A systematic optimization approach for assembly sequence planning using Taguchi method, DOE, and BPNN

https://doi.org/10.1016/j.eswa.2009.05.098Get rights and content

Abstract

Research in assembly planning can be categorised into three types of approach: graph-based, knowledge-based and artificial intelligence approaches. The main drawbacks of the above approaches are as follows: the first is time-consuming; in the second approach it is difficult to find the optimal solution; and the third approach requires a high computing efficiency. To tackle these problems, this study develops a novel approach integrated with some graph-based heuristic working rules, robust back-propagation neural network (BPNN) engines via Taguchi method and design of experiment (DOE), and a knowledge-based engineering (KBE) system to assist the assembly engineers in promptly predicting a near-optimal assembly sequence. Three real-world examples are dedicated to evaluating the feasibility of the proposed model in terms of the differences in assembly sequences. The results show that the proposed model can efficiently generate BPNN engines, facilitate assembly sequence optimisation and allow the designers to recognise the contact relationships, assembly difficulties and assembly constraints of three-dimensional (3D) components in a virtual environment type.

Introduction

In general, assembly involves the integration of components and parts to create a product or system through computer-aided design and manufacturing (CAD/CAM) systems. Assembly planning is a crucial design step for generating a feasible assembly sequence. Traditional assembly planning is manual and based on the experience and knowledge of industrial engineers; however, manual analysis does not allow the feasibility of assembly sequences to be easily verified. In the electronics industry, the approximate 40–60% of total wages was paid to assembly labors (Kalpakjian, 1992). The implementation of design for assembly (DFA) and design for manufacturing (DFM) resulted in enormous benefits, including the simplification of products, reduction of assembly product costs, improvement of quality, and shrinkage of time to market (Kuo, Huang, & Zhang, 2001). Good assembly sequence planning (ASP) has been recognised as a practical way of reducing operational difficulties, the number of tools and the working time (Lai & Huang, 2004).

De Fazio and Whitney (1987) adopted the concept of Bourjault (1984) to generate a complete set of assembly sequences. They generated sequences in two stages – creating the precedence relations between liaisons or logical combinations of liaisons in a product and verifying the liaison sequence. Homen de Mello and Sanderson (1991a) made a representation of the directed AND/OR graphs to create feasible assembly sequences. In addition, Kroll (1994) used graph-based procedures with conventional representations to reduce the number of sorting operations required. He then extended his previous approach from uniaxial assemblies to triaxial assemblies and presented a set of rules for resolving conflicts between multiple parents and multiple offspring. However, in practice most assembly companies use semi-automatic systems to generate an assembly plan and employ 2D cross-sectional views to represent their heuristic models (Lin & Chang, 1993).

Assembly planning is also regarded as “assembly by disassembling,” i.e., an assembly sequence results from systematically disassembling the final product and reversing the disassembling sequence (Lee, 1989). This approach usually employs the contact-based feature to represent the precedence relationships of the product. A designer can successively assign the assembly relations to form the assembly plan based on the precedence diagram. However, the contact-based precedence diagram cannot effectively express the complexity of the assigned assembly relations. An effective assembly plan must include other graphs, such as the explosion graph, the relational model graph, the incidence matrix, the assembly precedence diagram (APD), etc. In reality, few experts or engineers know exactly how to derive a correct explosion graph, draw a complete relational model graph or incidence matrix among the components, or determine a complete APD to generate an optimal assembly sequence (Chen et al., 2004b, Chen et al., 2008).

The other approach to Knowledge-based engineering (KBE) is a technology that allows an engineer to create a product model based on rules and the powerful CAD/CAM applications that used to design, configure and assemble products, examples of which include the so-called expert systems, web-based knowledge bases involving the engineering knowledge (i.e., Knowledge Fusion) and becoming an critical part of business strategy (Homen de Mello & Sanderson, 1991b). In addition, numerous researchers have employed an artificial intelligence (AI) tree search or graph search methodology to generate an assembly sequence (Chen et al., 2004a, Homen de Mello and Sanderson, 1991b). Unfortunately, the search space increases explosively when the number of components in a design grows. To relieve this combinational complexity, heuristic rules and genetic algorithms (GAs) have been used in the searching process (Chen et al., 2004a, Marian et al., 2003). Other studies have used the Hopfield and BPNN as the means to generate optimum or sub-optimum assembly sequences (Chen, 1990, Hong and Cho, 1995, Sinanoglu, 2006).

This study proposes a three-stage integrated approach with some heuristic working rules to assist the planner to obtain an optimal assembly plan. In the first stage, the Above Graphs with spatial constraints are used to create a correct explosion graph of the assembly model; these two graphs can be used to represent the correct geometric constraints among the assembly parts. In the second stage, a three-level relational model is developed to generate a complete relational model graph (RMG) and the incidence matrix. The relational model graph can be advanced and transformed into an assembly precedence diagram (APD), which is used to describe the assembly precedence relations of the parts. Based on these graphs, the designer can easily find feasible sequences and evaluate the difficulty of assembly. In the third stage, the CAD-based Knowledge Fusion (KF) programming language and BPNN engines via Taguchi method and design of experiment (DOE) are employed to validate the available assembly sequences. The three kinds of real-world toy products are utilised to evaluate the feasibility of the proposed model in terms of the differences in underlying assembly characteristics and predict a near-optimal assembly sequence according to the defined performance criteria.

Section snippets

The working concepts and procedures

The working concepts and procedures of the proposed approach are shown in Fig. 1. Initially, detailed data is input from a 2D engineering drawing and related assembly information into a CAD assembly package. Then, the correct explosion graph is developed using the transforming rules. Finally, the relational models are generalized to represent the assembly precedence relations, and an evaluating mechanism is then employed to find a global feasible solution. The planning process is recursive

Back-propagation neural network

In much of the literature, back-propagation neural networks (BPNNs) have been adopted because they have the advantages of a fast response and high learning accuracy (Chen and Hsu, 2007, Liu et al., 2001, Maier and Dandy, 1998, Yao et al., 2005). The superiority of a network’s functional approach depends on the network architecture and parameters, as well as the problem complexity. If inappropriate network architecture or parameters are selected, undesirable results may be obtained. Conversely,

Taguchi method

Taguchi’s parameter design method normally selects an appropriate formulation of the S/N ratio and calculates the S/N ratio for each treatment. There are three types of S/N ratios: nominal the best, the larger the better, and the smaller the better. Most engineers choose the highest S/N ratio treatment as the preliminary optimal initial process parameter setting. Taguchi method has also been used to design the parameters for neural networks in previous research (Khaw et al., 1995, Santos and

Optimization of the neural network parameters using RSM & Taguchi method

In this research, we applied the Taguchi method and DOE to obtaining the optimal parameter settings of the BPNN. Since the number of hidden layers did not have a significant effect on convergence, the number of hidden layer was set to 1. The controlling factors of Taguchi method are transfer function (Ft), the number of hidden neurons (Nh), learning rate (Rl), momentum (Mt), and Epochs (Ep). The numbers of neurons in the hidden layer under different levels were obtained by the method proposed

Illustrative examples

In this section, the examples of a toy car, a toy motorbike and a toy boat are used to demonstrate the generation procedures of assembly planning.

Conclusions

Theoretically, an assembly plan can be optimised based on the factors of shortest assembly time and assembly sequence optimisation. However, these are uncertain factors prior to the determination of the optimised assembly scheme and the completion of the jig and fixture. The proposed model adopts a three-stage integrated assembly planning approach to express the complexity of the assembly relations and to evaluate the feasibility of the respective assembly sequences in the design phase. The

Acknowledgement

Financial support from the National Science Council, Taiwan, ROC, under contract NSC 97-2221-E-216 -026 and Chung Hua University, under contract CHU-96-M-001.

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