generator thermal sensitivity analysis with support vector regression

8/3/2019 Generator Thermal Sensitivity Analysis With Support Vector Regression

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Generator Thermal Sensitivity Analysis with Support Vector Regression

Youliang Yang and Qing Zhao*

Abstract— Generator thermal sensitivity issue is studied inthis paper. Currently, thermal sensitivity test is usually adoptedin industries to determine if a generator has been experiencingthermal sensitivity problem. However, this kind of tests has itsown disadvantages. In this paper, Support Vector Regressionis utilized to provide some valuable information regardingthermal sensitivity in a rotating machine based on the normaloperational data of the machine. Experimental results on thesteam turbine generators show that the proposed method canbe used to track the generator condition related to the thermaleffects and make a recommendation to the on-site engineerswhether or not a thermal sensitivity test should be performed.

I. INTRODUCTIONElectrical machine condition monitoring plays an impor-

tant role in modern industries and it has been an active

research topic. Traditionally, electrical machines are allowed

to run until failure then they are either repaired or replaced.

Very limited information regarding the machine condition is

known before the machine is shutdown and hence resulting in

long machine downtime and great economic lost. Recently,

predictive maintenance strategy is adopted in many indus-

tries. In predictive maintenance, machine condition is moni-

tored continuously, and hence valuable information regarding

machine condition can be obtained before the machine is

shutdown and repaired and the machine downtime can be

greatly reduced.Predictive maintenance consists of various aspects. For

example, fault analysis needs to be performed and classi-

fication models can be built with artificial intelligence tech-

niques to classify and identify different machine conditions.

In addition, prognosis models can be built to predict the

future machine conditions and determine if the machine

is experiencing faults related condition degradation. The

machine condition trending based on importance machine

performance index can be carried out to determine when the

machine should be shutdown or a major maintenance/repair

should be scheduled. This way the number of unexpected

shutdown can be greatly reduced and the reliability is greatly

improved.

In this paper, a specific issue, generator rotor thermal

sensitivity, is studied. Thermal sensitivity is a phenomenon

caused by uneven heat distribution around an axis, e.g.

rotor, causing it to bend. Some common causes of generator

thermal sensitivity include shorted turns, blocked ventilation

or unsymmetrical cooling, insulation variation, wedge fit,

Y. Yang and Q. Zhao are with the Dept. of Electrical and ComputerEngineering, University of Alberta, Edmonton, Alberta, T6G2V4 Canada.Email: <youliang, qingz>@ualberta.ca, *: correspondingauthor

distance block fitting, etc. [1]. There are two types of thermal

sensitivity, reversible and irreversible. Normally thermal sen-

sitivity is confirmed and the severity is determined through

a standard test procedure commonly adopted in industries.

However, the thermal sensitivity test is destructive especially

when the machine has irreversible thermal sensitivity prob-

lem.

Support Vector Regression (SVR) has been widely used

in the field of electrical machine condition monitoring. Just

to name a few, in [2], a hybrid model is built with SVR

to predict the future state of a turbo generator. In [3], the

Least-Square Support Vector Machine (LS-SVM) combining

with wavelet decomposition is utilized to predict the futurevibration of a hydro-turbine generating unit. In this paper,

a model for vibration analysis is built with SVR that can

be useful in tracking machine conditions. It is applied to

analyze the thermal sensitivity issue for a type of steam

turbine generators. In this method, only normal machine

operational data are used to build the model. The results

can be used to recommend whether and when a necessary

thermal sensitivity test is needed. The rest of the paper is

organized as follows. The basic theory of SVR is reviewed

in section II. In section III, the background of generator

thermal sensitivity and the procedure of a thermal sensitivity

test are introduced. In section IV, after some discussions

on the industrial practice regarding thermal sensitivity andthe limitations, SVR models are built and the experimental

results are presented. Finally, the conclusion is provided in

section V.

I I . SUPPORT VECTOR REGRESSION

In SVR, the goal is to find a function f (x), which maps the

input to the output, while minimizing the difference between

the predicted value yi and the actual value yi based on

the loss function [4]. Suppose that there are training data

(x1, y1), (x2, y2), ..., (xN , yN ), where xi is the input and yi

is the output. In a linear case, f (x) can be expressed as

y = f (x) = wx + b (1)

where w is the weighted vector and b is a constant. While

trying to minimize the difference between the predicted value

and the actual value, in SVR, it is also desirable to keep

the function f (x) as flat as possible [4], which means wshould be as small as possible. One way to find a small wis to minimize the norm, i.e. ||w||2 =< w, w >. Thus, the

regression problem becomes to

min.1

2

N n=1

(yi − yi)2 +1

2||w||2 (2)

2010 American Control ConferenceMarriott Waterfront, Baltimore, MD, USAJune 30-July 02, 2010

WeB05.3

978-1-4244-7427-1/10/$26.00 ©2010 AACC 944



x

x

x

x

x

x

x

x

x

x

x

xx

xx

x

x

x

x

iξ

iξ

x

x

y

ε + y

ε − y

x

)(ˆ x y

Fig. 1. Linear SVR with slack variables

Quadratic error function is used in Eq. (2) to calculate the

error between the predicted value and the actual value. In

practice, the ǫ-insensitive error function is often used, which

can be mathematically expressed as

E ǫ(yi − yi) =

0, if |yi − yi| < ǫ

|yi − yi| − ǫ, otherwise(3)

Readers can refer to [5] for more details on error functions.

With the ǫ-insensitive error function, the regression problem

becomes to minimize

C N

n=1

E ǫ(yi − yi) +1

2||w||2 (4)

Where C is the trade-off between the flatness of f (x) and the

prediction error. In cases that with the optimal f (x), some

actual values may not lie within the region [y−ǫ, y+ǫ], slack

variables ξ and ξ need to be introduced so that for any given

actual value yi, it lies within the region [yi−ǫ−ξi, yi +ǫ+ξi]

(Please refer to Fig. 1). When yi lies above yi + ǫ, ξi > 0and ξi = 0. On the other hand, when yi lies below yi − ǫ,

ξi = 0 and ξi > 0. Thus, the objective function of the SVR

problem can be rewritten as

min. C N

i=1

(ξi + ξi) +1

2||w||2 (5)

subject to

ξi ≥ 0 (6)

ξi ≥ 0 (7)

yi ≤ yi + ǫ + ξi (8)

yi ≥ yi − ǫ − ξi (9)

The above optimization problem can be transformed into

a Lagrangian dual problem and the final predicted value is

given by [6]:

yi =N

i=1

(αi − αi)k(x, xi) + b (10)

where αi and αi are the Lagrange multipliers, and k is the

kernel function. Common kernel functions include linear,

polynomial, and radial basis functions (RBF) [7].

III. GENERATOR THERMAL SENSITIVITY

A. Causes of thermal sensitivity

As stated in [1], even for a rotor that has thermal sensitivity

issue, it is not affected much when the generator is operating

with low VAR. On the other hand, when the generator is op-

erating with a power factor lower than 0.85 lagging, a thermal

sensitive rotor will be affected and its vibration profile will

change. The rotor vibration may increase, decrease, or its

phase angle may change. Therefore, even with a thermal

sensitive rotor, a generator may not have any issues when

operating with low field current; however, its operation may

be greatly restricted at high field currents or VAR loads as

the rotor vibration excesses the acceptable limit.

Generator rotor thermal sensitivity can be classified into

two types: reversible and irreversible. When the thermal

sensitivity is reversible, rotor vibration changes as field

current varies. That is, when the field current increases, the

rotor vibration increases. Later on, when the field current

decreases, the rotor vibration will decrease as well. This type

of thermal sensitivity usually does not cause major problemsin practice and the rotor can be balanced so that its maximum

vibration will not excess the limit. If the rotor vibration does

not decrease after the field current is reduced, this type of

thermal sensitivity is called irreversible. This type of thermal

sensitivity is troublesome since the rotor vibration will keep

increasing, and the rotor may have to be taken off-line and

repaired in order to reduce the vibration. Readers can refer

to [1] for more details on some common causes of generator

thermal sensitivity and their thermal sensitivity types.

B. Thermal sensitivity test

A standard procedure for determining generator thermal

sensitivity is normally adopted. The purpose of this test is toisolate the machine vibration which is caused by MW (real

power) loading from that caused by VAR loading (reactive

power). Vibration changing with MW loading does not

indicate thermal sensitivity problem. The thermal sensitivity

test consists of 3 parts:

1) The thermal sensitivity test is started by loading the

generator with small MW and MVAR, 10MW and

0MVAR for example, and then MW gradually in-

creases to about 60% of its rated value and MVAR

will be reduced. At each stage, all the important read-

ings, such as the machine vibration, voltage, current,

temperature, etc. are recorded.

2) In the second step of the test, the generator MW is kept

constant while the field current continuously increases

to its rated value, so MVAR increases correspondingly.

It is important that the MVAR is high enough so that

the generator operates with a power factor lower than

0.85 lagging.

3) The last step of the thermal sensitivity test is the

reverse of the first 2 parts. The generator MVAR

decreases while the MW is kept constant, and then

the MW decreases and MVAR increases so that the

final generator MW and MVAR are back to the same

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10

-20

-10

40

30

20

10

706050403020

0 MW

MVAR

Fig. 2. Typical plot of machine output power during a thermal sensitivitytest

Stream

TurbineGenerator

Bearing 1X, 1Y Bearing 4X, 4YBearing 3X, 3YBearing 2X, 2Y

A

X YA

Axial view

Fig. 3. Typical layout of a BPSTG

values as when the test is started. The complete process

of the thermal sensitivity test is illustrated in Figure 2.

If the final machine vibration is similar to the vibration

when the test is started, it can be concluded that the

thermal sensitivity is reversible. Otherwise, if the final

machine vibration remains high, the thermal sensitivity

is irreversible and further maintenance actions may

need to be taken.

IV. SVR MODEL BASED ON MACHINE VIBRATION

TRACKING FOR THERMAL SENSITIVITY ANALYSIS

A. Experimental setup

Two back pressure steam turbine generators (BPSTG) used

in a local oil-sand company are investigated in this paper.

They are labeled as G1 and G2. Figure 3 shows a typical

layout of the BPSTG, which consists of a steam turbine and

a generator. They are 4 bearings in total for each generator

and two vibration sensors are installed on each bearing along

x and y axes of 90 degrees apart. During normal operation,

the machines are running at 3600 RPM and the vibration

waveform for each bearing is captured and updated every 2

hours.

B. Thermal component

The thermal sensitivity test serves 2 purposes. The first one

is to determine if there exists irreversible thermal sensitivity.

The other purpose is to determine the ‘size’ of the thermal

component, i.e. the difference between the vibration when the

generator is operating at the low MW and MVAR loading at

the beginning of the test and the vibration when the generator

is operating at the highest MW and MVAR during the test.

The difference has to be within a certain limit otherwise

the generator will not be able to run with its full capacity.

The method used to calculate the thermal component is as

follows:

0 20 40 60 80 100 120 140−1

0

1

Time (ms)

m i l

(a)

0 20 40 60 80 100 120 140

−1

0

1

Time (ms)

m i l

(b)

Fig. 4. Machine vibration waveform, (a) unfiltered, (b) 1X only

During the thermal sensitivity test, at each stage, the

machine vibration peak-to-peak value and its phase can be

recorded. However, it is believed that the vibration due to

thermal bow is mainly shown on 1X (one times) speed, which

is 60 Hz in this case; therefore, in order to eliminate the other

effects, the 1X vibration peak-to-peak value is used. Figure

4 shows a typical machine vibration waveform together with

1X component only. Thus, every cycle in the 1X vibrationwaveform in the x and y direction can be expressed by:

V x =1

2Axcos(θ − θx)

V y =1

2Aycos(θ − θy)

0 ≤ θ < 2π (11)

where Ax, Ay, θx, and θy are the 1X vibration peak-to-peak

value and phase angle in the x and y direction, respectively,

and they can all be recorded during the thermal sensitivity

test.

θy is subtracted by π/2 (or added by 3π/2 if θy−π/2 < 0)

since the vibration sensor x and y are 90o degree apart. Thus,

θy = θy − π/2

V y =1

2Aycos(θ − θy) (12)

To ensure V x and V y are larger than 0, constant terms, 1

2Ax

and 1

2Ay will be added to V x and V y, respectively. Hence,

V x =1

2Ax +

1

2Axcos(θ − θx)

V y =1

2Ay +

1

2Aycos(θ − θy) (13)

Finally, by iteration, a θ can be found which maximizes

the following equation,

V T =

V x

2+ V y

2(14)

The corresponding phase angle can be denoted as θT . At

this point, the overall maximum machine vibration can be

expressed by a vibration vector with magnitude V T and phase

angle θT .

The maximum vibration vector can be calculated for the

machine vibration at the start of the thermal sensitivity test

and at the point when the machine is operating at the highest

MW and MVAR during the test, and then the vibration

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1 2 3 4 50

-1

-2

-3

1

2

Low

Load

High Load

Thermal Component

mil

mil

-1

Fig. 5. Typical plot of the machine 1X vibration vector during a thermalsensitivity test

difference between those 2 conditions can be calculated.

Figure 5 is a typical plot of the vibration vector during a

thermal sensitivity test indicating the thermal component.

The above analysis is focused on the vibration difference

between the lowest load and the highest load of the machine

operation during the thermal sensitivity test. However, how

the machine vibration changes due to thermal sensitivity ina long term has not been taken into consideration. Also, if

the machine thermal sensitivity is irreversible, the thermal

sensitivity test can be destructive since the machine vibration

may become worse after the test. Moreover, when a machine

is undergone a thermal sensitivity test, it has to be removed

from the production line, so the productivity is reduced. It

is therefore desirable to determine whether or not a machine

has been experiencing thermal sensitivity issue by analyzing

normal machine operational data. In this paper, the SVR

technique is applied to build a model for this purpose.

Many different techniques can be used to build a system

model, including building a physical model. However, this

usually requires an in-depth understanding of the machine

structure. Hence, artificial intelligence techniques are often

preferred. Based on [8] and [9], SVR seems to be a better

choice over Neural Network (NN) and adaptive neuro-fuzzy

inference system (ANFIS) and therefore it is selected in

this paper. The method is tested on the two BPSTG and

some valuable preliminary information about rotor thermal

sensitivity problem is obtained.

C. SVR based vibration model

For tracking the machine vibration, a system model is

needed. In this case, the inputs of the model are the generator

output real power and reactive power, and the output of the

model is the machine 1X vibration. Other than the machine

output power, many other factors, such as the temperature of

the machine operating environment, may also have impacts

on the machine vibration. However, machine output power

can be directly controlled by the on-site engineers, and this

is why they are chosen as the inputs of the model. The model

built to predict the machine vibration based on the generator

output power can be mathematically expressed as

y = f (P, Q) (15)

(a)

(b)

Fig. 6. Plots of (a) V TX and (b) V TY , G1

where P and Q are the machine real and reactive power,

respectively, and y is the output related to machine 1X

vibration amplitude. If the model is properly trained and

the machine thermal sensitivity is irreversible, the difference

between the predicted vibration and the real vibration can be

shown in the thermal component analysis. Instead of using

the magnitude or phase angle of the vibration vector as the

model output, the vibration vector is decomposed into two

components by projecting to X and Y axes:

V T X = V T cosθT , V T Y = V T sinθT (16)

Thus, any changes in the magnitude and phase angle of

the machine 1X vibration are reflected in V T X and V T Y .

D. Case studies and the analysis results

In this section, SVR models are built for both G1 and G2

and used to track their vibrations. Based on previous thermal

sensitivity test results from the plant, it is known that G1

does not have serious problem since the thermal sensitivity isreversible. On the other hand, G2 may have serious thermal

sensitivity issue and it is irreversible. Vibrations for both

generators are analyzed separately in the following sections.

Fig. 6 shows the plots of V T X and V T Y of G1. The

vibration data is obtained during the period from Jan. to Aug.

2003 on bearing 4 and there are 2761 data points in total.

From Fig. 6, no obvious trend can be noticed. V T X and V T Y

do not seem to increase or decrease as time progresses. In

order to confirm that the machine condition did not change

during that period, SVR models can be built to predict the

machine vibration based on the machine output power. If the

machine condition indeed did not change during that period,

the model predicted vibration should be very close to thereal vibration as long as the model is properly trained.

When building the SVR models in this section, different

kernel functions have been tried, including linear and poly-

nomial kernel functions with different degrees. By trial and

error while taking the model training time into consideration

as well, polynomial kernel function with degree 2 is selected.

The first 700 data points are used to train the SVR models

and the prediction error is simply the difference between the

predicted vibration value and the real vibration value:

error = V ibrationT, actual − V ibrationT, predicted (17)

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(a)

(b)

Fig. 7. (a) SVR model prediction results for V TX , predicted values (red),actual values (blue), and (b) prediction error, G1

(a)

(b)

Fig. 8. (a) SVR model prediction results for V TY , predicted values (red),actual values (blue), and (b) prediction error, G1

Fig. 7 and 8 shows the SVR model prediction results along

with the real machine vibration and the prediction error. It

can be seen that, for both V T X and V T Y , the predictionresults are very close to the real values. The mean and

the standard deviation of the prediction error of V T X are

−0.024 and 0.2599, respectively, while they are 0.1202 and

0.5018 for V T Y . Also, from the error plots, there is no

clear trend that the prediction error increases or decreases

as time progresses. Therefore, it can be concluded that the

condition of G1 did not change during the period from Jan. to

Aug. 2003, and a thermal sensitivity test around this period

may not be necessary for G1. From the plots, it can also

be concluded that there is a direct relationship between the

machine output power and the machine 1X vibration. It is

possible to build an accurate model with machine real and

reactive powers as the model inputs to predict the machine1X vibration.

Similar analysis can be applied to generator G2. Fig. 10

shows the plots of V T X and V T Y of G2. The vibration data

is obtained from Jan. to Sep. 2003 on bearing 3 and there are

3123 data points in total. SVR models are built with the same

kernel function and parameter for V T X and V T Y , and again

the first 700 data points are used to trained the models. The

prediction results and prediction errors are shown on Fig.

11 and 12. From Fig. 11, it can be seen that the prediction

results are close to the actual values. The mean and standard

deviation of the prediction errors are 0.0114 and 0.2584,

respectively. On the other hand, on Fig. 12, starting from

data points around 1920, which corresponding to June 23,

2003 in actual date, the actual vibration starts to increase,

which causes the prediction error between the predicted V T Y

and the actual V T Y to increase and finally settles down at

data points around 2200, which corresponding to July 16,

2003 in actual date. The mean and standard deviation of theprediction errors are 0.5502 and 0.613, respectively. Hence,

the mean of the prediction error is much larger than those

in the other 3 cases. The prediction error can be further

analyzed with the moving window method to show how the

mean and standard deviation change more clearly. The results

are shown in Fig. 13, with 500 data points as the window

size and 100 data points as the moving size. From Fig. 13,

it is very clear that the mean of the prediction error starts to

increase rapidly after index 15, which is equivalent to index

1900 in the actual data point. If the vibration vectors are

plotted during the period from June 23 to July 16, the result

would be similar to Fig. 9. V T X did not change too much

during that period and it remained at about 2.5 mil, whileV T Y increased approximately from -1 to 1 mil. Thus, the

vibration vector moves from the forth quadrant to the first

quadrant.

From the Fig. 12, it is noticed that the model prediction

errors are small for the first 1800 data points, it can be

confirmed that the SVR model has been trained properly

and it should generate outputs accordingly with the changing

input power. Therefore the difference shown after the index

number 1920, is mainly due to the reason that the machine

condition has changed. The machine condition may change

due to many mechanical reasons, such as the machine may

have been taken off-line and maintenance work have been

performed to the machine, or some machine componentsare worn out. However, it has been confirmed that G2 was

continuously running for the whole period and there was

not any maintenance work done to the machine. Also, if

the machine condition is changed due to components wear

out, the process should be slow and the vibration should

change slowly instead of increasing abruptly as it is shown

in Fig. 12. Another possible cause for the machine condition

change is irreversible thermal sensitivity. By checking the

generator output powers, it is found out that, from June 23 to

27, the generator was operating with very high MVAR, such

as 25MW and 30MVAR, 45MW and 30MVAR, etc. Also,

G2 was considered running in the normal condition since

its peak-to-peak vibration is under the pre-defined limit and

the change of vibration cannot be noticed if the vibration

data was not processed by the method described previously

in this paper. Thus, considering all the analysis above, it

is believed that the vibration change is due to thermal

sensitivity. Based on the results, one could then recommend

a thermal sensitivity test to be scheduled to confirm this.

Since the valuable information about thermal sensitivity can

be obtained before the severe machine condition degradation

by analyzing past operational data, unexpected shutdowns

can be avoided.

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1 2 3 4 50

-1

1

mil

mil

-1

June 23, 2003

July 16, 2003

Change of vibration vector

Fig. 9. Change of vibration vector, G2

(a)

(b)

Fig. 10. Plots of (a) V TX and (b) V TY , G2

(a)

(b)

Fig. 11. (a) SVR model prediction results for V TX , predicted values (red),actual values (blue), and (b) prediction error, G2

(a)

(b)

Fig. 12. (a) SVR model prediction results for V TY , predicted values (red),actual values (blue), and (b) prediction error, G2

0 5 10 15 20 25 30−0.5

0

0.5

1

1.5

m i l

(a)

0 5 10 15 20 25 300.2

0.3

0.4

0.5

0.6

0.7

m i l

(b)

Fig. 13. SVR model prediction results for V TY , (a) mean, and (b) standarddeviation, G2

V. CONCLUSION

Generator thermal sensitivity is studied in this paper. Cur-

rently, in practice, a thermal sensitivity test can be performed

to determine if a generator has thermal sensitivity issue or

not. However, thermal sensitivity test has some disadvantages

and it is preferred to determine the thermal sensitivity prob-

lem based on the regular machine operational data. In this

paper, system model is built with SVR to predict the machine

vibration based on the machine output power. The proposed

method is applied to analyze the thermal sensitivity in 2

BPSTGs and experimental results show that the proposed

method can be used to keep track of the machine condition

and provide valuable information on whether the generator

has thermal sensitivity issue.

REFERENCES

[1] R.J. Zawoysky and W.M. Genovese. “Generator Rotor ThermalSensitivity-Theory and Experience”, GE Power Systems, New York,

2001.[2] L. Xiang, G.J. Tang, and C. Zhang. “Simulation of time series

prediction based on hybrid support vector regression”, Proceedings- 4th International Conference on Natural Computation, Vol, 2, 2008,pp.167–171.

[3] M. Zou, J. Zhou, Z. Liu, and L. Zhan, L. “A Hybrid Model forHydroturbine Generating Unit Trend Analysis”, Proceedings - Third

International Conference on Natural Computation, Vol. 2, 2007,pp.570–574.

[4] Alex J. Smola and B. Scholkopf, “A tutorial on support vectorregression”, Statistics and Computing, Vol. 14, 2004, pp.199–222.

[5] S.R. Gunn, “Support Vector Machines for Classification and Re-gression”, Technical Report, Faculty of Engineering, Science andMathematics, School of Electronics and Computer Science, Universityof Southampton, 1998.

[6] C.M. Bishop, Pattern Recognition and Machine Learning, Springer,New York, 2006.

[7] S. Abe, Support Vector Machine for Pattern Classification, Springer,London, 2005.

[8] Jang, J.R. (1993) “ANFIS: adaptive-network-based fuzzy inferencesystem”, IEEE Transactions on Systems, Man, and Cybernetics,May/June, Vol. 23, No. 6, pp.665–685.

[9] B. Samanta and C. Nataraj. “Prognostics of machine condition usingsoft computing”, Robotics and Computer-Integrated Manufacturing,Vol. 24, 2008, pp.816–823.

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generator thermal sensitivity analysis with support vector regression

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