SIS Review-May 18-19, 1999sis.ae.illinois.edu/Present/NASARvwSxn/4_Controls.pdf · 1999. 10. 29. · Diagram NASA Review Ma y 18-19, 1999 ID Algo rithm(s) Ice Detection & Senso r

Smart Icing SystemsFlight Controls and Sensors

NASA Review May 18-19, 1999

Principal Investigators: Tamer Ba�sar (CSL/ECE)

William Perkins� (CSL/ECE)

Petros Voulgaris (CSL/AAE)

Graduate Students: Wen Li (NASA Support)

James Melody� (CRI Support)

Eric Schuchard (Fellowship)

Undergrad Students: Eric Keller (NSF Support)

Thomas Hillbrand (Fellowship)

Eduardo Salvador (NSF Support)

* presenting

4-1

Smart Icing Systems

Smart Icing Systems Research Organization


Core Technologies

Aerodynamcs

and

Propulsion

Flight

Mechanics

Control and

Sensor

Integration

Human

Factors

Aircraft

Icing

Technology

IMS Functions

Characterize

Icing E�ects

Operate and

Monitor IPS

Envelope

Protection

Adaptive

Control

Flight Simulation

Demonstration

Safety and Economics

Trade Study

4-2

Smart Icing SystemsFlight Controls and Sensors


Goal: Improve the safety of aircraft in icing conditions.

Develop smart systems to improve ice tolerance.

Objectives:

1) Develop fast and reliable methods and algorithms for inight

identi�cation of aircraft ight dynamics.

2) Develop robust ice detection and classi�cation methods and al-

gorithms that incorporate identi�ed parameters and other avail-

able sensor information.

3) Investigate utility of control recon�guration to maintain ight

characteristics in the presence of icing.

Approach: Apply existing parameter identi�cation techniques to

parameter identi�cation of ight dynamics. Investigate detection

methods based on the identi�ed parameters. Evaluate performance

according to timeliness and accuracy of icing characterization.

4-3

Smart Icing Systems

Smart Icing Systems Research


THE CONTROL AND SENSOR

INTEGRATION GROUP

LTI - Linear, Time-Invariant

LTV - Linear, Time-VaryingEric Keller, Eduardo Salvador, Prof. Ba�sar

Thomas Hillbrand, Prof. Ba�sar

Wen Li, Prof. Voulgaris

Jim Melody, Prof. Ba�sar

Eric Schuchard, Prof. Perkins

Characterizaton

Flight

Simulation

Adaptation

LTI Longitudinal

Dynamics ID

LTI Longitudinal

Dynamics Detection

LTV Longitudinal

Dynamics ID

LTV Longitudinal

Dynamics Detection

Nonlinear 6-axis

Dynamics ID

Nonlinear 6-axis

Dynamics Detection

Adaptation/Handling

Event Recovery

Nonlinear Dynamics

Development

Sensor and Drag

Charact. Integration

4-4

Smart Icing Systems

Flight Controls and Sensors Outline


� Ice detection & characterization overview

� Identi�cation during maneuver

{ Batch Algorithm

{ Recursive Algorithm: H1

{ Recursive Algorithm: EKF

� Neural network detection & classi�cation during maneuver

� Identi�cation during steady level ight

� Summary & Conclusions

� Future Plans

4-5

Smart Icing Systems

Ice Characterization Block Diagram


ID

Algorithm(s)

Ice Detection

& Sensor Fusion

Envelope Prot

& IPS I/F

Flight

Dynamics

(depend on �)

Flight

Controller

+

other sensors� parameters

^� parameter estimates

output

input

^�

Pilot

Pilot

IPS

IMS

4-6

Smart Icing Systems

Icing Characterization Philosophy


� Icing matters to the extent that it a�ects the ight dynamics.

� E�ect of icing on ight dynamics is captured by parameter �.

� By observing behavior of dynamics, can infer the value of �

) Parameter Identi�cation (ID)

� From estimated parameter ^�(t), detect and classify icing e�ects.

� Icing detection will also incorporate

{ aerodynamic sensors

{ steady-state characterization

{ hinge moment sensing

{ external environmental sensors

) Sensor Integration

� Inform pilot of icing directly and via envelope protection

4-7

Smart Icing Systems

Longitudinal Flight Dynamics Model


Linearized model of longitudinal ight dynamics

_u = �g cos(�) + (Xu +XTu)u+X��+XÆEÆE

_w � Uq = �g� sin(�)+ Zuu+ Z��+ Z _� _�+ Zqq+ ZÆEÆE

_q = Muu+MTuu+M��+MT��+M _� _�+Mqq+MÆEÆE

where u forward velocity w downward velocity

� angle of attack q pitch rate

� pitch angle ÆE elevator angle

U , � trim conditions (i.e., linearization point)

and fM�, Z�, X�g are stability and control (S/C) derivatives.

Model v1.0 clean and iced (�ice = 1) S/C derivatives:

M� MÆE Mq Z� ZÆE Zq X� Xu +XTu

Clean -7.86 -10.44 -3.055 -378.7 -40.30 -19.70 13.71 -0.018

Iced -7.08 -9.40 -2.948 -342.7 -36.45 -19.43 13.90 -0.020

other derivatives are invariant to icing. Extensive simulation for this model has

shown that only M�, MÆE, and possibly Mq are useful for icing characterization.4-8

Smart Icing SystemsParameter ID Framework


� Let � := [M�; MÆE; Mq; Z�; ZÆE ; Zq; X�; (Xu+XTu)]T

be parameters to identify and convert ight dynamics to

_x = A(x; v)�+ b(x; v) + w

z = x+ n

where x = [q � � u]T state

v = ÆE input

z measured output

w state disturbance (a.k.a., process noise)

n measurement noise

� n(t) represents inaccuracies in the measurement,

e.g., instrument accuracy limitations

� w(t) represents unknown excitation of the ight dynamics,

e.g., turbulence, modeling error

� system excitation is necessary for identi�cation

� unknown exogenous signals n(t) and w(t) limit accurately of

estimated parameter

4-9

Smart Icing Systems

Parameter ID Algorithm Categorization


Objective: Given some information, , (e.g., input, output, and

state measurements) identify � accurately in the presence of w and n.

� Static algorithms: parameter estimate at any instant, ^�(tn), is

based solely on measurements at that instant, tn.

{ solve matrix equation

{ no solution when dim(x) � dim(�)

� Batch algorithms: static algorithms that process measurements

in batches: ^�(tm) depends on ftm�k; ::: ;tm�1; tmg

{ noise sensitivity depends on excitation level and batch period

� Recursive algorithms: parameter estimate is based on past and

present measurements: ^�(t) depends on [0; t]

{ characterized by di�erential equations with i.c.'s

{ convergence rate is a function of excitation level

4-10

Smart Icing Systems

Parameter ID Information Structures


ID algorithm depends on type of information available

� Full state derivative information (FSDI): input, state, and state derivative are

available,

t := (x(t); _x(t); u(t))

i.e., n = 0 and ( _q, _�, _u) and (q, �, �, u) are measured

� Full state information (FSI): input and state are available,

t := (x(t); u(t))

i.e., n = 0 and (q, �, �, u) are measured

� Noise perturbed full-state information (NPFSI): input and noisy measurement

of state are available,

t := (z(t); u(t))

i.e., n 6= 0

� Noise perturbed partial-state information (NPPSI): input and noisy

measurement of only part of the state are available

t := (z(t); u(t))

where z = Cx+ n, e.g., � is not measured.

4-11

Smart Icing Systems

Noise CharacterizationNASA Review May 18-19, 1999

Assume: n and w are zero-mean white Gaussian noise, hence

completely characterized by their covariances

Covariance of w:

� Consider turbulence as a vertical velocity perturbation

) only � is directly a�ected.

� Assume noise covariance equal to energy of _� for a 5Æ doublet

� _q �q � _� � _u

0Æ/s2 0Æ/s 0.026Æ/s 0 knot/s

Covariance of n:

� Instrument resolution speci�cations for NASA Twin Otter:

�q �� u

0.0167Æ/s 0.0293Æ 0.003Æ 0.076 knot

4-12

Smart Icing Systems

Identi�cation during Maneuver



INTEGRATION GROUP







Characterizaton

Flight

Simulation

Adaptation

LTI Longitudinal

Dynamics ID

LTI Longitudinal

Dynamics Detection

LTV Longitudinal

Dynamics ID

LTV Longitudinal

Dynamics Detection

Nonlinear 6-axis

Dynamics ID

Nonlinear 6-axis

Dynamics Detection

Adaptation/Handling

Event Recovery

Nonlinear Dynamics

Development

Sensor and Drag


4-13

Smart Icing Systems

Maneuver Icing Scenario


Icing Scenario:

� During a period of steady level ight, ice accretes but lack of

excitation limits parameter ID e�ectiveness.

� Afterwards, a maneuver is performed during which parameter ID

takes place.

Model of Scenario:

� Begin ID simulations at beginning of maneuver

� Parameters assumed constant over the maneuver

� Maneuver is modeled as an elevator doublet

� Use simple threshold (mean of clean and iced parameters) for

quick and dirty evaluation of algorithms

� Must also consider ID of clean aircraft for \false alarms"

Question: Is there a reliable indication of icing in a reasonable

amount of time?

4-14

Smart Icing Systems

Static Least-Squares FSDI ID


� Assume that _x(t), x(t), and u(t) are known, and take w(t) equal

to its mean, i.e., w(t) � 0.

� At each time instant, t, we have the system of n linear equations

in r unknowns, �:

A(xt; vt)� = _xt � b(xt; vt) (1)

where xt 2 IRn and � 2 IRr.

� Solve directly for ^�(t) using matrix least squares:

^� =

hATAi�1

AT ( _xt � b) (2)

� Solution will not exist if the rank of A is less than r, e.g., if r > n.

4-15

Smart Icing Systems

Batch Least-Squares FSDI ID


� Collect several measurements in batch and concatenate equations

A(xt1; vt1)� = _xt1 � b(xt1; vt1)

A(xt2; vt2)� = _xt2 � b(xt2; vt2)

...

A(xtm; vtm)� = _xtm � b(xtm; vtm)9>>=

>>;) Am� = _Xm � Bm

� Excitation ) nondegenerate equations for t1, t2, : : : , tm

) rank of Am is r with suÆcient number of measurements, m.

� Solve directly for ^�(tm) using matrix least squares:

^�(tm) =

�ATmAm��1ATm�

_Xm � Bm�

� By including disturbances, the error in the estimate, ~�(tm), is given by

~�(tm) =

�ATmAm��1ATmWm

with WTm :=

�w(t1)T w(t2)T � � � w(tm)T�

.

� If the system is poorly excited, or if the batch period is small, the error can

be very sensitive to w.

4-16

Smart Icing SystemsBatch Least-Squares FSI ID


� Extend to FSI case via integrating pre�lter.

� With x(t) and v(t) known, integration yields x = �At� + �bt + �wt where

_�At = A(x(t); v(t)), _�bt = b(x(t); v(t)), and _�wt = w(t).

� Pure integrator is not stable. In order to stabilize, include pole at �� < 0

_�At = �� At + A(x(t); v(t)); �AÆ = 0

_�bt = ��bt + b(x(t); v(t)); �bÆ = xÆ

� Apply matrix LS to pre�ltered equation

�At1� = xt1 ��bt1

...

�Atm� = xtm ��btm9=

; ) �A� = X � �B

� Then ~�=

��AT �A��1 �AT W where W is concatenated pre�ltered noise

_�wt = ��wt + w(t); �wÆ = 0

� NPFSI ?

) use measurement z in place of x, but sensitive to measurement noise.4-17

Smart Icing Systems

Batch LS Results: Clean & Iced w/ no

Measurement NoiseNASA Review May 18-19, 1999

Batch LS FSI Algorithm with Tb = 8 s, � = 10, and sampling rate 30 Hz

5Æ doublet maneuver over 10 seconds

with process noise but no measurement noise

Iced Aircraft Clean Aircraft

0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

Notice: A reliable indication of icing is not given for either MÆE or M�.

4-18

Smart Icing Systems







0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

Notice: A reliable indication of icing is not given for either MÆE or M�.

4-19

Smart Icing Systems





with process noise reduced by a factor of 100 in energy and no measurement noise


0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

Notice: A reliable indication of icing for both MÆE and M� is available in 1 s.

4-20

Smart Icing Systems

Recursive Parameter ID Algorithms


� Extended Kalman �lter (EKF):

{ augment the state with the parameters and estimate this augmented state

{ can accommodate both state disturbance and measurement noise

{ estimate may diverge, a.k.a. \lose lock"

{ can be generalized to time-varying parameters

{ very common in practice

� H1 identi�cation:

{ generalization of recursive least-squares (RLS) and least-mean-squares

(LMS)

{ guaranteed disturbance attenuation between disturbances and parameter

estimation error

{ can accommodate both state disturbance and measurement noise

{ persistency of excitation results in asymptotic convergence of estimate

for time-invariant parameters

{ can be generalized to time-varying parameters

4-21

Smart Icing Systems

H

1 FSDI AlgorithmNASA Review May 18-19, 1999

� Guaranteed disturbance attenuation level for any greater than some �

k�� ^�k2Q(x;v)

kwk2+ j�� ^�Æj2QÆ

� 2

where k�kQ is an L2 norm with a chosen weighting function Q(x; v) � 0 and

j � jQÆ is a weighted Euclidean norm with QÆ > 0.

� x, _x, and v are known. For > � parameter estimate ^� is given by

_^� = ��1A(x; v)T [ _x�A(x; v)^�� b(x; v)] ; ^�(0) = ^�Æ

_� = A(x; v)TA(x; v)� �2Q(x; u); �(0) = QÆ

where �(t) 2 IRr�r.

� Generally, � is unknown and may be in�nite.

� However, Q(x; v) := A(x; v)TA(x; v)) � = 1

= 1) generalized LMS estimator:

_^� = Q�1Æ

A(x; v)T [ _x�A(x; v)^�� b(x; v)]

� If " 1 the limiting �lter is the RLS estimator.

4-22

Smart Icing Systems

H

1 NPFSI AlgorithmNASA Review May 18-19, 1999

� input is known, but only noisy state measurement z = x+ n is available.

� Guaranteed disturbance attenuation level > �,

k�� ^�k2Q(x;v)

kwk2+ knk2+ j�� ^�Æj2QÆ + jxÆ � ^xÆj2

PÆ

� 2

where xÆ is actual initial state, ^xÆ is initial state estimate, and PÆ > 0.

� Both the state and the parameter must be estimated. For > �:�_^x

_^��

=

�0 A

0 0� �

^x^�

�+�

b0

�+��1�

I0

�(z � ^x) ;

_� = ��

0 A

0 0�

��

0 0

AT 0�

�+�

I 0

0 ��2Q

��

I 0

0 0�

�;

with �(t) 2 IR(n+r)�(n+r) and �(0) = diag(PÆ; QÆ).

� It can be shown that Q := �T2�2 yields � = 1, where �2 2 IRn�r is o�-diagonal

portion of �.

4-23

Smart Icing Systems

Recursive H1: Iced, No Measurement Noise


H1 FSDI Algorithm with = 3 and QÆ = (1� 10�6)I



0 5 10 15

0.9

0.95

1

1.05

1.1

1.15

1.2

MÆE

M�

time (s)

Norm

alizedEstim

ates

Notice: Using simple threshold, both M� and MÆE

give indication in < 1 s.

4-24

Smart Icing Systems

Recursive H1: Clean, No Measurement Noise


H1 FSDI Algorithm with = 3 and QÆ = (1� 10�6)I



false alarm scenario with various initial parameter estimation errors

M� parameter estimates MÆE parameter estimates

0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

Notice: M� and MÆE estimates never yield false

alarms using simple detection threshold.

4-25

Smart Icing Systems

Recursive H1: Iced, w/ Measurement Noise


H1 NPFSI Algorithm with = 3 and QÆ = (1� 10�7)I


with process noise and measurement noise

0 5 10 15

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

MÆE

M�

time (s)

Norm

alizedEstim

ates


give indication in < 1 s.

4-26

Smart Icing Systems

Recursive H1: Clean, w/ Measurement Noise







0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

Notice: M� and MÆE estimates never yield false

alarms using simple detection threshold.

4-27

Smart Icing Systems

Recursive H1: Iced, w/ Measurement Noise





0 5 10 15

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

MÆE

M�

time (s)

Norm

alizedEstim

ates


again give indication in < 1 s.

4-28

Smart Icing Systems

Recursive H1: Clean, w/ Measurement Noise







0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

0 5 10 150.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time (s)

Norm

alizedEstim

ate

Notice: M� gives false alarm for large

initial estimation errors.

Notice: MÆE estimates never cross the

threshold.

4-29

Smart Icing SystemsRecursive EKF ID Algorithm


� Kalman �lter provides state estimate. Recast the parameter ID problem into

a state estimation problem:

_x = A�+ b+ w

_� = 0

)y :=

�x

��

)

8>><>>:

_y =

�A(x; v)�+ b(x; v)

0

�+�

w0

�

z = [I 0] y+ n

� In the Kalman �lter framework, the state disturbance, measurement noise,

and initial state, yÆ, are assumed to be Gaussian with:

E fw(t)g � 0

E fn(t)g � 0

E fyÆg = �yÆ

cov fw(t); w(�)g = P(t)Æ(t� �)

cov fn(t); n(�)g = R(t)Æ(t� �)

cov fyÆ; yÆg = QÆ

Furthermore, w(t) and n(t) are assumed to be uncorrelated:

cov fw(t); n(�)g � 0

� For linear systems Kalman �lter provides minimum-variance, unbiased state

estimate.

� However, augmented system is always nonlinear ) extended Kalman �lter.4-30

Smart Icing Systems

Recursive EKF ID Algorithm (cont'd)


� Extended Kalman �lter: linearize the system about an estimated (augmented)

state trajectory.

� The resulting algorithm is:

_^y =

�A(^x; v)^�+ b(^x; v)

0

�+�(t)HT ^R(t)�1 [z �H^y]

_�(t) = D(^y; v)�(t) +�(t)D(^y; v)T + �P(t)��(t)HT ^R(t)�1H�(t)

where, � 2 IR(n+r)�(n+r), H = [I 0],

�P(t) =

�^P(t) 0

0 0�

; and; D(^y; v) =

"@

@^xA(^x; v)^�+ @@^xb(^x; v) 0

A(^x; v)T 0#

� For a linear system, ^P(t) = P(t) and ^R(t) = R(t)

^R(t) = R(t); ^P(t) = P(t); & �(0) = QÆ

are optimal, but not for a nonlinear system. Hence, ^P(t) = ^P(t)T � 0,

^R(t) = ^R(t)T > 0, and QÆ = QTÆ � 0 are used as algorithm design parameters.

4-31

Smart Icing SystemsRecursive EKF Results: Iced


EKF Algorithm with ^P (t) � 0:1I and ^R(t) � (1� 10�5)I



0 5 10 15

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

MÆE

M�

time (s)

Norm

alizedEstim

ates

Notice: Using the simple threshold, both

M� and MÆE give an indication in < 2 s.

4-32

Smart Icing Systems

Recursive EKF Results: Clean







0 5 10 150.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

time (s)

Norm

alizedEstimate

0 5 10 150.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

time (s)

Norm

alizedEstimate

Notice: Using simple threshold, both M� and MÆE give false alarms for all initial errors.4-33

Smart Icing SystemsRecursive EKF Results: Iced





0 5 10 15

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

MÆE

M�

time (s)

Norm

alizedEstimates

Notice: Using simple threshold, only MÆE yields a

reliable indication of icing.

4-34

Smart Icing Systems

Recursive EKF Results: Clean







0 5 10 150.8

0.85

0.9

0.95

1

1.05

1.1

1.15

time (s)

Norm

alizedEstimate

0 5 10 150.9

0.95

1

1.05

1.1

1.15

time (s)

Norm

alizedEstimate

Notice: Using simple threshold, both M� and MÆE give false alarms for all initial errors.4-35

Smart Icing Systems

Detection and Classi�cation during Maneuver



INTEGRATION GROUP







Characterizaton

Flight

Simulation

Adaptation

LTI Longitudinal

Dynamics ID

LTI Longitudinal

Dynamics Detection

LTV Longitudinal

Dynamics ID

LTV Longitudinal

Dynamics Detection

Nonlinear 6-axis

Dynamics ID

Nonlinear 6-axis

Dynamics Detection

Adaptation/Handling

Event Recovery

Nonlinear Dynamics

Development

Sensor and Drag


4-36

Smart Icing Systems

Detection and Classi�cation Formulation


Objective: Given parameter estimate, ^�(t), and other sensor information, reliably

detect the presence of icing and classify its severity in a timely manner.

Approach:

� Train neural networks (NN) to recognize correlations between parameter es-

timates, other sensor information, and icing.

� Activate the NN at beginning of maneuver

� Feed batch of sampled parameter estimates to NN.

� NN will take advantage of trends in parameter estimates, improving over

threshold detection.

� Use separate detection and classi�cation networks for eÆciency

Results to date:

� NN have been applied to H1 NPFSI identi�cation.

� Other sensor information has not yet been incorporated.

4-37

Smart Icing Systems

Neural NetworksNASA Review May 18-19, 1999

Neural Network Sigmoidal Activation Function

Input Nodes

Output Nodes

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

� NN are layered networks of interconnected nodes. Nodes ) activation func-

tions, lines ) weights, multiple lines are summed.

� Weighted sum of inputs to node plus a bias are input to activation function.

Often, sigmoidal activation functions are used.

� Sigmoidal activation functions generalize discrete switching.

� For a given structure (# of layers and nodes) training refers to optimization

of biases and weights based on a suite of test cases.

� NN are general enough to recognize complex nonlinear relationships, such as

between our sensor information and icing.

4-38

Smart Icing Systems

Neural Network vs. Threshold


� For detection based on parameter estimates alone, NN will take advantage

of any consistent temporal patterns in parameter estimates.

� If no consistent trends, NN will not perform better than thresholding at the

�nal estimate sample.

� Evaluate consistency of trends by running same simulations for various noise

realizations:

Recursive H1 NPFSI MÆE estimates Batch LS MÆE parameter estimates

0 5 10 150.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

time (s)

Norm

alizedEstimate

0 1 2 3 4 5 6 7 8 9 100.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

time (s)

Norm

alizedEstimate

4-39

Smart Icing SystemsRecursive H1 Detection Network


Detection Network Results

using �ve seconds of MÆE and M� estimates as input

elevator input doublets varying from 1Æ to 10Æ and from 5s to 15s

0 10 20 30 40 50 60 70 80 90 100 110

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

simulation case #

smaller amplitude doublets

ActualIcingLevel�ice

mark indication

clean

� iced

4-40

Smart Icing Systems

Recursive H1 Classi�cation Network


Four-level Classi�cation Network Results

using �ve seconds of MÆE and M� estimates as input

elevator input doublets varying from 1Æ to 10Æ and from 5s to 15s

0 10 20 30 40 50 60 70 80 90 100 110

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

simulation case #

smaller amplitude doublets

ActualIcingLevel�ice

mark �ice class.

0

2 1/3

+ 2/3

� 1

4-41

Smart Icing Systems

Identi�cation during Steady-Level Flight



INTEGRATION GROUP







Characterizaton

Flight

Simulation

Adaptation

LTI Longitudinal

Dynamics ID

LTI Longitudinal

Dynamics Detection

LTV Longitudinal

Dynamics ID

LTV Longitudinal

Dynamics Detection

Nonlinear 6-axis

Dynamics ID

Nonlinear 6-axis

Dynamics Detection

Adaptation/Handling

Event Recovery

Nonlinear Dynamics

Development

Sensor and Drag


4-42

Smart Icing Systems

Steady-Level Flight Icing Scenario


Icing Scenario:

� During steady level ight the clean aircraft passes through a \cloud" of icing

conditions and ice accretes continuously.

Model of Scenario:

� Use AcE accretion model with freezing fraction n= 0:2.

� Assume that airplane ies through icing \cloud" in time Tc, and that the LWC

along ight path has raised-cosine shape.

� Then AcE as a function of time is the solution of

ddtAcE =

�2[1� cos (2�t=Tc)] ; AcE(0) = 0

where assumed value of �ice(Tc) determines � from

�ice(t) = Z1(n)AcE(t) + Z2(n)[AcE(t)]2

Question: Can parameter ID augment steady-state characterization during

moderate turbulence?

4-43

Smart Icing Systems

Steady-Level Flight Icing Scenario (cont'd)


Assume: freezing fraction n= 0:2

Choose: icing cloud length Tc and �ice(Tc)

LWC AcE(t)

TcTc

Rdt

)

TcTc

ddtAcE � LWC � 1� cos(2�t=Tc) AcE(t) � t�

Tc2�sin(2�t=Tc)

�ice(t)

)

Tc

�ice(Tc)

�ice(t) = Z1(n)AcE(t) + Z2(n)[AcE(t)]2

4-44

Smart Icing Systems

Recursive H1 Time-varying Algorithm


� The actual parameters are allowed to vary with time, according to

_� = H�+Kd

where H and K are assumed to be known and d is (unknown) parametric

disturbance.

� For the FSDI case, we have guaranteed disturbance attenuation level > �,

k�(t)� ^�(t)k2Q(x;v)

kwk2 + kdk2 + j�� ^�Æj2QÆ

� 2

� For > � the algorithm is

_^� = H^�+��1AT [ _x�A^�� b] ; ^�(0) = ^�Æ

_� = ��H �HT��KKT�+ATA� �2Q(x; u); �(0) = QÆ

� In this case, H = 0 and K can be calculated from Z1(n), Z2(n), and the S/C

derivative �ice-coeÆcients.

� Note: MÆE is an input coeÆcient and cannot be estimated without input.4-45

Smart Icing Systems

Recursive H1 Results: Moderate Icing


H1 FSDI Algorithm with = 1:0001, Q = ATA, and QÆ = (1� 10�4)I

5 minute icing cloud with �nal icing value of �ice = 1


Actual and Estimated M�

0 1 2 3 4 5 6

0.9

0.92

0.94

0.96

0.98

1

1.02

^M�(t)

M�(t)

time (min)

Norm

alizedM

�Estim

ate | actual M�

| estimated M�

� � � classi�cation levels

| classi�cation delays

�ice Level Delay

0.2 17 s

0.4 24 s

0.6 31 s

0.8 43 s

1.0 > 100 s

4-46

Smart Icing Systems

Recursive H1 Results: Rapid/Severe Icing


H1 FSDI Algorithm with = 1:0001, Q = ATA, and QÆ = (1� 10�4)I

2 minute icing cloud with �nal icing value of �ice = 1:5


Actual and Estimated M�

0 0.5 1 1.5 2 2.5 3

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

^M�(t)

M�(t)time (min)

Norm

alizedM

�Estim

ate | actual M�

| estimated M�

� � � classi�cation levels

| classi�cation delays

�ice Level Delay

0.25 12 s

0.50 17 s

0.75 20 s

1.00 28 s

1.25 64 s

1.50 < 80 s

4-47

Smart Icing Systems

Conclusions


� Recursive H1 and EKF algorithms yield timely estimates during

maneuver with measurement noise.

� Batch estimation performs poorly with and without measure-

ment noise

� NN applied to recursive H1 during maneuver detected tailplane

icing correctly 97% of the time, for doublet inputs greater than 1Æ.

� NN applied to recursive H1 during maneuver classi�ed tailplane

icing correctly 97% of cases, for doublet inputs greater than 1Æ.

� For batch detection and classi�cation, NN will not improve over

threshold applied after some �xed period.

4-48

Smart Icing Systems

Issues/Near Term Plans


� Re�ne turbulence process noise model

� H

1 NPFSI algorithm during steady-level ight

� Batch LS algorithm during steady-level ight

� NN accuracy/excitation/batch time tradeo�

� ID of lateral dynamics

� Sliding or expanding window for NN detection during maneuver

� Detection with parameter ID and steady-state characterization4-49

Smart Icing Systems

Future Plans


� Uni�ed approach to various icing event types: lateral/longitudinal,

handling/performance

� Integrate sensor info into detection and classi�cation

� Extend ID and detection/classi�cation to full nonlinear dynamics

{ Apply linear-based algorithms to nonlinear model at trim point

{ Develop algorithms based on direct parameterization of non-

linear model

� Investigate adaptive control for handling event recovery, not just

prevention

� Support incorporation of algorithms into Icing Encounter Flight

Simulator

4-50

Smart Icing Systems

Flight Controls and Sensors Waterfall Chart


Federal Fiscal Years

98 99 00 01 02 03

ID of LTI DynamicsID of LTV Dynamics

Ice Detection for LTI Dynamics

Ice Detection for LTV Dynamics

ID of Nonlinear Dynamics

Sensor IntegrationDetection for Nonlinear Dynamics

Adaptation/Event Recovery

Support IE Flight Simulator

4-51

Documents

SIS Review-May 18-19, 1999sis.ae.illinois.edu/Present/NASARvwSxn/4_Controls.pdf · 1999. 10. 29. · Diagram NASA Review Ma y 18-19, 1999 ID Algo rithm(s) Ice Detection & Senso r