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20

A Regime Recognition Algorithm

for Helicopter Usage Monitoring

David He1, Shenliang Wu1 and Eric Bechhoefer2

1The University of Illinois at Chicago

2 Goodrich

USA

1. Introduction

The importance of regime recognition for structural usage monitoring of helicopters cannot

be overemphasized. Usage monitoring entails determining the actual usage of a component

on the aircraft. This allows the actual usage/damage from a flight to be assigned to that

component instead of the more conservative worst-case usage. By measuring the actual

usage on the aircraft, the life of the components can be extended to their true lifetime.

Usage monitoring requires an accurate recognition of regimes, where a regime is the flight

profile of the aircraft at each instant of the flight. For each regime, a damage factor is

assigned to each component that has usage. These damage factors are assigned by the

original equipment manufactures (OEMs) based on measured stresses in the aircraft when

undergoing a given maneuver. Therefore, it is important that the regimes can be recognized

correctly during the flight of the aircraft to avoid either underestimated or overestimated

damages for the aircraft. Another important aspect of regime recognition is related to the

certification of health usage and monitoring system (HUMS). As outlined in a document of

the Federal Aviation Administration (FAA) HUMS R&D Initiatives (Le, 2006), regime

recognition and monitoring has been identified as a high priority HUMS R&D short-term

task in the area of structural usage monitoring and credit validation. The certification

readiness and the aircraft applicability of regime recognition and credit validation are lower

in comparison to the overall HUMS assessment (12% to 18% and 59% to 82%, respectively).

These cited assessment results clearly show the weakness of current regime recognition

methods in HUMS.

Although important, not much work on regime recognition has been published. Two recent

research papers are worth mentioning here. The first paper (Teal et al., 1997) described a

methodology for mapping aircraft maneuver state into the MH-47E basic fatigue profile

flight regimes in a manner which ensures a conservative, yet realistic, assessment of critical

component life expenditure. They also presented the use of wind direction and magnitude

estimation and inertial/air data blending to obtain high fidelity airspeed estimation at low

speeds. An accuracy rate of 90% based on time was reported. This method basically is a

logical test. The system firstly identifies the maneuver based on flight dynamic data and

general principles of tandem rotor helicopter flight which are derived from flight experience

and mathematical models correlated with flight test results, then the aircraft maneuver state

is mapped directly into one of the basic fatigue profile flight regimes. The method is subject

Source: Aerospace Technologies Advancements, Book edited by: Dr. Thawar T. Arif,

ISBN 978-953-7619-96-1, pp. 492, January 2010, INTECH, Croatia, downloaded from SCIYO.COM

Aerospace Technologies Advancements

392

to the main weakness of logical test in dealing with the noisy measurement. If the measured

parameters were free of noise, logical tests would give accurate results. The second paper

(Berry et al., 2006) presented a regime recognition scheme implemented as a hierarchical set

of elliptical function (EBF) neural networks. Motivated to develop an automatic regime

recognition capability as an enhancement to the US Army’s Vibration Management

Enhancement Program (VMEP), the EBF neural networks were devised to simplify neural

net training and to improve the overall performance. The idea of using a hierarchical set of

neural networks is to group individual regimes into regime groups, including an unknown

regime group (regimes that cannot be classified as any regimes in one of the known regime

groups). Regimes in each group are classified by an individual net in the hierarchical set.

Regime recognition is carried out through a hierarchical process, e.g., if a regime cannot be

classified as the first regime group by the top net in the hierarchy it will be passed to the

lower level nets for further classification. In the paper, a total of 141 regimes of Sikorsky’s S-

92 helicopter were grouped into 11 groups, including “level flight”, “auto”, “climb”, “dive”,

and etc. As shown in the paper, the EBF neural network regime recognition scheme gave

near perfect classification results for “level flight” regimes. However, the results for

classification of all regime groups didn’t show a consistent effectiveness of the scheme. For

example, for “level flight” group the classification rate is 97.85% but it is 33.18% for “turns”

group. Because of the low classification rates for some groups, the scheme gave an overall

rate of 76.21%. In addition to the requirement for a large amount of data to train a neural

network, one variable that could also affect the performance of the scheme is the way by

which the regimes are grouped. Another limitation of neural network is that as it is a black-

box methodology, little analytical insights can be gained to enhance the regime recognition

process.

Regime recognition is basically a data mining problem, i.e., mining the measured parameter

data and mapping them to a defined flight profile. In this paper, the philosophy of data

mining is adopted for regime recognition. In particular, a regime recognition algorithm

developed based on hidden Markov model (HMM) is presented.

2. Regime recognition algorithm

Before presenting the data mining based approach for regime recognition, we first describe

the regime recognition problem from a data mining perspective as following. Suppose we

have Q regimes, denoted as },...,,...,,{ 21 Qi

ω

ω

ω

ω

ω

=

. By taking into account the time

factor in regime recognition, each individual regime at time t is expressed as i

ts

ω

=)( .

Given an observation sequence Tt RRRRR ......

21

=

, where T is the length of observations in

the sequence and each observation t

R is a O

×

1 vector, denoted as 12

{, ,..., ,... }

T

ttt tjtO

Rff ff=

with tj

f being the value of feature j of the tth observation and O the number of the features,

the objective is to identify regime sequence denoted as

{

}

)(),...,2(),1( Tsss

=

Ω

.

Accordingly, a hidden Markov model ),,( BA

π

λ

=

for regime recognition could be

characterized as follows:

1. The initial regime distribution }{ i

π

π

=

, where ])0([ ii sP

ω

π

=

=

, Qi

≤

≤

1.

2. The regime transition probability distribution }{ ij

aA

=

, where

])(|)1([ ijij tstsPa

ω

ω

=

=

+= , Qji

≤

≤

,1 .

3. The observation probability distribution in regime j

ω

,)}({ tbB j

=

, where

])([)( jtj tsRPtb

ω

== , Qj

≤

≤

1, Tt

≤

≤

1.

A Regime Recognition Algorithm for Helicopter Usage Monitoring

393

The estimation of ),,( BA

π

λ

=

is a crucial step if we want to compute the probability of a

system in regime i

ω

based on the estimated HMM model

∧

λ

. Generally, there are two main

stages in regime recognition using HMM. The first stage is the training stage. The purpose

of training stage is to estimate the three parameters of the HMM. The estimation of

),,( BA

π

λ

= is carried out through an iterative learning process of adjusting the model

parameters to maximize the probability )|(

λ

train

RP of producing an observation sequence

1

...

21 Ttrain RRRR =, given model

λ

. Therefore, at the end of training process, we could

obtain an estimated HMM model ),,(

∧∧∧∧ =iii

iBA

πλ

for each regime i

ω

. The second stage is

the testing stage. The purpose of testing is to calculate the probability of generating the

unknown observation sequence, given the estimated model Qi

i≤≤

∧

1 ,

λ

. Given a testing

observation sequence 2

...

21 Ttest RRRR = and a set of estimated models

⎭

⎬

⎫

⎩

⎨

⎧≤≤== ∧∧∧∧

QiBA iii

i1 ),,,(

πλλ

, log-likelihood LL of t

R from the observation sequence

2

...

21 Ttest RRRR = can be computed. Note that, in general, 21 TT ≥.

2.1 The training stage

The training stage is a process to determine model parameters from a set of training data. A

priori values of π, A, and B are assumed and observations are presented iteratively to the

model for estimation of parameters. Likelihood maximization is the basic concept behind

this estimation procedure. In each iteration, the goal is to maximize the expected log-

likelihood, i.e., logarithm of the probability that the model generates the observation

sequence. This iterative process continues until the change in log-likelihood is less than

some threshold and convergence is declared.

In an HMM, the observation probability is assumed to follow a Gaussian distribution.

Although, all of the classical parametric densities are unimodal, many practical problems

involve multimodal densities. In our algorithm, a Gaussian mixture model (GMM) is used.

Let ],...,...,,[ 21 Tk

Xxxxx= be the sample dataset and k

x is a 1

×

O vector. Let M be the

number of mixture components. There is no definition for the number of mixture

components per output distribution and there is no requirement for the number of mixture

components to be the same in each distribution. If 1

=

M

, it is the unimodal density case.

When 1>

M

, a mixture model can be expressed as:

∑

==

M

iiii XhwXp

1

),|()(

σμ

(1)

where )(Xp is the modeled probability distribution function and i

w is the mixture weight

of component i. Clearly, 1...

21

=

+

+

+

M

www , and 10

<

<

i

w for all Mi ,,2,1 "=.

),|( ii

Xh

σ

μ

is a probability distribution parameterized by ii

σ

μ

,, and can be computed

as:

Aerospace Technologies Advancements

394

i

O

d

ii

i

e

Xh

σπ

σμ

2

)2(

),|(

2

2

1

−

= (2)

where 2

i

d can be computed as:

[

]

t

iT

ik

ii

iddddd 222

2

2

1

2,...,,...,,=

)()( 12

iki

t

ikik

d

μσμ

−−= −xx , Tk ,...,2,1

=

(3)

Once w,

μ

and

σ

are determined, )( Xp is defined, i.e., the observation probability

distribution B. So the estimation problem of an HMM model ),,( BA

π

λ

=

is converted to

estimate ),,( wσ,μ,A

π

λ

=, where },...,,{ 21 M

μ

μ

μ

=

μ, },...,,{ 21 M

σ

σ

σ

=

σ,

},...,,{ 21 M

www=w. Here, the GMM parameters of each HMM model can be split into two

groups: the untied parameters that are Gaussian-specific and the tied parameters that are

shared among all the Gaussians of all the HMM states.

Although there is no optimal way of estimating the model parameters so far, local optimal is

feasible using an iterative procedure such as the Baum-Welch method (or equivalently the

expectation-modification method) (Rabiner, 1989; Levinson et al., 1983), or using gradient

techniques (Dempster, 1977). In order to facilitate the computation of learning, three

forward-backward variables are defined in the forward-backward algorithm:

1. The probability of the partial observation sequence, t

RRR ...

21 , and regime i

ω

at time t,

given model

λ

: ]|)(,...[)( 21

λ

ω

α

itt tsRRRPi

=

=

2. The probability of the partial observation sequence from t+1 to the end, given regime

i

ω

at time t and model

λ

: ],)(|...[)( 21

λ

ω

β

iTttt tsRRRPi

=

=

++

3. The probability of being in regime i

ω

at time t, and regime j

ω

at time t+1, given model

λ

and observation sequence t

R, i.e.,

],|)1(,)([),(

λωωξ

tjit RtstsPji =+==

We initialize forward variable as 0)(

0

=

=i

t

α

, for all Qi

≤

≤

1 at time 0

=

t, then in the

forward iteration, we calculate the forward variable )( j

t

α

by the following equations from

t = 1 to t = T:

)()()( 1

1

1+

=

+⎥

⎦

⎤

⎢

⎣

⎡∑

=tj

Q

iijtt Rbaij

αα

, where: 11

−

≤

≤

Tt , Qj

≤

≤

1 (4)

In the backward iteration, we compute the backward variable )(i

t

β

and ),( ji

t

ξ

after

initialization 1)(

=

i

T

β

at time t = T:

∑

==++

Q

jttjijt jRbai

111 )()()(

ββ

, where: 1,...,2,1

−

−

=

TTt , Qi

≤

≤

1 (5)

(

)

)|(

)()(

),( 11

λ

βα

ξ

train

ttjijt

tRP

jRbai

ji ++

=

(

)

∑∑

=

== ++

++

Q

i

Q

jttjijt

ttjijt

jRbai

jRbai

11 11

11

)()()(

)()(

βα

βα

, where: 1≤ i, j ≤ Q (6)

A Regime Recognition Algorithm for Helicopter Usage Monitoring

395

We define )(i

t

γ

as the probability of being in regime i

ω

at time t, given the observation

sequence and the model. Therefore, ∑

=

=

Q

jtt jii

1

),()(

ξγ

. So, ij

a

∧

, the estimated probability of

a regime transition from i

ts

ω

=

−

)1( to j

ts

ω

=)( , can be calculated by taking the ratio

between the expected number of transitions from i

ω

to j

ω

and the total expected number

of any transitions from i

ω

can be computed as:

∑

∑

=−

=

−

=

∧

1

1

1

1

)(

),(

T

tt

T

tt

ij i

ji

a

γ

ξ

, QjQi

≤

≤

≤

≤1,1 (7)

Then the estimated observation probability distribution )( jjj w,σ,μ in regime j

ω

can be

computed as:

∑

∑

=

∧

t

j

t

ttraintj

j

t

j

RE

w

w

μ

][

(8)

'

'][

jj

t

j

t

ttraintraintj

j

t

j

RRE ∧∧∧ −

∑

∑

=μμ

w

w

σ (9)

Note in equations (8)- (9), weights ∑

=−

=1

1)(

T

tt

j

tj

γ

w are posterior probabilities, ][ traintj RE is

the mathematical expectation of observation train

R at time t under regime j

ω

, ˆˆ

,

j

j

μσ are

both untied parameters of GMM, and the covariance type is full.

Similarly, the estimated initial regime distribution can be computed as:

),(

1i

i

γπ

=

∧

Qi

≤

≤

1 (10)

2.2 The testing stage

As mentioned before, testing is a stage to evaluate the likelihood of an unknown observation

belonging to a given regime. Since model ˆ(,, )

i iiii i

A

λπ

=μ,σ,w has been built up in the

training process, it can be used to calculate the log-likelihood LL of a testing observation

test

R based on model ˆi

λ

for regime i

ω

. This log-likelihood can be calculated efficiently

using the forward algorithm.

The probability that model ˆi

λ

produces observation test

R is computed as:

)()|( iRP i

test

αλ

=

∧

By definition, )(i

α

is the probability of generating test

R and ending in regime i

ω

, therefore,

)(])(|[])([)()|( testiitest

i

test RpitsRPitsPiRP

παλ

=====

∧

Qi

≤

≤

1 (11)

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396

In (11), )( testi Rp can be calculated from equation (1), and test

R in regime recognition is the

unknown signal. So, the log-likelihood value is computed as:

)]|([Ln i

testi RPLL

∧

=

λ

(12)

To classify a testing observation into one of Q regimes, train Q HMMs, one per regime, and

then compute the log-likelihood that each model gives to the testing observation, a set of

log-likelihood value },...,,...,,{ 21 Qi LLLLLLLLLL

=

will be obtained.

3. Algorithm validation

In this section, the developed regime recognition algorithm was validated using the Army

UH-60L flight card data.

The Army UH-60L flight card data was collected during a flight test and provided by

Goodrich. The intent of the flight test was to provide flight data which could be used to

refine and revise a preliminary set of regime recognition algorithms. The test pilots

annotated detailed flight cards with actual event times as maneuvers were conducted

during the UH-60L regime recognition flights. The on-board pilots maintained a detailed log

of the maneuvers, flight conditions, and corresponding event times encountered during the

mission flight. A total of 50 regimes were conducted with annotation in the flight test. A

limited amount of non-annotated actual flight data was used prior to the flight test to check

the functionality of the HUMS system. The recorded data was downloaded and processed

after the flight test.

For the Army UH-60L helicopter, a total of 90 preliminary regimes were defined by original

equipment manufacturer (OEM). Data of 22 basic aircraft parameters were collected from

sensors mounted on the aircraft, or sensors added to the Goodrich IMD-HUMS system for

regime recognition. These parameter data is used for the identification of events, control

reversals, and regimes. The parameter monitoring is performed during the whole ground-

air-ground (GAG) cycles, from rotor start to rotor shutdown, and takeoff to landing. Table 1

provides the list of parameters with their description collected from IMD-HUMS system for

regime recognition.

During the validation process, the dataset was randomly divided into two subsets: 70% of

data was used for training and 30% for testing. By using the training data, an HMM model

was built for each regime. Then the testing data was input into the trained HMM models to

compute the log-likelihood values. The maximum log-likelihood value indicates the

identified regime. The confusion matrix generated during the testing is provided in Table 2.

From the results in Table 2, we see that the overall accuracy of the regime recognition is

99%.

Note that in solving regime recognition using HMM, the training set is dependent on the

time sequence of maneuvers. Thus, it is able to find the regime or very complex grouped

maneuvers. On the down side, the training set is really too small to capture all of the various

maneuvers sequences that could be encountered. For example, it likely that from straight

and level, you could go in to a left turn, or a right turn. From a right turn, you can go back

to level, climbing right turn, diving right turn, or a higher angle of back turn. In reality, a

flight card should contain all of the mixed mode maneuvers.

A Regime Recognition Algorithm for Helicopter Usage Monitoring

397

Parameter

No.

Parameter

Name

Parameter

Description

1 WowDly WOW Delayed

2 LngFlg Landing Flag

3 TkOFlg Takeoff Flag

4 RollAt Roll Attitude

5 PtchAt Pitch Attitude

6 RdAlt Radar Altitude

7 YawDt Yaw Rate

8 AltDt Altitude Rate

9 LatDt2 Lateral Acceleration

10 VertAccl Vertical

Acceleration

11 MrRpm RPM of Main Rotor

12 CrNz

Corrected Normal

Acceleration

13 CalSpd Calibrated Airspeed

14 Vh

Airspeed Vh

Fraction

15 TGT

Turbine Gas

Temperature

16 RMS_Nz

RMS Normal

Acceleration

17 TEngTrq Torque 1/Torque 2

18 AOB Angle of Bank

19 CR_Pedal

Control Reversal

Flag

20 Cr_Colct Corrected

Collective Rate

21 Cr_Lat Corrected Latitude

22 Cr_Lon Corrected

Longitude

Table 1. Monitored parameters in IMD-HUMS system

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Regime 2 3 4 5 7 8 9 10 11 12 13 14 15 16

2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

3 1 0.99 1 0.99 1 1 1 1 1 1 1 1 1 1

4 1 1 0.99 1 1 1 1 1 1 1 1 1 1 1

5 0.05 0.66 0.26 0.97 1 1 1 1 1 1 1 1 1 1

7 1 1 1 1 0.99 0.5 1 1 1 1 1 1 1 1

8 1 1 1 1 0.95 1 1 1 1 1 1 1 1 1

9 1 1 1 1 1 1 0.99 1 1 1 1 1 1 1

10 1 1 1 1 1 1 0.97 1 0.98 1 0.93 0.99 1 1

11 1 1 1 1 1 1 1 1 1 0.93 0.91 0.98 1 1

12 1 1 1 1 1 1 1 1 1 0.99 0.87 0.96 1 1

13 1 1 1 1 1 1 1 1 1 0.99 1 1 1 1

14 1 1 1 1 1 1 1 1 1 1 1 0.96 1 1

15 1 1 1 1 1 1 1 1 1 1 1 1 0.98 1

16 1 1 1 1 1 1 1 1 1 1 1 1 0.93 0.9

17 1 1 1 1 1 1 1 1 1 1 1 1 0.98 1

19 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 1 1 1 1 1 1 1 1 1 1 1 1 1 1

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1

22 1 1 1 1 1 1 1 1 1 1 1 1 1 1

23 1 1 1 1 1 1 1 1 1 1 1 1 1 1

24 1 1 1 1 1 1 1 1 1 1 1 1 1 1

25 1 1 1 1 1 1 1 1 1 1 1 1 1 1

26 1 1 1 1 1 1 1 1 1 1 1 1 1 1

27 1 1 1 1 1 1 1 1 1 1 1 1 1 1

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1

36 1 1 1 1 1 1 1 1 1 1 1 1 1 1

37 1 1 1 1 1 1 1 1 1 1 1 1 1 1

40 1 1 1 1 1 1 1 1 1 1 1 1 1 1

41 1 1 1 1 1 1 1 1 1 1 1 1 1 1

42 1 1 1 1 1 1 1 1 1 1 1 1 1 1

43 1 1 1 1 1 1 1 1 1 1 1 1 1 1

44 1 1 1 1 1 1 1 1 1 1 1 1 1 1

45 1 1 1 1 1 1 1 1 1 1 1 1 1 1

46 1 1 1 1 1 1 1 1 1 1 1 1 1 1

48 1 1 1 1 1 1 1 1 1 1 1 1 1 1

49 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 2. The confusion matrix of validation test

A Regime Recognition Algorithm for Helicopter Usage Monitoring

399

Regime 2 3 4 5 7 8 9 10 11 12 13 14 15 16

50 1 1 1 1 1 1 1 1 1 1 1 1 1 1

51 1 1 1 1 1 1 1 1 1 1 1 1 1 1

52 1 1 1 1 1 1 1 1 1 1 1 1 1 1

53 1 1 1 1 1 1 1 1 1 1 1 1 1 1

54 1 1 1 1 1 1 1 1 1 1 1 1 1 1

55 1 1 1 1 1 1 1 1 1 1 1 1 1 1

56 1 1 1 1 1 1 1 1 1 1 1 1 1 1

57 1 1 1 1 1 1 1 1 1 1 1 1 1 1

59 1 1 1 1 1 1 1 1 1 1 1 1 1 1

60 1 1 1 1 1 1 1 1 1 1 1 1 1 1

61 1 1 1 1 1 1 1 1 1 1 1 1 1 1

63 1 1 1 1 1 1 1 1 1 1 1 1 1 1

64 1 1 1 1 1 1 1 1 1 1 1 1 1 1

65 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 2. The confusion matrix of validation test (Continued 1)

Regime 41 42 43 44 45 46 48 49 50 51 52 53 54 55

2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

3 1 1 1 1 1 1 1 1 1 1 1 1 1 1

4 1 1 1 1 1 1 1 1 1 1 1 1 1 1

5 1 1 1 1 1 1 1 1 1 1 1 1 1 1

7 1 1 1 1 1 1 1 1 1 1 1 1 1 1

8 1 1 1 1 1 1 1 1 1 1 1 1 1 1

9 1 1 1 1 1 1 1 1 1 1 1 1 1 1

10 1 1 1 1 1 1 1 1 1 1 1 1 1 1

11 1 1 1 1 1 1 1 1 1 1 1 1 1 1

12 1 1 1 1 1 1 1 1 1 1 1 1 1 1

13 1 1 1 1 1 1 1 1 1 1 1 1 1 1

14 1 1 1 1 1 1 1 1 1 1 1 1 1 1

15 1 1 1 1 1 1 1 1 1 1 1 1 1 1

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1

17 1 1 1 1 1 1 1 1 1 1 1 1 1 1

19 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 1 1 1 1 1 1 1 1 1 1 1 1 1 1

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1

22 1 1 1 1 1 1 1 1 1 1 1 1 1 1

23 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 2. The confusion matrix of validation test (Continued 2)

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Regime 41 42 43 44 45 46 48 49 50 51 52 53 54 55

24 1 1 1 1 1 1 1 1 1 1 1 1 1 1

25 1 1 1 1 1 1 1 1 1 1 1 1 1 1

26 1 1 1 1 1 1 1 1 1 1 1 1 1 1

27 1 1 1 1 1 1 1 1 1 1 1 1 1 1

28 1 1 1 1 1 1 1 1 1 1 1 1 1 1

36 1 1 1 1 1 1 1 1 1 1 1 1 1 1

37 1 1 1 1 1 1 1 1 1 1 1 1 1 1

40 1 1 1 1 1 1 1 1 1 1 1 1 1 1

41 1 1 1 1 1 1 1 1 1 1 1 1 1 1

42 1 0.99 1 1 1 1 1 1 1 1 1 1 1 1

43 1 1 0.99 1 1 1 1 1 1 1 1 1 1 1

44 1 1 1 0.98 1 1 1 1 1 1 1 1 1 1

45 1 1 1 1 0.99 1 1 1 1 1 1 1 1 1

46 1 1 1 1 1 1.00 1 1 1 1 1 1 1 1

48 1 1 1 1 1 1 0.99 1 1 1 1 1 1 1

49 1 1 1 1 1 1 1 1 1 1 1 1 1 1

50 1 1 1 1 1 1 0.97 1 0.97 1 1 1 1 1

51 1 1 1 1 1 1 1 1 1 0.99 1 1 1 1

52 1 1 1 1 1 1 1 1 1 1 0.93 1 1 1

53 1 1 1 1 1 1 1 1 1 1 1 0.96 1 1

54 1 1 1 1 1 1 1 1 1 1 1 1 0.97 1

55 1 1 1 1 1 1 1 1 1 1 1 1 1 0.98

56 1 1 1 1 1 1 1 1 1 1 1 1 1 1

57 1 1 1 1 1 1 1 1 1 1 1 1 1 1

59 1 1 1 1 1 1 1 1 1 1 1 1 1 1

60 1 1 1 1 1 1 1 1 1 1 1 1 1 1

61 1 1 1 1 1 1 1 1 1 1 1 1 1 1

63 1 1 1 1 1 1 1 1 1 1 1 1 1 1

64 1 1 1 1 1 1 1 1 1 1 1 1 1 1

65 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 2. The confusion matrix of validation test (Continued 3)

A Regime Recognition Algorithm for Helicopter Usage Monitoring

401

Regime 56 57 59 60 61 63 64 65

2 1 1 1 1 1 1 1 1 1

3 1 1 1 1 1 1 1 1 1

4 1 1 1 1 1 1 1 1 1

5 1 1 1 1 1 1 1 1 1.00

7 1 1 1 1 1 1 1 1 1

8 1 1 1 1 1 1 1 1 1

9 1 1 1 1 1 1 1 1 1

10 1 1 1 1 1 1 1 1 1.00

11 1 1 1 1 1 1 1 1 1.00

12 1 1 1 1 1 1 1 1 1.00

13 1 1 1 1 1 1 1 1 1

14 1 1 1 1 1 1 1 1 1.00

15 1 1 1 1 1 1 1 1 1

16 1 1 1 1 1 1 1 1 1.00

17 1 1 1 1 1 1 1 1 1

19 1 1 1 1 1 1 1 1 1

20 1 1 1 1 1 1 1 1 1

21 1 1 1 1 1 1 1 1 1

22 1 1 1 1 1 1 1 1 1

23 1 1 1 1 1 1 1 1 1

24 1 1 1 1 1 1 1 1 1

25 1 1 1 1 1 1 1 1 1

26 1 1 1 1 1 1 1 1 1

27 1 1 1 1 1 1 1 1 1.00

28 1 1 1 1 1 1 1 1 1.00

36 1 1 1 1 1 1 1 1 1

37 1 1 1 1 1 1 1 1 1

40 1 1 1 1 1 1 1 1 1

41 1 1 1 1 1 1 1 1 1

42 1 1 1 1 1 1 1 1 1

43 1 1 1 1 1 1 1 1 1

44 1 1 1 1 1 1 1 1 1

45 1 1 1 1 1 1 1 1 1

46 1 1 1 1 1 1 1 1 1

48 1 1 1 1 1 1 1 1 1

49 1 1 1 1 1 1 1 1 1

50 1 1 1 1 1 1 1 1 1.00

Table 2. The confusion matrix of validation test (Continued 4)

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Regime 56 57 59 60 61 63 64 65

51 1 1 1 1 1 1 1 1 1

52 1 1 1 1 1 1 1 1 1.00

53 1 1 1 1 1 1 1 1 1.00

54 1 1 1 1 1 1 1 1 1.00

55 1 1 1 1 1 1 1 1 1

56 0.97 1 1 1 1 1 1 1 1.00

57 1 0.98 1 1 1 1 1 1 1

59 1 1 1.00 1 1 1 1 1 1

60 1 1 1 0.99 1 1 1 1 1

61 1 1 1 1 0.99 1 1 1 1

63 1 1 1 1 1 0.99 1 1 1

64 1 1 1 1 1 1 0.98 1 1

65 1 1 1 1 1 1 1 0.98 1

Overall Accuracy 0.99

Table 2. The confusion matrix of validation test (Continued 5)

In addition to the validation test, the performance of the HMM based regime recognition

algorithm was compared with a number of data mining methods. These data mining

methods included: neural network, discriminant analysis, K-nearest neighbor, regression

tree, and naïve bayes. The results of the performance comparison test are provided in Table

3. In this test, to be consistent, data with the same regimes were used for all the data mining

methods. From Table 3, we can see that the HMM based regime recognition algorithm

outperforms all other data mining methods.

Note that in Table 3, the names of methods are defined as: HMM = hidden Markov model;

NN = neural network (back propagation); DA = discriminant analysis; KNN = k-nearest

neighbor; RT = regression tree; NB = naïve bayes.

4. Conclusion

In this paper, a data mining approach is adopted for regime recognition. In particular, a

regime recognition algorithm developed based on HMM was presented. The HMM based

regime recognition involves two major stages: model learning process and model testing

process. The learning process could be implemented off-board. In this process, Gaussian

mixture model (GMM) was used instead of unimodal density of Gaussian distribution in

HMM. Once the learning process is completed, new incoming unknown signal could be

tested and recognized on-board. The developed algorithm was validated using the flight

card data of an Army UH-60L helicopter. The performance of this regime recognition

algorithm was also compared with other data mining approaches using the same dataset.

Using the flight card information and regime definitions, a dataset of about 56,000 data

points labeled with 50 regimes recorded in the flight card were mapped to the health and

usage monitoring parameters. The validation and performance comparison results have

showed that the hidden Markov model based regime recognition algorithm was able to

accurately recognize the regimes recorded in the flight card data and outperformed other

data mining methods.

A Regime Recognition Algorithm for Helicopter Usage Monitoring

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Regime No. HMM NN DA KNN RT NB

2 0.01% 32.00% 16.00% 0.00% 12.00% 46.00%

3 0.10% 17.65% 23.53% 41.18% 100.00% 94.12%

4 0.06% 0.00% 84.62% 69.23% 100.00% 84.62%

5 10.30% 3.03% 0.00% 0.00% 39.39% 75.76%

7 2.51% 10.20% 5.10% 10.20% 3.06% 0.00%

8 0.26% 10.00% 6.67% 43.33% 0.00% 53.33%

9 0.04% 18.75% 62.50% 56.25% 100.00% 100.00%

10 0.66% 50.00% 50.00% 35.71% 100.00% 100.00%

11 1.02% 0.00% 26.67% 20.00% 13.33% 66.67%

12 0.92% 0.00% 0.00% 0.00% 100.00% 88.89%

13 0.05% 0.00% 0.00% 3.45% 100.00% 68.97%

14 0.21% 13.33% 6.67% 46.67% 100.00% 80.00%

15 0.09% 33.33% 33.33% 66.67% 100.00% 50.00%

16 0.88% 40.00% 100.00% 100.00% 100.00% 80.00%

17 0.12% 100.00% 100.00% 100.00% 100.00% 100.00%

19 0.11% 10.00% 0.00% 50.00% 100.00% 80.00%

20 0.09% 0.00% 0.00% 0.00% 0.00% 70.83%

21 0.09% 9.09% 36.36% 36.36% 100.00% 100.00%

22 0.01% 21.43% 14.29% 50.00% 100.00% 100.00%

23 0.07% 0.00% 9.09% 9.09% 100.00% 90.91%

Overall 0.88% 12.79% 15.58% 21.16% 47.44% 57.44%

Table 3. Results of performance comparison of various data mining methods (regime

recognition error rate)

5. References

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Le, D. (2006). Federal Aviation Administration (FAA) Health and Usage Monitoring System

R&D Initiatives. http://aar400.tc.faa.gov/Programs/agingaircraft/rotorcraft/

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Levinson, S. E., Rabiner, L. R., and Sondhi, M. M. (1983). An Introduction to the Application

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Rabiner, L. R. (1989). A Tutorial on Hidden Markov Models and Selected Applications in

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Teal, R. S., Evernham, J. T., Larchuk, T. J., Miller, D. G., Marquith, D. E., White, F., and

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