June 2012 

NASA/TM–2012-217586 

On Identifiability of Bias-Type Actuator-Sensor 

Faults in Multiple-Model-Based Fault Detection 

and Identification 

Suresh M. Joshi 

Langley Research Center, Hampton, Virginia 
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA scientific and technical information (STI) 

program plays a key part in helping NASA maintain 

this important role. 

The NASA STI program operates under the 

auspices of the Agency Chief Information Officer. 

It collects, organizes, provides for archiving, and 

disseminates NASA’s STI. The NASA STI 

program provides access to the NASA Aeronautics 

and Space Database and its public interface, the 

NASA Technical Report Server, thus providing one 

of the largest collections of aeronautical and space 

science STI in the world. Results are published in 

both non-NASA channels and by NASA in the 

NASA STI Report Series, which includes the 

following report types: 

 TECHNICAL PUBLICATION. Reports of 

completed research or a major significant phase 

of research that present the results of NASA 

Programs and include extensive data or 

theoretical analysis. Includes compilations of 

significant scientific and technical data and 

information deemed to be of continuing 

reference value. NASA counterpart of peerreviewed formal professional papers, but 

having less stringent limitations on manuscript 

length and extent of graphic presentations. 

 TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or of 

specialized interest, e.g., quick release reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis. 

 CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees. 

 CONFERENCE PUBLICATION. 

Collected papers from scientific and 

technical conferences, symposia, seminars, 

or other meetings sponsored or cosponsored by NASA. 

 SPECIAL PUBLICATION. Scientific, 

technical, or historical information from 

NASA programs, projects, and missions, 

often concerned with subjects having 

substantial public interest. 

 TECHNICAL TRANSLATION. 

English-language translations of foreign 

scientific and technical material pertinent to 

NASA’s mission. 

Specialized services also include organizing 

and publishing research results, distributing 

specialized research announcements and feeds, 

providing information desk and personal search 

support, and enabling data exchange services. 

For more information about the NASA STI 

program, see the following: 

 Access the NASA STI program home page 

at http://www.sti.nasa.gov

 E-mail your question to help@sti.nasa.gov

 Fax your question to the NASA STI 

Information Desk at 443-757-5803 

 Phone the NASA STI Information Desk at 

443-757-5802 

 Write to: 

 STI Information Desk 

 NASA Center for AeroSpace Information 

 7115 Standard Drive 

 Hanover, MD 21076-1320
National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton, Virginia 23681-2199 

 

June 2012 

NASA/TM–2012-217586 

On Identifiability of Bias-Type Actuator-Sensor 

Faults in Multiple-Model-Based Fault Detection 

and Identification 

Suresh M. Joshi 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics 

and Space Administration.
Abstract

This paper explores a class of multiple-model-based fault detection and identification

(FDI) methods for bias-type faults in actuators and sensors. These methods employ

banks of Kalman-Bucy filters to detect the faults, determine the fault pattern, and

estimate the fault values, wherein each Kalman-Bucy filter is tuned to a different

failure pattern. Necessary and sufficient conditions are presented for identifiability

of actuator faults, sensor faults, and simultaneous actuator and sensor faults. It is

shown that FDI of simultaneous actuator and sensor faults is not possible using these

methods when all sensors have biases.

1 Introduction

Failures in control effectors and sensors can cause poor performance or instability

in dynamical systems. In particular, faults in flight control systems for aircraft or

spacecraft can lead to loss of control and serious incidents. Therefore, rapid fault

detection and identification (FDI) in actuators and sensors is important for enhancing

flight safety. One approach to actuator and sensor FDI is based on multiple-model

methods [1], [2], which have been extended to detect faults and identify the fault

pattern as well as the fault values [3], [4]. Such methods typically use banks of

Kalman-Bucy filters (or Extended Kalman filters) and multiple hypothesis testing,

and have been reported to be effective for bias-type faults such as aircraft control

surfaces getting stuck at unknown values, or sensors (e.g., rate gyros) that develop

unknown constant or slowly-varying biases. The underlying requirement for these

methods is that the faults should be identifiable. Identifiability of bias-type faults

was considered in [4] and preliminary results were presented. This paper focuses in

greater detail on the identifiability of actuator faults, sensor faults, and simultaneous

actuator and sensor faults.

2 Actuator Faults

Consider a linear time-invariant system:

x ̇ = Ax + Bu + wp

y = Cx + ws (1)

where x ∈ Rn, u ∈ Rm, wp ∈ Rn, y ∈ Rl, ws ∈ Rl denote the state vector, control

vector, process noise, output vector, and sensor noise respectively, and A, B, C are

appropriately dimensioned matrices. wp and ws are usually assumed to be stationary

zero-mean Gaussian processes having constant covariance intensities.

Of the m actuators in the system, some may fail at unknown time instants. The

type of actuator failure addressed in this paper is a “stuck actuator” failure, which

produces a constant unknown input value (which is zero in the case of complete

actuator outage). Thus, in the kth failure pattern, if mk of the m actuators fail, the

1
system dynamics becomes

x ̇ = Ax +

X

j /∈Fak

bjuj +

X

j∈Fak

bju ̄j + wp

= Ax + B

kuk + B

k

u ̄

k + wp (2)

where Fak is the set of indices corresponding to the failed actuators, and  ̄uj denotes

the corresponding failure value (for example, deflection of a stuck control surface in

aircraft). There are up to 2m − 1 possible failure patterns for m actuators.  ̄u

k ∈

Rmk denotes the failure value for the kth failure pattern; u

k ∈ Rm−mk denotes the

input vector corresponding to the functioning actuators; B

k

denotes the columns

of B corresponding to the failed actuators Bk denotes the remaining columns of B

corresponding to the functional actuators.

In multiple-model-based methods, up to 2m mathematical models (including the

“no failures” case and up to 2m − 1 failure patterns) are constructed from (2) and a

corresponding bank of 2m Kalman-Bucy filters is designed. The fault is isolated and

the fault values  ̄uj are estimated by augmenting (2) with:

u ̄ ̇

j = waj

(3)

where wajis a fictitious zero-mean white noise process. Thus the augmented equation

corresponding to model k (failure pattern k) is

d

dt 

x

u

k



=

"

A B

k

0 0 # 

x

u ̄

k



+



Bk

0



u

k + wk

(4)

where w

k ∈ Rn+mk denotes the input noise vector consisting of the process noise wp

and the fictitious noise corresponding to  ̄u

k

. Denoting

ξ

k =



x

u ̄

k



(5)

the system corresponding to failure pattern k is expressed as

 ̇

ξ

k = A

k

ξ

ξ

k + Bk

ξ u

k + wk

(6)

y = [C 0]ξ

k + ws := Ck

ξ

ξ

k + ws (7)

where Ak

ξ

, Bk

ξ

are the augmented system- and input-matrices from (4).

The FDI approach employed in multiple-model-based methods is to design and

implement a bank of Kalman-Bucy filters (KBF), one corresponding to each of the

2

m models, and to determine (in real time) which model correctly represents the

actual fault pattern, using criteria such as highest conditional probability or the

smallest residual norm. The KBF corresponding to the correct model also gives an

unbiased minimum-variance estimate of the fault values. The KBF corresponding to

model k is given by

 ̇bξ

k = A

k

ξ

bξ

k + B

k

ξ u

k + Hk

(y − C

k

ξ

bξ

k) (8)

2
where bξ

k denotes the estimate of ξ

k and Hk

(a function of time) is the KBF gain.

From (6) and (8), the estimation error dynamics are given by

 ̇eξ

k = (A

k

ξ − HkC

k

ξ

)

eξ

k + w

k − Hkws (9)

where eξ

k = ξ

k − bξ

k. The residual (which is used in decision-making to determine

which fault model is “closest” to the actual system), is given by

rk = y − C

k

ξ

bξ

k = C

k

ξ

eξ

k + ws (10)

For the scheme to work, the error dynamics (9) must be asymptotically stable and

unbiased, i.e., the mean of eξ

k should converge to zero and its covariance should be

bounded ∀t ≥ 0.

For failure pattern k, if B

k

is not of full rank, it is not possible to distinguish

between fault values for actuators corresponding to linearly dependent columns of

B

k

. For example, for some failure pattern, if

B = [ ̄b1,

 ̄b2, ̄b3]

and if  ̄b3 = α1

 ̄b1 + α2

 ̄b2 for some constant α1, α2, the input terms due to the failed

actuators are

Bu ̄ =  ̄b1u ̄1 +  ̄b2u ̄2 +  ̄b3u ̄3

=  ̄b1( ̄u1 + α1u ̄3) +  ̄b2( ̄u2 + α2u ̄3) (11)

Thus only the aggregated fault values  ̄u1 + α1u ̄3, u ̄2 + α2u ̄3 can be estimated, and

u ̄1, u ̄2, u ̄3 cannot be estimated individually. Therefore it is assumed henceforth that,

for each failure mode, the fault inputs corresponding to linearly dependent columns

of B

k

have been aggregated and that B

k

is of full rank. As a result, the number

of distinguishable failure patterns (and the corresponding Kalman-Bucy filters) is

usually less than 2m − 1.

2.1 Actuator Fault Identifiability

For the Kalman-Bucy filter to work correctly, observability of the augmented system (6), (7) is essential. Unobservability can result in grossly erroneous estimates of

the augmented state vector and incorrect FDI. Furthermore, in the infinite duration

case, a KBF gain (constant) Hkthat stabilizes the system matrix in (9) exists only

if (Cξ, Aξ) is detectable, which is possible only if the the augmented zero-frequency

modes of Aξ are observable. Thus, the observability rather than detectability of

(Cξ, Aξ) is important. The following theorem gives a necessary and sufficient condition for observability.

Theorem 1. The pair (C

k

ξ

, Ak

ξ

) is observable iff all of the following conditions are

satisfied:

(i) l ≥ mk

(ii) the pair (C, A) observable, and

3
(iii) the system (C, A, B

k

) has no zeros at the origin.

Proof. Applying the PBH rank test [5], [C

k

ξ

, Ak

ξ

] is observable iff

rank





sI − A −B

k

0 sImk

C 0



 = n + mk for s = λ(A) and s = 0 (12)

where λ(.) denotes eigenvalue. The first n columns of the PBH test matrix are

independent (for all s) iff (C, A) is observable. For s 6= 0, the last mk columns are

mutually independent as well as independent of the first n columns, thus the test

matrix has a full rank. For s = 0, the rank condition (12) is satisfied iff l ≥ mk and

(C, A, B

k

) has no system zeros at s = 0. 

Remark 2.1. The zeros mentioned in Theorem 1 are system zeros of (C, A, B

k

),

which include transmission zeros and input decoupling zeros (idz) [6]. The idz’s are

simply the eigenvalues of A corresponding to the uncontrollable modes of (A, B

k

).

Because (C, A) is observable, there are no output decoupling zeros. Note that B

k

corresponds to failed actuators in failure pattern k; therefore, (A, B

k

) may not be

controllable for all k. For the corresponding models, Theorem 1 requires that the

uncontrollable modes must not have zero eigenvalues. If (A, B

k

) is controllable, the

system zeros are just the transmission zeros.

Remark 2.2. In practical implementation, the estimation is performed in a discretetime setting using discrete-time Kalman filters. The observability conditions of Theorem 1 are very similar, the only difference being that, in item (iii), the phrase “no

zeros at the origin” is replaced by: “no zeros at unity” (for the discretized version

of (C, A, B

k

ξ

)).

Remark 2.3. The unobservable subspace O

k

ξ of (C

k

ξ

, Ak

ξ

) can be obtained as follows

(after some manipulation and using the fact that (C, A) is observable)

O

k

ξ = N











C

k

ξ

C

k

ξ Ak

ξ

.

.

.

C

k

ξ

(Ak

ξ

)

(n+mk−1)











= N

"

A B

k

C 0

#

(13)

where N (.) denotes the null space. Thus the unobservable subspace of (C

k

ξ

, Ak

ξ

)

consists of the generalized eigenvectors of (C, A, B

k

) corresponding to the zeros at

the origin. If A is nonsingular, it can be seen that

O

k

ξ =

(" −A−1B

k

x2

x2

#

, x2 ∈ R

mk

)

(14)

For the case when A has one or more zero eigenvalues, the corresponding O

k

ξ

is still

non-trivial when (C, A, B

k

) has one or more zeros at the origin.

4
Remark 2.4. It is intuitively straightforward to see that a zero at the origin adversely affects the ability to estimate a constant fault value  ̄u, because input frequency components corresponding to the system zeros do not appear in the output.

Furthermore, a set of initial conditions exist such that y(t) is identically zero.

3 Sensor Bias

Suppose there are no actuator failures but q of the l sensors have unknown sensor

biases, (or are known to be prone to developing biases). Denote the bias-free part

and the biased part of the sensor output vector as y1 and y2 respectively, and the

corresponding output matrices as C1 ∈ R(l−q)×n, C2 ∈ Rq×n. Then the sensor output

equation is

y =



y1

y2



= Cx + ws =



C1x

C2x +  ̄y2



+ ws (15)

where  ̄y2 ∈ Rqis the sensor bias vector and C = [C

T

1 C

T

2

]

T

. As was done in the

case of linearly dependent columns of B

k

, it is assumed that linearly dependent

sensor outputs have been combined and C, C1, C2 all have full row ranks. (Biases

corresponding to linearly dependent sensors cannot be estimated individually and

must be aggregated).

For this sensor bias formulation, bias- and state-estimation does not require multiple models and a bank of KBFs, but requires only one KBF. Upon augmenting the

sensor bias  ̄y2 to the state vector, the system becomes

η ̇ :=

d

dt 

x

y ̄2



=



A 0

0 0 

η +



B

0



u + w

0

:=Aηη + Bηu (16)

y =



C1 0(l−q)×n

C2 Iq



η + ws := Cηη + ws (17)

where w

0 denotes the augmented process noise vector.

3.1 Sensor Fault Identifiability

The bias estimation approach involves constructing a KBF for the augmented system

(16), (17). As in the case of actuator faults, observability of (Cη, Aη) is essential for

the KBF to function correctly. The following theorem gives necessary and sufficient

conditions for observability.

Theorem 2. The pair (Cη, Aη) is observable iff the following conditions are satisfied:

(i) the pair (C, A) is observable, and

(ii) all zero-frequency modes of A are observable with respect to the bias-free sensor

outputs

5
Proof. Applying the PBH rank test, (Cη, Aη) is observable iff

rank









sI − A 0

0 sIq

C1 0

C2 Iq









= n + q for s = λ(A) and s = 0 (18)

The first n columns of the PBH test matrix are linearly independent ∀s iff (C, A)

is observable. For s 6= 0, the last q columns are mutually independent as well as

independent of the first n columns. For s = 0, the rank of the test matrix is n + q iff

rank





sI − A 0

C1 0

C2 Iq





s=0

= n + q (19)

Since elementary column operations do not change the column rank,

rank





sI − A 0

C1 0

C2 Iq





s=0

= rank











sI − A 0

C1 0

C2 Iq





s=0



In 0

−C2 Iq









= rank





sI − A 0

C1 0

0 Iq





s=0

(20)

Thus the rank of the PBH test matrix at s = 0 is n + q iff the first n columns are

linearly independent for s = 0, i.e., iff the zero-frequency modes of A are observable

with respect to C1. 

When all sensors have biases, i.e., q = l, (Cη, Aη) is observable iff A has no zero

eigenvalue, as stated below.

Corollary 2.1. If all sensors have biases, (Cη, Aη) is observable iff

(i) (C, A) observable, and

(ii) A has no zero eigenvalues.

Remark 3.1. For the case when all sensors have biases, the condition that A should

not have zero eigenvalues is rather restrictive, since many engineering systems have

free integrators in their dynamics. However, there does not appear to be an obvious

way of getting around this problem. Consider the effect of using output feedback

which moves the eigenvalues away from the origin, i.e.,

u = −Gy = −G(Cx +  ̄y) (21)

where G ∈ Rm×l, which gives the following closed-loop system (including the augmented state  ̄y);

η ̇ =



A − BGC −BG

0 0 

η + w := A

0

ηη + w (22)

y = [C I]η + ws (23)

6
The pair (Cη, A0

η

) is observable iff

rank





sI − A + BGC BG

0l×n sIl

C Il



 = n + l for s = λ(A − BGC) and s = 0 (24)

Proceeding as in the proof of Theorem 2, the first n columns are linearly independent

iff [C,(A−BGC)] is observable. For s 6= 0, the last l columns of the PBH test matrix

are mutually independent as well as independent of the first n columns. For s = 0,

since the rank of a matrix is unchanged by multiplication by an elementary matrix,

rank  In −BG

0 Il

  sI − A + BGC BG

C Il



s=0



= rank 

sI − A 0

C Il



s=0

(25)

The rank is n+l iff A has no eigenvalue at the origin. Thus, using feedback to move

the eigenvalue away from zero does not make the augmented closed-loop system

observable.

Remark 3.2. If A has one or more zero eigenvalues, the unobservable subspace

of (Cη, Aη) can be readily obtained. Defining Γ = [0q×(l−q) Iq]

T

, the unobservable

subspace is

Oη = N















C Γ

CA 0

CA2 0

.

.

.

.

.

.

CAn+q−1 0















(26)

That is, if (x

T

1

, xT

2

)

T ∈ Oη,

Cx1 + Γx2 = 0; [O]Ax1 = 0 (27)

where O = [C

T

, CT AT, . . . , CT An−1T]

T

, which yields (since (C, A) is observable):

Ax1 = 0; C1x1 = 0; C2x1 + x2 = 0 (28)

That is, x1 must be an eigenvector of A corresponding to a zero-frequency mode

of A that is unobservable with respect to C1. If all zero-frequency modes of A are

observable with respect to C1, then x1 = 0, therefore, x2 = 0, Oη = 0, and the

augmented system is observable, which is consistent with Theorem 2. If some zerofrequency modes of A are not observable with respect to C1, Oη can be characterized

as

Oη =

 x1

−C2x1



, x1 = eigenvector of A corresponding to unobservable 0-freq modes

(29)

Remark 3.3 In practice, the Kalman filter is implemented in a discrete-time setting,

and the condition (ii) in Theorem 2 changes to: “all modes corresponding to λ(A) =

1 are observable with respect to the bias-free sensor outputs” (for the discretized

version of A).

7
4 Simultaneous Actuator Faults and Sensor Bias

For the case with actuator fault pattern k, if q of the sensors have biases, the augmented system is given by

d

dt





x

u ̄

k

y ̄2



 :=  ̇φ =





A B

k

0

0 0 0

0 0 0



 φ +





Bk

0

0



 u

k + w00 (30)

:=Aφφ + B

k

φu

k + w00 (31)

y =



C1 0 0

C2 0 Iq



φ + ws = Cφφ + ws (32)

where w

00 is the augmented process noise vector. The following theorem gives necessary and sufficient conditions for observability.

Theorem 3. The pair (Cφ, Aφ) is observable iff

(i) l ≥ mk + q

(ii) the pair (C, A) is observable, and

(iii) the system (C1, A, B

k

) has no zeros at the origin.

Proof. Applying the PBH rank test, (Cφ, Aφ) is observable iff

rank













sI − A −B

k

0

0 sImk0

0 0 sIq

C1 0 0

C2 0 Iq













= n + mk + q for s = λ(A) and s = 0. (33)

The first n columns of the PBH test matrix are linearly independent for all s iff

(C, A) is observable. For s 6= 0, the last mk +q columns are mutually independent as

well as independent of the first n columns. For s = 0, the columns of the test matrix

are linearly independent iff the columns of the following (n+l)×(n+mk +q) matrix

(after applying elementary column operations as shown) are linearly independent:





sI − A −B

k

0

C1 0 0

C2 0 Iq





s=0





In 0 0

0 Imk0

−C2 0 Iq



 =





sI − A −B

k

0

C1 0 0

0 0 Iq





s=0

(34)

The columns of the above matrix are linearly independent iff (i) and (iii) hold. 

If all sensors have biases (q = l), condition (i) cannot be satisfied in the presence

of one or more actuator failures and the system is unobservable. This represents

a major limitation of this approach to FDI when actuator faults and sensor biases

are simultaneously present, and suggests that some alternate techniques should be

considered (perhaps for sensor FDI).

8
5 Conclusions

This paper explored in detail a class of fault detection and identification (FDI)

methods for bias-type faults in actuators and sensors, from the point of view of fault

identifiability. The methods employ a bank of Kalman-Bucy filters (KBFs) to detect

the faults, determine the fault pattern, and estimate the fault values. Each KBF

is tuned to a different fault pattern. Necessary and sufficient conditions were presented for identifiability of bias-type actuator faults, sensor faults, and simultaneous

actuator and sensor faults. The results indicate that caution should be exercised to

ensure fault identifiability for different fault patterns when using such methods. It

was shown that FDI of simultaneous actuator and sensor faults is not possible using

these methods when all sensors have biases.

References

1. Maybeck, P. S., and Stevens, R. D., “Reconfigurable Flight control

via Multiple Model Adaptive Control Methods”, IEEE Transactios on

Aerospace and Electronic Systems, Vol. 27, No. 3, 1991, pp.470-479.

2. Menke T., and Maybeck, P. S., “Sensor/Actuator Failure Detection in the

Vista F-16 by Multiple Model Adaptive Estimation”, IEEE Transactions

on Aerospace and Electronics Systems, Vol. 31, No. 4, 1995, pp. 1218-1228.

3. Ducard, P. G. and Geering, H. P., “Efficient Nonlinear Actuator Fault

Detection and Isolation System for Unmanned Aerial Vehicles”, Journal

of Guidance, Control, and Dynamics, Vol. 31, No. 1, 2008, pp. 225-237.

4. Sun, Joy Z., and Joshi, Suresh M., “An Indirect Adaptive Control Scheme

in the Presence of Actuator and Sensor Failures”, AIAA-2009-5740, Guidance, Navigation, and Control Conference , Chicago, August 10-13, 2009.

5. Kailath, T., “Linear systems”, Englewood Cliffs, N.J., Prentice-Hall,

1980, p. 366.

6. Sinha, P. K., “Multivariable Control- an Introduction”, New York: Marcel

Dekker, 1984, pp. 148-153.

9
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

On Identifiability of Bias-Type Actuator-Sensor Faults in 

Multiple-Model-Based Fault Detection and Identification 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Joshi, Suresh M.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20149

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 63

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

This paper explores a class of multiple-model-based fault detection and identification (FDI) methods for bias-type faults in 

actuators and sensors. These methods employ banks of Kalman-Bucy filters to detect the faults, determine the fault pattern, 

and estimate the fault values, wherein each Kalman-Bucy filter is tuned to a different failure pattern. Necessary and sufficient 

conditions are presented for identifiability of actuator faults, sensor faults, and simultaneous actuator and sensor faults. It is 

shown that FDI of simultaneous actuator and sensor faults is not possible using these methods when all sensors have biases.

15. SUBJECT TERMS

Actuator faults; Fault detection; Fault-tolerant control; Sensor faults

18. NUMBER

 OF 

 PAGES

14

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

17. LIMITATION OF 

 ABSTRACT

UU

Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

284848.02.05.07.02

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/TM-2012-217586

16. SECURITY CLASSIFICATION OF:

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and 

Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person 

shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 06 - 2012