An Integrated Optimization System for Plastic Injection Molding Using Taguchi Method, BPNN,

(1)

中華大學博士論文

運用田口方法、倒傳遞類神經網路、基因演算法及混合粒子群演算法與基因演算法於塑膠

射出成形最佳化系統之研究

An Integrated Optimization System for Plastic Injection Molding Using Taguchi Method, BPNN,

GA, and Hybrid PSO-GA

系所別：科技管理博士學位學程學號姓名： D09803025 丹尼 Denni Kurniawan 指導教授：陳文欽博士

中華民國 1 0 3 年 6 月

(2)

ᄔ!ा!

߈ԃٰǴଯϩη׷਑ᔈҔܭ৔рԋ׎(PIM)ϐמೌԋߏِೲǶԜѦǴӢғౢൻᕉ ਔ໔อǵౢࠔख़ໆᇸǵଯ߄य़ࠔ፦฻ᓬᗺǴ׳ᡣ༟ጤ৔рԋ׎ԋࣁౢ཰ᝡݾύޑғ ӸϐၰǶନԜϐѦǴ৔рԋ׎ޑᇙำࣗࣁፄᚇǴό፾྽ϐ׷፦ࡷᒧǵᇙำୖኧϷኳ ڀ೛ीǴ೿཮ቹៜ༟ጤᇙࠔϐࠔ፦ǶӢԜǴӵՖගϲౢࠔࠔ፦ϝࢂख़ाޑ᝼ᚒǶؼ ӳޑᇙำୖኧ೛ۓࢂᗉխ܈෧Ͽ༟ጤᇙࠔલഐޑځύ΋ᅿБݤǶၸѐ৔рԋ׎ޑᇙ ำୖኧ೛ۓǴӄһᒘπำৣޑ࿶ᡍᆶ၂ᇤݤǶฅԶǴԜݤჹܭፄᚇޑᇙำࡽคਏΨ όӝ፾ǶҁፕЎගрٿ໘ࢤന٫ϯس಍Ǵࣁפр৔рԋ׎ӭख़ࠔ፦੝܄ϐന٫ᇙำ

ୖኧಔӝǶҁࣴز٬ҔҖαБݤǵॹ໺ሀᜪઓ࿶ᆛၡ(BPNN)ǵ୷Ӣᄽᆉݤ(GA)Ϸష ӝಈηဂᄽᆉݤᆶ୷Ӣᄽᆉݤ(PSO-GA)аפрന٫ୖኧ೛ۓǶӧҁࣴزύஒᅙጤྕ

ࡋǵ৔рೲࡋǵߥᓸᓸΚǵߥᓸਔ໔Ϸհࠅਔ໔ࣁᇙำ௓ڋୖኧǴߏࡋᆶᙋԔࣁࠔ

፦੝܄Ƕ२ӃǴ೸ၸҖαޔҬ߄຾Չ L255⁶ჴᡍǶਥᏵҖαჴᡍݤளٰޑ่݀ीᆉߞ

ဦᚇૻКǴ٩Ᏽౢࠔࠔ፦פрᇙำୖኧಔӝǶځԛǴ٬Ҕᡂ౦ኧϩ݋ݤ(ANOVA)פ рӭࠔ፦੝܄ϐᇙำୖኧಔӝǶಃ΋໘ࢤ S/N Кന٫ϯǴၮҔॹ໺ሀઓ࿶ᆛၡ (BPNN)ࡌᄬ S/N КႣෳᏔǴ่ӝ S/N КႣෳᏔᆶ୷Ӣᄽᆉݤ(GA)຾Չӄୱཛྷ൨Ǵ٬

Ӛࠔ፦੝܄ϐ S/N Кॶ೿നεϯǴԜ໘ࢤஒ٬ᇙำᡂ౦फ़ԿനեǹಃΒ໘ࢤࠔ፦ന

٫ϯǴճҔॹ໺ሀઓ࿶ᆛၡࡌᄬࠔ፦ႣෳᏔǴ่ӝ S/N КႣෳᏔǵࠔ፦ႣෳᏔᆶష ӝಈηဂᄽᆉݤᆶ୷Ӣᄽᆉݤ(hybrid PSO-GA)຾Չ୔ୱֽ೽ཛྷ൨Ǵஒࠔ፦ၳ߈Ҟ኱

ೕ਱Ǵפрന಄ӝࠔ፦ೕ਱Ъᇙำനࣁᛙۓϐന٫ᇙำୖኧಔӝǶനࡕ຾Չᡍ᛾ჴ ᡍаຑ՗Ԝس಍ϐਏૈǶᡍ᛾ჴᡍ่݀ᡉҢǴҁࣴزϐന٫ϯس಍ό໻ගϲ༟ጤ႟

ҹϐࠔ፦ǴҭёԖਏफ़եᇙำᡂ౦Ƕ

ᜢᗖຒǺ༟ጤ৔рԋࠠǵҖαБݤǵᡂ౦ኧϩ݋ǵॹ໺ሀᜪઓ࿶ᆛၡǵ୷Ӣᄽᆉ ݤǵషӝಈηဂᄽᆉݤᆶ୷Ӣᄽᆉݤ!

(3)

Abstract

Applications of polymer material in injection molding application are growing very fast in last decades. Moreover, several advantages, such as short cycle time production, light weight of products, and high surface quality, make plastic injection molding (PIM) work as a solution for industries to survive in competitive world. Besides these advantages, PIM is a more complex process than it is previously thought. Inappropriate material selection, process parameters, part and mold designs can affect the quality of plastic products. Therefore, investigation to improve product quality still becomes an important issue to be conducted. A well-controlled parameter setting is one of the solutions to avoid or reduce defect in plastic products. Previously, process parameters in PIM relied on the technician's experience using trial-and-error approach. However, this approach is not effective and unsuitable for complex manufacturing processes. This study presents a two- stage optimization system to find optimal process parameters of multiple quality characteristics in the PIM process. The Taguchi method, back-propagation neural network (BPNN), genetic algorithms (GA), and combination of particle swarm optimization and genetic algorithms (PSO-GA) are used to find optimum parameter settings. Melt temperature, injection velocity, packing pressure, packing time, and cooling time are selected as initial process parameters. Length and warpage are employed as the product quality. The experimental work is conducted using the Taguchi orthogonal array.

According to the result from the Taguchi experiment, S/N ratio is calculated to find the best combination settings for product quality. Then, analysis of variance (ANOVA) is used to determine significant factors of the control parameters. Moreover, the S/N ratio predictor and quality predictor are constructed using BPNN. In the first stage optimization, S/N ratio predictor and GA are used to reduce variance of quality characteristic. In the second stage optimization, the S/N ratio predictor and quality predictor with hybrid PSO- GA are used to find optimal parameter settings for quality characteristic and stability of the process. Finally, three confirmation experiments are conducted to assess the effectiveness of the proposed system. Experimental results show that the proposed system not only improves the quality of plastic parts, but also reduces variability of process effectively.

Keywords: plastic injection molding, Taguchi method, ANOVA, BPNN, GA, PSO-GA.

(4)

Acknowledgment

First and foremost I would like to express heartfelt appreciation and sincere gratitude to Dr. Wen-Chin, Chen for providing me the opportunity to conduct this research under his guidance. His analytical skill, motivation, energy, and power have made the opportunity of my study extremely valuable and become unforgettable memory during my study in Taiwan. I am sure this will make a good foundation for me for my future as researcher and professional career as well. I also like to thank for all committee members for my final oral defense: Prof. Chung-Teh Sheng, Prof. Perng-Kwei Lei, Prof Wang-Ming Wen, and Prof.

Wei-Zao Deng (Simon).

I would like to thanks for Aceh government and Taiwan government for the scholarship during my study in Taiwan. Special thank also for Polyprecision Industrial Co.

Ltd. that allowing me for conducting the experiment in the company. I also would like to thankful for Chung Hua University, Ph.D. Program for Technology Management, Prof.

Kai-Wei Li, Prof. Chiu-Chi Wei, Prof. Wen-Long Yao, Prof. Charles Choi, Prof. Heng Ma, Prof. Yuwaldi Away, Prof. Riza Sulaiman, and Dr. Haslina Arshad.

All this work also dedicate for my parents, H. Sofyan Ibrahim Tiba (Alm.) and Hj.

Zuriati. I can never thank for my parents enough, and I am very happy for all support from them and all family members bang Apok, kak Yanti, kak Desi, Oki & Felly.

Special thanks for support and help during my study from all teachers, I really appreciate help from all friends during my study in Taiwan, Munira, Agus, Ikram, Iqbal, Okta, Rijalul, Intan, Nuri, Nina, Maliya, Bustami and all MSC members, Basrul, Nayan, Hendy, Arrad, Haikal, Reza, Omar and all ICA members, Raymon, Charles, Dr. Mohannad, Muhammad Jamal and family, Sam and family, Ms. Hichi and all Activity Center in CHU, Apple and all MINT members, Ashley, Anita and all International Office crew, bro Abdul Razak, (Alm.) Pn Pura and family, and all of crew from 144 Laboratory Artificial Intelligence and Automations, especially for Dr. Persie, Dr. Dai, Dr. Gong-Loung Fu, Wang lao-tse. Dyan, Aibar, Handsome boy, Denin, Mickey, and all friends that I cannot put in this dissertation book.

Denni Kurniawan (Ϗѭ) Ph.D. Program for Technology Management, Chung Hua University,

2014/06/05

(5)

List of Tables

Table 1 Effect of injection molding parameters for product quality ... 16

Table 2 Summary of plastic injection molding in previous studies ... 18

Table 3 Comparison several methods for experimental design ... 23

Table 4 The L₄(2³) orthogonal array ... 23

Table 5 The C_p value scales ... 46

Table 6 The process capability Ca value hierarchy ... 47

Table 7 Cpk value classification ... 47

Table 8 The range for parameter settings ... 51

Table 9 Taguchi orthogonal array ... 52

Table 10 Specifications of plastic injection molding machine ... 57

Table 11 Specification of PBT material ... 59

Table 12 Recommended molding processing window for PBT 2100 ... 59

Table 13 The level and ranges of parameter settings ... 64

Table 14 Experimental parameters of the Taguchi orthogonal array ... 64

Table 15 Experimental results for length ... 65

Table 16 Experimental results for warpage ... 66

Table 17 Parameter settings for highest S/N ratio of length and warpage ... 68

Table 18 ANOVA analysis for length ... 68

Table 19 ANOVA analysis for warpage ... 69

Table 20 Settings for S/N ratio predictor (BPNN_SN) ... 70

Table 21 Settings for quality predictor (BPNNQ) ... 72

Table 22 The best parameter settings for Taguchi method ... 74

Table 23 Optimal parameter settings for the first stage optimization ... 75

Table 24 Optimal parameter settings for the second stage optimization ... 76

Table 25 Search values and setting values for confirmation experiment ... 78

Table 26 Results of confirmation experiments for product length and warpage ... 78

Table 27 Comparison verification experiment ... 81

(8)

List of Figures

Figure 1 Flowchart of this dissertation ... 5

Figure 2 Illustration of plastic injection molding machine ... 8

Figure 3 Schematic plastic injection molding process ... 9

Figure 4 Volume variation for crystalline and amorphous materials ... 14

Figure 5 The variation of shrinkage caused by processing and design parameters ... 15

Figure 6 Quadratic loss function ... 21

Figure 7 Illustration of L4(2³) orthogonal array ... 23

Figure 8 Flowchart of the Taguchi method ... 25

Figure 9 Biological neural network... 27

Figure 10 Nonlinear model of a neuron ... 28

Figure 11 ANN activation functions ... 29

Figure 12 Architecture of multilayer perceptron ... 34

Figure 13 Flow chart of Genetic Algorithm ... 37

Figure 14 One point crossover processes ... 38

Figure 15 Two-point crossover processes ... 39

Figure 16 Uniform crossover processes ... 39

Figure 17 Mutation process ... 40

Figure 18 Flowchart of PSO ... 41

Figure 19 General classification of the optimization methods... 43

Figure 20 Capability index C_p ... 45

Figure 21 Center positions of offset levels ... 46

Figure 22 Flowchart of the proposed research ... 50

Figure 23 Architecture of BPNN for the proposed system ... 55

Figure 24 Victor Taichung VS-80 PIM Machine ... 58

Figure 25 Control panel of injection molding machine ... 58

Figure 26 Experimental mold... 60

Figure 27 Proposed plastic part ... 60

Figure 28 Dimension of plastic product ... 61

Figure 29 Mitutoyo digital slide caliper ... 62

Figure 30 NV300T laser measurement ... 62

(9)

Figure 31 The measurement method for the length ... 63

Figure 32 The measurement method for the warpage ... 63

Figure 33 BPNNSN training performance ... 70

Figure 34 Zigzag line of BPNNSN for length ... 71

Figure 35 Zigzag line of BPNNSN for warpage ... 71

Figure 36 BPNN_Q training performance ... 72

Figure 37 Zigzag line of BPNN_Q for length ... 73

Figure 38 Zigzag line of BPNNQ for warpage ... 73

Figure 39 Comparison of lengths between Taguchi method, first stage and proposed system ... 79

Figure 40 Comparison of warpage between Taguchi method, first stage and proposed system ... 80

(10)

CHAPTER 1 Introduction

Injection molding is commonly used to produce plastic products, because it can produce a large amount of product in a very short time with low production cost. Plastic injection molding (PIM) has several advantages, such as short cycle time production, light weight of products, and high surface quality. There are several sequences in a PIM process such as plastication, injection, packing, cooling, ejection and quality control process.

Besides of these advantages, PIM is a more complex process than it is previously thought.

Inappropriate mold design, material, and parameter settings can produce defects in the plastic parts. The plastic products are very complex designed and it is difficult to predict the final product results. The quality of plastic products depends on the material selection, process parameters, the design of part and mold. Inappropriate of these factors, will produce several defects such as warpage, shrinkage, flash, sink marks and weld lines.

Among those defects, warpage is considered as the most important defect and it has been investigated by many researchers. To prevent these defects occur in PIM process and to improve product quality, many studies had been conducted by optimizing process parameter settings. This chapter is arranged in the following manner. The first section gives an overview of plastic injection molding process. The second section presents the problems related to PIM. Then, the motivation behind the research undertaken in this dissertation is discussed in the third section. Finally, the last section provides outline of this dissertation.

Section 1 Background and Motivation

Plastic injection molding (PIM) is a very important process to produce plastic parts.

PIM is suitable to use for mass production of products because it is easy to convert raw material to be a plastic product in a single automation process. Other advantages of utilization of PIM, such as easy to produce, light, corrosion resistance, easy to shape, and low processing cost. There are several processes of injection molding to produce plastic parts: plastication, injection, packing, cooling, and ejection. Even though most engineers argue that this is an easy process, but in the practice PIM process is more complex than it

(11)

is thought. Inappropriate material selection, process parameters, part and mold designs can affect the quality of plastic products. Several defects that frequently occur in the PIM process for instance warpage, shrinkage, sink marks, and weld lines. In many studies, researchers give more focus to reduce warpage compared to other defects. It is because warpage easily affect the appearance and functions of plastic products.

One of the solutions to reduce warpage is by optimizing parameter settings in PIM.

In the past, process parameters during PIM were mostly relied on the technician's experience. They determined the initial process parameter settings by using trial-and-error methods. However, this attempt requires high cost, time consuming, and depends highly on the experience of the technicians as well. Then, many studies used the Taguchi method to determine the best combination of process parameters for improving product quality.

However, the Taguchi method is not suitable to find the optimal parameter settings for continuous value, and it has difficulties when it is used for multiple response problems.

Therefore, advanced methods are highly demanded to optimize the PIM process to produce high quality of plastic products. Recently, integration of the Taguchi method and optimization methods found as the answer to obtain more reliable system to found the optimum parameter settings in improving product quality. Some studies showed that combination of several intelligent and optimization system will give a better solution for the real word applications. The combination of these systems is called as hybrid optimization system. Even though a hybrid system can be a good solution to solve the problems, but inappropriate of proposed combination will be the weakness. Thus, it is depends on the components constitute the hybrid to make it as good or bad solution.

Selecting the right components to build a good hybrid system will ensure the system to give the optimal solution for the problems.

According to previous studies, many researchers only focused on optimizing the process parameters to improve quality in PIM using various methods, but they did not asses the stability of the process. Therefore, besides improving the quality of plastic parts, this study also gives attention to the stability of the process. This study proposes a systematic technique using the Taguchi method, BPNN, GA, and hybrid PSO-GA is used to optimize process parameters. The optimization system has two stages. First, the Taguchi method is used to find the best combination of initial parameter settings for product length and warpage. The experimental data is used to construct S/N ratio predictor and quality predictor by using BPNN. In the first stage optimization, combination of S/N ratio

(12)

predictor and GA is used to reduce the variability of the process and consistency of product quality. In the second stage, the S/N ratio predictor and the quality predictor with the hybrid PSO-GA are used in the second stage optimization. The objective of the second stage is to find the optimal settings for quality characteristic and stability of the process.

The proposed system not only promotes the quality of plastic parts, but also reduces the manufacturing process variables.

Section 2 Problem Statement and Recognition

Process parameter settings are very important and have direct effect for quality of plastic product in PIM. Unsuitable parameter settings also can initiate defect and unstable quality in production process. Previously, trial-and-error method was often performed by engineers to get the best parameter settings. However, this method is not efficient because it is time consuming and unsuitable for complex manufacturing process. Even though the Taguchi method was applied in many studies, but this method cannot be used to find optimal parameter settings for continuous values. The application of the Taguchi method is only used to get the best combination of process parameters. Moreover, many studies also only focused on the optimizing the process parameters, but did not assess the stability of the process. Therefore, this study not only focusing on the optimal process parameters to improve the multiple qualities of plastic parts, but also the stability of the process. A systematic technique using the Taguchi method, BPNN, GA, and hybrid PSO-GA are used to optimize parameter setting for optimal quality characteristics of plastic parts and to reduce more stable of the process.

Section 3 Research Objectives

The objectives of this dissertation is to obtain optimal process parameters using a two stage optimization system for improving multiple quality characteristics and to reduce variability in plastic injection molding process. Therefore, in order to obtained the process parameters optimization system, the main purposes as follows:

Firstly, the Taguchi method is used to get initial parameter settings for product length and warpage. Since the Taguchi method difficult to find optimal settings for continuous value, and also for multiple response problems, then this study is expected to overcome this shortcoming.

(13)

Second, this study expected to find the correlation of process parameters and quality characteristics of plastic parts. The important of process parameters for product length and warpage also can be identify based on data of the experiment.

Third, S/N ratio predictor and quality predictor are used to map relationship of control factors and responses of experiment. The S/N ratio predictor and quality predictor are constructed from data of previous experiment. The estimation and true value from experiment will be compare to assess the accuracy of the predictor.

Fourth, the utilization of the Taguchi method, BPNN, GA, and hybrid GA-PSO optimization methods and experimental procedures to optimize parameter settings.

Also to asses if the combination of optimal parameters from those methods will improve product quality and make the process better in variability.

Fifth, by applying a two stage optimization system, it is expected to have a better quality of plastic products (length and warpage). Moreover, the proposed system believed to reduce variability of process for both quality characteristics.

Section 4 Guide of Dissertation

This dissertation is divided into six step to as illustrate in Fig. 1. The title of this dissertation is “An Integrated Optimization System for Plastic Injection Molding using Taguchi Method, BPNN, GA, and Hybrid PSO-GA”. The expectation of this study is to find optimal process parameters to improve multiple quality characteristics and reducing variability of PIM process. The detail of this dissertation will be addresses as follows:

Chapter 1 Introduction

This chapter presents background and motivation of the study, reveals all problems from previous studies, and the objectives of this research.

Chapter 2 Literature Review

This chapter reveals the literature review that related to this research. Plastic injection molding, the Taguchi method, artificial neural network, genetic algorithm, particle swarm optimization, and process capability index, are among the topics discuss in this chapter.

(14)

! " #

$

Figure 1 Flowchart of this dissertation

Chapter 3 Research Methodology

Design of proposed system and detail implementation of each method will be discuss in this chapter.

Chapter 4 Experiment and Result Analysis

Chapter 4 discloses the result and analysis of the experiment, which conducted in Chapter 3. Moreover, detail procedure of experiments, the sequence of proposed system is expected to find optimum parameter settings to improve product quality and reduce variability of the process also discussed in this chapter.

(15)

Chapter 5 Confirmation Experiment for Proposed Optimization System

Chapter 5 presents the confirmation experiment, which is necessary to examine the effectiveness of proposed system. Confirmation of the Taguchi method, the first stage optimization and the second stage optimization conducted are exhibited within this chapter.

Chapter 6 Conclusion and Future Works

In this chapter, all important findings during the study will be concluded within this chapter. Suggestion for the future work related to the study is discloses here.

(16)

CHAPTER 2 Literature Review

Plastic injection molding is the most important process for manufacturing plastic parts. According to many literatures, many factors should be given attention to produce high quality of plastic products. Optimization of process parameters is often used to improve the quality of plastic parts. In previous studies, combination of several optimization methods is used in order to improve the product quality. This chapter reveals the introduction about plastic injection molding, such as the machine, the process, selection of control process parameters, responses in the previous studies, and the implementation of optimization method in plastic injection molding. Moreover, this chapter also presents the basic of the Taguchi method, artificial neural network, genetic algorithm, particle swarm optimization, soft computing and hybrid system, and process capability indices, which are used to optimize process parameter settings in molding of plastic parts.

Section 1 Plastic Injection Molding

1. Previous Study in Plastic Injection Molding

Plastic injection molding (PIM) is the most important method in polymer processing.

This process grows very fast in the last decades and it is always used in many industries.

There are several types of PIM machine, but generally, they are divided into two major parts: injection unit and clamping unit. The functions of injection unit is to plasticizing the pallets and force the melt into the mold under specific pressure. This unit consists of several parts such as plastic feeding hopper, heating cylinder (barrel), screw, and nozzle.

The clamping unit works to hold the mold closely during the injection and actuates the ejector when it opens. This unit should be strong enough to resist large force generated by injection pressure. The clamping mechanism could be a hydraulic press or a mechanical lever system. Mold is placed within clamping unit. Mold is the tool to shape material into a desired product. There are several types of mold, but generally two-piece of molds are used in many industries. Mold is not simply two halves with a single cavity. A mold is moving plates with a resin flow system where placed gates, runner, and a sprue. Another important part of PIM machine is the controller, which is a programmable computer to control whole

(17)

units and processes in PIM machine, such as attaining and holding the desired process variables, controlling the cooling system, and actuating the clamp mechanism and mold system. The illustration of PIM machine is shown in Fig. 2.

Figure 2 Illustration of plastic injection molding machine Source: Banerjee (2006)

Generally, the plastic injection molding cycle consists of several phases: closing the mold, injecting, cooling and packing, open the mold, and ejecting the part. The cycle in PIM process will repeats from closing the mold process. Illustration of the process in plastic injection molding process is shown in Fig. 3. The process in PIM begins when two- pieces mold is closing, then the polymer material is put into the barrel and heated to its melting temperature. The melting plastic accumulates at the front of the barrel as the screw retracts to the rear of barrel. Then, the melting polymer is injected into the cavity through a gate under high pressure. When the filling process is nearly completed, the cavity is kept at a constant pressure for the packing pressure. The packing pressure is utilized to fill the remaining volume of the cavity to avoid or to minimize the shrinkage defect during cooling process. After the plastic parts are formed during the cooling process, then the final process is to eject the product from the mold. Some of the injection molding machines, equipped with the ejector device that makes the plastic parts easier to be ejected and collected. After this process, the cycle repeats from closing the mold process.

(18)

Figure 3 Schematic plastic injection molding process Source: Banerjee (2006)

(19)

Several advantages, such as short cycle time production, light weight of products, and high surface quality, make Plastic Injection Molding (PIM) work as a solution for industries to survive in the competitive world. Besides these advantages, to obtain a high quality of plastic product, process in PIM is more complex than it is previously thought.

Inappropriate mold design, material, and parameter settings will produce defects in the plastic parts. Many researchers conducted investigation to minimize defects in PIM (Kusic, et al., 2013; Mohammad et al., 2011; Oktem, 2011; Oktem et al., 2007; Shi et al., 2012;

Tzeng, et al., 2012; Wang, et al., 2013). Typical responses problem in PIM, including:

minimizing warpage (Chen et al., 2009; Deng et al., 2010; Gao & Wang, 2009; Kurtaran &

Erzurumlu, 2006; Sun et al., 2010), shrinkage (Altan, 2010; Kamaruddin et al., 2010;

Prashantha et al., 2009), sink mark (Mathivanan & Parthasarathy, 2009), flash (Xu et al., 2012), short shot (Chiang et al., 2011; Park & Ahn, 2004), weld-line (Ozcelik et al., 2012), minimizing cycle time (Chauhan & Ahmad, 2012), designing of cooling channel (Hassan et al., 2010; Park & Dang, 2010; Postawa et al., 2008), minimizing clamp force (Yin et al., 2011a), and reducing weight (Chen et al., 2008; Yang & Gao, 2006).

According to the previous studies, most of researchers focused the research on reducing warpage, since it affects the appearance and the function of plastic parts (Mostafa et al., 2011; Oktem, 2011; Shi et al., 2012; Tzeng et al., 2012). There are several reasons for the occurrence of warpage, such as differences in shrinkage that causes deformation, non-uniform mold temperature in the mold plate, differences in material properties, not uniform in material temperature, type of filler, processing parameter condition, differences in part thickness, and the placement of fluid core inside the part (Bociaga et al., 2010). To prevent warpage, it is important to assure the uniformity of the temperature across the part.

Minimizing of warpage for thin-walled parts and parts with application for optics is also possible by optimizing parameter settings. Typical process parameters or control factors give a contribution for a good quality of plastic product. Several process parameters such as melt temperature, mold temperature, cooling time, packing pressure, packing time, injection time, gate locations and injection velocity are potential influences the product quality (Attia & Alcock, 2011; Chen et al., 2009; Zhao & Gao, 1999).

A well-controlled parameter setting is one of the solutions to avoid or to reduce these defects. Previously, process parameters in PIM process relied on the technician's experience using trial-and-error approach. However, this approach is not effective and unsuitable for complex manufacturing processes. Then, many studies used the Taguchi

(20)

method to determine the best combination of process parameters for improving product quality (Altan, 2010; Fei et al., 2011; Oktem et al., 2007; Ozcelik et al., 2010; Ozcelik &

Sonat, 2009; Sun et al., 2010). However, the Taguchi method is not suitable to find the optimal parameter settings for continuous value, and it has difficulties when it is used for multiple response problems (Chen et al. 2009; Hao, 2010; Xu et al., 2011). As solutions, several methods such as Back-Propagation Neural Network (BPNN), Response Surface Methodology (RSM), Design of Experiment (DOE), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) were applied to optimize parameter settings in plastic injection molding (Berti & Monti, 2013; Dang & Park, 2011). In Ozcelik and Erzurumlu (2005) research, warpage of a thin shell plastic part was successfully reduced over 40% using a combination of DOE, RSM, FEA and GA. Yin et al. (2011) presented reduction of warpage value by 32.9% using the BPNN and Finite Element Analysis (FEA). In their study, they stated that process parameters can be optimized with the help of a prediction system, where BPNN was used to predict the relationship between parameter settings and warpage value. Chen et al. (2009) presented the investigation of reducing shrinkage using RSM. Four process parameters were used (injection velocity, packing pressure, mold temperature, and melt temperature). The result from confirmation experiment found that the error of experimental data and predicted values were relatively small.

Recently, many studies investigate a combination of optimization methods in improving product quality of plastic parts. The combination of several optimization systems is called hybrid optimization system and it is believed that it offers a better solution (Idoumghar, 2011; Mhamdi et al., 2011; Nakano, et al., 2010; Song et al., 2008;

Zhang & Wu, 2012). Since each optimization, has its own strengths and weaknesses, then a hybrid system is a good solution to solve problems by empowering each method and abandoning their weaknesses. Chen et al. (2012a) used BPNN, Simulated Annealing (SA) and PSO to obtain the best combination of parameter settings for precise product length and minimized warpage. Kurtaran and Erzurumlu (2006) presented the combination of RSM and GA to minimize warpage of thin shell parts. In their study, mold temperature, melt temperature, packing pressure, packing time, and cooling time were considered as initial process parameters. Moreover, the RSM model was combined with GA to find optimum process parameter values. The combination system successfully reduced warpage by about 46%. Resendiz and Rull-Flores (2013), determined the optimal variable selection using combinational Mahalanobis-Taguchi System (MTS), Binary PSO (BPSO), Binary

(21)

Ant Colony Optimization (NBACO), and Gompertz Binary PSO (GBPSO) in application of automotive pedals components. In Wang et al. (2013) study, they developed a combination of BPNN and PSO to find the optimal setting and to estimate the production cost of plastic parts in injection molding manufacturing. They successfully reduced the number of variables and they found that GBPSO is the fastest computational method compared to BPSO and NBACO algorithm.

2. Selection of Control Factors in PIM

Many factors affect the quality of plastic parts, such as the setting of process parameters, the mold system, part geometry and plastic materials (Bociaga & Jaruga, 2006).

Many studies reported the importance of appropriate determination of process parameters to obtain high quality of product. Engineer or user must select the feasible and tractable control factors that influence the product result in PIM process. Unsuitable of determination parameter settings can cause many production problems. Many studies select different number of process parameters that potentially influence the quality of product in plastic injection molding such as melt temperature, mold temperature, injection pressure, injection velocity, injection time, packing pressure, packing time, cooling temperature and cooling time (Kurtaran & Erzurumlu, 2006; Zhao & Gao, 1999).

Generally, many literatures investigated the improvement of plastic part using different control process parameters. For example, Shi et al. (2009) used six process parameters (mold temperature, melt temperature, injection time, packing pressure, packing time, and cooling time) to determine the optimal process parameter settings to reduce warpage defect.

Park and Dang (2010) used six process parameters (diameter of cooling channel, thermal conductivity, thickness of mold, injection temperature, coolant temperature, and pitch direction) to optimize the cooling channel in PIM. Sun et al. (2010) selected five process parameters (mold temperature, melt temperature, injection time, packing pressure, and packing time) to verify the optimal initial process parameters and reduce warpage of digital camera case. Yin et al. (2011b) applied five parameter settings (mold temperature, melt temperature, packing pressure, packing time, and cooling time) to minimize warpage and clamp force that used in PIM process. In Ozcelik and Sonat (2009) study, they used four process parameters (packing pressure, melt temperature, packing time, and mold temperature) to minimize warpage of a thin shell plastic product. Kurtaran et al. (2005) utilized five process parameters (mold temperature, melt temperature, packing pressure,

(22)

packing time and cooling time) to predict and to minimize warpage of plastic product.

Ozcelik et al. (2010) selected four process parameters (melt temperature, packing pressure, cooling time, and injection pressure) to optimize the mechanical properties of injection molding test part. Four control factors were selected in Chen, Su and Lin (2009) research:

injection velocity, packing pressure, mold temperature, and melt temperature. Those factors were chosen as initial parameters to minimize shrinkage of thin shell molded part.

In addition, a large number of parameters were used in Chen et al. (2012b) study. Initially, eight process parameters (cooling time, mold temperature, melt temperature, injection velocity, packing pressure, injection pressure, packing time, and VP switch) were used in the research. After a screening process using design of experiment and ANOVA analysis, the number of control parameters was reduced to five factors (melt temperature, injection velocity, injection pressure, packing pressure, and packing time). Therefore, the selection of control process parameters is very important in PIM process.

Feasible and tractable control parameters need to be selected in order to get a good product quality of plastic product. Several techniques are used to select initial process parameters, such as expert experience, previous studies and brainstorming. In order to have an effective experiment, it is very important to have basic understanding of the processes and products. Discussion with the expert about the products is one of the effective tool for guiding the experiment become success. Brainstorming can be helpful to get feasible alternative of the selection control factors for the experiment. Brainstorming also can be used to determine the experiment objectives, alternative quality characteristics, and to identify means of measuring quality characteristics.

3. Defects in PIM

As mentioned in the previous section, most of research in PIM focused on reducing warpage in plastic parts. Warpage is a distortion of the plastic products surface from the intended shape of the design. There are several causes that make warpage occurs in plastic parts, such as differences in shrinkage that causes deformation, non-uniform mold temperature in the mold plate, differences in material properties, not uniform in material temperature, type of filler, processing parameters condition, differences in part thickness, and the placement of fluid core inside the part (Bociaga et al., 2010). Achieving good product by minimizing as low as possible of warpage is a complicated task due to the presence and interaction of many factors in the process.

(23)

Differential shrinkage can lead to warpage occur in plastic parts. The variation in shrinkage can be caused by molecular and fiber orientation, temperature of the molded part, and variable of packing, or different pressure levels as material solidifies across the part thickness. When shrinkage is different and anisotropic across the parts and the parts thickness, then warpage will occur that caused by the internal stress. The shrinkage of molded plastic parts can be about 20 percent of the volume, when measured at the processing temperature and the ambient temperature. Crystalline and semi-crystalline materials are very vulnerable to thermal shrinkage, while the amorphous materials tend to have less shrinkage. The crystallites will be occur when crystalline materials are cooled below the transition temperature. On the other hand, the amorphous material does not change with the phase change. As the result, crystalline and semi-crystalline materials have a greater difference in specific volume (∆υ) between the melt phase and solid phase (Potsch, 1995). Fig. 4 illustrates the shrinkage of crystalline and semi-crystalline with amorphous material. An example of crystalline polymer material is Polybutylene terephthalate (PBT). This material is a type of polyester and it is appropriate to be used as insulator in many electronics products. Another advantages of PBT material is good resistant to solvents, resistant for shrinkage during forming, mechanically strong, and can be treated with flame retardants.

Figure 4 Volume variation for crystalline and amorphous materials Source: Potsch (1995)

(24)

Excessive of shrinkage, beyond the acceptable level, can be caused many factors such as: low injection pressure, short cooling time, high melt temperature, high mold temperature, and low holding pressure. The processing and design parameters that affect part shrinkage can be illustrated by Fig. 5.

Figure 5 The variation of shrinkage caused by processing and design parameters

Process parameters in plastic injection molding such as melt temperature, mold geometry, injection velocity, packing time, packing pressure, and cooling time will affect the quality of plastic products. Previously, the settings for these control parameters fully relied on trial-and-error approach. Technician’s need to change the setting when defects occur in the plastic parts. Table 1 shows general recommendations based on trial-and-error approach for defects on plastic products (Bollin, 2010). For example, when flash defect occur on the plastic part, then technicians need to adjust the settings manually, either to decrease melt temperature, injection pressure, cycle time, or increase clamp pressure.

Adjusting the settings manually one-by-one will make this approach not effective, time consuming and unsuitable for complex manufacturing process. Therefore, other approaches using the Taguchi method and optimization methods will make the process to find optimum parameter settings more effective and efficient.

Packing pressure

Shrinkage

Packing time

Shrinkage

Part thickness

Shrinkage

Melt temperature

Shrinkage

Mold temperature

Shrinkage

Injection rate

Shrinkage

(25)

Table 1

Effect of injection molding parameters for product quality

Defect Adjustment for Parameter Settings

Poor surface finish

Increase shot size

Increase injection pressure and/or speed Increase melt temperature

Increase mold temperature Increase cycle time

Flash

Decrease melt temperature Decrease injection pressure Decrease cycle time

Improve mold venting Increase clamp pressure

Weld lines

Increase injection pressure

Increase packing time and pressure Increase melt temperature

Increase mold temperature

Sinks or Voids

Increase injection pressure

Increase packing time and pressure Increase melt temperature

Decrease mold temperature

Warpage

Increase mold temperature

Increase injection pressure and/or velocity Increase packing time and pressure

4. Categories of problems in Experiment

There are different types of problems in experimental work, such as to maximizing the strength of products, minimizing defects, and so on. However, the problems can be divided into five categories: smaller-the-better, larger-the-better, and target value (Barker, 2005). The smaller the better is the first category, which the concern in this type of the problem is to minimize the characteristics as close as possible to zero. There is no limit how small the characteristics could be, the ideal value is zero. To get as the values as low as possible requires focusing on the average and on reducing the variation of the process.

The second category of the problem in the experiment is the larger-the-better. In this type of problem, the overriding concern is getting some characteristics as high as possible. For larger-the-better experimental case, there is no limit on how high the characteristics value

(26)

could be, and the ideal value is infinity. Moreover, the third category is target value. In this type category, the characteristics should be as close as possible to the target value. In this category, the only acceptable characteristic value is the value which is very close to the target. In order to get the closest value on the target, then average value of experiments as close as the target as possible and minimizing the variation around this target. Reducing variation on the experiments are very important, because it can reduce the number of defects which can be improve the quality of products. Moreover, by reducing variations, wider operating windows making the process easier to control.

5. Optimization Methods in PIM

Several studies reveal that combination of different intelligent and optimization system will give a better solution for the real-world applications. The combination of these systems is called as hybrid optimization system, implemented firstly in soft computing by Lotfi Zadeh (Negnevitsky, 2005). The combination of probabilistic reasoning, fuzzy logic, neural network and evolutionary computation form is the core of soft computing system.

Since each method has its own strengths and weaknesses, then a hybrid system is a good solution to overcome this problem by empowering the strengths of each method and to abandons their weaknesses. However, the best solution can only be obtained by selecting the right components. In previous studies, researchers combined optimization methods such as GA, PSO, SA, and others to improve the quality of plastic product. In research conducted by Chen et al. (2009), combination of the Taguchi method, BPNN, and genetic algorithm (GA) were used to optimize process parameters in PIM for product length and weight. Deng et al. (2010) applied integration of mode pursuing sampling (MPS), GA, and Kriging surrogate modeling to minimize warpage in food tray plastic part. The summary of previous studies about optimization methods, parameter selection, and the target of in plastic injection molding is shown in Table 2.

(27)

Table 2

Summary of plastic injection molding in previous studies

Researcher Method Target Parameter settings

Altan (2010) Taguchi method

BPNN Shrinkage

Melt temperature Injection pressure Packing pressure Packing time

Chen & Lin (2013)

Taguchi method BPNN

GA

Length Warpage

Melt temperature Injection velocity Packing time Packing pressure Cooling time

Chen et al. (2009)

Taguchi method BPNN

GA

Length Warpage

Melt temperature Injection velocity Injection pressure VP switch over Packing pressure Packing time

Chen et al. (2009) DOE Warpage

Melt temperature Mold temperature Injection speed Packing pressure

Chen et al. (2012a)

Taguchi method BPNN

SA PSO

Length Warpage

Melt temperature Injection velocity Injection pressure Packing pressure Packing time

Chen et al. (2012b)

DOE RSM GA

Length Warpage

Cooling time Mold temperature Melt temperature Injection velocity Packing pressure Injection pressure Packing time VP switch over Chiang et al.

(2011) Taguchi method Warpage

Short shot

Mold temperature Melt temperature Injection speed Packing pressure

Gao & Wang (2009)

Kriging surrogate

DOE Warpage

Packing time Packing pressure Mold temperature Melt temperature Injection time

(28)

Table 2 (Continued)

Kamaruddin et al.

(2010) Taguchi method Shrinkage

Melt temperature Injection pressure Holding pressure Holding time Cooling time

Mathivanan &

Parthasarathy (2009)

DOE

RSM Sink mark

Melt temperature Mold temperature Injection time VP switch over Packing time Packing pressure Rib-to-wall ratio Rib-gate distance

Ozcelik et al.

(2012) FEA

Weld line Tensile strength

Melt temperature Packing pressure Mold temperature Injection pressure Injection time Packing time Cooling time Cycle time

Prashantha et al.

(2009) Taguchi method Warpage

Shrinkage

Injection speed Holding pressure Back pressure Screw speed

Sun et al. (2010)

DOE RSM GA

Warpage

Mold temperature Melt temperature Injection time Packing pressure Packing time

Wang et al. (2013)

BPNN PSO GA

Cost estimation

Price materials Plastic materials Density

Volume Surface area Wall thickness Length of products Width of products Height of products Projection area

(29)

Table 2 (Continued)

Xu et al. (2012) NNs PSO

Weight Flash Shrinkage

Melt temperature Mold temperature Injection pressure Injection time Holding pressure Holding time Cooling time

Section 2 Taguchi Method

1. Basic Concept

The Taguchi method is a statistical method that developed by Dr. Genichi Taguchi after World War II. This method is an easy technique to use and to get the good quality of design with computational cost efficiency. The size of experimentation can be reduced significantly and process productivity can be improved by implementing orthogonal array.

In addition, the implementation of orthogonal array also will minimize the effect of the source of experimentation variability.

There are three major contributions of the Taguchi method for quality improvement:

the loss function, orthogonal arrays, and robustness (Roy, 2001). The idea of loss function is for estimating the monetary loss caused by lack of quality (Taguchi, 1990). The illustration of quadratic loss function is shown in Fig. 6. The loss function estimates loss even though the products are made within the specification limits. If the products different from the target specifications, there is some loss. The mathematical model in which loss is a quadratic function of the deviation of the quality of interest from its target value. Eq. (1) shows the equation for the Taguchi loss function. Based on this concept, then quality improvement can be obtained from data.

The Taguchi loss function:

( ) (y m)2

L y =k − (1)

where k is constant, y is actual measurement, and m is target value.

(30)

Figure 6 Quadratic loss function

The second major contribution is the utilization of orthogonal arrays for efficient experiments and to analyze the experimental data. Orthogonal array not only used to measure the effect of a factor on the average result, but also to determine the variation from the mean as well (Peace, 1993). In addition, another advantage of orthogonal array is the relationship among control factors. All levels of the control factors occur an equal number of times. This will make the balance experiment and allow the effect of one factor under the investigation can be separable from the effects of the other factors. Even though orthogonal array has balance experimental design, but it also efficient. The design of an orthogonal array does not require all combination of factors be tested. As a result, cost efficiency can be obtained by utilize orthogonal array.

Another advantage of the Taguchi method is the concept of robustness. There are two types of the concept of robustness based on the standpoint: for product and for process.

The robustness for product can be defined as the ability of the products to perform consistently as designed with minimal effect from changes in uncontrollable operating influences. Meanwhile, the robustness for the process is the ability of the process to produce consistently good product with minimal effect from changes in uncontrollable manufacturing influences. The Taguchi method can be used to control the significant factors that feasible to control, and minimized the factors that cannot be controlled.

There are three stages or phases in the Taguchi method; they are system design, parameter design, and tolerance design. In system design, the idea about something new from early development is conceived and tested in stage. Next, in parameter design, the

(31)

Tolerance design stage is used to establish the acceptable range of variability of the settings and to analyses the optimum combination suggested by parameter design. The procedure of the Taguchi method execution is as following the procedure:

1) Determining the control factors, noise factors, and quality characteristics of the product or process

2) Identifying the levels of each factor and appropriate orthogonal array table

3) Executing ANOVA analysis, in addition to determine the significant control factors and minimize the impact for uncontrollable factors

4) Performing the confirmation experiments using the optimal parameter settings

2. Taguchi Design and Orthogonal Array

Experimental design should be perform before the experimental work is conducted.

This stage is very important to get reliable data. Generally, there are three experimental techniques in conducting experiment: factorial design, the Taguchi method, and random design (Barker, 2005). If we have a small numbers of variables or factors with a few levels, then factorial design is an appropriate technique to be used. Experimental work using factorial design is used to test all possibilities of all combinations. This technique is very good to be used when the interaction between variables are assumed strong and very important. However, when the control factors and level become higher, then huge number of experiments should be conducted.

As mentioned in previous section, orthogonal array from the Taguchi method provide efficiency in the experiment. Similar information as performed in factorial design with fewer experiments can be done using the Taguchi method. Instead of perform all possible combination of control factors, the Taguchi method has ability to assess all pairs of combinations in some more efficient way. In random design, experimental conditions with high probability create a near optimal design. However, this design tends to work poorly for small number of experiments, but works well for large systems. Comparison of several methods in experimental work recorded in Table 3.

(32)

Table 3

Comparison several methods for experimental design

Factorial Design Taguchi Method Random Design

Factors 1~3 3~50 > 50

Interactions between control

factors important Few Few

Contributions of control

factors Significant Few Very few

The selection of orthogonal array and the number of factors should be done before conducting the experiment. It is essential to understand the standard nomenclature for describing the design of orthogonal array. For example, the L₄(2³) orthogonal array is selected for the experiment as illustrated in Fig. 7. The subscript of L, which is 4, represents the number of experimental runs or combination of factors which is in the experiment. The 2 value means that 2 levels experiment within each column. The 3 value which is shown as the exponent of 2, informs that the number of columns or factors are available within the orthogonal array. The experimental run of L₄(2³) is shown in Table 4.

Figure 7 Illustration of L₄(2³) orthogonal array

Table 4

The L4(2³) orthogonal array

Experiment (run) Control factor

A B C

1 1 1 1

2 1 2 2

3 2 1 1

(33)

3. Signal-to-Noise Ratio

Determination of quality variations can be defined by implementing signal-to-noise (S/N) ratio. Dr. Taguchi has generalized the concept of S/N ratio as used in the communication industry and has applied it for the evaluation of measurement (Taguchi et al., 2005). The consistency of quality characteristics and the best combination of parameters can be decided by applying the result from S/N ratio. The flowchart for the Taguchi method is shown in Fig. 8. According to the flowchart, the first step in the Taguchi method is to determine experimental plan, controllable factors and levels. The orthogonal array is developed to run the experiment. After experimental work is conducted, then S/N ratio can be calculated using several formulations: smaller-the-better, larger-the- better, and nominal-the-best (Peace, 1993; Taguchi, 1990). In plastic injection molding, the best combination of parameter settings can be determined using the result of S/N ratio value. Most of engineers are often use the highest value of S/N ratio as the preliminary optimal parameter settings. There are three types of S/N ratio: smaller-the-better, larger- the-better, and nominal-the-best as shown in Eqs. (2), (3), and (4), respectively.

Smaller-the-better:

2 1

/ 10 log 1

n i i

S N y

n ₌

= − ⋅ (2)

Larger-the-better:

2 1

1 1

/ 10 log

n

i i

S N = − ⋅ n ₌ y ₍₃₎

Nominal-the-best:

( )

² ²

/ 10 log y m

S N = − ⋅ − +S (4)

(34)

Figure 8 Flowchart of the Taguchi method

where y_i is the response value of a specific treatment under i replications, m is the target value, n is the number of replications, y is the average of all y_i values, and S is the standard deviation of all y_i values. The S/N ratio result is presented in response graph and table.

The purpose of statistical analysis using ANOVA determines significant control factors in the experiment. There are several steps of ANOVA calculations as follows:

1) Calculate total sum of squares (SST) and sum of squares between (SSB) for the result with SSB deducted from SST to obtain sum of square within (SSW). SST is the total sum of squares combined within group and between different groups. The formulation for SST, SSB, and SSW are shown in Eqs. (5), (6), and (7) respectively.

(35)

SST =SSW +SSB (5) (X_i X )_k

SSW = − (6)

(X X)2

k k

SSB= N − (7)

where X_i is one fraction in pooled samples, X is mean of pooled samples, X_k is mean of each category or group, N_k is sample size of each group.

2) Calculate two degrees of freedom corresponding to SSB and SSW.

3) Obtain the ratio of SSB or SSW to corresponding degree of freedom and estimate the variance of one parent population in two mean square estimates.

4) Calculate F ratio.

Finally, according to the experimental result, the best combination of parameter settings can be determined and verify the result of optimal parameters by conducting confirmation experiment.

4. Multiple quality characteristics in Taguchi method

In the Taguchi method, the best combination of parameters can be defined by calculate the signal-to-noise (S/N) ratio from the experimental data. The calculation of S/N ratio is based on the requirement: smaller-the-better, larger-the-better, and nominal-the- best. Then, the best combination parameter settings can be determined by the highest S/N ratio value. It is very easy to find the best settings if only one response is calculate.

However, the difficulties is facing when multiple responses should be determined in the experiments. Multiple responses of quality characteristics cannot be neglected in real- world. Therefore, there are several techniques to overcome the problem of multiple responses in the experiments using the Taguchi method. Refaie et al. (2010) present four responses in the experiments (LP error, RP error, LH error, and RH error). Their proposed approach using calculation of level weight from each control factors to solve the problem for multiple responses using the Taguchi method. In another study, Chen and Lin (2013) determined the best parameter settings of multiple responses using the Taguchi method by calculate of average settings from the highest values of S/N ratio of length and warpage.

The result from their study, the Taguchi method and integration with optimization methods successfully improve the quality of plastic parts.

(36)

Section 3 Artificial Neural Network

1. Overview of Neural Network

Artificial neural network (ANN) can be defined as a model of reasoning based on the human brain (Negnevitsky, 2005). An artificial neural network consists of several numbers of interconnected neurons, which are analogous to the biological neurons in the brain and connected by weighted link passing signal from one neuron to another. A neuron consists of a cell body called soma, a number of fibers called dendrites, and a single long fiber called axon. Dendrits are branches for a network around soma, the axon stretches out to the dendrites and somas of other neurons. Fig. 9 illustrates the schematic of neural network. The neurons are connected to the external environment from input and output layers. A neuron receives several signals from the input links, then computes an activation level and sends the information as an output signal through the output links. The output signal can be the final solution to the problem or be an input to other neurons. Neural networks have capability to learn, when they use experiences to improve the performance.

Figure 9 Biological neural network Source: Negnevitsky (2005)

Neural network has ability to learn and generalize, which means it can produce reasonable outputs for inputs that not faced during the training phase. This will make ANN has ability to solve complex problems that are difficult. However, ANN cannot solve the solution by working individually, but need to integrate with a consistent system engineering approach. There are several useful properties and capabilities of ANN, such as:

(37)

nonlinearity, input-output mapping, adaptively, evidential response, contextual information, fault tolerance, uniformity of analysis and design, and neurobiology analogy.

There are three basic elements in ANN model as shown in Fig. 10. The interconnecting link or synapses differentiate by the weight. An input signal is connected to neuron and multiplied by the synaptic weight. The weight of an artificial neural network can be within positive and negative values. An adder for summing the input signals, weighted by synapses of the neuron. Activation function is a function to limit the permissible amplitude range of the output signal to some finite value. An external bias also applied in the neuron model in Fig. 10. The bias is used to increase or decrease the net input of the activation function.

Figure 10 Nonlinear model of a neuron

The weights are the basic function of long-term memory in neural networks, and the learning ability is performing by repeated adjustment of these weights. Each neuron receives a number of input signals from its connections, while the output signal is transmitted through the neuron’s outgoing connection. The neuron computes the weighted sum of the input signals and then compares it with the result of the threshold value. For example, if the net input is less than the threshold value, then the neuron output is -1. But when the input value is greater than or equal to the threshold value, then the neuron becomes activated and the output reaches a value +1. Mathematical model for describing a neuron is describing in Eq. (8) as follows:

(38)

1 m

k kj j

j

u w x

=

= ₍₈₎

and,

(u b )

k k k

y =ϕ + (9)

where x₁, x2, …, xm are the input signals; w_k1, wk2, …, wkm are the synaptic weights of neuron k; uk is the linear combiner output; bk is the bias; ϕ(⋅) is the activation function; and yk is the output signal of the neuron.

2. Activation Functions

Activation functions work to defines output of neurons in terms of the induced local field. There are three basic types of activation functions: threshold function, sigmoid function, and piecewise-linear function. These activation functions are depicted in Fig. 11.

Threshold function

Sigmoid function

Piecewise-linear function

Figure 11 ANN activation functions

Threshold function

The threshold activation functions also called as hard limit function or Heaviside function. This type of activation function is expressed as:

1, if 0 ( ) 0, if 0

ϕ υ = ^≥

< (10)

The output of neuron k employing such a threshold functions as following:

1, if 0 0, if < 0

yk υ

υ

= ≥ (11)

An Integrated Optimization System for Plastic Injection Molding Using Taguchi Method, BPNN,

中 華 大 學 博 士 論 文

An Integrated Optimization System for Plastic Injection Molding Using Taguchi Method, BPNN,

GA, and Hybrid PSO-GA

Abstract

Acknowledgment

Table of Contents

List of Tables

List of Figures

CHAPTER 1 Introduction

Section 1 Background and Motivation

Section 2 Problem Statement and Recognition

Section 3 Research Objectives

Section 4 Guide of Dissertation

CHAPTER 2 Literature Review

Section 1 Plastic Injection Molding

1. Previous Study in Plastic Injection Molding

2. Selection of Control Factors in PIM

3. Defects in PIM

4. Categories of problems in Experiment

5. Optimization Methods in PIM

Section 2 Taguchi Method

( )

Section 3 Artificial Neural Network

中華大學博士論文