src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2017 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
  92     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  93         self._pre_run(Parameters)
  94         #
  95         if self._parameters["EstimationOf"] == "Parameters":
  96             self._parameters["StoreInternalVariables"] = True
  97         #
  98         L     = Xb.size
  99         Alpha = self._parameters["Alpha"]
 100         Beta  = self._parameters["Beta"]
 101         if self._parameters["Kappa"] == 0:
 102             if self._parameters["EstimationOf"] == "State":
 103                 Kappa = 0
 104             elif self._parameters["EstimationOf"] == "Parameters":
 105                 Kappa = 3 - L
 106         else:
 107             Kappa = self._parameters["Kappa"]
 108         Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
 109         Gamma  = math.sqrt( L + Lambda )
 110         #
 111         Ww = []
 112         Ww.append( 0. )
 113         for i in range(2*L):
 114             Ww.append( 1. / (2.*(L + Lambda)) )
 115         #
 116         Wm = numpy.array( Ww )
 117         Wm[0] = Lambda / (L + Lambda)
 118         Wc = numpy.array( Ww )
 119         Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
 120         #
 121         # Opérateurs
 122         # ----------
 123         if B is None:
 124             raise ValueError("Background error covariance matrix has to be properly defined!")
 125         if R is None:
 126             raise ValueError("Observation error covariance matrix has to be properly defined!")
 127         #
 128         H = HO["Direct"].appliedControledFormTo
 129         #
 130         if self._parameters["EstimationOf"] == "State":
 131             M = EM["Direct"].appliedControledFormTo
 132         #
 133         if CM is not None and "Tangent" in CM and U is not None:
 134             Cm = CM["Tangent"].asMatrix(Xb)
 135         else:
 136             Cm = None
 137         #
 138         # Nombre de pas identique au nombre de pas d'observations
 139         # -------------------------------------------------------
 140         if hasattr(Y,"stepnumber"):
 141             duration = Y.stepnumber()
 142         else:
 143             duration = 2
 144         #
 145         # Précalcul des inversions de B et R
 146         # ----------------------------------
 147         if self._parameters["StoreInternalVariables"]:
 148             BI = B.getI()
 149             RI = R.getI()
 150         #
 151         # Initialisation
 152         # --------------
 153         Xn = Xb
 154         if hasattr(B,"asfullmatrix"):
 155             Pn = B.asfullmatrix(Xn.size)
 156         else:
 157             Pn = B
 158         #
 159         self.StoredVariables["Analysis"].store( Xn.A1 )
 160         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 161             self.StoredVariables["APosterioriCovariance"].store( Pn )
 162             covarianceXa = Pn
 163         Xa               = Xn
 164         previousJMinimum = numpy.finfo(float).max
 165         #
 166         for step in range(duration-1):
 167             if hasattr(Y,"store"):
 168                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 169             else:
 170                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 171             #
 172             if U is not None:
 173                 if hasattr(U,"store") and len(U)>1:
 174                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 175                 elif hasattr(U,"store") and len(U)==1:
 176                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 177                 else:
 178                     Un = numpy.asmatrix(numpy.ravel( U )).T
 179             else:
 180                 Un = None
 181             #
 182             Pndemi = numpy.linalg.cholesky(Pn)
 183             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 184             nbSpts = 2*Xn.size+1
 185             #
 186             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 187                 for point in range(nbSpts):
 188                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 189                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 190             #
 191             XEtnnp = []
 192             for point in range(nbSpts):
 193                 if self._parameters["EstimationOf"] == "State":
 194                     XEtnnpi = numpy.asmatrix(numpy.ravel( M( (Xnp[:,point], Un) ) )).T
 195                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 196                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 197                         XEtnnpi = XEtnnpi + Cm * Un
 198                     if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 199                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 200                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 201                 elif self._parameters["EstimationOf"] == "Parameters":
 202                     # --- > Par principe, M = Id, Q = 0
 203                     XEtnnpi = Xnp[:,point]
 204                 XEtnnp.append( XEtnnpi )
 205             XEtnnp = numpy.hstack( XEtnnp )
 206             #
 207             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 208             #
 209             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 210                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 211                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 212             #
 213             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 214             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 215             for point in range(nbSpts):
 216                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 217             #
 218             if self._parameters["EstimationOf"] == "Parameters" and self._parameters["Bounds"] is not None:
 219                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 220             else:
 221                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 222             #
 223             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 224             #
 225             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 226                 for point in range(nbSpts):
 227                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 228                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 229             #
 230             Ynnp = []
 231             for point in range(nbSpts):
 232                 if self._parameters["EstimationOf"] == "State":
 233                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], None) ) )).T
 234                 elif self._parameters["EstimationOf"] == "Parameters":
 235                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], Un) ) )).T
 236                 Ynnp.append( Ynnpi )
 237             Ynnp = numpy.hstack( Ynnp )
 238             #
 239             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 240             #
 241             Pyyn = R
 242             Pxyn = 0.
 243             for point in range(nbSpts):
 244                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 245                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 246             #
 247             d  = Ynpu - Yncm
 248             if self._parameters["EstimationOf"] == "Parameters":
 249                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 250                     d = d - Cm * Un
 251             #
 252             Kn = Pxyn * Pyyn.I
 253             Xn = Xncm + Kn * d
 254             Pn = Pnm - Kn * Pyyn * Kn.T
 255             #
 256             if self._parameters["Bounds"] is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 257                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,0])),axis=1)
 258                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(self._parameters["Bounds"])[:,1])),axis=1)
 259             #
 260             self.StoredVariables["Analysis"].store( Xn.A1 )
 261             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 262                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 263             if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 264                 self.StoredVariables["Innovation"].store( numpy.ravel( d.A1 ) )
 265             if self._parameters["StoreInternalVariables"]:
 266                 Jb  = 0.5 * (Xn - Xb).T * BI * (Xn - Xb)
 267                 Jo  = 0.5 * d.T * RI * d
 268                 J   = float( Jb ) + float( Jo )
 269                 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 270                     self.StoredVariables["CurrentState"].store( Xn )
 271                 self.StoredVariables["CostFunctionJb"].store( Jb )
 272                 self.StoredVariables["CostFunctionJo"].store( Jo )
 273                 self.StoredVariables["CostFunctionJ" ].store( J )
 274                 if J < previousJMinimum:
 275                     previousJMinimum  = J
 276                     Xa                = Xn
 277                     if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 278                         covarianceXa  = Pn
 279             else:
 280                 Xa = Xn
 281             #
 282         #
 283         # Stockage supplementaire de l'optimum en estimation de parametres
 284         # ----------------------------------------------------------------
 285         if self._parameters["EstimationOf"] == "Parameters":
 286             self.StoredVariables["Analysis"].store( Xa.A1 )
 287             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 288                 self.StoredVariables["APosterioriCovariance"].store( covarianceXa )
 289         #
 290         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 291             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 292         #
 293         self._post_run(HO)
 294         return 0
 295
 296 # ==============================================================================
 297 if __name__ == "__main__":
 298     print('\n AUTODIAGNOSTIC \n')