A Regime Recognition Algorithm for Helicopter Usage Monitoring

Abstract

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.

Full text

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

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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.

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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:

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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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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.

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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
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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.

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