AIM-92-2466-CP

SENSOR FAILURE DETECTION AND ISOLATION IN FLEXIBLE STRUCTURES USING THE EIGENSYSTEM

REALIZATION ALGORITHM

David C. zimmermanJF Terri L. Lyde

University of Florida Gainesville, Florida 3261 1

ABSTRACT

Sensor I'ailure detection and isolation (FDI) for I'lexil~lc structures is approached from a system realization perspective. Instead of using hardware or analytical model redundancy, system realization is utilized to provicle an experimental model based reclundancy. 'l'hc FDI algorithm utilizes the IEigensystcm Realization Algorithm to determine a minimum-order state space realization of the structure in the presence of noisy measurements. The FIJI algorithm utilizes statistical comparisons of successive reali~ations to detect and isolate the failed sensor component. I h e to the nature in which the FDI algorithm is formulated, it is also possible to classify the failure mode of the sensor. Kesultsare presented using 1 ~ 0 t h numerically simulated and actual experimental data.

1 . INTRODUCTION

I'hc clesign. control. and maintenance of future large space structures (LSS) offcrs many new and different challenges for engineers. The economic requirement of light weight structurescoupledwith the large physical dimensions needed to meet mission ol7jectives necessitates the use of active vibration control. The large number of actuators and sensors required I'or precise control of LSS together with the clesire for long periods of operation between maintenance periods lx-ings about the need for a reliable monitoring system to detect actuator and sensor 1';tilures. I t can easily be shown that in a typical large space structure control system with 400 components. each with an exponential distribution of time to friilure with a mean time to failure of 100,000 hours. one can expect a component failure every 10 clays. I n this paper, an algorithm to detect. isolate, and clnssib sensor I'ailures for flexible structure control systems is presented.

Early I'ault cletection schemes were based on hardware redundancy. Hardware redundancy schemes use three (or more) sensors for each physical quantity that is to I x measured. 'l'hc three sensor outputs arc

'~ssistant Professor. Aerospace Engineering Member AIAA

'currently Staff Engineer. Lockheed ('orp., Marietta. (icorgia

then compared at regular time intervals. A sensor output not agreeing completely with the other two is then flagged as being faulty. For LSS, the high cost of Ix)th space qualified hardware as well as launch costs may make hardware duplication inreasihle. More recent schemes are based on analytical redundancy which eliminates the need for extra hardware. Analytical redundancy is the use of a mathematical model to analytically generate signals that would otherwise be produced by redundant hardware. 'J'hese functionally redundant schemes employ state estimation, parameter estimation, adaptive filtering. variable threshold logic, statistical decision theory and various combinatorial and logical operations.

During the last three decades, many rcsearchcrs have addressed the development of on-line lailure detection methods1. 'I'hese efforts were stimulated hy the advent of cheaper and faster digital computers and the increasing complexity and sire of the operating physical systems. 'I'here have been a numher or application studies of FDI techniques including some actual applications to either process plants or laboratory experiments using real time equipment. As a few examples. Watanahe and ~limmcll>lau2 demonstrated fault detection strategies for nonlinear chemical reactors. Shiozaki et a ~ . ~ diagnosed fault\ in pipeline systems using signed directional graphs. ~ c r r ~ used Kalman filters to detect faults in inertial navigation systems. Ikckert et a ~ . ~ used Kalrnnn filters for fault identification on the NASA F;X digital fly-by-wire aircraft. Finally Raruh and ('hoe5and vanderVelde7 have investigated FIjI systems I'or flexible structures.

Along with the many different areas of applications for fault detection systems comes many different techniques. All fault detection schemes are in one way or another based on the use or reduncluncy, i.e. on static or dynamic relationships among measured variables. The idea to replace hardware redundnnc ;Y with analytical redundancy was originated l?y I3enrd . Beard proposed methods of self-reorganizatit,n to maintain closed loop stability. ' Ihe prohlem of identifying Failures and changes in the system sensors was solved by comparison of the outputs of ol,scrvers. Mehra and peschonY introduced a general proccclurc for FDI in dynamic systems with the aid o f a single Kalman filter. An innovation sequence was generated and subjected to statistical tests ofwhiteness, mean and

covariance. Knowing the time histories of the output variables under normal conditions, the deviations under faulty conditions are detected hy statistical decision theory. Montgomery and ('aglayanl" pro~x~secl the Hayesian decision theory which uses several Knlman filters. A hank of m parallel Kalman filters designed for a set of m-1 possible failure modes is used with h pothesis testing to detect failures. ? . L . 1)eckcrt et al: descr~be a I'unctional redundancy scheme combined with dual sensor redundancy of the process. F?iilure identification is accomplished on the basis of the functional relationships among the outputs of dissimilar instruments by performing sequential probability ratio tests of the differences among the outputs. A similar concept called the Generalized 1 .ikelihood 'I'est was proposed by Daly et al . l l . Several contributions to F L ~ I with s t ak estimation methods using either observers or Kalman filters were made by ('lark12. I n 1977, ('lark published the Dedicated Ohserver Scheme (DOS) for FDI using a bank of Luenbcrger observers, each driven by one sensor output. I f none o f the sensors fails, all of the reconstructed state vectors converge to the actual state vector. I f one of the sensors fails. then a difference occurs in the output vector of the corresponding observer. This can he used to identify the faulty sensor. 'li) handle the HI1 problem in the resence of random 9 disturbances, ('lark and ('ampbelll- moddied the DOS scheme hy using a dedicated Kalman filter for each of the sensors. but instead of driving each filter by a single sensor output. it is driven by three sensor outputs where each filter is sensitiaed to faults in a single sensor.

In the Fr)I schemes described so far, the errors of the reconstructed states that are employed for FIII are affected by hot h sensor malfunctions and variations of the 17rocessparametcrs. Insensitivity to parameter variations as a design specification was first included in the ohserver design hy Frank and el let-14. They extended the dedicated observer scheme by duplicating the olxervers to allow distinction between parameter variations and instrument malfunctions. Several other approaches to the robustness problem were proposed by ~ e l k o u r a l ~ . and Frank and ~ e l l e r l ~ . A general approach of creating robustness in FDI systems has heen pursued over the years by ('how and ~ i l l s k ~ l ~ , Lou, Willsky, and vergheselx, and many others. 'I'hey look to the prohlem of rohust residual generation from the viewpoint of analytical redundancy relations, and have introduced the concept of general parity checks.

I n this paper. a failure detection. isolation. classif'ication algorithm is developed for LSS. The algorithm makes use of system realizations obtained I'rom the Eigensystem Realization Algorithm ERA)^'. I t is assumed that a nominal realization for the LSS is ohtaincd hefore any sensor failure has occurred. The 1.3)I algorithm is based on comparing future realimtions of the LSS to the nominal case.

2. PROBLEM FORMULATION

2.1 Structural Formulation

('onsider a n-L)OF structural model with feedback control,

ME + Ih- + Kw = B,,g ( 1 )

where M, I), and K are the n x n analytical mass, damping, and stiffness matrices, w is a n x 1 vector of positions, B, is the n x m actuator influence matrix, y is the m x 1 vector of control forces, and the overdots represent differentiation with respect to time. 'l'his second-order model can be recast in first-order stace space form as

where is referred to as the state matrix and is referred to as the control inlluence matrix,

In addition, the r x 1 output vector y 01' sensor measurements is given by.

where C is the output influence matrix.

Equations (3) and (4) constitute the continuous time model for the llexible structure. Similarly, the structure can be modelled in discrete time form as,

x(k + 1) = A-(k) + Bg(k) - (4)

yik) = ('xik) ( 5 )

where A and €3 are derined as

A = en;-" B = (h) - I"e-xd~fi

The triplet of constant matrices [A,H,C\ IS termed a realization of the LSS. (;wen the structure realization, one can determine the response to any known input. It should be noted that any system has an infinite number of realizations which will predrct the identical response to any input. 'To see this, def~ne a coord~nate transformation as

x = 7'~ - (7)

Substitut~on of Eq. (7) ~ n t o Eqs. (4) and (5) yield.

The effect of input ~ ( k ) on output y(k) will he the wme whether Eqs. (4)-(5)or Eqs. (8)-(9)are used. Thus. the

triple [T-lAl: T I B , ('I.] = [ A , H . (' / is also a

realization for the LSS.

2.2 System Realization

For the F1)I algorithm proposed, the Eigensystem Kealizntion Algorithm (ERA) is utilized to determine the structure realization1? ERA is an extension of minimum realization theory2" to handle the case o f noisy measurement data. A unique approach based on ;I generalized Hankel matrixis used in conjunction with the singular value decomposition to arrive at a minimum order state-space realization which preserves input - output characteristics. Thus, the output of EKA is the matrix triple [T-'AT T ~ B , ('TI = [A', 13', (''1 . The Hankel matrix is obtained from the

impulse response of the structure. The impulse response may be obtained from an impact hammer test of the structure a by taking the inverse FFT of the frequency response Sunctions measured from a forced measurement of the structure.

2.3 Sensor Failure Detection and Isolation

I'he method proposed to detect sensor failures is based on the comparison of two realizations for the same system. If {Ai,Hi,('j, i = 1.2) are two minimal realimtions of the same system. then there exist a unique ~nvertiblc matrix 7' such that2'

I'urthermore, 'I' can be slxxified as

where W; and Vi are the controllability and ol~servability matrices for each system given as,

The approach of the proposed fault detection and isolation algorithm is to detect failures by comparing the two realizations. One realization in the comparison will be defined as the nominal case, the realization hefore any sensor has failed. The other realizations will he compared to this one. To detcrmine whether or not a sensor failure has occurred. the output inlluence matrix will Ix examined.

11' [A,,,I3,,.(',,I is the nominal realization for the structure and [AI.B 1.C'l J is another realization, then lrom 1x1. (10)

As with all systems, noise will be present and a fully pupulated error matrix E can he defined as,

When a sensor fails, it would be expected that one of the rows of E will be greater in magnitude than the others. By comparing the magnitude ol'the error of each row, the sensor failure can be isolated. Seven failure criteria are used to isolate the failed sensor,

F, = rmean (abs(E)) - ( 16a)

F, = rmean (E) - ( 1 W)

F, = rnorm (E) - ( I6c)

E, = rmean (abs((',,))

411 E = rnorm (C,)

where the rmean operator is the average of each row, the rnorm operator is the 2-norm of each row, ahs is the absolute value operator, and isEi normalized to unit Largest component. The element location corresponding lo the largest value ofEi indicates which sensor has failed. The failure criteria E7 is a composite of the other six failure criteria.

In the case that the I-lankel matrix is determined from an impact test, the FI3I algorithm must account for the possbility that impacts of different magnitude are used. The difference in magnitude can I>e approximated by comparing the element I7y element ratio of to C,,. This matrix is referred to as the scale factor matrix. In determining the magnitude difference, the most dissimilar row of the ratio matrix is ignored because the failed sensor will not provide correct scale factor information. The dissimilar row is chosen as the row whose row mean differs from the matrix mean to the greatest extent.

In addition, the noise floor of the sensor/structure system must be determined before any failure has occurred. As stated earlier, the error matrix E will always be nonzero even when there is no actual sensor failure if there is any noise present in the system. 'I'hus, a noise floor for the matrix E must hc determined so that the case of no sensor failure can also Ile determined from inspecting the error matrix. l'his noise floor can be determined l y applying the FI)I algorithm several times before any sensor fails.

2.4 Failure Classification

Due to the nature in which failures are being detected, it is possible to classify some of the types of failures that will occur by inspecting the error matrix E and the scale factor matrix. In this FJjI algorithm, the sensor failure is classified as one of four sensor failure

classes: complete sensor failure (no output), gain error failure, random signal output falure, and state correlated failure. Each of these different types of I'ailurcs show up in the realbation in a different manner, as will he demonstrated in the examples. In this section, each failure mode is described and techniques for determining from the FDI algorithm the class of sensor failure is discussed.

('omplete sensor failure is the case when the output from the sensor is identically zero

y,, = O + noise (17)

where yit is the output of the ill1 sensor in a failed mode. In this case, there is no corruption of the ERA identified eigenvalues by the output of the faulty sensor. If the measured data 1s noise free, the row of the identified C matrix corresponding to the failed sensor will he identically zero. With noise present, the mean of the row will he statistically close to zero. Thus, once the FI)I algorithm isolates the faulty sensor, the row mean of the (' matrix is examined to check for the zero output condition. This classification can also be veril'icd by checking the element by element inverse of the scale tactor matrlx. In this matrix, each element in the faulty row is k i n g divided by a small number (in the no noise case by zero). Thus, the magnitude of each element o f the row corresponding to the failed sensor will he much greater than the other rows.

A gain fa~lure is when the sensor outputs the correct waveform, except that it has been scaled by a constant scalar factor a

In the noise free case. there is no effect of the gain

Finally, a state-correlated failure is one in which the sensors output is dependent on the state vector

y , ~ = fi + noise (20)

where h is a vector of constants. Again, in the noise free case there is no effect of a state-correlated I'aili~re on the ERA identified eigenvalues. If the FL)I algorithm cannot classify the failure as any of the other previously discussed failure modes, it defaults to a state correlated failure. In essence, the zero output and gain failures are just special cases of a state correlated failure. In the zero output case, the 1? vector is identically zero. In the gain failure case, the h vector is again zero except at one of the element locations.

3. EXAMPLES

Two examples are provided. One consists ol' a system where the experimental data is "simulated" using a numerical simulation. 'I'he second example consists of a laboratory demonstration of the algorithm.

3.1 Example #1 - 4 Degree of Freedom Struct~~ral Model

In this first example, a four degree of freedom structure as shown in Fig. 1 is used as a test-hed. 'l'he nondimensional mass, stiffness, and damping constants are given as m = 1. k = 5 and c = 2. It is assumed that each structural displacement is measured. 'I'his model is used to generate time histories for input into the FIJI algorithm. To better simulate a real world environment, a random noise signal is addcd to the output of each sensor. 'Table 1 provides a summary of each "numerical experiment" performed. 'I'he sampling time for each experiment is 0.10 seconds.

The FllI algorit hm classifies the failure as a gain failure when the standard deviation is less than 10% of the mean. 7'he value of 10% is an arbitrary setting which should be adjusted hased on the noise floor level and the particular structure of interest.

failure on the ERA identitled eigenvalues. The FI)I

Random noise failure is the case where the sensor outputs a random time series

y,, = noise (19)

algorithm calculates the mean and standard deviation of the row elements of the scale factor matrix

k m+

corresponding to the failed sensor. In the no noise

where i t is assumed that the noise has zero mean. In this case, the ERA identified eigenvalues are effected, the degree to which is dependent on the KMS level of the noise in comparison to the RMS level of the other sensors. 'l'hus, a random signal failure is flagged when a large shift in the ERA identified eigenvalues is ol~served.

Figure 1 - Four Degree of Freedom Structure 'Test (lase

The nominal case was excited with a unit impulse and had no noise added. The eigenvalucs for the system determined by ERA are shown In 'Iiible I .

The first exper~ment is used to establish the noise Iloor of the system. 'I he data was corrupted with 15% n o w and there was no sensor failure. 7'he dilterence in lmpulse magnitude was accounted for usmg the scale factor matrix. The 2-norm of the error matrix was 0.0132. The ratio of the 2-norm of the error matrix to the 2-norm of (',, was 0.0510. Several other "noi.;yV test cases were run with lower levels of noise: each resulted In error norms lower than the 15% noise case. ' I hus, any realization with norms less than the above norms will be classified as no failure.

case. these elements would all be eaual to one another.

- -

- m+

k m+

k m+ k

- -

-

-

Fl'nl>le 1 - Summary of Numerical Experiments

Exper~ment 2 illustrates the case in which there is no sensor failure. l 'he output time histories are corrupted with 2.5% noise. The scale factor matrix is shown in 'Iiible 2a. The fourth row 1s determined to be the mo\t dissimilar; the resulting scale factor is determined to be 0.9997. The FD1 algorithm then compensates for the magnitude difference by dividing

I I,y the s a l e l'actor and then calculating the error matrix shown In lable 2h. l 'he 2-norm of the error matrvt and the 2-norm of the error matrix t o the 2-norm of (',, is 0.0018 and 0.0069 respectively. Since thew are helow the noise threshold, the FIII algorithms correctly concludes that there is no sensor failure.

For thc remain~ng experiments, the error norms

were all greater than the established noise Iloor, and will not be reported. The results of the seven failure criteria applied to the remaining numeria11 "experiments" are summari7ed in 'Iiihle 3. Is~~rther discussion on the numerical "experiments" follow.

Experiment 3 illustrates the case when a sensor is dead, i.e., the sensor has no output. 'I'he output data was not corrupted with noise. The scale faclor is calculated to be 0.9977 and the realizedltransformed output influence and error matrices are given in lilhles 4a and 4b respectively. When the sensor has no output, the row corresponding to that sensor will have a row mean close to zero. This is used to classify the failure as sensor number one failing with no output.

Fail ure 'lype

-

-

None

No Output Sensor # l

Random Sensor #4

Sine Sensor # 3

Gain Sensor #2

Gain Sensor #3

Correlated Sensor #1

P

n

I i~ilurc I )clcctccl

-

-

None

No Output Sensor # l

Random Sensor #4

CJnclassified Sensor f 3

('orrelated Sensor #2

Gain Sensor #3

Correlated Sensor #1

Noise (76)

0

15

2.5

0

2.5

5

7

10

5

Iixlxrinicnl #

Nominal

1

2

3

4

5

6

7

X

L)rce Applied

Impulse Mag = 1

Impulse Mag = 3

Impulse Mag = 1

Impulse Mag = 1

Impulse Mag = 2

Impulse Mag= 1

Impulse Mag = 3.5

Impulse Mag = 1.4

Impulse Mag = I

KRA eigenvalues

-0.13 + 1.42i -0.46 + 2.70i -0.34 + 3.40i -0.06 + 4.18i

-0.13 + 1.42i -0.46 + 2.71i -0.34 + 3.40i -0.06 + 4.18i

-0.13 + 1.42i -0.48 + 3.40i -0.33 + 3.40i -0.06 + 4.1Xi

-0.13 + 1.42i -0.46 + 2.70i -0.34 + 3.40i -0.06 + 4.18i

-0.15 + 1.38i -0.43 + 3.12i -0.4 1 + 4.33i -1.92+31.4i

-0.00 + 1.00i -0.10 + 1.42i -0.23 + 3.1 li -0.01 + 4.14i

-0.13 + 1.42i -0.47 + 2.70i -0.35 + 3.39i -0.07 + 4.18i

-0.14 + 1.42i -0.47 + 2.7 1i -0.37 + 3.4li -0.07 + 4.17i

-0.14 + 1.42i -0.50 + 2.71i -0.38 + 3.3% -0.07 + 4.17i

Table 2a - Scale Factor Matrix

%ble 213 - Error Matrix for Experiment Number 2

Table 3 - Summary of Experiments/Failure Criteria

n Experiment # I Fl

Table 4a - Realized Output Influence Matrix - Experiment Number 3

Table 4b - Error Matrix for Experiment Number 3

Experiment 4 illustrates the case when a sensor classfies the failure correctly as a random output ou tputsa random signal. l 'he KMS value of the failure. 'I'he large error made in the calculation ol'the random signal was chosen t o be the same order of scale factor indicates that the FUI algorithm may mugnitudc as the other sensor signals. The scale encounter dil'ficulties when the failed sensor output factcw is calculated to be 2449 and the error matrix is KMS level is of the same order of magnitude as the true givcn in ' IWe 5. t h e Sailure is identified as sensor sensor signals. number four. .l'he large shift in the EKA eigenvalues

'Ihble 5 - Error Matrix for Experiment Number 4

In experiment 5. the third sensor outputs a sine three indicate sensor numher 1. tfowever, the wave with t'requcncy 1 radlsec. I'he frequency of the cumulative indicator indicates sensor number 3. 'l'hus, sine wave is identil'ied by the ERAalgorithm asa mode sensor numher 3 is flagged as having failed, hut IS not of vilmtion, along with the first, third, and forth actual classified. However, in inspecting the eigenvalues. the structural modes of vibration. The scale factor is presence of a previously undamped mode of vibration calculated to be 0.6773 and the error matrix is given in at 1 radtsec would seem to indicate that the failed Xihle 6. Inspectmg Table 3, it is seen that three of the sensor is outputting a pure harmonic signal. talurc criteria indicate sensor three as failing, whereas

.IBble h - Error Matrix Sor Experiment Nuniher 5

I n experiment 6, the second sensor outputs a sensor with zero output corrupted with noise (an random signal whose KMS magnitude is much smaller infinite gain reduction). l 'he scale factor is identified than the other signals. This represents the case of a as 3.2857 and the error matrix Tor this case is shown in

3ithlc 7. J'he failure criteria indicates correctly that sensor two has failed. However, the FI)I algorithm in some sense incorrectly classifies the failure as a state correlated failure. 'This incorrect classification is due to the fact that the small random signal does not greatly influence the ERA identified eigenvalues, nor does the

l3ble 7 - Error Matrix for

error or scale factor matrices indicate any other form of failure. In a certain sense, this is also a correct classification for this failure in that the constanls multiplying the states are all zero as previously discussed.

Experiment Number 6

In experiment 7, a gain error o f 0.7 is introduced simulated for sensor f l . The correlated sensor failure into the signal conditioning unit for sensor number 3. output is given by, '1.h~ data i&orrupled with iO% noise. l 'he error matrix

-

is given in 'lhble 8. l 'he FD1 algorithm indicates sensor y,, = [0.1 0.2 0.3 0.4 0.0 0.0 0.0 0.01 y,, - + noise

th;ee has failed. I he failure i<classified asa gain error where Is the senu,r Outl,uts, y l f is the hecause the row in the scale factor matrix the first sensor in the f;,iled -I.he sc;,le corresponding to the failed sensor has a standard deviation which is less than 10% of its mean value. In factor is identified as 1.1365 and the error matrix is

other words, the numbers comprising the third row are given in 7Bble 9. 7'he FIII algorithm flags sensor one

all close to one another. as the failed sensor. Because none of the other sensor failure classifications are met, the FDI correctly

In experiment 8, a correlated sensor failure is classifies the failure as a slate correlated failure.

Table 8 - Error Matrix for Experiment Number 7

'I'ahle 9 - Error Matrix for Experiment Number 8

3.2 Example #2 - Cantilever Beam Experiment

I i ) further illustrate the FD1 method, experiments were conducted using a cantilevered beam with two accelerometers attached as shown in Figure 2. The c f l heam has length 0.84 m. a mass per unit length of 2.364 kglm. a moment of inertia of3.02e-09 m4and a ~ o u n g ' s Modulus of 70 (;Pa. 'I'he measured natural freauencies 6 5 4 3 2 1 and damping ratios for the first three rn;,des of vibration arc f l = 7.04 Hz. f7 = 44.02 Hz. f7 = 122.63 Figure 2 - Experimental Beam

Four different experrments were conducted with directly calculate the scale factor matrix, in that with the cnnt~levercd beam. 'I hese experiments are only two sensors the most dissimilar row is not uniquely summari7ed in 1Bhle 10. The sampling time for each defined. At the same time, one would not want to experiment was 0.002 sec. ERA analysis was applied include both sensors in the scale factor matrix using 100 time points of data. Data acquisit~on calculation. Therefore, the scale factor was cnlculwtctl capahlrties led to the constraint of only placlng two with the sensor which was known to he good. Xble 11 sensor.; on the beam. I herefore, 11 is not possible to presents the results of the seven failure criteria.

'l'able 10 - Summary of Cantilever Beam Experiments

'Ihble 11 - Summary of Cantilever Beam ExperimentsIFailure ('riteria

'!'he first experiment simulates a gain error in the first sensor. The gain was increased by a factor of 10. l 'he scale factor was calculated to be -0.02. which from performing the experiment is known to be incorrect hcaiuse thc impulse was applied in the same direction. 'l'he error in the scale factor is attributed to a single large negative clement in the scale factor matrix. If the clement is ignored. the scale factor is calculated to be O.hX, which appears t o he more reasonable. However, hecause an FI)1 algorithm should require no human intervention, the results listed use the -0.02 scale factor. The row norms of the nominal (' matrix are 0.47 (row 1 ) and 0.30 (row 2). This is expected because sensor one is located at the tip of the cantilever beam. 'I'he row norms of the (' matrix for experiment one are

Experiment #

.

1.32 (row 1) and 0.08 (row 2). One can ol3viously see the effect of using a poor scale factor. However, the gain difference can he seen by the relative magnitude difference hetween the two row norms. An approximation to the gain error can bc calculated from

Failure Type ERA Natural Frequencies (Hz)

7.04

where the subscripts exp and nom refer to the current experiment and nominal test case respectively. Llsing Eq. (21). the gain error is approximated as 10.53. However, it should be noted that the scale factor matrix does not pass the standard deviation test f o r gnin

Failure Detected

fnilurc. 'Thus, the F1)I algorithm classifies the failure as a state correlated failure.

-1 he second c~pcriment simulates a gain error in the second sensor. I'he gain was increased by a factor of 10. ' I he scale Factor is calculated to he 0.73. Again, the scale Pactor matrix docs not pass the standard dcv~ation test and the failure is classified as state correlated.

1:xperiment three simulatesa random signal error in the second sensor. l 'he KMS level of the random noise was of the same order of magnitude as the true

signal (sensor #I). The scale Factor was calculated to be 4.78, although it should be noted that one element of the scale factor matrix greatly increases the average. Hecause of the large eigenvalue shift in the fundamental frequency, the FDI algorithm classil'ies the failure as a random output.

Experiment four replaces accelerometer two with a broken accelerometer. The realized (' matrix is shown in 'Iable 12. 'The failure is classit'ied as a zero output failure because the row average of realized (' matrix is -0.00028.

Table 12 - Realized (' Matrix

4. SUMMARY

A sensor fatlure detection and isolation (FDI) algorithm has been presented which utilizes system rcali7ation theory. Instead of using hardware or analytical model redundancy, system realization is utili~ed to provide an experimental model based redundancy. 'l'he FL)I algorithm utilizes the Eigensystem Realization Algorithm to determine a minimum-order state space realization of the structure in the presence of noisy measurements. The FDI algorithm then compar& successive realizations to detect and isolate the failed sensor component. Due to the nature in which the FI)I algorithm is formulated, ., it is also possible to classify the failure mode of the sensor.

'I'he algorithm has heen demonstrated to perform well in the presence of noise. Some difficulties have been encountered when the RMS output of the failed sensor is of the same order of magnitude as the KMS outputs of the other sensors.

ACKNOWLEDGEMENTS

'I he authors greatly appreciate the support received from the Florida Space Grant Consortium Interinstitutional Space Research Program. In addition, the work of the second author was partially s ~ ~ p p ) r t c d by a Ilarris Fellowship. The experimental equipment used in this research was obtained under NSP grant number MSM-8806869, grant monitor Dr. E. Marsh. '1 he authors would also like to thank Ilrs. Jer-Nan Juang, L. Horta and E. Garcia for discussions concerning the Eigensystem Realization Algorithm.

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