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 240             #
 241             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 242                 for point in range(nbSpts):
 243                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 244                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 245             #
 246             Ynnp = []
 247             for point in range(nbSpts):
 248                 if self._parameters["EstimationOf"] == "State":
 249                     Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], None) ) )).T
 250                 elif self._parameters["EstimationOf"] == "Parameters":
 251                     Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], Un) ) )).T
 252                 Ynnp.append( Ynnpi )
 253             Ynnp = numpy.hstack( Ynnp )
 254             #
 255             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 256             #
 257             Pyyn = R
 258             Pxyn = 0.
 259             for point in range(nbSpts):
 260                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 261                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 262             #
 263             d  = Ynpu - Yncm
 264             if self._parameters["EstimationOf"] == "Parameters":
 265                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 266                     d = d - Cm * Un
 267             #
 268             Kn = Pxyn * Pyyn.I
 269             Xn = Xncm + Kn * d
 270             Pn = Pnm - Kn * Pyyn * Kn.T
 271             #
 272             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 273                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 274                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 275             Xa = Xn # Pointeurs
 276             #
 277             # ---> avec analysis
 278             self.StoredVariables["Analysis"].store( Xa )
 279             if self._toStore("APosterioriCovariance"):
 280                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 281             # ---> avec current state
 282             if self._toStore("InnovationAtCurrentState"):
 283                 self.StoredVariables["InnovationAtCurrentState"].store( d )
 284             if self._parameters["StoreInternalVariables"] \
 285                 or self._toStore("CurrentState"):
 286                 self.StoredVariables["CurrentState"].store( Xn )
 287             if self._parameters["StoreInternalVariables"] \
 288                 or self._toStore("CostFunctionJ") \
 289                 or self._toStore("CostFunctionJb") \
 290                 or self._toStore("CostFunctionJo"):
 291                 Jb  = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
 292                 Jo  = float( 0.5 * d.T * RI * d )
 293                 J   = Jb + Jo
 294                 self.StoredVariables["CostFunctionJb"].store( Jb )
 295                 self.StoredVariables["CostFunctionJo"].store( Jo )
 296                 self.StoredVariables["CostFunctionJ" ].store( J )
 297             if self._parameters["EstimationOf"] == "Parameters" \
 298                 and J < previousJMinimum:
 299                 previousJMinimum    = J
 300                 XaMin               = Xa
 301                 if self._toStore("APosterioriCovariance"):
 302                     covarianceXaMin = Pn
 303         #
 304         # Stockage final supplémentaire de l'optimum en estimation de paramètres
 305         # ----------------------------------------------------------------------
 306         if self._parameters["EstimationOf"] == "Parameters":
 307             self.StoredVariables["Analysis"].store( XaMin )
 308             if self._toStore("APosterioriCovariance"):
 309                 self.StoredVariables["APosterioriCovariance"].store( covarianceXaMin )
 310             if self._toStore("BMA"):
 311                 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(XaMin) )
 312         #
 313         self._post_run(HO)
 314         return 0
 315
 316 # ==============================================================================
 317 if __name__ == "__main__":
 318     print('\n AUTODIAGNOSTIC\n')