src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 #-*-coding:iso-8859-1-*-
   2 #
   3 #  Copyright (C) 2008-2015 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  = ["APosterioriCovariance", "BMA", "CurrentState", "CostFunctionJ", "Innovation"]
  86             )
  87
  88     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  89         self._pre_run()
  90         #
  91         # Paramètres de pilotage
  92         # ----------------------
  93         self.setParameters(Parameters)
  94         #
  95         if self._parameters.has_key("Bounds") and (type(self._parameters["Bounds"]) is type([]) or type(self._parameters["Bounds"]) is type(())) and (len(self._parameters["Bounds"]) > 0):
  96             Bounds = self._parameters["Bounds"]
  97             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
  98         else:
  99             Bounds = None
 100         if self._parameters["EstimationOf"] == "Parameters":
 101             self._parameters["StoreInternalVariables"] = True
 102         #
 103         L     = Xb.size
 104         Alpha = self._parameters["Alpha"]
 105         Beta  = self._parameters["Beta"]
 106         if self._parameters["Kappa"] == 0:
 107             if self._parameters["EstimationOf"] == "State":
 108                 Kappa = 0
 109             elif self._parameters["EstimationOf"] == "Parameters":
 110                 Kappa = 3 - L
 111         else:
 112             Kappa = self._parameters["Kappa"]
 113         Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
 114         Gamma  = math.sqrt( L + Lambda )
 115         #
 116         Ww = []
 117         Ww.append( 0. )
 118         for i in range(2*L):
 119             Ww.append( 1. / (2.*(L + Lambda)) )
 120         #
 121         Wm = numpy.array( Ww )
 122         Wm[0] = Lambda / (L + Lambda)
 123         Wc = numpy.array( Ww )
 124         Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
 125         #
 126         # Opérateurs
 127         # ----------
 128         if B is None:
 129             raise ValueError("Background error covariance matrix has to be properly defined!")
 130         if R is None:
 131             raise ValueError("Observation error covariance matrix has to be properly defined!")
 132         #
 133         H = HO["Direct"].appliedControledFormTo
 134         #
 135         if self._parameters["EstimationOf"] == "State":
 136             M = EM["Direct"].appliedControledFormTo
 137         #
 138         if CM is not None and CM.has_key("Tangent") and U is not None:
 139             Cm = CM["Tangent"].asMatrix(Xb)
 140         else:
 141             Cm = None
 142         #
 143         # Nombre de pas identique au nombre de pas d'observations
 144         # -------------------------------------------------------
 145         if hasattr(Y,"stepnumber"):
 146             duration = Y.stepnumber()
 147         else:
 148             duration = 2
 149         #
 150         # Précalcul des inversions de B et R
 151         # ----------------------------------
 152         if self._parameters["StoreInternalVariables"]:
 153             BI = B.getI()
 154             RI = R.getI()
 155         #
 156         # Initialisation
 157         # --------------
 158         Xn = Xb
 159         if hasattr(B,"asfullmatrix"):
 160             Pn = B.asfullmatrix(Xn.size)
 161         else:
 162             Pn = B
 163         #
 164         self.StoredVariables["Analysis"].store( Xn.A1 )
 165         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 166             self.StoredVariables["APosterioriCovariance"].store( Pn )
 167             covarianceXa = Pn
 168         Xa               = Xn
 169         previousJMinimum = numpy.finfo(float).max
 170         #
 171         for step in range(duration-1):
 172             if hasattr(Y,"store"):
 173                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 174             else:
 175                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 176             #
 177             if U is not None:
 178                 if hasattr(U,"store") and len(U)>1:
 179                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 180                 elif hasattr(U,"store") and len(U)==1:
 181                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 182                 else:
 183                     Un = numpy.asmatrix(numpy.ravel( U )).T
 184             else:
 185                 Un = None
 186             #
 187             Pndemi = numpy.linalg.cholesky(Pn)
 188             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 189             nbSpts = 2*Xn.size+1
 190             #
 191             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 192                 for point in range(nbSpts):
 193                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(Bounds)[:,0])),axis=1)
 194                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(Bounds)[:,1])),axis=1)
 195             #
 196             XEtnnp = []
 197             for point in range(nbSpts):
 198                 if self._parameters["EstimationOf"] == "State":
 199                     XEtnnpi = numpy.asmatrix(numpy.ravel( M( (Xnp[:,point], Un) ) )).T
 200                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 201                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 202                         XEtnnpi = XEtnnpi + Cm * Un
 203                     if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 204                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(Bounds)[:,0])),axis=1)
 205                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(Bounds)[:,1])),axis=1)
 206                 elif self._parameters["EstimationOf"] == "Parameters":
 207                     # --- > Par principe, M = Id, Q = 0
 208                     XEtnnpi = Xnp[:,point]
 209                 XEtnnp.append( XEtnnpi )
 210             XEtnnp = numpy.hstack( XEtnnp )
 211             #
 212             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 213             #
 214             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 215                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(Bounds)[:,0])),axis=1)
 216                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(Bounds)[:,1])),axis=1)
 217             #
 218             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 219             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 220             for point in range(nbSpts):
 221                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 222             #
 223             if self._parameters["EstimationOf"] == "Parameters" and Bounds is not None:
 224                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 225             else:
 226                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 227             #
 228             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 229             #
 230             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 231                 for point in range(nbSpts):
 232                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(Bounds)[:,0])),axis=1)
 233                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(Bounds)[:,1])),axis=1)
 234             #
 235             Ynnp = []
 236             for point in range(nbSpts):
 237                 if self._parameters["EstimationOf"] == "State":
 238                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], None) ) )).T
 239                 elif self._parameters["EstimationOf"] == "Parameters":
 240                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], Un) ) )).T
 241                 Ynnp.append( Ynnpi )
 242             Ynnp = numpy.hstack( Ynnp )
 243             #
 244             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 245             #
 246             Pyyn = R
 247             Pxyn = 0.
 248             for point in range(nbSpts):
 249                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 250                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 251             #
 252             d  = Ynpu - Yncm
 253             if self._parameters["EstimationOf"] == "Parameters":
 254                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 255                     d = d - Cm * Un
 256             #
 257             Kn = Pxyn * Pyyn.I
 258             Xn = Xncm + Kn * d
 259             Pn = Pnm - Kn * Pyyn * Kn.T
 260             #
 261             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 262                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(Bounds)[:,0])),axis=1)
 263                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(Bounds)[:,1])),axis=1)
 264             #
 265             self.StoredVariables["Analysis"].store( Xn.A1 )
 266             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 267                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 268             if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 269                 self.StoredVariables["Innovation"].store( numpy.ravel( d.A1 ) )
 270             if self._parameters["StoreInternalVariables"]:
 271                 Jb  = 0.5 * (Xn - Xb).T * BI * (Xn - Xb)
 272                 Jo  = 0.5 * d.T * RI * d
 273                 J   = float( Jb ) + float( Jo )
 274                 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 275                     self.StoredVariables["CurrentState"].store( Xn )
 276                 self.StoredVariables["CostFunctionJb"].store( Jb )
 277                 self.StoredVariables["CostFunctionJo"].store( Jo )
 278                 self.StoredVariables["CostFunctionJ" ].store( J )
 279                 if J < previousJMinimum:
 280                     previousJMinimum  = J
 281                     Xa                = Xn
 282                     if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 283                         covarianceXa  = Pn
 284             else:
 285                 Xa = Xn
 286             #
 287         #
 288         # Stockage supplementaire de l'optimum en estimation de parametres
 289         # ----------------------------------------------------------------
 290         if self._parameters["EstimationOf"] == "Parameters":
 291             self.StoredVariables["Analysis"].store( Xa.A1 )
 292             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 293                 self.StoredVariables["APosterioriCovariance"].store( covarianceXa )
 294         #
 295         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 296             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 297         #
 298         self._post_run(HO)
 299         return 0
 300
 301 # ==============================================================================
 302 if __name__ == "__main__":
 303     print '\n AUTODIAGNOSTIC \n'