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Accepted Manuscript

Title: Incipient fault detection in induction machinestator-winding using a fuzzy-Bayesian change point detectionapproach

Authors: Marcos F.S.V. D’Angelo, Reinaldo M. Palhares,Ricardo H.C. Takahashi, Rosangela H. Loschi, Lane M.R.Baccarini, Walmir M. Caminhas

PII: S1568-4946(09)00221-XDOI: doi:10.1016/j.asoc.2009.11.008Reference: ASOC 723

To appear in: Applied Soft Computing

Received date: 20-7-2008Revised date: 27-5-2009Accepted date: 15-11-2009

Please cite this article as: M.F.S.V. D’Angelo, R.M. Palhares, R.H.C. Takahashi, R.H.Loschi, L.M.R. Baccarini, W.M. Caminhas, Incipient fault detection in inductionmachine stator-winding using a fuzzy-Bayesian change point detection approach,Applied Soft Computing Journal (2008), doi:10.1016/j.asoc.2009.11.008

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

dx.doi.org/doi:10.1016/j.asoc.2009.11.008

dx.doi.org/10.1016/j.asoc.2009.11.008

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Incipient fault detection in induction machine

stator-winding using a fuzzy-Bayesian change

point detection approach

Marcos F. S. V. D’Angelo a, Reinaldo M. Palhares b,

Ricardo H. C. Takahashi c,∗, Rosangela H. Loschi d,

Lane M. R. Baccarini e, Walmir M. Caminhas f

aDepartment of Computer Science - UNIMONTES,

Av. Rui Braga, sn, Vila Mauriceia, 39401-089, Montes Claros - MG - Brasil

bDepartment of Electronics Engineering, Universidade Federal de Minas Gerais,

Av. Antonio Carlos 6627 - 31270-901, Belo Horizonte - MG - Brazil

cDepartment of Mathematics, Universidade Federal de Minas Gerais

dDepartment of Statistics, Universidade Federal de Minas Gerais

eDepartment of Electrical Engineering, Universidade Federal de Sao Joao del-Rei,

Praca Frei Orlando, 170 - Centro - 36307-352, Sao Joao del-Rei - MG - Brazil

fDepartment of Electrical Engineering, Universidade Federal de Minas Gerais

Abstract

In this paper the incipient fault detection problem in induction machine stator-

winding is considered. The problem is solved using a new technique of change point

detection in time series, based on a two-step formulation. The first step consists of a

fuzzy clustering to transform the initial data, with arbitrary distribution, into a new

one that can be approximated by a beta distribution. The fuzzy cluster centers are

Preprint submitted to Applied Soft Computing 27 May 2009

* Manuscript

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determined by using a Kohonen neural network. The second step consists in using

the Metropolis-Hastings algorithm for performing the change point detection in the

transformed time series generated by the first step with that known distribution.

The incipient faults are detected as long as they characterize change points in such

transformed time series. The main contribution of the proposed approach is the

enhanced resilience of the new failure detection procedure against false alarms,

combined with a good sensitivity that allows the detection of rather small fault

signals. Simulation and practical results are presented to illustrate the proposed

methodology.

Key words: Incipient fault detection, induction machine stator-winding, fuzzy

clusters, Bayesian analysis, Metropolis-Hastings algorithm

1 Introduction

Induction motors are the most important electric machinery for different in-

dustrial applications. Faults in the stator windings of three-phase induction

motor represent a significant part of the failures that arise during the motor

lifetime. When these motors are fed through an inverter, the situation tends to

become even worse due to the voltage stresses imposed by the fast switching

of the inverter [1]. From a number of surveys, it can be realized that, for the

induction motors, stator winding failures account for approximately 30% of

all failures [2] [3].

The stator winding of induction machine is subject to stress induced by a

variety of factors, which include thermal overload, mechanical vibrations and

∗ Corresponding author. email:[email protected].

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voltage spikes. Deterioration of winding insulation usually begins as an inter-

turn short circuit in one of the stator coils. The increased heating due to this

short circuit will eventually cause turn to turn and turn to ground faults which

finally lead the stator to break down [4].

Although there is no experimental data that indicate the time delay between

inter-turn and ground insulation failure, it is believed that the transition be-

tween the two states is not instantaneous. Therefore, early detection of inter

turn short circuit during motor operation can be of great significance as it

would eliminate subsequent damage to adjacent coils and the stator core, re-

ducing repairing cost and motor outage time [5] [6].

However, early stages of deterioration are difficult to detect. In general, most

of the previous references present approaches for dealing with abrupt faults

in the stator winding, which are easier to be detected than incipient faults. In

spite of these difficulties, a great deal of progress has been made on induction

machine stator-winding incipient fault detection. Methods that use voltage

and current measurements offer several advantages over test procedures that

require machine to be taken off line or techniques that require special sensors

to be mounted on the motor [7]. Other methods, in the context of abrupt

fault detection related to the stator-winding, can be found in [8], [9], [10], [11],

[12]. Other types of faults in induction machines, such as dynamic eccentricity,

unbalanced rotors, bearing defects and broken rotor bars have been tackled

via other approaches of fault detection that are specific for each case (see [13]

for details and further references).

In this paper, a new two-step formulation for incipient fault detection in the

stator windings of induction machines is proposed. The proposed methodology

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deals with the fault detection problem as a change point detection problem

over the time series of the rms (root mean square) values of stator currents.

The change point detection algorithm is based on a fuzzy set technique and

a Markov Chain Monte Carlo (MCMC ) method. The proposed method, dif-

ferently from former techniques, does not require any prior knowledge about

statistical properties of the time series before the application of the MCMC

procedure. This is made possible by the first step, in which a fuzzy set tech-

nique is applied in order to cluster and to transform the initial time series

(about which there is no a priori knowledge of its distribution) into a time

series whose probability distribution can be approximated by a beta distribu-

tion. Specifically in the first step, a Kohonen network is used to find centers of

the clusters, and in the sequel the fuzzy membership degree is computed for

each point of the initial time series, generating a time series with beta distribu-

tion. This new time series, generated in the first step, allows to systematically

apply the same strategy to detect the change point via a MCMC method with

a fixed reference distribution: the beta distribution. The Metropolis-Hastings

algorithm [14] is used to perform the change point detection. The main idea in

this paper is to apply the change point detection strategy in a data sequence

that carries information of relevant physical variables of the dynamic system.

A change point detection gives support to the hypothesis of fault occurrence.

The research on the theme of change point detection in time series has been

performed in the context of several applications, such as financial series [15],

ecological series [16], hydrometeorological time series [17], etc. The main tech-

niques presented in the literature are statistical tests and Bayesian analysis. In

the change point detection problem the standard statistical test is the CUSUM

(Cumulative Sum). The CUSUM test proposed by [18] is widely used in the

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change point detection, and applications of this method can be seen in [19],

[20], and [21], as well as its modifications and extensions. However other type

of statistical approaches can be considered as the two step presented in [22]

which is based on learning the statistical properties of the process. In the con-

text of Bayesian analysis different MCMC methods may be used as, for exam-

ple, the Metropolis-Hastings, Gibbs sampling (see [14] and references therein),

and reversible jump MCMC (see [23] and references therein). In the Bayesian

analysis context, the product partition model (PPM) proposed by [24] may be

used to model uncertainties that exist in a sequence of random quantities. The

PPM has also been applied to the identification of multiple change points in

the mean of data modeled by Gaussian distribution, as presented in [25] and

[26]. In [27] the PPM has been extended to identify multiple change points

both in the mean and variance of Gaussian-distribution data. However, all

those previous approaches necessarily demand some type of prior knowledge

about the time series, namely the type of distribution that models the data

set. An important contribution of the approach proposed in this paper is the

possibility of dealing with data with unknown probability distributions.

The main contribution of the proposed approach, however, is related to the

enhanced resilience of the new failure detection procedure against false alarms,

combined with a good sensitivity that allows the detection of rather small fault

signals. This property comes from the adopted PPM model, which assumes

explicitly that just one change can occur within the time window under anal-

ysis, performing a search for the most provable change point, and calculating

the probability of such point being effectively a change point. The behavior of

the resulting failure detection system contrasts with the outcome of other ap-

proaches, which search for any change point, assuming implicitly that several

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change points can occur: such approaches lead either to too sensitive systems

(which cause false alarms) or to too insensitive systems (which will not detect

several faults). Simulation and experimental results illustrate such comparison

of the proposed method with other approaches.

The paper is organized as follows. Section II presents and analyzes the in-

duction machine simulation considering the case of incipient fault on stator-

winding. Section III describes the methodology used for change point detec-

tion. Section IV shows the simulations and experimental results for on–line

incipient fault detection in induction machine stator-winding. Finally, section

V presents the concluding remarks.

2 Induction machine modeling and simulation with turn-to-turn

short-circuit in stator winding

Many studies have shown that a large proportion of induction machine faults

are related to the stator-winding [8], [9], [10], [11]. The induction machine

stator-winding is subject to stress due to many factors, which include thermal

overload, mechanical vibration and peak voltage caused by a speed controller.

The deterioration of insulation usually begins as a short-circuit fault of the

stator-winding. This section describes the model that is employed here for

the simulation of inter-turn short-circuits in the stator windings of induction

machines.

This work employs a generic model for the machine [12], valid for any dq

(direct and quadrature) axis speed obtained by the Park’s transformation [28].

Representing the currents, voltages and electromagnetic flows by i, v and λ,

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the resistance, leakage and mutual inductance by r, Ll and Lm, the phases a,

b and c by indexes a, b and c, the windings of the stator and rotor by indexes

s and r, the stator and rotor voltages equations become:

[vs] = [rs][is] +d[λs]

dt(1)

[vr] = [rr][ir] +d[λr]

dt(2)

where

[vs] = [ vas1 vas2 vbs vcs]T

[vr] = [ var vbr vcr]T

[is] = [ ias ias − if ibs ics]T

[ir] = [ iar ibr icr]T

[λs] = [ λas1 λas2 λbs λcs]T

[λr] = [ λar λbr λcr]T

In the above, the index as2 represents the shorted turns and if is the current

in the short-circuit. Figure 1 represents the schematic diagram of a motor with

an inter-turn short-circuit.

In the model proposed in reference [12], the stator windings voltages are given

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Fig. 1. Representation of stator windings of a motor with inter-turn short circuit.

by:

Vds +2

3μrsifcosθ = rsids +

dλds

dt+ ωλqs (3)

Vqs +2

3μrsifsinθ = rsiqs +

dλqs

dt+ ωλds (4)

V0s +1

3μrsif = rsi0s +

dλ0s

dt(5)

The rotor circuit equations are the same as for traditional symmetrical model.

The stator and the rotor electromagnetic flows of stator in dq axis, are given

by:

λds = Lsids + Lmidr − 2

3μLsifcosθ (6)

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λqs = Lsiqs + Lmiqr − 2

3μLsifsinθ (7)

λ0s = Llsi0s +μ

3Llsifsinθ (8)

λdr = Lridr + Lmids − 2

3μLmifcosθ (9)

λqr = Lriqr + Lmiqs − 2

3μLmifsinθ (10)

The voltage and the induced electromagnetic flow in the short-circuit turns

are given by:

vas2 = μrs(idscosθ + iqssinθ − if ) +dλas2

dt(11)

λas2 = μLls(iqssinθ + idscosθ − if ) + μLm(iqssinθ +

+idscosθ + iqrsinθ + idrcosθ − 2

3μif) (12)

The electromagnetic torque is given by:

T =3

2

p

2Lm(iqsidr − idsiqr) − p

2μLmif iqr (13)

The induction machine stator current simulation results for a fault in which

5% of turns in the phase a become in short-circuit after the time 0.72s are

shown in the Figures 2–4. The root mean square (rms) current values are

illustrated in Figures 5–7. Notice that when a short-circuit occurs in phase

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a, the increase in the current of phase a is greater than that of phases b and

c. The fault detection methodology proposed here is based on finding such

events of non-balanced changes in the current rms values.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−30

−20

−10

0

10

20

30

40

Fault

time (s)

i as

Fig. 2. Current of phase a.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−30

−20

−10

0

10

20

30

40

Fault

time (s)

i bs

Fig. 3. Current of phase b.

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−40

−30

−20

−10

0

10

20

30

Fault

time (s)

i cs

Fig. 4. Current of phase c.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24

4.5

5

5.5

6

6.5

time (s)

i as

Fig. 5. rms current of phase a.

3 Change point detection methodology

In this section, the proposed two-step formulation to the change point detec-

tion problem is detailed. Consider a time series signal in which a change point

is to be detected. The first step consists in transforming the given time series

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0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24

4.5

5

5.5

6

6.5

time (s)

i bs

Fig. 6. rms current of phase b.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24

4.5

5

5.5

6

6.5

time (s)

i cs

Fig. 7. rms current of phase c.

into another one with beta distribution using a fuzzy set technique [29]. In

order to illustrate how this is done, the following time series is used:

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y(t) =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

p1 + 0.1 ∗ ε(t) − 0.1 ∗ ε(t − 1), if t � m,

p2 + 0.1 ∗ ε(t) − 0.1 ∗ ε(t − 1), if t > m

(14)

where p1 is the first operation point (the mean value before the change point),

p2 is the second operation point (the mean value after the change point), ε(t)

is a noise signal with π(·) distribution and m is the change point. The figure

8 shows the time series y(t) with fixed p1 = 1, and p2 = 2, ε(t) ∼ U(0, 1)

(uniform distribution in the interval [0, 1]), m = 30 and 60 samples.

0 10 20 30 40 50 600.8

1

1.2

1.4

1.6

1.8

2

2.2

Samples

y(t

)

Fig. 8. Time series with fixed p1 = 1, and p2 = 2, ε(t) ∼ U(0, 1), m = 30 and 60

samples.

Definition (Fuzzy Cluster Centers) Let y(t) be a time series, and consider

a positive integer k. Define the set

C = {Ci | min{y(t)} ≤ Ci ≤ max{y(t)}, i = 1, 2, . . . , k}

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such that it solves the minimization problem:

mink∑

i=1

∑y(t)∈Ci

‖ y(t) − Ci ‖2 . (15)

The set C = {Ci, i = 1, 2, . . . , k} which minimizes (15) is called the cluster

center set for the time series y(t). The fuzzy membership degree (or fuzzy

membership function value) of the fuzzy relation y(t) ∈ Ci (which means y(t)

belongs to each cluster Ci) is given by:

μi(t) �⎡⎣ k∑

j=1

‖y(t) − Ci‖2

‖y(t) − Cj‖2

⎤⎦−1

(16)

�

Notice that, given a set C of cluster centers, it is an easy task to measure the

distance of each point in the time series y(t) to each center Ci. The problem

of finding the centers can be solved, for instance, via K-means [30], C-means

[31], and Kohonen network [32]. In this paper, the Kohonen network technique

is used.

The proposed fuzzy clustering to transform a given time series into a new one

is described below:

(1) Input the time series y(t);

(2) Find Ci, i = 1, 2, the elements of the cluster center set for y(t) using the

Kohonen network (as illustrated in figure 9 considering, for example, the

time series in (14)).

(3) Compute the fuzzy membership degree given in (16), for each sample

of the time series, y(t), with respect to each center Ci (as illustrated in

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figure 10 considering, for example, the time series in (14)).

0 10 20 30 40 50 600.8

1

1.2

1.4

1.6

1.8

2

2.2

Samples

y(t

)

Fig. 9. Time serie centers: ‘×’ denotes both the min{y(t)} and max{y(t)} and ‘◦’denotes the centers found using the Kohonen network.

0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

1

Samples

μi(

t)

Fig. 10. Membership function, μ1(t)(· · · ) and μ2(t)(− − −).

Notice that, since the idea is to find just one change point, only two centers

are to be found. The function μ1(t) defines a new time series, in which the

change point is to be detected.

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Further, it is clear that the distributions of μ1(t), according to (16), are con-

fined in the interval [0, 1]:

• if y(t) −→ C1 then μ1(t) −→ 1−

• if y(t) −→ C2 then μ1(t) −→ 0+

• if C1 −→ C2 then μ1(t) −→ 12

• if y(t) ⊂ [C1, C2] then μ1(t) ⊂ [0, 1]

and using the Kullback-Leibler divergence [33] one may conclude that the

distributions of μ1(t) shape a family of beta distribution with different input

parameters: for μ1(t), t ≤ m, one obtains a beta(a, b) distribution, or beta(c, d)

distribution, if t > m. For example, in the case in which there is a change point

in the time series, the parameter a is greater than the parameter b in the beta

distribution of μ1(t) if t ≤ m and the parameter c is smaller than the parameter

d in the beta distribution of μ1(t) if t > m. Figure 11 presents an illustration

of the distributions of μ1(t) for the time series (14). This empirical test has

been performed for several time series with different probability distributions,

always leading to the same family of beta distributions after the clustering

technique.

Since the clustering technique maps the original time series, with arbitrary

probability distribution, into a new time series μ1(t) with a beta probabil-

ity distribution function, this fixed statistical model can be assumed in the

Bayesian formulation to detect the change point in the transformed time se-

ries (second step). In this paper, the Metropolis-Hastings algorithm is used,

since it is a powerful and simple strategy. The goal of the Metropolis-Hastings

algorithm [14] is to construct a Markov chain that has a specified equilibrium

distribution π.

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0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 10

5

10

15

a

b

Fig. 11. Distributions of: (a) μ1(t), t ≤ m and; (b) μ1(t), t > m.

Define a Markov chain as follows. If Xi = xi, then draw a candidate value Y

from a distribution with density fY |X(y) = q(xi, y). The q function is known as

the transition kernel of the chain. It is a function of two variables, the current

state of the chain xi and the candidate value y. For each xi, the function

q(xi, y) is a density which is a function of y.

The candidate value Y is then accepted or rejected. The probability of accep-

tance is

α(x, y) = min

(1,

π(y)

π(xi)

q(y, xi)

q(xi, y)

)(17)

If the candidate value is accepted, then set Xi+1 = Y , otherwise set Xi+1 = Xi.

Thus, if the candidate value is rejected, the Markov chain has a repeat in the

sequence. It is possible to show that under general conditions the sequence

X0, X1, X2, ... is a Markov chain with equilibrium distribution π.

In practical terms, the Metropolis-Hastings algorithm can be specified by the

following steps:

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Metropolis-Hastings Algorithm

(1) Choose a starting value x0, the number of iterations, R, and set the

iteration counter r = 0;

(2) Generate a candidate value y using the reference distribution given by

q(xr, y);

(3) Calculate the acceptance probability in (17) and generate u ∼ U(0, 1);

(4) Compute the new value for the current state:

xt+1 =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

y, if α(x, y) ≥ u,

xt, otherwise

(5) If r < R, return to step 2. Otherwise stop.

Notice that, as discussed previously, the clustering technique generates a trans-

formed time series with the following distribution:

y(t) ∼ beta(a, b), for t = 1, ..., m

y(t) ∼ beta(c, d), for t = m + 1, ..., n

The parameters to be estimated for the Metropolis-Hastings algorithm are a,

b, c, d and the change point m. In this type of algorithm, the choice of non-

informative priors is performed usually from “flat” distributions, for example:

a ∼ gamma(0.1, 0.1)

b ∼ gamma(0.1, 0.1)

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c ∼ gamma(0.1, 0.1)

d ∼ gamma(0.1, 0.1)

m ∼ U{1, 2, ..., n}, with p(m) =1

n

These distributions, with parameters 0.1, have been chosen for the purpose of

spreading the whole parametric space.

The reference distribution, used in Step (2) of the Metropolis-Hastings algo-

rithm to generate the candidate value to the change point m, is computed

as:

q(m | a, b, c, d)∝ q(m, a, b, c, d) (18)

∼m∏

i=1

G(a + b)

G(a)G(b)ya−1

i (1 − yi)b−1

n∏i=m+1

G(c + d)

G(c)G(d)yc−1

i (1 − yi)d−1

where a, b, c and d are generated by priors distribution and G(k) ∼ gamma(k, 1).

The final analysis is performed as: the change point, m, is obtained by checking

where the maximum of q(m | a, b, c, d) occurs, with the exception of the border

points of the distribution (if the maximum occurs on such points, then there

is no change point). Figure 12 shows the result when applying the proposed

methodology for p1 = 1, p2 = 2, e(t) ∼ U(0, 1), and m = 30. The function q

can be interpreted as a probability of change in the time series at the instant

m.

This methodology is applied, in the next section, in the problem of incipient

fault detection problem in induction machine stator winding – which is stated

as a change point detection problem.

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0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Samples

q(m

|a,b

,c,d

)

Fig. 12. Result of the methodology proposed for p1 = 1, p2 = 2, e(t) ∼ U(0, 1), and

m = 30.

4 Implementation and results of the proposed methodology

In this section, the implementation details are described, and both simulation

results and experimental results are presented. A block diagram of the system

can be seen in Figure 13. The system monitors the instantaneous values of

the motor currents ias, ibs, ics and the rotor speed ω. Firstly, the analogical

measurements are converted in digital data through an A/D converter. Then,

the root mean square (rms) value of each phase current is calculated over a

period of time.

Let i denote the rms value associated to the current whose instantaneous

value is i. In the case of the induction machine with delta connection, the

fault detection is performed by the following rule set, and considering the

Figure 1:

IF m(ias) ∼= m(ibs) > m(ics) THEN fault in phase b;

IF m(ias) ∼= m(ics) > m(ibs) THEN fault in phase a;

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Fig. 13. Block diagram of the proposed methodology

IF m(ibs) ∼= m(ics) > m(ias) THEN fault in phase c;

IF m(ibs) ∼= m(ics) ∼= m(ias) THEN fault free.

In the case of the induction machine with star connection, the rule set for

fault detection should be adapted as follows:

IF m(ias) > m(ibs) ∼= m(ics) THEN fault in phase a;

IF m(ibs) > m(ias) ∼= m(ics) THEN fault in phase b;

IF m(ics) > m(ias) ∼= m(ibs) THEN fault in phase c;

IF m(ibs) ∼= m(ics) ∼= m(ias) THEN fault free.

where m(ν) indicates the probability of change in the time series of variable ν.

This probability of change is given by the change point detection algorithm, as

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described in the former section. It should be noticed that the rms values of the

stator currents in an induction motor change their values several times within

a normal operation cycle. Under normal conditions, these changes should be

balanced, i.e., similar changes should occur in the three phases. The idea

behind these rule sets is to detect changes in the rms values of the currents

that are not balanced between the phases: these changes are related to faults.

4.1 Simulation Results

The simulation results of incipient fault detection in the stator winding of

an induction machine with star connection are shown in Figures 14–19, con-

sidering the rule set for star connection and 0.1% of turns in short-circuit in

phase a. These results have been obtained by simulation of the induction ma-

chine using the model described in Section 2 and the change point detection

methodology presented in Section 3.

As can be seen from Figures 15, 17 and 19, the fault detection has been per-

formed in the correct time and in the correct phase, with the system indicating

that the probability of change in the current of phase a is about 60%, while

the probability of change in the currents of phases b and c are below 10%,

with a clear unbalancing of the changes between the phases. The system has

also correctly indicated that the fault has occurred in phase a. For the case of

fault-free and noise-free simulation, the probability of change in each current

phase results null when using the proposed approach.

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0 50 100 150 200 2504.16

4.165

4.17

4.175

4.18

4.185

4.19

4.195

4.2

4.205

4.21Ia

Fig. 14. rms current of phase a: ias with 0.1% of turns in short-circuit in phase a

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 15. Probability of indication of change point detection in current ias

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0 50 100 150 200 250

4.086

4.088

4.09

4.092

4.094

4.096

4.098

4.1

4.102Ib

Fig. 16. rms current of phase b: ibs with 0.1% of turns in short-circuit in phase a

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Fig. 17. Probability of indication of change detection in current ibs

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0 50 100 150 200 250

4.19

4.195

4.2

4.205

4.21

4.215Ic

Fig. 18. rms current of phase c: ics with 0.1% of turns in short-circuit in phase a

0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Fig. 19. Probability of indication of change detection in current ics

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4.2 Practical Results

Figure 20 illustrates the experimental setup. It consists of a 3HP , 220/380V ,

60Hz, 4 poles, squirrel-cage induction machine.

Phase windings are composed by two phase groups with three coils in each

one. Each coil is composed of 33 turns. Figure 21 shows details of the connec-

tion diagram of the stator windings. The induction motor is specially wound

with tapping that allows a turn-to-turn fault insertion in one of the phases

(Figure 22).

Fig. 20. Experimental test bed

A mechanical load is provided by a separate dc generator feeding a variable

resistor. In order to allow tests to be performed at different load levels, the dc

excitation current and load resistor are both controllable. The data acquisition

system consists of:

• three hall effect current sensors (LEM, LTA50P);

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Fig. 21. Connection diagram of stator winding

Fig. 22. Photograph showing the stator terminals

• three hall effect voltage sensors (LEM, LV 100-300);

• analog input board (National Instruments PCI 6013).

In all experimental tests, the stator windings of the motor have delta con-

nection. When short-circuits were introduced, a shorting resistor was used in

order to limit the value of the short-circuit current, thus protecting the motor

windings from complete failure.

The Figures 23 – 25 show the instantaneous currents of phases a (ias), b (ibs)

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and c (ics) with ∼ 1.5% of turns in short-circuit in phase b. The short-circuit

has been established at the time t ∼= 2s. Figures 26 – 28 show the rms value

currents of phases a (ias), b (ibs) and c (ics), for the same experiment.

The results of incipient fault detection in induction machine stator winding are

shown in Figures 29–31, considering the rule set for delta connection and 1.5%

of turns in short-circuit in phase b. To illustrate a change point detection using

the proposed approach, the fault-free and incipient fault cases are considered.

For the fault-free case (Figures 29a, 30a and 31a) Figures 29c, 30c and 31c

show that the probability of change in each current phase is null when using

the proposed approach. For the incipient fault case (Figures 29b, 30b and

31b), the detection of the fault has been performed in the correct time instant

and in the correct phase, as shown in Figures 29d, 30d and 31d. In this case,

the system indicates that the probability of change in the currents of phases

a and b is approximately 10%, while the probability of change in the current

of phase c is null, with a clear unbalancing of the changes between the phases.

These informations lead the system to indicate (correctly) that the fault has

occurred in phase b.

For comparison purposes, two other methods have been considered:

• The classical CUSUM statistical method [19].

• The direct use of a fuzzy clustering technique as the one presented in Sec-

tion 3.

To illustrate how a change point detection using the classical CUSUM works,

the fault-free and incipient fault cases are considered. For the fault-free case,

Figures 32 c, 33 c and 34 c show that the CUSUM generates several “false

alarm” indications. For the case of incipient fault with 1.5% of turns in

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0 0.5 1 1.5 2 2.5 3 3.5−15

−10

−5

0

5

10

15

i as

t(s)

Fig. 23. Instantaneous current of phase a: ias with ∼ 1.5% of turns in short-circuit

in phase b

0 0.5 1 1.5 2 2.5 3 3.5−15

−10

−5

0

5

10

15

i bs

t(s)

Fig. 24. Instantaneous current of phase b: ibs with ∼ 1.5% of turns in short-circuit

in phase b

short-circuit in phase b, the CUSUM method detects nearly the same change

point that has been indicated by the proposed methodology, as shown in Fig-

ures 32 d, 33 d and 34 d.

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0 0.5 1 1.5 2 2.5 3 3.5−15

−10

−5

0

5

10

15

i cs

t(s)

Fig. 25. Instantaneous current of phase c: ics with ∼ 1.5% of turns in short-circuit

in phase b

0 0.5 1 1.5 2 2.5 3 3.58.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55

8.6

8.65

i as

t(s)

Fig. 26. rms current of phase a: ias with ∼ 1.5% of turns in short-circuit in phase b

A possible approach for detecting faults could be the direct examination of

the fuzzy set membership transformed variable from step 1 of the proposed

algorithm to indicate the position of the change-point. This approach has been

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0 0.5 1 1.5 2 2.5 3 3.57.7

7.8

7.9

8

8.1

8.2

8.3

8.4

i bs

t(s)

Fig. 27. rms current of phase b: ibs with ∼ 1.5% of turns in short-circuit in phase b

0 0.5 1 1.5 2 2.5 3 3.57.7

7.75

7.8

7.85

7.9

7.95

8

i cs

t(s)

Fig. 28. rms current of phase c: ics with ∼ 1.5% of turns in short-circuit in phase b

evaluated, with the results shown in Figures 35, 36 and 37, where the fault-free

case is presented. It should be noticed that the membership functions indicate

several false alarms, as in the case of the CUSUM.

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ipt0 0.5 1 1.5 2

8.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55a

t(s)

i as

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8c

t(s)

q(m

|a,b

,c,d

)

0 1 2 3 48.2

8.3

8.4

8.5

8.6

8.7b

t(s)

i as

0 1 2 3 40

0.02

0.04

0.06

0.08

0.1

0.12d

t(s)

q(m

|a,b

,c,d

)

Fig. 29. a - ias in free-fault case; b - ias with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ias for fault-free case; d - Change detection

in current ias with ∼ 1.5% of turns in short-circuit in phase b

It should be also noticed that the same membership function value signal,

combined with the Metropolis-Hastings algorithm in the proposed new algo-

rithm, prevents the detection of false alarms. This enhanced behavior is due

to the explicit quantification of the “probability of change” that is performed

by the Metropolis-Hastings algorithm, with the explicit assumption that just

one change can occur. This endows the proposed algorithm with the ability

to distinguish effective changes in a signal from mere stochastic fluctuations

in the raw fuzzy membership signal.

Other methods could be considered for the same fault detection problem, such

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ipt0 0.5 1 1.5 2

7.7

7.8

7.9

8

8.1

8.2a

t(s)

i bs

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5c

t(s)

q(m

|a,b

,c,d

)

0 1 2 3 47.7

7.8

7.9

8

8.1

8.2

8.3

8.4b

t(s)

i bs

0 1 2 3 40

0.02

0.04

0.06

0.08

0.1d

t(s)

q(m

|a,b

,c,d

)

Fig. 30. a - ibs in fault-free case; b - ibs with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ibs for fault-free case; d - Change detection

in current ibs with ∼ 1.5% of turns in short-circuit in phase b

as recursive estimation and identification schemes. However, these methods

require the specification of a model for the residual generation process as well

as the definition of decision thresholds. The proposed methodology does not

depend on such kind of information.

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0 0.5 1 1.5 27.7

7.75

7.8

7.85

7.9

7.95

8a

t(s)

i cs

0 0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25

0.3

0.35c

t(s)

q(m

|a,b

,c,d

)

0 1 2 3 47.7

7.75

7.8

7.85

7.9

7.95

8b

t(s)i cs

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5d

t(s)

q(m

|a,b

,c,d

)

Fig. 31. a - ics in fault-free case; b - ics with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ics for fault-free case; d - Change detection

in current ics with ∼ 1.5% of turns in short-circuit in phase b

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0 0.5 1 1.5 28.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55a

t(s)

i as

0 0.5 1 1.5 20

0.02

0.04

0.06

0.08

0.1

0.12

0.14c

t(s)

CU

SU

M

0 1 2 3 48.2

8.3

8.4

8.5

8.6

8.7b

t(s)i a

s

0 1 2 3 40

0.05

0.1

0.15

0.2d

t(s)

CU

SU

M

Fig. 32. a - ias in fault-free case; b - ias with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ias for fault-free case; d - Change detection

in current ias with ∼ 1.5% of turns in short-circuit in phase b

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0 0.5 1 1.5 27.7

7.8

7.9

8

8.1

8.2a

t(s)

i bs

0 0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25c

t(s)

CU

SU

M

0 1 2 3 47.7

7.8

7.9

8

8.1

8.2

8.3

8.4b

t(s)i b

s

0 1 2 3 40

0.05

0.1

0.15

0.2d

t(s)

CU

SU

M

Fig. 33. a - ibs in fault-free case; b - ibs with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ibs for fault-free case; d - Change detection

in current ibs with ∼ 1.5% of turns in short-circuit in phase b

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0 0.5 1 1.5 27.7

7.75

7.8

7.85

7.9

7.95

8a

t(s)

i cs

0 0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25c

t(s)

CU

SU

M

0 1 2 3 47.7

7.75

7.8

7.85

7.9

7.95

8b

t(s)i cs

0 1 2 3 40

0.02

0.04

0.06

0.08

0.1

0.12d

t(s)

CU

SU

M

Fig. 34. a - ics in fault-free case; b - ics with ∼ 1.5% of turns in short-circuit in

phase b; c - Change detection in current ics for fault-free case; d - Change detection

in current ics with ∼ 1.5% of turns in short-circuit in phase b

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ipt0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

8.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55a

t(s)

i as

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1b

t(s)

μ 1t a

nd μ 2t

Fig. 35. a - ias in fault-free case; b - Intersection between μ1t and μ2t indicating

change in current ias for fault-free case

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.87.7

7.8

7.9

8

8.1

8.2a

t(s)

i bs

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1b

t(s)

μ 1t a

nd μ 2t

Fig. 36. a - ibs in fault-free case; b - Intersection between μ1t and μ2t indicating

change in current ibs for fault-free case

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.87.7

7.75

7.8

7.85

7.9

7.95

8a

t(s)

i cs

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1b

t(s)

μ 1t a

nd μ 2t

Fig. 37. a - ics in fault-free case; b Intersection between μ1t and μ2t indicating change

in current ics for fault-free case

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5 Conclusions

In this paper a novel fuzzy/Bayesian methodology for change point detection

in time series has been used to treat the on-line fault detection problem in

induction machine stator-winding. The methodology is based on a two-step

formulation: Firstly, a fuzzy clustering generates a transformed time series

with beta distribution. In the second step, a Metropolis-Hastings algorithm

is used to detect the probability of the occurrence of a change point in the

transformed time series. This two-step formulation allows a systematic efficient

way to solve a change point detection problem, which is employed for detecting

incipient faults as change points that occur in some system signal.

The proposed methodology has as advantages, compared to other techniques

for the FDI problem, the fact that no mathematical models of the motor and

no previous knowledge of signal statistical distributions are necessary, and also

an enhanced resilience against false alarms, combined with a good sensitivity

that allows the detection of rather small fault signals.

This methodology has been successfully applied: Simulation and experimental

results have been presented as evidences of the effectiveness of the proposed

methodology, even in the case of faults that cause very low level disturbances.

Acknowledgments

This work has been supported in part by the Brazilian agencies CNPq and

FAPEMIG.

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