Comparison of Two Ground-based Mass Estimation Methods on Real Data - PowerPoint PPT Presentation

Comparison of Two Ground-based Mass Estimation Methods on Real Data R. Alligier D. Gianazza M. Ghasemi-Hamed N. Durand ENAC/MAIAA - IRIT/APO International Conference on Research in Air Transportation, 2014 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 1 / 31

Objective Context Two mass estimation methods: Adaptive method [Schultz et al., 2012] Least square method [Alligier et al., 2013] A comparison was done on synthetic data [Alligier et al., 2013] In this work: comparison on real data Mode-C radar data + weather data Actual mass not known Comparison of the trajectory prediction accuracies R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 2 / 31

Objective R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 3 / 31

Objective R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 3 / 31

Objective R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 3 / 31

Objective R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 3 / 31

An energy-rate oriented approach Newton’s laws dv 2 = power ( mass ) 1 dt + g dz 2 dt mass � �� � � �� � energy-rate f ( mass ) f is given by a physical model of the forces Using past positions given by radar We compute the observed energy-rate from radar data We search a mass such that: � � observed energy-rate = f mass R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 4 / 31

Computing the power mass provided by BADA 1 The adaptive method [Schultz et al., 2012] 2 The least square method [Alligier et al., 2012] 3 Experimental setup 4 Results 5 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 5 / 31

Computing the power mass provided by BADA 1 The adaptive method [Schultz et al., 2012] 2 The least square method [Alligier et al., 2012] 3 Experimental setup 4 Results 5 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 6 / 31

A Point Mass Model Lift Path angle Drag Thrust Weight m . dV TAS = Thr − D − m . g . sin ( γ ) dt R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 7 / 31

A simplified model (longitudinal+vertical) V TAS . dV TAS + g . dz = ( Thr − D ) . V TAS dt dt m � �� � � �� � energy-rate power mass z : altitude Thr (Thrust): thrust of the engines D (Drag): drag of the aircraft m : mass V TAS (True Air Speed): velocity in the air dV TAS : longitudinal acceleration dt dz dt = V TAS . sin ( γ ) : rate of climb R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 8 / 31

A physical model V TAS . dV TAS + g . dz = ( Thr − D ) . V TAS dt dt m � �� � � �� � power energy-rate mass R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 9 / 31

A physical model V TAS . dV TAS + g . dz = ( Thr − D ) . V TAS dt dt m � �� � � �� � power energy-rate mass BADA model Max climb thrust: Thr = f ( T , V TAS , z ) Drag: D = f ( T , V TAS , z , m ) R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 9 / 31

A physical model V TAS . dV TAS + g . dz = ( Thr − D ) . V TAS = f ( T , V TAS , z , m ) dt dt m � �� � � �� � � �� � BADA model power energy-rate mass BADA model Max climb thrust: Thr = f ( T , V TAS , z ) Drag: D = f ( T , V TAS , z , m ) R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 9 / 31

Equation at a given point = ( Thr − D ) . V TAS V TAS . dV TAS + g . dz = f ( T , V TAS , z , m ) dt dt m � �� � � �� � � �� � BADA model energy-rate power mass Using radar and weather data, we know: dV TAS dz T , z , dt , V TAS , dt R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 10 / 31

Equation at a given point = ( Thr − D ) . V TAS V TAS . dV TAS + g . dz = f ( T , V TAS , z , m ) dt dt m � �� � � �� � � �� � BADA model energy-rate power mass Using radar and weather data, we know: dV TAS dz T , z , dt , V TAS , dt The resulting equation: P ( m ) E = f ( T , V TAS , z , m ) = m ���� � �� � energy-rate � �� � BADA model P , a known function R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 10 / 31

Computing the power mass provided by BADA 1 The adaptive method [Schultz et al., 2012] 2 The least square method [Alligier et al., 2012] 3 Experimental setup 4 Results 5 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 11 / 31

The adaptive method [Schultz et al., 2012] Principle Assuming an initial guess m 0 At each point i , the mass m i is estimated using m i − 1 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 12 / 31

The adaptive method [Schultz et al., 2012] Principle Assuming an initial guess m 0 At each point i , the mass m i is estimated using m i − 1 � � P i m i E i = m i R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 12 / 31

The adaptive method [Schultz et al., 2012] Principle Assuming an initial guess m 0 At each point i , the mass m i is estimated using m i − 1 � � � � P i m i P i m i E i = ⇔ m i = m i E i R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 12 / 31

The adaptive method [Schultz et al., 2012] Principle Assuming an initial guess m 0 At each point i , the mass m i is estimated using m i − 1 � � � � � � P i m i P i m i P i m i − 1 E i = ⇔ m i = ≃ m i E i E i R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 12 / 31

The adaptive method [Schultz et al., 2012] Principle Assuming an initial guess m 0 At each point i , the mass m i is estimated using m i − 1 � � � � � � P i m i P i m i P i m i − 1 E i = ⇔ m i = ≃ m i E i E i At each new point i : m i = P i ( m i − 1 ) E i R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 12 / 31

Introduction of the sensitivity parameter β [Schultz et al., 2012] The previous update formula can be rewritten:   − 1     � � m i − 1 E i − P i ( m i − 1 )   m i = m i − 1 1 +   P i ( m i − 1 ) m i − 1     � �� �   error on the energy rate when using m i − 1 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 13 / 31

Introduction of the sensitivity parameter β [Schultz et al., 2012] The previous update formula can be rewritten:   − 1     � � m i − 1 E i − P i ( m i − 1 )   m i = m i − 1 1 +   P i ( m i − 1 ) m i − 1     � �� �   error on the energy rate when using m i − 1 Introducing a sensitivity parameter β i : � � �� − 1 m i − 1 E i − P i ( m i − 1 ) m i = m i − 1 1 + β i P i ( m i − 1 ) m i − 1 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 13 / 31

Logic of the sensitivity parameter β [Schultz et al., 2012] β low ⇒ point i has nearly no impact, m i ≃ m i − 1 β is dynamically adjusted according ∆ ˙ E i , . . . , ∆ ˙ E i − p Update rule [Schultz et al., 2012] � � ∆ ˙ E i − ∆ ˙ � � E avg if i > 0 and ∆ ˙ � � E i > 0 . 0001 and � < 3 � � ∆ ˙ E avg � then β i = max ( 0 . 205 , β i − 1 + 0 . 05 ) else β i = 0 . 005 R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 14 / 31

Logic of the sensitivity parameter β [Schultz et al., 2012] � � �� − 1 m i − 1 E i − P i ( m i − 1 ) m i = m i − 1 1 + β i P i ( m i − 1 ) m i − 1 This mechanism increases robustness If ∆ ˙ E i repeatedly high in the same order of magnitude, β will increase, strengthening adaptation Isolated low or high ∆ ˙ E i has a lower impact on adaptation R. Alligier, D. Gianazza, M. Ghasemi-Hamed, N. Durand (ENAC) Estimation of the Aircraft Mass ICRAT 2014 15 / 31