A multi-principle module identification method for product platform design
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Abstract
In today’s competitive global business environment, platform strategy presents an opportunity for manufacturing companies to juggle increased customer demand for customized products and the inherited complexity and increased development cost that comes with it. The goal of this paper is to support module identification as an essential part of a module-based platform strategy approach. Based on various existing methods, this paper abstracted three principles, which include an internal clustering principle, an external independence principle, and an overall stability principle. The three principles should be holistically considered, and be simultaneously satisfied during the module identification. Both conceptual and mathematical modeling of the proposed multi-principle module identification method are elaborated. Then an improved strength Pareto evolutionary algorithm (ISPEA2) is used to address the multi-principle module identification problem and find the Pareto-optimal set. A fuzzy compromise selection method base on fuzzy set theory is also used to select the best compromise Pareto solution. An industrial case study in a turbo expander manufacturing company is provided to illustrate practical applications of the research. Finally, the result obtained by the proposed approach is compared with other established optimization approaches.
Key words
Module identification Modularization principles Multi-objective optimization Improved strength Pareto evolutionary algorithm (ISPEA2) Turbo expander一种支持产品平台设计的多准则模块划分方法
抽象的
目的
研究多准则约束下的产品模块划分方法, 为企业 建立稳健的模块化产品平台奠定基础。
方法
采用改进的多目标进化算法对建立的多准则模块 划分数学模型求解, 并采用模糊集合评价机制进 行最优解的寻取, 得到基于多准则模块划分方法 的产品模块划分结果。
结论
通过改进的多目标进化算法求解多准则模块划分 模型, 能够得到有效支持产品平台设计的产品模 块划分方案。 通过与已有优化方法的比较验证了 本文提出的多准则模块划分方法的优越性。
关键词
模块划分 模块化准则 多目标优化 改进的强 度帕累托进化算法 透平膨胀机1 Introduction
In today’s highly competitive global business environment, platform-based strategy has been proven to be beneficial for enterprises to reduce cost, increase product variety, decrease product lead time, cope with the emerging customized requirements, and improve manufacturing flexibility (Simpson, 2004). There are two basic types of platforms, namely, the module-based platform and the scale-based platform. The former depends on different configurations of modules to generate a variety of products, whereas the latter scales one or multiple variables of the platform to create products of varying performances (Li et al., 2008).
- 1.
Internal interactions clustering viewpoint
The internal clustering viewpoint requires that components with a high degree of interactions should be clustered to form an individual module (Yu et al., 2011). In other words, the interactions between components within a module must be maximized. Therefore, this principle is also known as the ‘internal clustering principle’, which represents a well-known principle in module design. In the past, a number of other clustering algorithms have been developed to cluster components based on their interactions (Tseng et al., 2008). Sanchez (1993) suggested that the aim of module design is to identify components with a high degree of interactions. Sosa et al. (2004) analyzed the internal interactions from the energy, material, spatial, and informational aspects. Ulrich (1995) suggested that modules are identified in a way that interactions within a module might be high.
- 2.
External interactions independence viewpoint
The external independence viewpoint suggests that the coupling degree between different modules must be minimized (Ulrich, 1994). The primary purpose is to keep different modules independent of each other as much as possible. Therefore, this viewpoint is also called the ‘external independence principle’, which is a well-known modularization principle. Part of the modularity definition states that “the unintended interactions between modules are minimized”. Huang et al. (2006) adopted a fuzzy clustering matrix to evaluate the external interaction value in the matrix by five basic recycling attributes. Kimura et al. (2001) took multi-characteristics into consideration, such as technological stability, functional upgrade ability, long life, and so on. Umeda et al. (2008) proposed a modular identification method that derives modular structure based on both life cycle properties and geometric information.
- 3.
Overall system reliability viewpoint
The objective of modular identification is to separate the system into independent modules (Newcomb et al., 1996). It is important to evaluate modularity within a holistic view of the total system. The overall system reliability viewpoint requires that the components that may affect the same set of functional requirements should be grouped together to form a module. Hence, components within a module should address the same set of functional requirements. Therefore, certain functional requirements will ideally only be affected by one particular module. This viewpoint is called the ‘overall reliability principle’. Ji et al. (2013) proposed an effectiveness-driven modular design method which takes all effectiveness scenarios into consideration and balances the granularity and composition of modules among all possible forms during the clustering process. The modularity is evaluated in a holistic view of the total system. Li et al. (2013) proposed a holistic integrated product modularisation method based on flow analysis, a design structure matrix and fuzzy clustering to compose a flexible platform. Holtta-Otto and de Weck (2007) used a singular value modularity index and a non-zero fraction to analyze the degree of modularity in view of the total system.
Based on a thorough investigation of different existing methods, there has been little attempt to integrate the three principles and regard them together as a to-be-solved multi-objective optimization problem (MOOP). This paper proposes the three modularization principles that should be holistically considered and simultaneously satisfied during the module identification.
It is important to point out that each of these three principles is deliberately chosen to address a particular aspect. For instance, the external independence principle aims to minimize the complexity, whereas the overall reliability principle’s goal is to improve the quality. Additionally, these principles are not entirely isolated, but rather mutually related. Hence, the three principles should be simultaneously satisfied in order to achieve the design goal.
Recently, evolution multiobjective optimization, which applies evolution computation to multiobjective optimization has attracted a great deal of attention (Feng et al., 2010; Cheng et al., 2013; Martínez-Morales et al., 2013; Gao et al., 2014). Many multiobjective genetic algorithms have been proposed. The recent research includes strength Pareto evolutionary algorithm (SPEA) (Zitzler and Thiele, 1998), nondominated sorting genetic algorithm (NSGA) (Srivans and Deb, 1995), niched Pareto genetic algorithm (NPGA) (Horn and Nafpliotis, 1994) and some improved versions, strength Pareto evolutionary algorithm 2 (SPEA2) (Zitzler et al., 2001), and nondominated sorting genetic algorithm-II (NSGA-II) (Deb, 2002). This paper focuses on a multi-principle module identification method and used an improved strength Pareto evolutionary algorithm (ISPEA2) to address the previously introduced multi-principle modularization problem. A fuzzy-based mechanism is also used to extract a Pareto-optimal solution as the best compromise in trying to eliminate the imprecise nature of a human decision.
2 Conceptual modeling of multi-principle modularization
From the above discussions, it is evident that the three modularization principles are not unfamiliar to the design community. Furthermore, each principle has been individually adopted by different methods. However, there has been little attempt to integrate the three principles and regard them together as a to-be-solved MOOP. This section presents the conceptual modeling of the proposed multi-principle module identification method. The identified principles are treated as a ‘three objectives’ optimization problem, and the ISPEA2 is used to find the Pareto-optimal set. The fuzzy-based selection mechanism is also used to extract the best Pareto-optimal solution (Abido, 2006).
3 Mathematical modeling of multi-principle modularization optimization problem
3.1 Internal clustering principle
- 1.Construct the interaction matrix between components where is the interactions between the pth and qth components within the module M_{ i }.
- 2.
Calculate the internal clustering degree within the modules
3.2 External independence principle
3.3 Overall reliability principle
- 1.
Build the probability matrix of every physical component
For the probability matrix F of every physical component in meeting every functional requirement (Kreng and Lee, 2003), where \(f_{ib}^{v}\) means the probability that the bth component contained within the ith module, and M_{ i } will meet the vth functional requirement. According to the evaluation theory of fuzzy mathematics, the values of \(f_{ib}^{v}\) are subjectively assigned by the designer according to the scales of 9, 7, 4, 1, 0, with the scores of 9 to 0, each representing highest, higher, middle, lower, lowest probability, respectively. This specific scale was chosen as it has proven effective in various previous studies for similar settings (Wang et al., 2006). - 2.
Develop a mathematical optimization model of the overall reliability
Considering the fuzzy entropy of product design requirements and the distribution of product differentiation (Kreng and Lee, 2003), the reliability I of the product is$$I = {{\sum\limits_{i = 1}^M {\sum\limits_{v = 1}^\eta {{w_v}E(DR_v^i}})\left[ {1 - {{SSD_v^i} \over {{{(SSD_v^i)}_{\max}}}}} \right]} \mathord{\left/{\vphantom {{\sum\limits_{i = 1}^M {\sum\limits_{v = 1}^\eta {{w_v}E(DR_v^i}})\left[ {1 - {{SSD_v^i} \over {{{(SSD_v^i)}_{\max}}}}} \right]} M}} \right. \kern-\nulldelimiterspace} M},$$(7)$$E(DR_v^i) = {{- 1} \over {\ln ({N_i})}}\sum\limits_{b = 1}^{{N_i}} {\left\{{{{f_{ib}^v} \over {\sum\limits_{b = 1}^{{N_i}} {f_{ib}^v}}}\ln \left[ {{{f_{ib}^v} \over {\sum\limits_{b = 1}^{{N_i}} {f_{ib}^v}}}} \right]} \right\}},$$(8)where w_{ v } stands for the weight of the vth functional requirement; \(E({\rm DR}_{v}^{i})\) reflects the fuzzy entropy between the ith module with the vth functional requirement; \({\rm SSD}_{v}^{i}\) means the sum of different mean square values of the vth functional requirement of the ith module; and \(\overline{f_{i}^{v}}\) describes the average probability of different components within the ith module to meet the vth functional requirement (Kreng and Lee, 2003).$$SSD_v^i = \sum\limits_{b = 1}^{{N_i}} {{{\left({f_{ib}^v - \overline {f_i^v}} \right)}^2}},\;\;\overline {f_i^v} = \sum\limits_{b = 1}^{{N_i}} {{{f_{ib}^v} \mathord{\left/{\vphantom {{f_{ib}^v} {{N_i},}}} \right.\kern-\nulldelimiterspace} {{N_i},}}}$$(9)
3.4 Constraint conditions
4 Multi-principle modularization optimization based on ISPEA2
4.1 Constraint conditions
4.2 Improved strength Pareto evolutionary algorithm
ISPEA2 is a new model of multi-objective genetic algorithm (MOGA) that features more effective crossover, and it will result in diverse solutions in both objective and variable spaces (Kim et al., 2004). ISPEA2 can be regarded as a particular type of SPEA2 with three additional mechanisms (Kim et al., 2004): (i) neighborhood crossover that allows crossing over individuals located near each other in the objective space; (ii) mating selection that reflects all good solutions within the archive; (iii) application of two archives to maintain diverse solutions in both objective and variable spaces.
4.3 Best compromise solution based on fuzzy set theory
5 Case study
5.1 Turbo expander and multi-principle module identification base date calculation
List of key components of the turbo expander
No. | Name |
---|---|
1 | Fuselage |
2 | Base |
3 | Fan volute |
4 | Nozzle |
5 | Expander impeller |
6 | Rotor |
7 | Fan cove |
8 | Expander impeller |
9 | Sensor holder |
10 | Operation panel |
11 | Axis sensor |
12 | Machine switches |
13 | Turbocharger impeller |
14 | Joint bearings |
15 | Inlet pipe |
16 | Gland |
17 | Cold box |
18 | Reducing valve |
19 | Exhaust pipe |
20 | Support bracket |
21 | Oil cooler |
22 | Oil filter |
23 | Aftercooler |
24 | Closures |
25 | Bladeless diffuser |
26 | Inlet chamber |
27 | Return pipe |
28 | Pneumatic membrane |
29 | Sheet heat exchanger |
30 | Tank |
31 | Three screw pump |
32 | Thermostatic valve |
33 | Bladder accumulators |
34 | Electric control box |
35 | Anti-spill plug |
36 | Oil window parts |
37 | Cooling water valve |
38 | Magnet sensor |
39 | Spindle |
40 | Intermediates |
41 | Bearing pedestal |
42 | Nameplate |
Coupling matrices between interacting components of the turbo expander
K _{1} | K _{2} | K _{3} | K _{4} | … | K _{39} | K _{40} | K _{41} | K _{42} | |
---|---|---|---|---|---|---|---|---|---|
K _{1} | 1 | 0.246 | 0.463 | 0.445 | … | 0.433 | 0.365 | 0.634 | 0.459 |
K _{2} | 0.246 | 1 | 0.267 | 0.734 | … | 0.172 | 0.262 | 0.641 | 0.125 |
K _{3} | 0.463 | 0.267 | 1 | 0.243 | … | 0.249 | 0.328 | 0.238 | 0.021 |
K _{4} | 0.445 | 0.734 | 0.243 | 1 | … | 0.416 | 0.179 | 0.315 | 0.196 |
K _{5} | 0.257 | 0.561 | 0.147 | 0.256 | … | 0.261 | 0.563 | 0.173 | 0.257 |
K _{6} | 0.563 | 0.435 | 0.318 | 0.349 | … | 0.483 | 0.319 | 0.276 | 0.191 |
K _{7} | 0.247 | 0.364 | 0.342 | 0.369 | … | 0.376 | 0.183 | 0.524 | 0.361 |
K _{8} | 0.339 | 0.098 | 0.517 | 0.716 | … | 0.423 | 0.542 | 0.621 | 0.116 |
… | … | … | … | … | … | … | … | … | … |
K _{37} | 0.361 | 0.473 | 0.432 | 0.846 | … | 0.161 | 0.347 | 0.362 | 0.475 |
K _{38} | 0.637 | 0.452 | 0.367 | 0.662 | … | 0.627 | 0.433 | 0.516 | 0.269 |
K _{39} | 0.433 | 0.172 | 0.249 | 0.416 | … | 1 | 0.467 | 0.316 | 0.244 |
K _{40} | 0.365 | 0.262 | 0.328 | 0.179 | … | 0.467 | 1 | 0.246 | 0.319 |
K _{41} | 0.634 | 0.641 | 0.238 | 0.315 | … | 0.316 | 0.246 | 1 | 0.317 |
K _{42} | 0.459 | 0.125 | 0.021 | 0.196 | … | 0.244 | 0.319 | 0.317 | 1 |
Probability matrix of each component in satisfying the customer requirement
P ^{1} | P ^{2} | P ^{3} | P ^{4} | P ^{5} | P ^{6} | P ^{7} | P ^{8} | P ^{9} | P ^{10} | |
---|---|---|---|---|---|---|---|---|---|---|
K ^{1} | 9 | 1 | 4 | 7 | 4 | 9 | 0 | 1 | 9 | 4 |
K ^{2} | 7 | 9 | 4 | 0 | 4 | 7 | 9 | 4 | 7 | 1 |
K ^{3} | 7 | 7 | 4 | 9 | 4 | 9 | 4 | 7 | 9 | 4 |
K ^{4} | 9 | 7 | 7 | 4 | 0 | 1 | 7 | 7 | 4 | 7 |
K ^{5} | 1 | 9 | 7 | 4 | 7 | 1 | 7 | 9 | 4 | 9 |
K ^{6} | 7 | 1 | 4 | 7 | 7 | 4 | 9 | 7 | 4 | 7 |
K ^{7} | 7 | 4 | 4 | 9 | 4 | 9 | 1 | 7 | 1 | 9 |
K ^{8} | 4 | 4 | 7 | 1 | 7 | 9 | 7 | 4 | 7 | 4 |
K ^{9} | 7 | 9 | 9 | 7 | 4 | 7 | 9 | 7 | 9 | 7 |
K ^{10} | 7 | 4 | 1 | 7 | 7 | 4 | 4 | 4 | 0 | 1 |
K ^{11} | 9 | 7 | 1 | 0 | 4 | 4 | 0 | 1 | 4 | 4 |
K ^{12} | 7 | 7 | 4 | 1 | 1 | 7 | 9 | 9 | 7 | 4 |
K ^{13} | 4 | 7 | 7 | 9 | 4 | 9 | 4 | 4 | 7 | 7 |
K ^{14} | 7 | 4 | 1 | 9 | 4 | 4 | 1 | 4 | 0 | 1 |
K ^{15} | 9 | 4 | 4 | 7 | 4 | 1 | 4 | 0 | 4 | 7 |
K ^{16} | 7 | 7 | 4 | 7 | 1 | 7 | 7 | 7 | 9 | 0 |
K ^{17} | 4 | 1 | 4 | 9 | 7 | 9 | 4 | 1 | 4 | 7 |
K ^{18} | 7 | 7 | 0 | 1 | 7 | 4 | 4 | 9 | 7 | 4 |
K ^{19} | 4 | 4 | 7 | 4 | 4 | 9 | 9 | 7 | 4 | 7 |
K ^{20} | 9 | 1 | 4 | 0 | 7 | 4 | 7 | 9 | 1 | 9 |
… | … | … | … | … | … | … | … | … | … | … |
K ^{40} | 0 | 7 | 9 | 4 | 7 | 7 | 9 | 0 | 7 | 1 |
K ^{41} | 4 | 1 | 4 | 0 | 1 | 1 | 0 | 4 | 1 | 7 |
K ^{42} | 1 | 0 | 1 | 7 | 1 | 0 | 1 | 1 | 7 | 0 |
Relative weight for every customer requirement
Customer requirement | Relative weight |
---|---|
Motion reliability | W_{1}=0.108 |
Expansion ratio | W_{2}=0.219 |
Security | W_{3}=0.126 |
Thermal deformation | W_{4}=0.063 |
Noise | W_{5}=0.061 |
Product dimensions | W_{6}=0.105 |
Quality | W_{7}=0.059 |
Durability | W_{8}=0.148 |
Modeling | W_{9}=0.067 |
Wear rate | W_{10}=0.044 |
5.2 Multi-objective optimization by ISPEA2 and best compromise solution
Based on the three modularization principles, the design variable is set as δnd_{ i }, and the objective functions include: (1) the clustering degree within modules must be maximized; (2) the coupling degree between modules must be minimized; and (3) the overall reliability of modules must be maximized.
The multi-principle modularization was carried out under the constraint conditions explained in Section 3.4. The component combination is treated as the gene fragment in a genetic algorithm and the initial population is generated according to the mode of random combination. As the searching performance of ISPEA2 will slow down after accession, the value of generation times K is to be set at a moderate level. The chosen parameters are set as follows: generation times K=400, initial population size N=150, crossover rate P_{c}=0.8, and mutation rate P_{m}=0.02. In terms of the chromosome minimum length which represents the quantity of modules, the minimum length M_{min} is set to be 2, and the maximum length M_{max} to be 12.
Based on the research methodology explained in Section 4.3, the best, most suitable compromise solution is selected based on fuzzy set theory. According to the result of chromosome constitutions and design variable values, six modules are identified: the final modularity scheme of the turbo expander is: (1) frame module {1, 2, 3, 7, 10, 20, 40, 42}; (2) expander module {4, 6, 8, 18, 19, 28, 39, 41}; (3) turbo module {13, 14, 25, 26}; (4) lubrication module {15, 16, 22, 24, 27, 30, 31, 35, 36}; (5) cooler module {17, 21, 23, 29, 32, 37}; and (6) control module {9, 11, 12, 33, 34, 38}.
5.3 ISPEA2 vs. other approaches
Comparison of different algorithms
Algorithm | Computing time (s) | Quantity of non-dominated solution (%) | Crossover probability (%) |
---|---|---|---|
ISPEA2 | 54.37 | 37.60 | 86 |
NSGA-II | 86.42 | 28.30 | 81 |
SPEA2 | 72.68 | 34.10 | 74 |
6 Conclusions
This paper attempts to support the module identification by integrating fundamental principles. Based on a thorough study of numerous existing methods, this paper abstracted three principles that should be holistically considered and simultaneously satisfied in the module identification: (1) internal clustering principle, (2) external independence principle, and (3) overall reliability principle. The resulting multi-principle modularization problem is solved as a MOOP. Both conceptual and mathematical modeling of the proposed multi-principle modularization method is presented. The ISPEA2 is used to find an optimal solution that satisfies all three principles. The fuzzy-based selection mechanism is used to extract a Pareto-optimal solution as the best compromise to eliminate the imprecise nature of human decision-making.
The ISPEA is compared with two other established multi-objective optimization methods in terms of computing time, quantity of non-dominated solutions, and crossover probability. The result reveals that the ISPEA2 demonstrated a better performance than the NSGA-II and SPEA2 in terms of both computing efficiency and accuracy to solve the multi-principle module identification problem.
It is also expected that the proposed new method will help deepen the understanding of modularization, and to enhance modularization effectiveness in practice. Future research will include recent hybrid heuristics for optimization and the application of the proposed method in a more complex product, for instance from the automotive or aerospace domain.
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