single-input-rule-modules connected fuzzy
TRANSCRIPT
SINGLE-INPUT-RULE-MODULES CONNECTED FUZZY INFERENCE SYSTEM AND ITS APPLICATIONS TO
F~UREMODE AND EFFECT ANALYSIS
Jong Chiao Haur
Master of Engineering (Electronic and Computer)
2015
Pusnf Khidmat Maklumat Akad n' ;' UNlVEftSJTI [\liALAYSIA. 'ARA',-;
SINGLE-INPUT-RULE-MODULES CONNECTED FUZZY INFERENCE SYSTEM AND ITS APPLICATIONS TO FAILURE
MODE AND EFFECT ANALYSIS
JONG CHIAN HAUR
A thesis submitted in fulfilment of the requirements for the degree of Master of Engineering
(Electronic and Computer)
Faculty of Engineering
UNIVERSITI MALAYSIA SARA W AK
2015
Pus:., Khidmat Makl mat Ak:ld ll': UNIV£flSrn MA.LAYS!A Sfl.kA' .'
SINGLE-INPUT-RULE-MODULES CONNECTED FUZZY INFERENCE SYSTEM AND ITS APPLICATIONS TO FAILURE
MODE AND EFFECT ANALYSIS
JONG CHIAN HAUR
A thesis submitted in fulfilment of the requirements for the degree of Master of Engineering
(Electronic and Computer)
Faculty of Engineering
UNIVERSITI MALAYSIA SARA W AK
2015
For my beloved family and friends
ii
ACKNOWLEDGEMENT
First of all, I would like to express my gratitude to God for giving me a
wonderful life, spirit and wisdom to complete this project and thesis report.
Special appreciation to Dr. Tay Kai Meng, for his patience and guidance.
Thanks to my beloved friends, especially Whilly Chan and Chai Kok Chin, and my
family for their kindness, care and support during my three years of Master study in
UNIMAS.
Last but not least, I would like to thank all lecturers and staff of Faculty of
Engineering for their teachings and technical advices and supports from time to time.
Also, speciai gratitude is dedicated to everyone who directly or indirectly offered
their help to make this project successful.
111
ABSTRAK
Fuzzy inference systems (FlS) tradisi seperti Mamdani FIS model dan T-S
FIS model telah mengalami dua kelemahan utama, iaitu (i) ia sukar dan tidak praktis
membentuk satu peraturan fuzzy asas yang lengkap apabila jumlah peraturan
peraturan diperlukan adalah besar , dan (ii) pencapaian ciri-ciri keekanadaan di
dalam pemodelan FlS. Matlamat tesis ini adalah untuk menganalisis penggunaan FIS
yang agak baru, iaitu, Single-Input-Rule-Modules (SIRMs) bersambungan FIS dan
satu teorem yang diringkaskan, sebagai penyelesaian untuk kelemahan-kelemahan
yang dinyatakan sebelum ini. Selain itu, satu prosedur ujian keekanadaan telah
digunakan untuk menilai pencapaian harta keekanadaan secara empirik. Dalam tesis
ini, kebolehgunaan SIRMs bersambungan FIS, satu teorem yang diringkaskan, dan
prosedur ujian keekanadaan, dalam aplikasi masalah dunia sebenar (iaitu, Failure
Mode and Effect Analysis (FMEA) dan masalah pengawalan paras air) telah
didemostrasikan. Prosedur FMEA yang baru dengan SIRMs bersambungan FIS dan
teorem diringkaskan telah dicadangkan. Teorem yang diringkaskan telah digunakan
sebagai formulasi pengawalan untuk membenarkan SIRMs bersambungan FIS model
dalam FMEA dapat dibinakan. Selain itu, kebergunaan prosedur yang dicadangkan
dalam bidang pertanian, iaitu sarang burung yang boleh dimakan (EBN)
pemprosesan dan industri semikonduktor telah aitunjukkan. Sumbangan tesis ini ada
tiga segi, (i) memudahkan satu teorem dan keekanadaan ujian untuk aplikasi dunia
sebenar, (ii) prosedur FMEA baru dengan SIRMs bersambungan FIS dan (iii) kajian
kes mengenai pemprosesan EBN dan industri semikonduktor
iv
ABSTRACT
/Two major shortcomings of the traditional fuzzy inference systems (FISs)
e.g., Mamdani FIS and T -S FIS models, are (i) its difficulty to form a complete fuzzy
rule base when the number of required rules is large, and (ii) the fulfillment of
monotonicity property. The aims of this thesis are to analyze the use of a relatively
new FIS, i.e., Single-Input-Rule-Modules (SIRMs) connected FIS, and a simplified
theorem, as a solution for aforementioned shortcomings. Besides, a monotonicity
test procedure is used to evaluate the fulfillment of monotonicity property,
empiricall,J In this thesis, lhe applicability of lhe SIRMs connected FIS, its
simplified theorem, and a monotonicity test procedure; to real world problems (i.e.,
Failure Mode and Effect Analysis (FMEA) and a water level control problems) are
demonstrated. A new FMEA procedure with the SIRMs connected FIS and the
simplified theorem is proposed. The simplified theorem is adopted as the governing
equations to allow the SIRMs connected FIS model in FMEA to be constructed.
Besides, the usefulness of the proposed FMEA procedure in agriculture i.e., edible
bird nest (EBN) processing and semiconductor industry are demonstrated. The
contributions of this thesis are three folds, (i) simplification of a theorem and
monotonicity test for real world applications, (ii) a new FMEA procedure with the
SIRMs connected FIS and (iii) case studies on BBN processing and semiconductor
industry
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Pusat hirlmat Maklumat Akad r ' " UNIVI IT( MA YSlA S RA\\i\..
TABLE OF CONTENTS
Contents Page
Acknowledgement III
Abstrak IV
Abstract V
Table of Contents VI
List of Tables Xl
List of Figures XIII
List of Abbreviations XVI
CHAPTER 1 INTRODUCTION ~
1.1 Overview 1
1.2 Problem Statements 3
1.3 Objectives 4
1.4 Scope of the Project 4
1.5 Research Methodology 5
1.6 Thesis Organization
vi
i
6
Chapter 2 Literature Review
2.1 Introduction 8
2.2 Fuzzy Set Theory 9
2.2.1 Trapezoidal, Triangular and Gaussian Fuzzy Sets 10
2.2 .2 Operation on Fuzzy Sets 11
2.3 Fuzzy Inference System (FIS) 12
2.3.1 Fuzzy If-Then Rules 13
2.3.2 Fuzzy Reasoning 13
2.3.3 A General Paradigm for Conventional FIS Models 14
2.3.4 SIRMs Connected FIS 17
2.4 Monotonicity Property 19
2.4.1 Related Works 19
2.5 Monotonicity Test and Related Works 20
2.6 Failure Mode and Effects Analysis (FMEA) 22
2.6.1 The Conventional FMEA Procedure 23
2.6.2 Shortcomings of the Traditional RPN Model 25
2.6.3 Improvements of FMEA 26
2.7 Summary 30
CHAPTER 3 THE MONOTONICITY PROPERTY OF SIRMS CONNECTED
FUZZY INFERENCE SYSTEM
3.1 Introduction 31
3.2 A Zero-Order SIRMs Connected FIS 32
3.3 An Analysis of Fuzzy Rule Reduction 33
3.4 The Monotonicity Property of the SIRMs Connected FIS Model 35
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1
3.5 Water Level Control Problem 37
3.5.1 Background 37
3.5.2 A Fuzzy Controller for the Water Level Control Problem 38
3.5.3 Fuzzy Membership Function Design 39
3.5.4 Fuzzy Rule Gathering 40
3.6 Simulation Results and Discussions 40
3.6.1 Stimulation Result of Water Tank Model 40
3.6.2 Monotone Index/Test 42
3.7 Summary 44
CHAPTER 4 SIRMS CONNECTED-BASED FUZZY FAILURE MODE AND
EFFECT ANALYSIS METHODOLOGY
4.1 Introduction 46
4.2 Background and Motivations 47
4.2.1 Background 47
4.2.2 Motivations 48
4.3 The Proposed Fuzzy FMEA Procedure 49
4.3.1 A SIRMs Connected FIS-Based RPN Model 50
4.3.2 Fuzzy Membership Functions Design 51
4.3.3 Fuzzy Rule Gathering 55
4.4 Simulation Results and Discussions 56
4.4.1 An Analysis of Fuzzy Rule Reduction 56
4.4.2 Risk Evaluation Results With the SIRMs Connected FIS
Based RPN Model 57
4.4.3 Surface Plots 61
Vlll
4.4.4 Monotonicity Index! Test 63
4.5 Summary 65
CHAPTER 5 AN APPLICATION OF FUZZY FAILURE MODE AND EFFECT
ANAL YSIS TO EDIBLE BIRD NEST PROCESSING
5.1 Introduction 66
5.2 Background and Motivations 67
5.3 Edible Bird Nest Production 70
5.3.1 Geographical Locations 70
5.3.2 EBN Production 71
5.3.3 Swiftlets Fann and Fanning Process. 72
5.3.4 Harvesting 74
5.3.5 EBN Cleaning 75
5.3.6 EBN Drying and Reshaping 78
5.3.7 Storing and Packaging 81
5.4 Application of SIRMs Connected PIS-Based RPN Model to
Edible Bird Nest Processing 82
5.4.1 Scale Tables and Fuzzy Membership Functions Design 82
5.4.2 Fuzzy Rule Gathering 85
5.5 Results And Discussions 86
5.5.1 An Analysis of Fuzzy Rule Reduction 86
5.5.2 Surface Plots 87
5.5.3 Monotonicity Test 90
5.6 The FMEA Tables and Discussions 90
5.6.1 Swiftlets Fanning 99
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I
5.6.2 Harvesting 101
5.6.3 EBN Cleaning 101
5.6.4 EBN Drying and Reshaping 102
5.6.5Storing and Packaging 103
5.7 Summary 104
CHAPTER 6 CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORKS
6.1 Conclusions 105
6.2 Recommendations for Future Works 106
REFERENCES 107
LIST OF PUBLICATIONS 119
x
LIST OF TABLES
Table Page
3.1 The evaluation of the efficiency of the SIRMs connected FIS model on the
fuzzy rule reduction 35
3.2 Results with the monotonicity test 44
4.1 The scale table for Severity (S) 52
4.2 The scale table for Occurrence (0) 53
4.3 The scale table for Detect (D) 53
4.4 Failure risk evaluation, ranking, and prioritizption results using the RPN and
SIRMs connected FIS-based RPN model for the test handler process 58
4.5 Results with the monotonicity test 64
5.1 The scale table for Severity (S) 82
5.2 The scale table for Occurrence (0) 83
5.3 The scale table for Detect (D) 83
5.4 Results with the monotonicity test 90
5.5 FMEA table for Swiftlets farming (P.l) 92
5.6 FMEA table for Harvesting (P.2) 93
5.7 FMEA table for EBN Cleaning (P.3) 94
5.8 FMEA table for EBN Drying and Reshaping (PA) 94
5.9 FMEA table for Storing and Packaging (P.5) 95
5.10 FMEA table for Tool and Facility Maintenance for Swiftlets farming (M.l) 96
Xl
1
5.11 FMEA table for Tool and Facility Maintenance for Harvesting (M.2) 97
5.12 FMEA table for Tool and Facility Maintenance for EBN Cleaning (M.3) 97
5.13 FMEA table for Tool and Facility Maintenance for EBN Drying and
Reshaping (M.4) 98
XlI
LIST OF FIGURES
Figure Page
1.1 Research methodology 5
2.1 Trapezoidal fuzzy set 10
2.2 Triangular fuzzy set 10
2.3 Gaussian fuzzy set 11
2.4 A general paradigm for conventional FIS models by Mendel (2001) 14
2.5 Fuzzy reasoning procedure of Mamdani FIS model operation (Ross, 2009) 15
2.6 The fuzzy If-Then rule of the Mamdani FIS model 15
2.7 An illustration of Sugeno FIS model operation (Jang et ai, 1997) 16
2.8 Block diagram of a SIRMs connected FIS model 17
2.9 Fuzzy rules for a zero-order SIRMs connected FIS model 18
2.10 Conventional FMEA procedure (Pillay and Wang, 2003) 23
3.1 Fuzzy rules for a zero-order SIRMs connected FIS model 32
3.2 A fuzzy rule for a conventional FIS model 33
3.3 Comparable fuzzy sets with a fuzzy ordering A ~ B 35
3.4 Water level control problem 37
3.5 Fuzzy rules for the SIRMs FIS-based RPN model 38
3.6 The membership functions ofSI RM - 1 (i.e., LEVEL) 39
3.7 The membership functions ofSI RM - 2 (i.e., RATE) 39
XllI
,..
3.8 Fuzzy rules for the SIRMs connected FIS model that is embedded in a 40
controller
3.9 Response of the controller subject to the square wave signal 41
3.1 0 Variation of the water level error versus to time 41
3.11 Response of the controller subject to a sinusoidal signal pattern 42
3.12 Response of the controller subject to a sawtooh input signal 42
4.1 The proposed fuzzy FMEA methodology with a SIRMs connected FIS-
based RPN model 49
4.2 Fuzzy rules for the SIRMs connected FIS-based RPN model 51
4.3 The membership functions of Severity (S) 54
4.4 The membership functions of Occurrence (0) 54
4.5 The membership functions of Detect (D) 54
4.6 Fuzzy sets of RPN output 55
4.7 Fuzzy rules for the SIRMs connected FIS-based RPN model 56
4.8 Inference outputs of 51RM - 1 61
4.9 Inference outputs of51RM - 2 61
4.10 Inference outputs of 51RM - 3' 61
4.11 A surface plot ofFRPN versus Occurrence (0) and Detect (D) with Severity 62
(S) is 10
4.12 A surface plot of FRPN versus Severity (S) and Detect (D) with Occurrence 62
(0) is 10
4.13 A surface plot of FRPN versus Severity (S) and Occurrence (0) with Detect 63
(D) is 10
5.1 Geographical locations of two swiftlets farms and two EBN production 70
plants in Sarawak, Malaysia
xiv
l
I
5.2 The EBN production process 71
5.3 A swift1ets fann in Sarikei 72
5.4 The management functional block diagram of a swiftlets fann 73
5.5 Raw EBNs in a swift1ets fann 74
5.6 A raw EBN accommodated by baby swiftlets 75
5.7 A flow chart for the EBN cleaning process 76
5.8 Cleaning of a raw EBN with a pincer 77
5.9 The tools used in the EBN cleaning process 77
5.10 A flow chart for the drying and reshaping process 79
5.11 The mold which is used in the molding process. 80
5.12 The oven which is used for drying the EBNs 81
5.13 The membership functions for Severity (S) 84
5.14 The membership functions for Occurrence (0) 84
5.15 The membership functions for Detect (D) 84
5.16 The fuzzy sets for the RPN output 85
5.17 Fuzzy rules for the SIRMs FIS-based RPN model 86
5.18 Inference outputs of SIRM - 1 87
5.19 Inference outputs ofSIRM - 2 87
5.20 Inference outputs of SIRM - 3 88
5.21 A surface plot ofFRPN versus Occurrence (0) and Detect (D) with Severity 88
(S) islO
5.22 A surface plot of FRPN versus Severity (S) and Detect (D) with Occurrence 89
(0) islO
5.23 A surface plot of FRPN versus Severity (S) and Occurrence (0) with Detect 89
(D) islO
xv
LIST OF ABBREVIATIONS
AHP
D
DEA
EBN
FCM
FIS
FMEA
FPR
FRPN
MAFMA
MCDM
MP
MRA
o
RPN
S
SlRMs
TOPSIS
PCR
Analytical Hierarchy Process
Detect
Data Envelopment Analysis
Edible Bird Nest
Fuzzy Cognitive Map
Fuzzy Inference System
Failure Mode and Effect Analysis
Fuzzy Production Rule
Fuzzy Risk Priority Number
Multi-Attribute Failure Mode Analysis
Multi-Criteria Decision Making
Mathematical Programming
Min Max Regret Approach
Occurrence
Risk Priority Number
Severity
Single-Input-Rule-Modules
Technique Order Preference by Similarity to Ideal Solution
Polymerase Chain Reaction
xvi
CHAPTER!
INTRODUCTION
1.1 Overview
Fuzzy sets and systems have gone through substantial development since the
introduction of fuzzy set theory by Zadeh (1965) about four decades ago. It has been
widely utilized in a variety of applications ranging from control engineering (Cai and
Zhang, 2008), pattern recognition (Ajiboye and Weir, 2005), risk assessment (Tay
and Lim, 2006), image processing (Lee et al.. 2005), robotics (Chatterjee et al ..
2008), and so on. In particular, fuzzy inference system (FIS), as one of the earliest
applications of fuzzy sets theory, has become one of the most successful applications
(Feng, 2006). An FIS model with fuzzy if-then rules can model the qualitative
aspects of human knowledge and reasoning processes without employing precise
quantitative analyses (Jang, 1993). Indeed, FIS has proven to be a successful control
approach to many complex nonlinear systems 'or even nonanalytic systems (Feng,
2006).
Mamdani FIS (Mamdani, 1971, 1976) and Takagi-Sugeno FIS (Takagi and
Sugeno, 1985) models are the earliest mathematical models with fuzzy sets.
Regardless of the popularity of Mamdani and Takagi-Sugeno FIS models, they suffer
from the "combinatorial rule explosion" issue, i.e., their complexity increases
1
exponentially, with the number of input dimension (Yubazaki et aI., 1997; Lee et aI.,
2003; Jin, 2000). Consider a traditional FIS model (e.g., Mamdani and Takagi
Sugeno FIS models), i.e., y = I (xv ... xn) with fuzzy if-then rules as follows;
II Xl is Al AND ",xn is An Theny is B
where An and B are fuzzy sets of input and output, respectively. With a traditional
FlS model, the number of fuzzy rules and the number of the parameters increase
exponentially, as the number of input parameters increases (Yubazaki et al., 1997).
Thus, it is difficult to develop or tune a traditional FIS model with many input
parameters (Seki et aI., 2010).
Over the years, several methods have been developed as solutions to the
"combinatorial rule explosion" issue. Examples are fuzzy rule reduction techniques
(Jin, 2000; Yen and Wang, 1999), hierarchical FIS (Lee et aI., 2003; Lin and Huang,
1998; Haber et al" 1998), and Single-Input-Rule-Modules (SIRMs) connected FIS
models (Yubazaki et al., 1997; Seki et al., 2010). In this thesis, the focus is on the
use of a SIRMs connected FIS model, as a solution to the "combinatorial rule
explosion" issue. SIRMs connected FIS model is chosen because of its simplicity.
A number of SIRMs connected FIS models exist in the literature. The zero-order
SIRMs connected FIS model was first propos~d by Yubazaki et al. (1997) for fuzzy
control with plural inputs. A functional-type SIRMs connected FIS model was
further proposed by Seki et al. (2010) in which a consequence has been generalized
as a mathematical function.
2
1.2 Problem Statements
In this thesis, the focus is on two highlighted shortcomings relating to FIS modeling;
(i) the "combinatorial rule explosion" (Yubazaki et aI., 1997; Lee et aI., 2003; Jin,
2000); and (ii) the fulfillment of monotonicity property (Seki et aI., 2010; Seki and
Tay, 2012; Tay and Lim, 2011). The first shortcoming suggests that a traditional FIS
model requires a large number of fuzzy rules, and it is a tedious process for obtaining
a complete set of fuzzy rules (Yubazaki et aI., 1997; Lee et aI., 2003; Jin, 2000). The
second shortcoming suggests that it is difficult and yet important to fulfill the
monotonicity property in many real world applications (Seki et aI., 2010; Seki and
Tay, 2012; Tay and Lim, 2011).
As a solution to the first shortcoming, a SIRMs connected FIS model is adopted.
As a solution to the second shortcoming, the theorem proposed by Seki et al. (2010)
are simplified and adopted as the governing equations for FIS modeling. In short,
Seki et aI.' s theorem (2010) suggests that a SIRMs connected FIS model is satisfying
the monotonicity property if the fuzzy membership functions are compare-able and a
set of monotonically-ordered fuzzy rules is available. Besides, while the SIRMs
connected FIS model and its monotonicity property has been studied, it is not sure
how these findings could be useful in undertaking real-world problems. Hence, this
thesis aims to demonstrate how the theorem which proposed by Seki et al. (2010)
could be implemented in practice. Besides, it is also difficult to visualize or evaluate
the monotonicity property (Tay et aI., 2012; Tay et aI., 2012; Tay and Lim, 2011) of
a SlRMs connected FIS. As such, the use of a monotonicity test (Tay et aI., 2012;
Tay et aI., 2012; Tay and Lim, 2011) to evaluate the monotonicity property
empirically is presented here in this thesis.
3
1.3 Objectives
The objectives of this thesis are as follows :
• To analyse the usefulness of SIRMs connected FIS in FIS modeling
problem.
• To apply the theorem proposed by Seki et al. (201O) in overcome the
issues related to the monotonicity property.
• To evaluate the monotonicity property of the constructed SIRMs
connected FIS model empirically.
• To formulate SIRMs connected FIS model, Seki et a!. 's theorem (20l0)
and monotonicity test to Failure Mode and Effect Analysis (fMEA) and
a control problem.
1.4 Scope of the Project
In this thesis, a zero-order SIRMs connected FIS model and its mathematical
conditions (i.e., Seki et a!. 's theorem (20l0)) to be of monotonicity property are
studied. The use of the zero-order SIRMs connected FIS model, together with the
mathematical conditions in two real world applications (i.e., to FMEA and a water
level control problem). A case study relating to edible bird nest (EBN) industry in
Sarawak, Malaysia is reported. The details of.discussions relating to FMEA, EBN
and water controller level are reported in the respective chapters. To evaluate the
monotonicity property fulfillment, a monotonicity test (Tay et a!., 2012; Tay et a!.,
2012; Tay and Lim, 2011) is implemented.
4
Pusat Khidmat Maid rna Akadl'rr'" IN V[ R' T I 1\lALAYSIA SARA\\n..
1.5 Research Methodology
The research methodology is depicted in Figure 1.1. Firstly, the background and
literatures relating to the subjects of interest were reviewed. The efficiency of the
SlRMs connected FIS model for fuzzy rule reduction is evaluated. The mathematical
conditions from Seki et al. (2010) are simplified. The monotonicity test (Tay et ai.,
2012; Tay et ai., 2012; Tay and Lim, 2011) is further adopted to evaluate the
monotonicity property of the SIRMs connected FIS model empirically.
[ Start J +
l Literature review J +
Analysis of the efficiency of the SIRMs connected FIS model on fuzzy rule reduction ..
Simplification ofSeki et aI's theorem (2010) and the monotonicity test
.J Application to water level control problem ,
Development of new fuzzy FMEA methodology with a monotonicitypreserving SIRMs connected FIS-based RPN model.
I + +
Case study 1: Semiconductor industry I
Case study 2: EBN processing 1y
I .. I
Conclusion and recommendation,
[ End ]
Figure 1.1 Research methodology
5
To illustrate the usefulness of the findings, an application to a water level
control problem is demonstrated. Besides, an FMEA methodology procedure with a
monotonicity-preserving SIRMs connected FIS-based Risk Priority Number model
(RPN) is developed. Seki et at.'s theorem (2010) is adopted as the governing
equation for preserving the monotonicity property of the proposed SIRMs connected
FIS-based RPN model. A case study on the semiconductor industry and a case study
on Edible Bird Nest (EBN) processing are further conducted to evaluate the
usefulness of the proposed FMEA model. Finally, concluding remarks and
suggestions for future works are presented.
1.6 Thesis Organization
This thesis is organized as follows. The research background is first described
in Chapter 1. Furthennore, problem statements and motivations are explained. The
research methodology, objectives, and scope of the project are also presented in
Chapter 1.
Literature relating to fuzzy set theory and related works are presented in
Chapter 2. Besides, the monotonicity property and the background of the
monotonicity testing techniques are briefly discussed in the chapter.
A zero-order SIRMs connected FIS model and its mathematical conditions
(i.e., Seki et al.'s theorem (2010» to be of monotonicity property are presented in
Chapter 3. An approach to evaluate the monotonicity property fulfillment of SIRMs
connected FIS, (i.e., the monotonicity index (Tay and Lim, 2011 b; Tay et at., 2012b,
2012c) are further implemented in the chapter. A SIRMs connected FIS-based water
level controller is further demonstrated to illustrate the usefulness of the simplified
theorem and the monotonicity index.
6