NASA/TM-2009-215948

An Amplitude-Based Estimation Method for

International Space Station (ISS) Leak

Detection and Localization Using Acoustic

Sensor Networks

Jialin Tian and Eric I. Madaras

Langley Research Center, Hampton, Virginia

November 2009
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NASA/TM-2009-215948

An Amplitude-Based Estimation Method for

International Space Station (ISS) Leak

Detection and Localization Using Acoustic

Sensor Networks

Jialin Tian and Eric I. Madaras

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

November 2009
Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802
Acronym List

FEM Finite Element Method

FMM Fast Marching Method

ODE Ordinary Differential Equation

ISS International Space Station

RMS Root Mean Square
Table of Contents

Abstract 7

1. Introduction 8

2. ISS Surface Mesh Distance Computation 9

3. Amplitude-Based Leak Detection and Localization Algorithm 12

3.1 Amplitude-Distance Decaying Function Model 13

3.2 Acoustic Sensor Network Placement Strategy 14

3.3 Leak Detection and Localization Method 18

4. Conclusions and Future Work 21

References 22

6
Abstract

The development of a robust and efficient leak detection and

localization system within a space station environment presents

a unique challenge. A plausible approach includes the

implementation of an acoustic sensor network system that can

successfully detect the presence of a leak and determine the

location of the leak source. Traditional acoustic detection and

localization schemes rely on the phase and amplitude

information collected by the sensor array system. Furthermore,

the acoustic source signals are assumed to be airborne and farfield. Likewise, there are similar applications in sonar. In solids,

there are specialized methods for locating events that are used in

geology and in acoustic emission testing that involve sensor

arrays and depend on a discernable phase front to the received

signal. These methods are ineffective if applied to a sensor

detection system within the space station environment. In the

case of acoustic signal location, there are significant baffling

and structural impediments to the sound path and the source

could be in the near-field of a sensor in this particular setting.

In the case of structural methods, the signal that we receive from

a structure-borne sensor has no discernable phase front to

detect. We propose a solution that is able to overcome these

challenges by utilizing the structural uniqueness of the space

station node module. This method emphasizes the amplitude

decaying properties of the acoustic signals and the surface mesh

system of the module. These two underlying components are

employed to solve the leak localization problem. In the

amplitude-based estimation method, a discrete mesh system is

constructed for the International Space Station Node Module; a

distance matrix that contains the shortest paths (geodesic paths)

on the station surface is then generated using the discrete mesh.

The sensors are characterized by the amplitude-distance

decaying function using experimental data sets. The pre-defined

components are applied to the detection and localization

algorithm during real-time operation. This approach is

especially effective when computational and physical resources

are limited since the most required algorithmic elements are predetermined and stored in the memory.

7
1. Introduction

The development of a robust and efficient leak detection and localization system within a space

station environment presents a unique challenge. A plausible approach includes the

implementation of an acoustic sensor network system that can successfully detect the presence of

a leak and determine the location of the leak source. Traditionally, acoustic target detection and

localization schemes involve methods such as maximum likelihood estimation, sensor-array

beamforming, least-square filtering, and other types of stochastic estimation techniques [1-5].

Most of those systems are designed specifically for far-field detection scenarios in which the

acoustic signals travel within an airborne environment. The distances between the sensors and the

source are extracted based on a Cartesian coordinate system. These localization algorithms are

usually designed using the phase and amplitude information received at the sensor array. For our

particular problem, the location of the leak cannot be easily derived using the conventional

acoustic detection solutions because the space station node module features a near-field and

structure-borne setting that presents two unique challenges to the leak localization problem. First

of all, the measured relative phase information among sensors is inadequate in a near-field

situation. Furthermore, there are significant baffling and structural impediments to the sound

path in this particular setting. Secondly, the acoustic signal travels within a structure-borne

environment, which implies that the sensor-to-leak distances cannot be estimated based on a

Cartesian coordinate system as is typically used in airborne acoustics. Instead, the signal travels

along a geodesic path in a curved space; in other words, the signal travels along the shortest path

between points on the station module surface.

Likewise, there are similar applications in sonar [7-9]. These methods follow acoustic

methods using advanced signal processing techniques and have been well developed for naval

applications. In the case of leak localization, these methods are of interest, but obviously, the

medium of transmission is distinctive and not relevant. In solids, there are specialized methods

for locating events that are used in geology and in acoustic emission testing that involve sensor

arrays and depend on a discernable phase front being detected by the receiving sensor [10-13]. In

our case, the structure-borne signal generated by a leak has no discernable phase front to detect.

Therefore, these methods are ineffective if applied to a sensor detection system within the space

station environment. Signal processing methods that involve cross correlating signals from an

array of sensors can derive relative phase information that can be used to indicate relative

directions from groups of sensor [14]. That technology is another possible method that is being

investigated for this purpose.

We propose a solution that is able to overcome many of the challenges of structure-borne

sound detection of leak noise by utilizing the structural uniqueness of the space station node

module. This method emphasizes the amplitude decaying properties of the acoustic signals and

the surface mesh system of the module. These two underlying components are employed to solve

the leak localization problem. This approach is especially effective when computational and

physical resources are limited since the most required algorithmic elements are pre-determined

and stored in the memory. The algorithm can be summarized in the following steps: (1)

construct a discrete mesh representation for the station module (for illustration purposes, we have

generated a two-dimensional flattened map of a module); (2) design a sensor network system that

optimizes the number of sensors and their placements subject to a set of constraints; (3) at each

node in the mesh, compute the acoustic field amplitudes generated by a leak, for demonstration

purposes, we can simulate this step with the following two sub-steps: (A) compute the geodesic

distances from the sensors to every location on the mesh and (B) characterize the amplitudedistance decaying function with an approximated 1/distance (1/r) relation, which is justified from

8
experimental data measurements; (4) detect the presence of a leak signal based on an amplitude

threshold; (5) localize the leak signal using the amplitude measurements, the pre-computed

distances, and the amplitude-distance decaying function. The first three procedures are predetermined; therefore they do not consume any real-time computational resources on-board. The

last two steps are performed during the real-time detection and localization process.

In Section 2, we discuss the techniques of constructing a mesh model for an ISS NODE

Module (Figure 1) and generating the geodesic distance matrix using the fast marching method.

In Section 3, we present the characterization of the amplitude-distance decaying function, the

sensor network placement strategy, and the proposed leak detection and localization algorithm.

Figure 1. A high-resolution mesh for the ISS NODE Module.

2. ISS Surface Mesh Distance Computation

This section describes the techniques for creating a distance matrix that contains the shortest

surface (geodesic) paths between points on a discretized ISS mesh model. The distance

information is stored and can be retrieved during the real-time leak localization process. Figure 2

depicts the necessary steps for generating a distance table of an ISS module based on a predefined discrete mesh system. In the initial step, a low-resolution FEM triangulated mesh system

is constructed. The mesh is defined in the (vertex, face) format. The number of points or vertices

should be selected such that it is coarse enough to ensure fast and efficient computation, and it is

also refined enough to guarantee an accurate identification of the leak location. An example of a

two-dimensional flattened triangulated uniform mesh of an ISS NODE module can be seen in

Figure 3.

9
Construct a Map the sensor Compute the distances Store the

triangulated coordinates into the between sensors to each distance table in

mesh system nearest vertices vertex on the mesh the memory

Map the sensor system into a

Cartesian coordinate system

Design an acoustic

sensor system

Figure 2. ISS surface mesh distance computation algorithm procedure.

Figure 3. A geodesic path from an arbitrary source to a sensor on the 2-D flattened

triangulated mesh of ISS NODE.

Once the mesh system is obtained for a particular NODE module, the next step involves

the mapping of an acoustic sensor/detector system onto the mesh system. The design criteria of

the sensor system include the number of sensors and their placements. Because the signal

amplitude diminishes very rapidly as a function of distance, the sensor system must be sufficient

enough to detect a leak signal from the background noise. In general, at any arbitrary location on

the module, a leak signal needs to be detectable by at least two sensors simultaneously to produce

a reasonable location estimate. In general, this suggests dispersing the sensor locations uniformly

throughout the structure. Please refer to Section 3.2 for further discussion on sensor network

10
designs. The physical locations of the sensors are mapped into a Cartesian coordinate system,

and then into the nearest vertices on the triangulated mesh model.

In the following stage, the shortest surface distances between sensors to each vertex on

the mesh are computed and stored in memory. To compute the shortest surface distance between

two points on the NODE module, we adopt the fast marching method (FMM). The FMM is a

numerical solution for finding the shortest surface path between two points on an arbitrary surface

using an iterative algorithm. The algorithm is performed on the discrete mesh system that has

been obtained in the previous step. The computation of the shortest geodesic path, P, between A

and B can be summarized in two steps. Given the input as the triangular mesh S and two points

A and B on the surface of S, the algorithm generates an output of a discrete geodesic P joining

A and B. In the first step, the initial approximation Pp is obtained; the polygonal curve Pp

joining vertices A and B is constructed using the FMM [15-17].

Figure 4. The distance gradient plot from an arbitrary location at Sensor 1 to the rest of the

vertices (points) on the mesh.

The FMM solves for Eikonal equation JVTJ =1, where T(P) is the geodesic distance

from point A to any point P on S. Once T is computed for every vertex, the following ordinary

differential equation (ODE) is solved d () = —VT; Â(s) is the geodesic path. In the second

step, the initial estimate Pi, i = 0 , 1, ... is iteratively corrected until it reaches a desirable

11
approximation Pn of P. In Figure 3, the geodesic path between an arbitrary source and a sensor

is illustrated on the triangulated uniform mesh of an ISS NODE that was generated earlier.

Figure 4 represents the geodesic distance from an arbitrary location at Sensor 1 to the rest of the

vertices (points) on the mesh in a gradient plot. Lastly, the computed distance matrix of a predefined sensor network is stored in the memory, which can be expressed as Dr(v), in which r

denotes the vertex number of the sensors/receivers and variable v represents an arbitrary

location/vertex on the mesh model. The distance information can be retrieved during real-time

leak localization process, which will be discussed in the following sections.

3. Amplitude-Based Leak Detection and Localization Algorithm

The leak detection and localization algorithm is designed based on knowing the acoustic field

amplitudes. For demonstration purposes, we have calculated the acoustic fields based on our

observation that the amplitudes measured by acoustic sensors are roughly inversely proportional

to the distances between the sensors and the leak on a logarithmic scale. Intuitively, we can see

that for an arbitrary leak location, sensors in the near vicinity of the leak measure high-amplitude

signals whereas sensors further away from the leak source obtain low-amplitude measurements.

An amplitude-distance decaying (attenuation) function is obtained using experimental data sets.

The polynomial coefficients that represent the decaying function are computed and stored in the

memory. For detailed derivation of the amplitude-distance decaying function, please refer to

Section 3.1.

The detection and localization process includes several steps as depicted in Figure 5.

Initially, the real-time acoustic measurement is compared with the stored background noise

profile. If the RMS value of the difference between the current measurement and the background

noise exceeds a threshold level, then a leak is detected, otherwise the decision sequence loops

back. When a leak signal is detected, the algorithm selects three to four sensors that have the

strongest leak signal strengths. This selection procedure is necessary because the signal amplitude

diminishes very rapidly, as a function of distance, the sensors that are further away from the leak

may not be able to detect the leak signal; therefore, only the strongest amplitude measurements

hold essential information that can be used by the localization algorithm.

In the next stage, the algorithm iterates through every vertex on the mesh model. At each

location, the surface distances from that location to the selected sensors are retrieved to generate a

distance estimation function. Using the amplitude-distance decaying polynomial coefficients, we

derive a real-time distance function via inversion. This function is correlated to the distance

estimation function to produce a correlation coefficient. This calculation is repeated until the

correlation coefficient is obtained for every location on the mesh model. In principle, the vertex

with the highest coefficient value corresponds to the most likely location of the leak; however, in

practice the level of random noise in the measurement may skew the position of the estimate. In

addition, the real-time amplitude-distance decaying characteristics may be slightly different from

the previously determined polynomials during real-time operation.

12
Background Surface distance

noise profile table

Compare the Yes Select Generate

real-time Detecting a sensors that distance

signal against leak? have the estimates using

the noise strongest the surface

profile signals distance table Estimate the location

of the leak by

computing the

distance correlation

No coefficients

Generate a realReal-time amp^ tude time distance measurements function using

the acoustic se the amplitudedistance function

Amplitude-distance

decaying

polynomials

Figure 5. The amplitude-based leak detection and localization algorithm path.

3.1. Amplitude-Distance Decaying Function Model

The fundamental principle of the amplitude-distance localization method is based on the

knowledge of the signal strength throughout the structure. We have observed in our

measurements that the signal strength measured by a detector is roughly inversely proportional to

the detector-to-source distance on a logarithmic scale. For instance, the detector observes a larger

signal if a leak source is located nearby; conversely, the detector observes a smaller signal or no

signal if a leak source is further away. This amplitude-distance decaying function can be

characterized by the detector’s performance specifications. For the specific type of sensors in

our application, the amplitude-distance decaying function is determined using a set of

experimental measurements. The amplitude data were obtained at several distances from the leak

source. The decaying amplitude as a function of distance can be derived by interpolating the

experimental data set, which is shown in Figure 6. Next we characterize the decaying slope using

a 4th order polynomial function. Since the slope is highly nonlinear, we apply the polynomial

fitting to the logarithm of the amplitudes, which can be written as f (d) = log(a) where f (•), d,

and a represent the polynomial function, the distance parameter, and the amplitude variable,

respectively. The resulting approximation is shown in Figure 7. The blue curve indicates the

logarithmic interpolated amplitude-distance function whereas the red curve features its

polynomial approximation. The inversion of the amplitude-distance function will be employed

to predict the distances from real-time sensor measurements.

13
010 50 100 150 200 250

Distance [inches]

Figure 6. The interpolated amplitude-distance decaying function.

0.5'0 50 100 150 200 250 300

Distance [inches]

Figure 7. The logarithmic amplitude-distance decaying function (blue) and its polynomial

approximation (red).

3.2. Acoustic Sensor Network Placement Strategy

In this section, we discuss the topic of choosing a suitable acoustic sensor network for the

detection system. Our goal is to determine the number of sensors and their corresponding

placements so that the cost is minimized while the sensor coverage is maximized. The number of

sensors used in the distributed sensor network typically represents the cost factor. The constraint

or requirement of the system is stated as every location inside the station module must be

detectable by at least two sensors simultaneously for the leak location to be estimated accurately.

This design problem can be treated as a combinatorial optimization problem, and the solution can

be obtained by solving a system of linear equations. An alternative approach that involves an

iterative technique is more desirable since it is computationally efficient for a large number of

unknowns [18-20].

14
Figure 8. An example of the pair-wise distance matrix for all vertices on the mesh of Figure 4.

Figure 9. The detection probability as a function of distance.

In the iterative algorithm, we first compute a geodesic distance matrix that contains the

pair-wise distances among all vertices on the ISS mesh. An example of the distance matrix that is

based on the mesh in Figure 4 can be seen in Figure 8. The sensor coverage in the placement

algorithm will be determined from the distance matrix. We assume that the probability of

detection by the acoustic sensor varies exponentially as a function of the distance between the

target and the sensor in the following approximation:

15
1, dij < Dl

,

P(dij) = e— ̧dij

, Dl <— dij <— Du ,

10, dij > Du .

In this case, we assume the probability of detection is 1 if the target-to-sensor distance dij is less

than Dl = 10 inches, and the probability of detection is 0 if the target-to-sensor distance is

greater than Du = 150 inches. If the target-to-sensor distance is between 10 and 150 inches, the

probability of detection is an exponential function of the distance with parameters A = 0.01 and

 ̄ = 0.5. The detection probability function is shown in Figure 9.

The miss probability (the probability of failing to detect the target) matrix is defined as

M(dij) = 1 — P(dij). Starting with one sensor, the algorithm iterates through each location

(vertex) on the mesh model. At each location, the total value of the miss probability matrix is

computed. The optimal sensor placement is determined to be the location that minimizes the total

miss probability value. The miss probability matrix is updated after the placement of that

particular sensor. The algorithm iterates with additional sensors until the total miss probability

value is minimized. In Figure 10(a), the detection probability function is illustrated using the

pair-wise distance matrix in Figure 8 and the probability detection function P(dij). Figure 10(b)

rescales the image in Figure 10(a) to accentuate the details in the plot.

'200C4t101 6001 8001 000' 1^1 V 72L10i r4^ I^ 800 10 ] PZUU

`llertex,number' Vkex number

Figure 10. The detection probability: (a) the pair-wise probability detection function, and (b) its

rescaled image.

16
Figure 11. An example of the sensor placement strategy. The

sensor network is shown in green; the coverage is shown in yellow

for each individual sensor (shown in red). The minimum number of

sensors required is seven to guarantee each location to be covered

by at least two sensors simultaneously.

17
For the node mesh model shown in Figure 4, we apply the placement technique as

described previously. The resulting placement configuration is shown in Figure 11. In this case,

we impose that each location must be detectable by at least two sensors simultaneously. The

required minimum number of sensors is seven. In practice, installing sensors at those exact

locations may not be feasible because it can be difficult and time-consuming to place sensors in

certain spots on-board of a space station. The easiest place to install a sensor is near the hatch

doors and end cone areas. Figure 12 shows an alternative configuration of the sensor network

(sensors are shown in green). In this case, eight sensors are required to accurately detection the

leak location; a detection example will be given in the following section for this particular sensor

placement.

3.3. Leak Detection and Localization Method

In the preceding sections, we have obtained the three required components of the real-time leak

detection and localization process. The first component is the mesh representation of the ISS

node model, in which the physical locations on the ISS node surface are mapped into

corresponding vertices on the mesh. The second component is the sensor-network design. The

locations of a number of acoustic sensors are strategically selected such that the sensor coverage

is optimized subject to physical constraints of the ISS node geometry. The third component is a

computation of the acoustic field. This was accomplished by pre-computing the surface distance

matrix Dr(v) , which contains the geodesic distances from the sensors to all other locations on

the mesh. Then for demonstration purposes, we computed the acoustic field as an inverse

distance formula using amplitude-distance decaying polynomial f (d) = log(a). The sensor-toleak distance is determined based on the inversion of f (d).

Suppose a leak is present at location vp, the detection system measures the received

maximum amplitudes Ar; max and compares them to a threshold level. The system then identifies

the incoming signal as a leak. Using the inverse amplitude-distance decaying polynomial

function, the distances between the sensors and the leak can be estimated from

^dr = f — 1

log(Ar;max ). Next, we will determine the actual leak location using ^dr and the precomputed matrix Dr(v). The localization algorithm iterates through all vertices vl,l = 1, ... , L

on the mesh. At each vertex, the distances between that particular vertex and the sensors are

computed from Dr(v); we denote this term as dr(va), a E [1, LI. Then we compute the

correlation coefficient between ^dr and dr(va), and store the resulting coefficient. This process is

repeated for all vertices vl, l = 1, ... , L. The vertex number that corresponds to the maximum

correlation coefficient is the optimal estimate of the leak source location. The correlation

computation can be formulated as

P(vl) = P 

(

^

dr, dr(vl

)

)

cov 

(

^dr, dr (vl

))

=

O'd^

r

O'dr(vl )

E { [^dr — μ^drI [dr (vl) — μdr (vl) I }

= for l = 1, ... , L,

O'd^

r

O'dr( vl

)

18
whereas cov(.) denotes the covariance operation and E{ .} denotes the expectation operation, and

Q is the standard deviation. The optimal estimate of the leak location ^vo is determined to be the

vertex number that maximizes the correlation coefficient, for instance, p(^v0) = max p(v): In

v

Figure 12, four leak sources (shown in red) are placed at random locations on the mesh model.

We apply the algorithm described in this section to the leak, and the results are shown in Figure

13. These images contain the correlation coefficient gradients from our detection results. The

four leak sources are colored in white. The concentrated dark red indicates high correlation

coefficient value, which implies the leak source is most likely to be found within those areas.

For the locations that are further away from the leak, the coefficient value decreases as shown in

blue.

Figure 12. An example sensor placement and leak source configuration.

The eight sensors are shown in green whereas the four leak sources are

shown in red.

19
Figure 13. Correlation coefficient gradient plots for four random leak sources (shown in white).

20
In an ideal situation, the location that has the highest correlation coefficient corresponds

to the leak source position. However, in practice the estimate can be affected by two factors.

First, the random noise level in the amplitude measurements may skew the coefficient values.

Second, the pre-determined amplitude-distance decaying function can be slightly different from

the real-time amplitude-distance relationship, which causes the distance calculation to be slightly

offset.

4. Conclusions and Future Work

The development of a robust and efficient leak detection and localization system within a space

station environment presents a unique challenge. Most of the commonly known acoustic leak

detection and localization systems are designed for far-field detection scenarios in which the

acoustic signals travel within an airborne environment. These methods are ineffective if applied

to a sensor detection system within the space station environment. In which case, a detection

system that is capable of locating the leak in a near-field and structure-borne environment is

required.

In this paper, we propose a novel technique that employs an amplitude-based method for

ISS leak detection and localization using acoustic sensor networks. This method utilizes the

structural uniqueness of the space station node module and emphasizes the amplitude decaying

properties of the acoustic signals and the surface mesh system of the module. In this algorithm, a

discrete mesh system is constructed for the ISS Node Module initially. A distance matrix that

contains the shortest paths (geodesic paths) on the station surface is then generated using the

discrete mesh. The sensors are characterized by the amplitude-distance decaying function using

experimental data sets. The pre-defined components are applied to the detection and localization

algorithm during real-time operation. This approach is especially effective when the

computational and physical resources are limited since the most required algorithmic elements are

pre-determined and stored in the memory.

The leak location is determined from the correlation coefficients between the estimated

sensor-to-leak distances and the distances computed from amplitude measurements. The

accuracy of the estimation can be affected by measurement distortions such as random noises. To

compensate for the distortions, the spread of the correlation gradient can be taken into

consideration. One method is to find the location that has the highest concentration of top

coefficient values, and use it as the final estimate. Another method is to interpret the data as the

level of confidence from a probabilistic standpoint instead of pin-pointing out a single location.

These issues will be addressed in future research.

21
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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)

01-11 - 2009 Technical Memorandum

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

An Amplitude-Based Estimation Method for International Space Station

(ISS) Leak Detection and Localization Using Acoustic Sensor Networks 5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

Tian, Jialin; Madaras, Eric

5e. TASK NUMBER

5f. WORK UNIT NUMBER

4017 69.06.03.04.02.12

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

NASA Langley Research Center REPORT NUMBER

Hampton, VA 23681-2199

L-19789

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

National Aeronautics and Space Administration NASA

Washington, DC 20546-0001

11. SPONSOR/MONITOR'S REPORT

NUMBER(S)

NASA/TM-2009-215948

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 18 - Spacecraft Design, Testing and Performance

Availability: NASA CASI (443) 757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The development of a robust and efficient leak detection and localization system within a space station environment presents a

unique challenge. A plausible approach includes the implementation of an acoustic sensor network system that can

successfully detect the presence of a leak and determine the location of the leak source. Traditional acoustic detection and

localization schemes rely on the phase and amplitude information collected by the sensor array system. Furthermore, the

acoustic source signals are assumed to be airborne and far-field. Likewise, there are similar applications in sonar. In solids,

there are specialized methods for locating events that are used in geology and in acoustic emission testing that involve sensor

arrays and depend on a discernable phase front to the received signal. These methods are ineffective if applied to a sensor

detection system within the space station environment. In the case of acoustic signal location, there are significant baffling and

structural impediments to the sound path and the source could be in the near-field of a sensor in this particular setting.

15. SUBJECT TERMS

Acoustic sensor networks; Geodesic surface distance; ISS node module; International Space Station (ISS); Leak detection and

localization; Spacecraft leak localization algorithm; amplitude-based estimation method

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON

ABSTRACT

PA

OF

a. REPORT b. ABSTRACT c. THIS PAGE PAGES Help Desk email: he p (

lp@sti.nasa. ov g )

19b. TELEPHONE NUMBER (Include area code)

U U U UU 24 (443) 757-5802

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