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CHAPTER 4

FUZZY LOGIC BASED CLASSIFICATION OF

VIBRATIONS USING LabVIEW

4.1 INTRODUCTION

Intelligent techniques are versatile in signal classification and

estimation. Prominent techniques like fuzzy logic, artificial neural networks,

genetic algorithms plays a significant role in signal classification and are

helpful in developing various continuous control schemes. This chapter

presents the effectiveness of fuzzy logic concept in classifying the vibration

signals based on their frequency levels in order to determine the nature of

fault in the rotating machinery. These frequency signals are given to fuzzy

logic system through on line mode.

4.2 DESIGN REQUIREMENT

Erkki Jantunen et al (2006) presented an expert system for condition

monitoring of rotating machinery. Statistical analysis and regression analysis

of monitoring parameters with laboratory test and mathematical equations

were presented. Based on the statistical readings, a fuzzy classification is

proposed between lower and upper limits of classes. Readings of fuzzy

classification are tabulated and further an industrial installation model is

mentioned with microcontroller based hardware box as Universal Local

Intelligent Module using CAN bus.

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The proposed method aims to develop a fuzzy classifier for

classifying more than 2 level of vibration. Also, it is well taken the point of

demonstrating an efficient intelligent virtual vibration analyser than the

quoted model.

Abhijit Mukherjee et al (2002) promoted a predictive maintenance

technique for health monitoring using transient vibration response. They

explained a clear functional flow diagram, schematic of damage, and

graphical illustration for different strain time trends. Local detection and

Intensity estimation were presented using Fuzzy integrated Neural network

for predicting location and intensity of damage. This technique explained only

the classification of damage. But the proposed method illustrated the causes

for the classification, for the vibration behaviour and its range in graphic

environment.

Jie Liu et al (2010) implemented presented a real time condition

monitoring system for the prevention of degradation and malfunctions of the

performance of machinery. With respect to kurtosis ratio reference function

an Enhanced diagnostic scheme was proposed with Neuro Fuzzy classifier

using feed forward NN, Recurrent NN, ANFIS and NF predictor. A vibration

analysis was conducted for comparing parameters of healthy bearing against

rolling-element faults, inner and outer race defects. Upon comparing the

different schemes an adaptive NF classifier was found to be suitable for

vibration analysis and classification.

This work dealt with kurtosis ratio based modal shape for the

diagnostic scheme for a bearing set up. A equivalent study in the proposed

research has been conducted to classify the rotating machinery signal as an

online method for fuzzy based classification. Chapter 5 of this thesis

demonstrates neural network based functional classification for the predictive

maintenance.

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4.3 PROPOSED METHODOLOGY

In the thesis, a fuzzy logic based classifier has been proposed for the

vibration signals obtained from rotating machinery through proper signal

conditioning. The proposed techniques triangular membership function has

been selected based on its suitability for linearly classifying the frequency

range. LabVIEW based graphic source code is executed for the classification

as per the algorithm in the sub section.

4.4 SIGNAL FLOW ALGORITHM FOR FUZZY

CLASSIFICATION

Based on the following algorithm signal flow, a fuzzy logic based

system is classified into different levels with respect to the fault at the rotating

machinery.

Step 1: Signals from sensors are interfaced to Fuzzy classifier through

Signal conditioning and processing unit.

Step 2: FL_create antecedent.vi acts to creates an antecedent, or IF portion,

of a rule for a fuzzy system.

Step 3: Creates a consequent, or THEN portion, of a rule for a fuzzy system.

Step 4: Creates a membership function for a linguistic variable.

Step 5: Creates a linguistic variable for a fuzzy system.

Step 6: Configures the linguistic variables of the fuzzy system.

Step 7: Estimates the membership grade.

Step 8: Displays the classified values.

Step 9: Displays the respective fault.

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4.5 SIGNAL FLOW CHART FOR FUZZY CLASSIFIER

Figure 4.1 Flowchart for fuzzy classifier

START

Assign input (sensor output),

Compare rule base and create variable

Select membership function

(NI_Fuzzy_Logic_API.lvlib)

Concatenate elements

Is classify between present

linguistic variable?

Display the class

YES

NO

Plot variable and membership grade

Plot variable and membership grade

Display the fault

START

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4.6 FUZZY CLASSIFIER

The proposed fuzzy based vibration classifier system has been

configured as indicated in Figure 4.1 by using LabVIEW based graphical

programming environment.

In this system, the signals from accelerometer output are assigned to

be input variables for the fuzzy logic system. An antecedent by IF portion as a

rule for fuzzy system by FL_create Antecedent.vi. An antecedent consists of

three parts: an input linguistic variable, an operator that specifies whether to

calculate the degree of membership or the degree of non-membership of the

input linguistic variable within a linguistic term, and a linguistic term.

Also a consequent is created for THEN portion in the same manner.

Created linguistic variables are read based on the selected membership

function, i.e. triangular membership function in the proposed system for its

linearity. Based on the linguistic variables for a fuzzy system, interactive

decision is taken based on the rule formation. Signal classification is done as

explained in the successive sections, and hence respective fault is being

identified.

4.7 FUZZY SYSTEM TERMINOLOGIES IN LabVIEW BASED

SYSTEM

This LabVIEW based Fuzzy system has the following

terminologies:

Variables:

Configures the linguistic variables of the fuzzy system.

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Input variables:

Lists the input variables in the fuzzy system. It includes variable

operations like Add, Edit, Delete.

Input variable membership functions:

Plots the membership functions for the input variable.

Output variables:

Lists the output variables in the fuzzy system. It includes variable

operations like Add, Edit, Delete.

Output variable membership functions:

Plots the membership functions for the output variable selected in

the Output variables list.

Rules: Configures the rules for the fuzzy system.

Rule has the following operative components such as Add , Delete,

Move Rule Up, Move Rule Down, Add Antecedent, Delete Antecedent,

Add Consequent, Delete Consequent, Antecedent connective, Degree of

support, Consequent implication.

Test System :

Tests the fuzzy system according to input values specified. It has

Input variables, Input values, Output variables, Output values

Input/Output relationship:

Displays a 3D surface graph that plots the Output variable against

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Input variable 1 and Input variable 2. This graph also indicates the location

of the current input and output values.

Plot Variables:

Specifies the variables are wants to display in the Input/Output

relationship graph.

Number of input 1 samples:

Specifies the number of samples of Input variable 1 one wants to

plot on the Input/Output relationship graph.

Number of input 2 samples:

Specifies the number of samples of Input variable 2 one wants to

plot on the Input/Output relationship graph.

Invoked Rules:

Displays the rules that apply to the current input and output variable

values as well as the corresponding rule weights.

4.8 FUZZY LOGIC

Fuzzy logic is a method of rule-based decision making used for

expert systems and process control. Fuzzy logic differs from traditional

Boolean logic in that fuzzy logic allows partial membership in a set.

Traditional Boolean logic is two-valued in the sense that a member either

belongs to a set or does not. Values of one and zero represent the membership

of a member to the set with one representing absolute membership and zero

representing no membership. Fuzzy logic allows partial membership, or a

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degree of membership, which might be any value along the continuum of zero

to one.

4.9 FUZZY SYSTEM

A fuzzy system is a system of variables that are associated when

using fuzzy logic. A fuzzy controller uses defined rules to control a fuzzy

system based on the current values of input variables. Fuzzy systems consist

of three main parts: linguistic variables, membership functions, and rules.

4.10 FUZZIFICATION

Fuzzy logic uses linguistic variables instead of numerical variables.

The process of converting a numerical variable (real number or crisp variable)

into a linguistic variable (fuzzy number) is called fuzzification. The simplest

form of membership function is the triangular membership function and it is

used in Figure 4.2 as the reference.

Figure 4.2 Fuzzy logic block diagram

Fuzzy Rule Base Fuzzy Inference Engine

Fuzzification

Defuzzification

Crisp input values

Crisp output values

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4.11 MEMBERSHIP FUNCTION

1. Trapezoidal Membership Function

2. Gaussian Membership Function

3. Bell Shape Membership Function

4. Sigmoidal Membership Function

5. S Membership Function

6. Membership Function

7. Triangular Membership Function

4.11.1 Triangular Membership Function

The triangular membership function is specified by three parameters

{a , b , c } as follows and its diagrammatic representation is shown in

Figure 4.3.

0 x < a

(x-a)/ (b-a) a x b

(c-x)/(c-b) b x c

0 x > c

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Figure 4.3 Triangular membership function

4.12 DEFUZZIFICATION

There are a few ‘Defuzzification’ methods by which fuzzy to crisp

value conversion could have been obtained, if a closed loop system is

preferred.

The reverse of fuzzification is called defuzzification. The use of

FLC inference engine produces the required output in a linguistic form. Riley

et al (1997) and Renwang et al (2010) and discussed about vibration

monitoring and fuzzy algorithms. According to this citation on real world

equipment, the linguistic variables have to be transformed to crisp output. The

centre of weight method is the best well-known defuzzification method and it

is used in this work.

µ

1

a b c

t

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1. Max membership principle

2. Centroid method

3. Weighted average method

4. Mean max membership

5. Centre of sums

6. Centre of largest area

7. First (or last) of maxima

4.12.1 Centroid Method

This method is also known as the centre of area or centre of gravity

defuzzification. It is the most commonly used technique and is very accurate.

The centroid defuzzification technique is expressed in Equation 4.1 and

shown in Figure 4.4.

z =( )

( ) (4.1)

where

Z * is the defuzzification output, C(z) is the aggregated

membership function and Z is the output variable.

Figure 4.4 Centroid method

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4.12.2 Center of Sums

This is faster than many defuzzification methods and the method is

not restricted to symmetric membership functions. This process involves the

algebraic sum of individual output fuzzy sets, instead of their union.

However, there are two drawbacks: the intersecting areas are added twice, and

the method also involves finding the centroids of the individual membership

functions.

z

n

k

k

z

z

n

k

k

dzzC

dzzC

z

1

1

)(

)(

* (4.2)

where

the symbol is the distance to the centroid of each of the respective

membership functions which has been expressed in Equation 4.2 and shown

in Figure 4.5.

Figure 4.5 Center of sums

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4.12.3 Centre of Largest Area

If the output fuzzy set has at least two convex sub regions, then the

centre of gravity (i.e. z is calculated using the centroid method) of the convex

fuzzy sub region with the largest area is used to obtain the defuzzified value

z of the output. This is shown graphically in Figure 4.6 and given

algebraically Equation 4.3,

z =( )

( ) (4.3)

where c is the convex sub region that has the largest area making upc . This

condition applies in the case when the overall output c is not a convex. In the

case when c is convex, z*is the same quantity as determined by the centroid

method or the centre of largest area method.

Figure 4.6 Centre of Largest Area

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4.13 LabVIEW BASED SIGNAL CLASSIFICATION USING

FUZZY LOGIC SYSTEM

Figure 4.7 is the source code for the signal flow algorithm illustrated

in LabVIEW.

Figure 4.7 LabVIEW Source Code for Vibration Classifier

The frequency from the real time rotating machine varies from 0 to

700Hz. This is classified into fuzzy linguistic variables as low, very low,

normal, high and very high.

The membership function is created in the range of 0-100 Hz, 90-

200 Hz, 190-300 Hz, 290-300 Hz, 390-400 Hz.

4.14 SIGNAL CLASSIFICATION

Frequency based classification of specified rotating machinery

vibration signals are indicated as mentioned in Table 4.1.

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If the frequency of the machine lies in 0-100Hz then it is designated

as ‘Very Low’.

If the frequency lies in between 100-200Hz, it is designated as

‘Low’.

If the frequency lies in 200-300Hz, it is designated as ‘Normal’.

If the frequency lies in 300-400Hz, it is designated as ‘High’.

If the frequency lies in 400-700Hz, it is designated as ‘Very high’.

Table 4.1 Range and Level classifications of Vibration Signals

S.NoFrequency

Range in Hz

Classified

Level

Machinery

Fault Remarks

1 0-100Hz Very low Improper

Mounting

Poor

Maintenance

2 100-200Hz Low Casing

looseness

Careless

installation

3 200-300Hz Normal Misalignment Abrupt

loading

4 300-400Hz High. Bearing

Damage

Ageing of

bearings

5 400-700Hz Very high Rotor

unbalance Loose joints

In Table 4.1 the corresponding machinery faults and remarks on the

cause of the faults are also enlisted. These five levels are categorized based on

the frequency range only. Because high frequency vibration with lower

amplitude will have less effect on the machine, whereas frequency

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discrimination over the spectrum will fetch the details regarding machinery

faults and hence the diagnosis.

Figure 4.8 Fuzzy Classification (High)

Rotating machinery under test has ‘High’ frequency composition,

for the particular machinery class is mentioned Figure 4.8. The machinery set

up studied for this research, indicates the problem due to bearing damage, and

it corresponds to the frequency 389.41Hz, which in the 300 – 400Hz and

classified by fuzzy as high. The amplitude is also indicated as 1.22 V.

The successive section shows still higher frequency classification as

displayed in Figure 4.9. The rotating machinery under test has ‘Very High’

frequency composition, for the particular machinery class. It has been

classified Rotor unbalance or Rotor misalignment problem due to the inner

race or outer mount. This case corresponds to the frequency 476.33Hz, which

in the 400 – 700Hz and classified by fuzzy as Very high with amplitude

1.54 V.

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Figure 4.9 Fuzzy Classification (Very High)

Figure 4.10 displayed in the next page, it is found that the rotating

machinery under the test has ‘Low’ frequency composition, for the particular

machinery class. In the machinery set up studied for this research, it indicates

the problem due to casing looseness due to improper installation during

commissioning. it corresponds to the frequency 153.34Hz, which in the

100 – 200Hz and classified by fuzzy as high. The amplitude is also indicated

as 785.54 mV.

‘Very low’ frequency composition is depicted in Figure 4.11. and

the rotating machinery under the test has ‘Very Low’, for the particular

machinery class. It has been classified as a Mounting problem. This case

corresponds to the frequency 53.98Hz, which in the 0 – 100Hz and classified

by fuzzy as ‘Very high’ with amplitude 500.28mV. Normally a disturbing

noise arises during this frequency. Chaofu Zhu et al (2010) discussed about

calibration of low frequency vibration calibration. However, periodical

maintenance will eradicate this problem.

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Figure 4.10 Fuzzy Classification (Low)

Figure 4.11 Fuzzy Classification (Very Low)

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Figure 4.12 Fuzzy Classification (Normal)

To mention the 200 to 300Hz, it has been designated as ‘Normal’ as

portrayed in Figure 4.12. It is found that the rotating machinery under the test

has ‘Normal’ frequency composition, for the particular machinery class. It

does not replicate machine under normal condition. Ashok Chettri et al (2007)

have discussed about monitoring natural frequencies during ‘normal’

operating conditions of machinery. Balamurugan et al (2004) discussed about

estimation of vibration frequencies.

With the above references, a fuzzy logic linguistic variable its

classification has been named as ‘Normal’. In this particular frequency of

243.87 Hz in 200 – 300 Hz range, with amplitude 462.06mV, the machine is

found suffer from ‘Misalignment’. This particular case has occurred due to

the sudden loading on the machinery or input power interruption. When

changing from certain load to rest, also this frequency class has been inferred.

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The above program is illustrated with LabVIEW and hardware set

up test motor with deliberate introduction of problems. It is recorded with

frequency and amplitude for multiple cases. After the study, the range of

frequencies and assumption on causes for faults were classified. These

classifications are applicable for the machinery undertaken for this research

only.

Figure 4.13 LabVIEW Block diagram of Fuzzy Classifier for Vibration

Frequency

LabVIEW based block diagram shown above in Figure 4.13

executes the signal acquisition part of the fuzzification. This includes

membership function selection, membership grading, Fuzzy set determination

for evaluating the input signal. Since the real time signals are interfaces, to

control the continuous operation, without interrupting the hardware loop,

WHILE is configured to exectute the requirement. However, stopping the

execution and aborting the programme is also possible.

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4.15 COMPARISON OF FUZZY CLASSIFIER WITH PREVIOUS

METHODS

The results found in Table 4.2, are the sample readings mentioned

in the previous section.

Table 4.2 Performance Comparison on Fuzzy Logic based

Classification of Vibrations

S.No Method Fuzzy

levels

Degree of

effectiveness

in 5 point

scale

Remarks and

special feature

1 Erkki Jantunen et al

(2006)

2 2.6 Statistical

Methods

2 Abhijit Mukherjee et

al. (2002)

4 3.2 With ANN

3 Jie Liu et al (2010) 5 3.9 Kurtosis with

NF and FF

4 Proposed method 5 4.1 Real time, on

line

The proposed method is being compared with others based on the

Fuzzy levels of classification, degree of effectiveness and special features

adapted in the method. Other feature may include mathematical procedure,

algorithm, simulation and experiment.

The proposed method has used 5 levels with a degree of

effectiveness in 4.1 in point scale. Mathematical approach will not fetch any

real time signal analysis. But the proposed method has implemented suitable

hardware mentioned in Figure 3.18. Since it is a LabVIEW based system,

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acquisition of real time signal and classification are dynamic. This proves that

the proposed method is more efficient than the previous methods in terms of

the aspects taken. The same has been illustrated graphically in Figure 4.14.

Figure 4.14 Frequency and amplitude comparison of Fuzzy logic based

Vibration Classification

This graph clearly indicates the sample readings displayed in

Figures 4.10, 4.11, 4.12, 4.13 and 4.14. Each classification has been shown in

the X axis and respective amplitude in mV and Frequency in Hz are plotted.

The dip in the frequency, 243.87, indicates, ‘Misalignment’ may occur with

increasing amplitude, i.e. forceful vibration with increasing frequency

component. Otherwise, the plot need not be linear because vibration signals,

textures or signature are complex and random, in time and frequency domain.

0

200

400

600

800

1000

1200

1400

1600

1800

Very Low Low Normal High Very High

Frequency Hz

Amp mV

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4.16 SUMMARY

The classification of vibration using fuzzy logic is described and

found to be useful to identify signal level. It helps to identify the probability

of fault which could occur during the operation. Fuzzy classification closely

categorizes the frequency variation and data logs the frequency and respective

amplitudes based on triangular membership. Since it has been configured

through a graphical environment, it is user friendly and the classification can

be done on a real time basis. The proposed method is found to be efficient in

variable classification and in the novelty of the method.