Mechanical Diagnostics System Engineering in IMD HUMS

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Vergennes, VT 05491. 802-877-4758. Eric.Mayhew@Goodrich.com. Abstract—The Goodrich Integrated Mechanical Diagnostics. Health and Usage System ...
Mechanical Diagnostics System Engineering in IMDHUMS Eric Bechhoefer Goodrich Fuels and Utility Systems Vergennes, VT 05491 802-877-4875 [email protected] Eric Mayhew Goodrich Fuels and Utility Systems Vergennes, VT 05491 802-877-4758 [email protected] Abstract—The Goodrich Integrated Mechanical Diagnostics 12 Health and Usage System (IMD-HUMS) , mechanical diagnostics functionality is the integration of disparate subsystems. When the aircraft is in the appropriate capture window, the primary processing unit (PPU) commands the vibration processing unit (VPU) to capture vibration data and a tachometer reference. This time domain data is processed by standard and proprietary algorithms to generate component condition indicators (CI). These CI are statistics, which when used with a priori configuration data, are mapped into component health indicators (HI). The VPU passes the component HI data to both the PPU and the data transfer unit for ground station display.

This paper addresses the system engineering required to integrate the vibration processing, decision algorithms, thresholding and filtering to give the operator the best representation of component health. The integration of the system allows IMD-HUMS to have a high degree of certainty in the information given to the operator. This information could potentially improve maintenance practices, lowing aircraft operating cost while improving aircraft safety. The system engineering insures that the recommendation for component maintenance has a low probability of false alarm while maintaining a high probability of component fault detection.

The PPU, taking the HI data for a component, can determine if the component has a degraded health state. If the component is degraded, the PPU can generate an exceedance message to be reviewed during maintenance debrief. After the flight, all CI and HI data are stored in a data base and is available for display against an aircraft, composite component (e.g. line replaceable unit) and the component itself.

1. INTRODUCTION ..................................................... 1 2. THE CALCULATION OF A HEALTH INDEX ............ 2 3. ON BOARD EXCEEDANCE MONITORING................ 5 4. CONCLUSIONS ....................................................... 7 REFERENCES............................................................. 7 BIOGRAPHY .............................................................. 8

TABLE OF CONTENTS

1. INTRODUCTION

The acquisition process is complicated by noise from internal sources (non synchronous gears, shafts and bearing not under analysis) and external sources (changes in airspeed, torque, weight, etc). The HI becomes, in essence, a statistical indicator of the components health. As such, the best estimator of component health is calculated using a Kalman filter. This reduces variance in the data prior to display of the component HI to the aircraft operator. This filtered HI is called the DHI (Display Health Indicator). The DHI uses a priori information and sampling theory to build the best available representation of health of the component.

The IMD-HUMS system functionalities, such as:

1 1 2

0-7803-9546-8/06/$20.00© 2006 IEEEAC paper #1068, Version 2, Updated Dec 20, 2005

1

performs

a

number

of



Operational Usage Monitoring: Provides tracking of flight events in time to record actual usage in various flight conditions.



Structural Usage Monitoring: Provides detection of various flight conditions/regimes of flight. Applies stress factors germane for each flight regime to specific equipment.



Exceedance & BIT Monitoring: Detects specific events related to aircraft operation to trigger maintenance actions. Provides in-flight as well as ground station notifications as required. In-flight

monitoring of all avionics maintenance actions. •



BIT to trigger

associated with higher level languages. This allows the system engineer to operate on, functionally, any condition indicator available for a given component, and report the calculated/mapped component health to both the PPU and Ground Station.

Pilot/Maintainer Debrief: Provides interface and procedure to efficiently collect inputs from the pilot, crew, and maintenance personnel. Trouble Shooting Provides specific user interfaces design to address known maintenance and troubleshooting procedures. Provides graphing capability that pulls up historical data within the database on the Fleet Management Work Station. The user can trend and plot any captured parameter to assist with trouble shooting or engineering evaluations of many systems on the aircraft.

Health Indicator Calculation There are a number of potential algorithms that could be used to calculate health. Derivation of health will be an ongoing exercise. The algorithms will mature as experience is gained with identifying faulted components. Currently, the health algorithms are based on the component type. Different components (and there underlying CIs) have different distributions and behavior. One aspect of system engineering is using the appropriate health calculation algorithm, based on the a priori information such as component failure modes, knowledge of the CI algorithm, and the distribution of the CI.

Finally, Mechanical Diagnostics & Prognostics: Capability to measure and track the status of gears, bearings, and shafts. Provide early detection of evolving flaws prior to becoming faults or equipment failures.

As an example, we can investigate the health algorithm for Shaft. For shaft force unbalance or dynamic unbalance, the shaft order 1 (SO1) magnitude will be excited. SO1 is vibration synchronous with 1 times the shaft RPM. For a bent shaft, it is typical to see SO1 and SO2 (shaft order 2, e.g. vibration twice the synchronous rpm). For shaft misalignment, misaligned bearing or mechanical looseness, SO1, SO2 and SO3 (shaft order 3) are excited. Because these indicators capture most shaft failure modes, these will be used for HI calculation.

The system engineering of Mechanical Diagnostic function takes into account the distribution of the condition indicators (CI), mapping the CI into an HI such that the operator has confidence that an alarm indicator requires maintenance. This is the first step into an On Condition maintenance practice.

2. THE CALCULATION OF A HEALTH INDEX

One could hypothesize that the real and imaginary part of the Fourier transform used to calculate magnitude at the SO1 frequency are zero mean and Gaussian, with some unknown variance:

The IMD-HUMS system is a data driven system. Not only does this facilitate reapplication across aircraft, but allows changes to the a priori libraries as component knowledge evolves without recertification of software. The a priori data consist of a representation of the helicopter drive train, such as: the relationship between sensors, shaft, bearing and gears. In addition, a priori data consists of a health algorithm script, called configurable health, and the threshold data.

Re ~ N (0, β ) Im ~ N (0, β )

(1)

The measured CI is then:

Configurable Health

CI =

X 2 +Y2

(2)

As the installed fleet of IMD-HUMS becomes larger, the amount of data collected and analyzed will increase. Within this data will be components in the process of failure. This fault data will be used to better understand the fault process, resulting in improved methodologies for diagnostics and prognostics. Normally, fielding new algorithms would require re-certification and test of the flight software. However, with the implementation of configurable health, new health algorithms are fielded as an update to configuration. This greatly reduces the cost associated with certification and test. Additionally, it allows customers to specify their own health algorithms.

or a function of Gaussian distributions. It can be shown analytically that this distribution is Rayleigh (see Bechhoefer). The measured CIs, for nominal (e.g. undamaged) shaft, parametric are shown to be Rayleigh like. A test of the distribution, using a distribution fitting procedure (such as the χ2 Goodness of Fit) will indicate the distribution to be almost Rayleigh and not Gaussian. The departure from Rayleigh is due to some components having dynamic imbalance (e.g. the assumption that the Real and Imaginary components are zero mean is violated for some components due to imbalance).

Physically, configurable health resembles a pseudo code, with all of the standard operators, logical and flow controls

Knowing that the shaft when damaged will excite a SO1, SO2 and SO3, a test can be built that maps the HI to 2

measure the deviation away from the population of nominal shafts. For example, one can take the maximum of the three normalized CIs (e.g. CI divided by the CI standard deviation). This mapping can take into account the distribution of CI values such that a health indicator (HI) value of .9 (defined as alarm) has a small probability of occurring in the population of nominal aircraft shafts (i.e. the probability of reporting a shaft in alarm is the PFA – the probability of false alarm, is small). This will give the operator confidence that the component is in fact damaged when HUMS reports it as damaged. Alternatively, the operator can define limits (e.g. manufacture’s limits) for which a component shall be reported. In this case, the PFA can be calculated for the given threshold from the CDF of the distribution.

where t is a t-statistic with n-2 degrees of freedom. Simply stated, if the confidence (α) is .025 percent (e.g. only 2.5 percent chance that t > t-statistic(.975,df) or t < tstatistic(.0.25,df ), one much reject the null hypothesis. For large sample sizes (n > 40), the t statistic approaches the Gaussian distribution. For shaft, it is predominately the case that one must reject the null hypothesis: there is statistically significant correlation. However this test does not indicate the degree correlation. One can calculate the covariance for a component across all aircraft (e.g. the grand covariance) and test this against each aircraft. As an example, the correlation coefficient associated with the covariance of an engine input shaft sampled from the H-60 utility helicopter is:

The Order Statistic as HI The maximum of a set of independent, identical distribution is an Order Statistic (OS). The OS is, again, a function of distributions, and can be found using the method of moment (see Wackerly). The PDF of the OS is:

g ( x ) = n[F ( x )]

n −1

f (n )

(3)

z=

Once the measured CIs are normalized by dividing by the CI standard deviation, the distributions are identical. The Rayleigh distribution shape parameter, β, is the variance in the underlying Gaussian distributions. The measured variance for the Rayleigh distribution is a function of β: σ2 = (2-π/2)*β2. By dividing the CI by the standard deviation of the CI, the distributions are identical with: β = (1 /(2-π/2))0.5 = 1.5264

(4)

A/C

(5)

To state that there is no covariance, (e.g. correlation is zero and that CI are independent), we need to prove this with some level of confidence that ρ is zero. Let one define the null hypothesis as: Ho ρ = 0, vs. the alternative hypothesis: H1 ρ > 0. This testing procedure can be verified using Pearson Produce Moment Correlation Coefficient (see Sheskin). This test is defined at:

t = ρ n−2

1− ρ 2

z r1 − z r 2

(7)

1 1 − n1 − 3 n2 − 3

where zr1 is the Fisher transformed value for the correlation from the first population, and zr2 is the Fisher transformed value for the correlation from the second population. The z is a normal Gaussian statistic. Example: Engine 1 Input Shaft, torque < 30 (Table 1.)

The assumption of independence is not as strong. Independence requires that the correlation coefficients between CI to be zero. Correlation coefficient is defined as:

σ x2, y = σ xσ y

ρ2,3 = 0.06,

We can now test the hypothesis that the covariance for each aircraft is the same as the covariance (e.g. and by extension the correlation) across all aircraft: Ho ρk = ρGrand, (the populations represented by the two samples are equal) vs. the alternative hypothesis: H1 ρk != ρGrand (the populations are not equal). The test statistic is:

where n is the number of identical distributions being sampled.

ρ x, y

ρ1,3 = 0.20,

ρ1,2 = 0.1635,

Z ρ1,2

Z ρ1,3

A/C 1 A/C 2

-1.26312 -0.83769

A/C 3

1.67684

0.08357 0.61812 2.33427 8

A/C 4 A/C 5

1.75394 -0.03613

-1.72067 1.24205

A/C 6

-0.09852

1.86508

A/C 7

-1.42555 -0.95239 0.42307 A/C 8 1 0.17419 A/C 9 -1.44741 -0.88177 A/C 10 -0.4552 4.21417 Table 1. Test Statistic for Correlation

(6)

3

Z ρ2,3 0.43739 7 -0.68272 2.34703 1 0.29425 1 -0.33697 0.44703 9 0.04400 4 2.00747 2 -1.0162 -1.56725

The highlighted statistics reject the null hypothesis (e.g. covariance is statistically different). It must be noted that, predominately, the covariance across aircraft are similar. Given that, the correlation is relatively small (see above). While this violates the condition of independence for the order statistic, it does not have a significant effect on the distribution OS when correlation is low, as is the case with Shaft.

Substituting the f(x), F(x) into the OS function gives an OS PDF of:

[

(

f ( x ) = 3 1 − exp − x 2 2β 2

)]

2

(

The expected value and variance can then explicitly be calculated: ∞

E[x] = ∫ xf ( x )dx,

It should be noted that this is difficult to quantify analytically the effect of correlation. However, we can contrive an experiment and derive the PDF under correlation and compare this to the OS (figure 1). It is difficult to construct a correlated Rayleigh distribution, so the Gaussian was used in this experiment. The coloring process was performance by multiplying a random Gaussian distribution by the inverse whitening matrix (Bechhoefer), then taking the OS of this correlated distribution. While the PDFs are different, the critical values are nearly identical. Since the PFA is set with the critical value, it is assumed that correlation does not have a significant effect and the threshold set for the OS will be representative or PFA observed in a fleet of aircraft.

[ ]

0



E x = ∫ x 2 f ( x )dx, 2

[ ]

V [x ] = E x 2 − E [x ]

2

Using β of 1.5264, the expected value is 2.785 and the variance is 0.784. Figure 2 is the PDF of the OS compared to a Gaussian distribution with the same mean value and varaince (figure 2). 0.5

Correlated OS OS

OS Gaussian

PDF

PDF

0.3

0.4

0.2

0.3

0.1

0.2

0

0

1

2

3

4

5

6

X

0.1 0

(11)

0

0.4

0.5

)

x β 2 exp − x 2 2β 2 (10)

-2

-1

0

1

2

3

4

Figure 2 OS PDF vs. Gaussian PDF

5

The OS PFA (probability of false alarm give a nominal part) is 1-CDF. While there is no close form inverse CDF for the OS, it is a relatively simple procedure to select a threshold value, x, such that the PFA is any desired value.

Figure 1 Correlated OS vs OS The Rayliegh Order Statistic

Now consider mapping the OS to a HI. With the OS PDF and CDF, the engineer can tailor the health algorithm to suit the operator’s requirements for PFA. As an example, consider a case where the engineer set the best 5% components as zero HI (e.g. HI will track 95% of all components – the best 5% are not an issue). Additionally, the engineer requires the system to have PFA for alarm of 10-3 (e.g. the HI reports Alarm, when in fact the component is good with a probability of 10-3). Finally, alarm is defined at a HI value of .9. The two critical values are found using the CDF. The CDF for .05 is 1.463, while the PFA (1CDF) for 10-3 is a value: 6.1. The HI algorithm becomes:

It has been shown that the CI distribution for shaft is a Rayleigh distribution, with a probability density function (PDF) of:

(

f ( x ) = x β 2 exp − x 2 β 2

)

(8)

The Rayleigh cumulative distribution function (CDF) is the integral of the PDF:

(

F ( x) = 1 − exp − x 2 2 β 2

)

(9)

4

HI =

[max(so1 σ

so1

]

)

drive the order statistic to approaching the Rice distribution. One can then calculate the PFA (e.g. 1-CDF) of using the Rice CDF, with a s of 2G’s, and a critical value of 5.7 G’s. The 5.7 G’s value is the critical value for a Rayleigh distribution exceeding 6.1 with normalized beta of 1.5264. The PFA would then be: 0.0085. If the SO1 was 4 G’s, the PFA would be 0.148. It is apparent in that as the component becomes more damaged, the probability of false alarm increases in a non-linear fashion. This can be problematic for automated decision tools.

, so 2 σ so 2 , so3 σ so 3 − 1.463 * .9 (12) (6.1 − 1.463)

The HI mean value and variance are then: E[HI] = (2.785 - 1.463)*.9/(6.1-1.463) = 0.26 V[HI] = 0.784*(.9/(6.1-1.463)) 2 = .029 The variance will be used to optimally weight the Kalman filter.

3. ON BOARD EXCEEDANCE MONITORING

PFA for Damage Components Now that the PDF is known for HI values of nominal components, "what if" conditions can be tested in order to evaluate the performance of the system when the component has wear. One can, for example, evaluate the PFA when the component is not nominal: e.g. when the true magnitude of the component is no longer zero, but some real value which does not require maintenance, say 2 Gs. While damaged, the component is not yet to a state that requires repair (e.g. because it does not require maintenance, a maintenance indication would be a false alarm). In this type of model, the Real and Imaginary parts of the Fourier transform associated with SO1, SO2 or SO3 are no longer zero. In this model, the distribution is now: Re ~ N ( g1 , β )

The IMD-HUMS system has the capability to be configured to issue exceedances with selected, flight critical components. When such a component exceeds an alarm threshold, the Ground station raised an exceedance messages. Automating the reporting of an exceedance which could result in spurious maintenance action: this adds a burden to the system engineer to ensure that the reporting is accurate. As noted, as a component becomes damages, it will be more likely to raise an exceedance. Additionally, the HI itself has a variance of 0.029 (standard deviation of 0.17). This requires some variance reducing technology to estimate the true component health despite the inherent variance in the system. There are a number of circumstances where kinematic models are appropriately used to smooth data or calculate derivatives under noise. Since the health is relatively stationary in time, this is a good candidate. Experience has shown that fault propagation is slow compared to the acquisition rate. Knowing this, a Wiener process acceleration (piecewise linear model) was chosen (see Bierman). This model can easily be solved using the Kalman Filter.

(13)

Im ~ N (g 2 , β )

where the true eccentricity is:

s = g12 + g 22

(14)

This distribution is related to the Rayleigh, and is known as the Rice distribution [Proakis]. The PDF of the rice distribution is:

P( M ) = x

(

)

(

⎞ ⎛− x2 + s2 2 ⎟ I xs β 2 exp⎜ 2β 2 ⎠ o β ⎝

)

Kalman Filter Onboard HI Smoothing The Kalman filter is a kimematic model in which a filter gain is set optimally based on the measurement and system variance and a priori knowledge on the state acceleration (e.g. how fast can the system change over time). The batch process for Kalman Filter is:

(15)

where I0 is the 0-th order Bessel function of the first kind. The CDF is: F (M ) = 1 − Q1 ⎛⎜ s , x ⎞⎟ ⎝ β β⎠

State Propagation Xt|t-1 = F Xt-1|t-1 Predicted Covariance Pt|t-1 = F Pt-1|t-1F’ + Q W = Pt|t-1 H’ [H Pt|t-1 H’ + R]-1 Kalman Gain State Covariance Pt|t = (I – WH) Pt|t-1 State Update X t|t = Xt|t-1 + W(Y-H Xt|t-1) Where: t|t-1 is the condition statement (e.g. t given the information at t-1) X is the state information (x, xdot, x dot dot) Y is the measured data W is the Kalman Gain P is the state covariance matrix

(16)

where Q1 is Marcum’s Q function. We will assume that for a SO1 defect that the β is constant and that the SO1 variance from an engine input shaft with a value of 0.8881, taken from historic data. Since the normalized SO1 value will be larger than the SO2/SO3 values (e.g. because the component is defective), it will 5

Q H R

is the process noise model is the measurement matrix is the measurement variance

s 3 + bs 2 + cs − 1 = 0

Where b = λ/2-3 and c = λ/2+3. Substituting again, s = y – b/3, which allows us to obtain

Ordinarily, there is a fair amount of overhead associated with propagating the state covariance. Since the system is stationary under normal condition, we make the assumption that state covariance is constant by taking the limit of the state covariance as the number of acquisitions become infinitely large.

1 T3 2 T2 T

1 T2⎤ 2 ⎥ T ⎥ ⎥ 1 ⎥ ⎦

where p = c-b2/3 and q = 2b3/27 – bc/3 – 1. substitution yields, y = z-p/3z and:

⎛ − q ± q 2 + 4p 3 / 27 ⎞ ⎟ z=⎜ ⎜ ⎟ 2 ⎝ ⎠

(17)

⎡1 T ⎢ F = ⎢0 1 ⎢0 0 ⎣

s = z − p 3z − b 3

1 T ⎤ 2 ⎥ T ⎥ 1 ⎥ ⎦

(18)

4(1 − α )

= λ2

β = 2(2 − α ) − 4 1 − α α = 2β − β 2

(19)

(20)

The first example (Figure 3.) is the left engine input shaft from a H-60 helicopter. The cyan is the raw HI value, and the black line is the fixed gain Kalman filter of the HI. SO1 is blue, SO2 is green and SO3 is magenta. Despite the apparent step in SO1 vibration, the Kalman filter response quickly to the change in state. Figure 4 is an example of the H-60 Generator Input Shaft. While SO1 is trending higher, it is SO2 that is driving the OS. Note that the Kalman filter effectively smoothes the OS. In this case (figure 4), one could surmise that because SO1, SO2 and SO3 are responding to the fault, that this is a shaft misalignment or mechanical looseness. Historically, maintainers have seen coupling failures with this components.

(21)

Lambda is defined as the target maneuver index:

λ =T 2σv σm

(22)

where (T2 σv ) is the motion of uncertainty and σm is the observer uncertainty. This provides the explicit solution for the gain coefficients in terms of s, for which a cubic equation is obtained. This leads to:

(

2λs = 4(1 − s ) 1 − s 2

)

(27)

Shaft Examples

From this, the solution can be deduced by the following series of substitutions is:

α = 1 − s 2 , β = 2(1 − s )2 , γ = 2λs

(26)

For implementation on the aircraft, the system engineer can make some simplifying assumptions: The time between acquisitions is relatively constant, about 8 per hour: T (delta time) will be set at 8 per hour = 0.125 hr. As noted the HI variance is .029 (e.g. measurement noise). The acceleration (e.g. how fast the system evolves) is set to a value of .00005. This was chosen by assuming that Health for a damage component would change from 0 to 1 in 100 hours, implying at rate of change of 0.01/hr. Acceleration is that: .5 * .012, or 0.00005. The filter gain, W, is then 0.0488, 0.0097, 0.0005 and is hard coded into the application. This reduced the HI variance to 0.0204*(0.0488)^2 = 4.8858e-5, greatly smoothing the HI.

In a similar method as depicted for the piecewise constant acceleration model, it can be show (see Bierman) that the optimal, steady state filter gain coefficients are: γ2

3

from which the gain coefficients α-β-γ can be directly calculated.

We will define the Kalman gain as: ⎡ ⎤ ⎡ g1 ⎤ ⎢ α ⎥ ⎢ ⎥ lim t→∞ W = ⎢g 2 ⎥ = ⎢ β ⎥ ⎢ T ⎥ ⎢⎣g 3 ⎥⎦ ⎢ γ ⎥ ⎢⎣ 2T 2 ⎥⎦

1

A final

of which the negative cubic root should be chosen. This yields:

The state transition matrix, F, is: 2

(25)

y 3 + py + q = 0

The piecewise constant Wiener acceleration model is a third order model, such that the process noise is: ⎡1 T 4 ⎡1 T 2⎤ ⎢ 4 ⎢ 2 ⎥ 2 2 1 T Γ = ⎢ T ⎥, Q = Γ ⋅ Γ σ v = σ v ⎢ T 3 ⎢ 12 2 ⎢ 1 ⎥ T ⎣ ⎦ ⎣⎢ 2

(24)

(23)

Rewriting and substituting: 6

300

400

500

SO1 SO2 SO3

600 1

0 12

0.6

3

0.4

2 0.2

1 200

300 400 Acquisistion

500

0 600

7

SO1 SO2 SO3

Shaft Order G's

6

100

150

200

SO2 SO3

0.8 0.6

6 0.4

4

0.2

100

200

300 400 Acquisistion

500

0 600

While fault detection will allow actionable maintenance to be performed, we still have little information on useful life remaining: we can assure the operator that a component is damages, but we have little ability to indicate the time remaining to failure (expect antidotal based on test stand and real world failures). This is the realm of prognostics. It is believe that the system engineering practiced here will assist in the development of failure models which will, eventually, enable prognostics. We have been experimenting with stochastic systems using the HI statistics and have met with limited success in prognostics. Currently, we are exploring the integration of physical based models which are stochastically driven by HI statistics in an attempt to improve the prognostics model. Regardless, a good understanding of the underlying stochastic process of the component and its distribution can not but improve the performance of a system.

250 1 0.8 0.6

4 0.4

3 2

0.2 1 50

600 SO1 1

Figure 5 Generator Shaft

5

0 0

500

8

0 0

Health 's

50

400

2

Figure 3 Engine Input Shaft 0 8

300

0.8

4

100

200

10

5

0 0

100

Health 's

200

Shaft Order G's

Shaft Order G's

6

100

Health 's

0 7

100 150 Acquisistion

200

0 250

Figure 4 Generator Input Shaft Figure (5) is an example where the HUMS identified the component as in a state of failure when initially installed. In this case, SO1 was driving the OS, although it is clear that SO2 and SO3 are in addition high. When maintenance was performance, the spline coupling was found to be damaged.

REFERENCES [1] Bechhoefer, E., Bernhard A., “HUMS Optimal Weighting of Condition Indicators to Determine the Health of a Component”, American Helicopter Society #60, Baltimore, USA, 2004. [2] Bechhoefer, E., “Method and apparatus for determining the health of a component using condition indicators” USPTO, 6,728,658, April 27, 2004 [3]Bierman, G., Factorization Methods for Discrete Sequential Estimation , Academic Press, New York, 1977 or A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974 [4]Proakis, John, G., Digital Communications, McGraw-Hill, Boston MA, 1995, page 45-46 [5]Sheskin, David, J., Handbook of Parametric and Nonparametric Statistical Procedures, CRC Press, Boca Raton, 1997, page 95 - 99.

4. CONCLUSIONS By taking a broad, system approach to mechanical diagnostics, we are able to provided actionable information to the operator on the health of a component. This methodology allows the system engineer to assure the operator, with a high degree of certainty, that when HUMS indicates a damaged component (e.g. the HI of a component greater than .9), the component is in need of maintenance. This assurance builds confidence in HUMS and will assist in the transition to condition based maintenance.

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[6]Wackerly, D., Mendenhall, W., Scheaffer, R., Mathematical Statistics with Applications, Buxbury Press, Belmont, 1996

BIOGRAPHY Dr. Bechhoefer is retired Naval aviator with a M.S. in Operation Research and a Ph.D. in General Engineering, with a focus on Statistics and Optimization. Dr. Bechhoefer has worked at Goodrich Aerospace since 2000 as a Diagnostics Technical Lead. He has previously worked at The MITRE Corporation in the Signal Processing Center. ERIC MAYHEW is the Vibration Diagnostics Technical Lead at Goodrich Fuel and Utility Systems. Mr. Mayhew has 8 years of experience in the area of vibration diagnostics and fielding diagnostic systems. Mr. Mayhew has developed automated analysis packages as well as many data replay tools. He is a member of the American Helicopter Society (AHS) and the Machinery Failure Prevention Technology (MFPT). He has a B.S. in Mechanical Engineering from Clarkson University.

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