A Novel Modular Disassembly Design Method for CNC Machine Tools based on PSOA and TOPSIS

 Abstract: Disassembly is one of the crucial issues for the green remanufacturing of obsolete CNC machine tools. Meanwhile, modular design method is the guarantee of disassembly rationality, which can maximize economic and environmental benefits. However, modular disassembly processes of CNC machine tools are more uncertainty in system structures and component conditions. On the basis of summarizing the existing research, disassembly module modeling of CNC machine tools is implemented. For one advantage, the rough set theory is utilized to cluster the parts into different disassembly modules. For another, disassembly information model is constructed by the disassembly multi-constrained graph. Secondly, multi-objective mathematical model which contains disassembly time, disassembly benefit and disassembly complexity is built. A novel particle swarm optimization algorithm (PSOA) improved by niche technology is applied to the disassembly sequence planning. Last but not least, this work also evaluates the disassembly scheme of CNC machine tools based on the technology for order preference by similarity to an ideal solution (TOPSIS). Evaluation indicator system is established and the comprehensive weight of evaluation indicators is determined by the respective advantages of entropy weight method (EWM) and analytic hierarchy process (AHP). A case study is conducted to illustrate the feasibility of the proposed models and methods. The results of this work can contribute to the selection of the optimal modular disassembly scheme of CNC machine


Introduction
Obsolete CNC machine tools have formed large-scale remanufacturing resources. Reasonable dismantling can not only improve the utilization rate of disused CNC machine tools, but also reduce the adverse effect on the environment [1][2]. Hence, modular disassembly design extends the traditional design to the life-cycle design in the purpose of enhancing the product detachability [3].
Related works on modular disassembly design are divided into three aspects, which are disassembly module modeling, disassembly sequence planning and disassembly scheme evaluation. Disassembly module modeling consists of disassembly module partition and disassembly information modeling. Disassembly module partition can effectively avoid the explosion of information combination in the disassembly sequence planning [4]. Tseng et al. [5] added some disassembly criteria such as contact type, combination type, tool type and accessed direction to the liaison graph model, and a grouping genetic algorithm was utilized to cluster parts into modules. Smith et al. [6] applied the atomic theory to address design modularization problems based upon the given green principles. Ji et al. [7] quantified and aggregated modularity measures by multiple attributes of part similarity. Chang et al. [8] applied the design structure matrix built on the modular concept to group different parts together. Qiu et al. [9] proposed a disassembly module partition technology for configurable product based on disassembly constraint relation weighted design structure matrix. The constraint relationship in ·3· modules is strong coupling and the constraint relationship between modules is weak coupling. From what have been described above, disassembly module partition was a process that clusters parts with high correlation value into the same modules in terms of module partition criteria. Nevertheless, the fuzzy relationship among the parts was seldom considered during the disassembly module partition, which led to the poor quality of the acquired disassembly modules. Disassembly information modeling expresses the geometric relationship, connection relationship and disassembly constraint relationship among the parts [10]. Moore et al. [11] obtained the disassembly precedence matrix from product CAD models and built a disassembly petri net model for recycling and remanufacturing. Zhang et al. [12] defined disassembly multi-constrained graph to describe disassembly attribute information. Vyas et al. [13] extracted disassembly relevant information from product CAD models and determined the disassembly feasibility of each component which is represented as a disassembly precedence matrix. Yu et al. [14] analyzed the disassembly information on automobile parts and established the disassembly network graph by using AND/OR graph. Thus it could be seen that disassembly information model represented the disassembly precedence relationship among the parts in the form of a graph model. However, disassembly information model could be depicted by corresponding basic disassembly information list. Resolving the disassembly sequence planning problem is under the driving of certain constraints and goals [15]. Li et al. [16] utilized the disassembly constraint graph to generate possible disassembly operations and genetic algorithm was employed to acquire optimal disassembly sequence. Dong et al. [17] presented an automatic disassembly sequence generation approach from hierarchical attributed liaison graph representation. Smith et al. [18] created a disassembly sequence structure graph model (DSSG) and used rules to search feasible solutions from the DSSG. Zhang et al. [19] defined some disassembly constraint factors and adopted the fuzzy-rough set mapping model to generate the optimum parallel disassembly sequence. Kim et al. [20] represented possible disassembly sequences using an extended process graph, and a branch-bound algorithm is proposed to decrease the search space. Tian et al. [21] took the uncertain part quality and varying operational cost into consideration and presented a hybrid intelligent algorithm integrating fuzzy simulation and artificial bee colony to solve graphbased disassembly sequence. Although the graph and intelligent algorithm in solving disassembly sequence were committed by researchers, traditional methods paid more attention to transform the disassembly sequence planning problem into a single-objective optimization problem. The quality of solutions depended on the cognitive level of decision-makers. Disassembly scheme evaluation is actually a multi-criterion optimization decision problem [22]. Das et al. [23] presented a multi-factor model including disassembly time, disassembly accessibility, disassembly tool and disassembly force to evaluate the detachable performance of products. Sun et al. [24] established a disassembly efficiency evaluation model on the basis of parts failure rate and its disassembly time. Tian et al. [25] proposed a novel dual-objective optimization model which combined the energy consumption with the traditional economic criteria. Feng et al. [26] constructed some indicators on disassembly scheme evaluation and a fuzzy integral method was applied in evaluating the obtained disassembly schemes. Yuan et al. [27] built a comprehensive disassembly evaluation model based on the fruit fly algorithm, crossover efficiency and extension-gray correlation degree and evaluated the disassembly schemes in terms of time, economy and environment. Hence, indicator choice, indicator quantification and weight determination were significant problems for disassembly scheme evaluation. However, previous studies often considered that evaluation indicators were independent from each other and failed to take advantage of the subjective and objective methods comprehensively in determining weight.
In comparison with the existing studies, three distinctive contributions have been made in this paper: (1) The rough set theory is applied to the disassembly module partition of CNC machine tools and the disassembly information model is constructed by the disassembly multiconstrained graph.
(2) Multi-objective mathematical model which contains disassembly time, disassembly benefit and disassembly complexity is built. The PSOA improved by niche technology is utilized to solve the mathematical model.
(3) The grey correlation theory and the Euclidean distance are imported into the TOPSIS. The comprehensive weight of evaluation indicators is determined by the respective advantages of the EWM and the AHP.
The rest of this paper is organized as follows. Section 2 illustrates the disassembly module modeling of CNC machine tools, and disassembly sequence planning of CNC machine tools is analyzed in Section 3. Section 4 presents the disassembly scheme evaluation of CNC machine tools. A case study is presented in Section 5. Finally, Section 6 concludes our work.

·4·
2 Disassembly module modeling 2.1 Analysis on module partition criteria From the perspective of facilitating disassembly modeling, decreasing disassembly cost, reducing disassembly complexity and protecting the environment, module partition criteria are summarized as functional interaction criterion, disassembly difficulty criterion, material similarity criterion and contact type criterion.
(1) Functional interaction criterion. The functional interaction criterion divides the parts with strong functional interaction into the same module, which can achieve the purpose of strong coupling within the modules and weak coupling among the modules.
(2) Disassembly difficulty criterion. The disassembly difficulty criterion, which is generally determined by part connection types, clusters the parts with large disassembly difficulty into the same modules.
(3) Material similarity criterion. The material similarity criterion divides the parts with same or similar materials into the same module, which is conducive to the material recycling and ensures the material performance.
(4) Contact type criterion. The different spatial position relationship among the parts brings about different contact types. Meanwhile, different contact types determine different disassembly complexity among the parts.
The definition of module partition criteria among the parts is described and quantified as Figure 1.

Correlation analysis among the parts based on rough set theory
The correlation value is generally quantified with fuzzy and imprecise value which can affect the construction quality of disassembly modules. Rough set theory can effectively analyze the uncertain information and rough number is proposed based on the rough set theory which expresses its size in the form of interval [28]. The upper limit and the lower limit of the interval can not only reflect the size of data, but also reflect the distribution of data. The quality of disassembly modules can be effectively improved by analyzing the correlation value among the parts with the rough number.
(1) Construction of the rough number ( , ) g h i j t expresses that expert g (1≤g≤G) marks the correlation value between part i and j on the criterion h. The correlation value between part i and j is described as , the rough number can be obtained as follows [29]. Table 1 The correlation value between part i and j Expert h=1 h=2 h=3 h=4 where h  is the weight of module partition criterion h, which is determined by the AHP. The comprehensive incidence matrix R can be established with Eqs. (4), (5).

Relationship type Value
where Lij is the lower limit of interval, Uij is the upper limit of interval and n is the number of the parts.
(3) Clustering solution and result optimization The transitive closure method is used to transform the comprehensive incidence matrix into fuzzy equivalent matrix and the result of module partition can be obtained by using upper threshold value U  and lower threshold value U   , part i and j belong to the same module. Otherwise, part i and j belong to the different modules. Although clustering parts with upper and lower threshold values can be better than using single threshold value, the selection of threshold values will affect the quality and number of disassembly modules. The clustering principle is to ensure higher cohesion degree within the modules and lower coupling degree among the modules [30]. Thus, the cohesion degree and coupling degree can be utilized to guide the reasonable selection of the upper and lower threshold value.
The cohesion degree K MI of module K and the coupling degree NI  between module α and β are defined as follows.
. The total cohesion degree MI, the total coupling degree NI and the ratio γ between MI and NI are described as follows.
where N is the number of the modules. The larger the value of γ is, the higher the quality of the disassembly modules is. Therefore, the value of γ can be used to guide the selection of threshold values.

Disassembly information modeling based on disassembly multi-constrained graph
It is inevitable to analyze the connection relationship and constraint relationship among the modules after the disassembly module partition is completed. Disassembly multi-constrained graph is a variant of disassembly hybrid graph, which can effectively reveal the disassembly constraint information and disassembly precedence information. Disassembly multi-constrained graph can be defined by a quintuple, which is represented as follows.
where   12 , ,..., indicates all the disassembly modules, Ep is physical constraint which illustrates that there are direct contact and identical disassembly precedence among the disassembly modules, Esp is powerful physical constraint which represents that there are direct contact and different disassembly precedence among the disassembly modules, Er is spatial constraint which describes that there are disassembly precedence but without direct contact among the disassembly modules, C is linkage constraint. Figure 2 is a paradigm of disassembly multiconstrained graph.

·6·
five types, and the conversion time is shown as The objective function for disassembly time, called t F , can be obtained as follows. (2) The objective function for disassembly benefit There are generally the following processing ways for the disassembled modules: reusing directly, reusing after remanufacturing, recycling and wasting directly. The first three ways can bring some benefits. What's more, the disassembly cost mainly includes the cost of tools and labors. Thus, we have the following objective function for disassembly benefit.
where i z is the benefit value of reusing directly of module

The PSOA improved by the niche technology
(1) Updated rules for the position and velocity of particle The position of particle is defined as a disassembly sequence. For example, the position of particle i can be indicated as   12 , ,..., The velocity of particle is defined as a transformation sequence that adjusts the disassembly sequence. For instance, the velocity of particle i can be expressed as   12 , ,...,  is the inertia weight factor. 1 c and 2 c are acceleration factors. 1 r and 2 r are random numbers between zero and one. The updated formulas for the position and velocity of particle i are presented as follows.
(2) Updating and filtrating of non-dominated solutions based on the niche technology The algorithm produces a set of non-dominated solutions after each iteration and how to deal with the non-dominated solutions correctly is a crucial problem. This paper adopts the elite set to preserve the non-dominated solutions of each iteration and utilizes the niche technology to determine the fitness of particles in the elite set. The niche number of particle i are defined as follows.
where K is the size of the population, ( ( , )) sh d i j is the sharing function, ( , ) d i j is the distance between particle i and j, U is the number of optimization objective functions, share  is the niche radius, α is the parameter that controls the shape of the sharing function.
When the number of non-dominated solutions in elite set exceeds the maximum capacity, the non-dominated solutions with low fitness are deleted. Besides, the selection of optimal individual position and group position can affect the efficiency of the algorithm. The optimal individual position can be selected by the dominant relationship. If the current position of particle i dominates the historical optimal individual position, the historical optimal individual position is updated. Otherwise, the historical optimal individual position is unchanged. The optimal group position can be selected randomly according to the fitness of particles in elite set. The implementation steps of particle swarm optimization algorithm is described as Figure 3. (2) Indicators about disassembly economy Disassembly cost (C1) consists of the tool cost and labor cost, which is formulated as where t is the total disassembly time, (3) Indicators about disassembly environment In the process of disassembly, parts with low material compatibility should be disassembled as soon as possible. The purpose is to prevent the chemical corrosion and the reduction of material performance. Besides, the larger the proportion of discarded modules is, the higher the pressure on environment is. Therefore, the material compatibility among the parts (E1) and the proportion of discarded modules (E2) can be expressed as

·8·
where , ij ZL is the material compatibility value between part i and j, which can refer to the Table 1

Evaluation of disassembly schemes based on TOPSIS
Hence, the weighted standardized decision matrix B can be acquired as follows. (4) Calculation of the relative closeness degree After the dimensionless processing of the Euclidean distance and the grey correlation value, the relative closeness degree between disassembly scheme i and ideal solutions, denoted by i c  , can be presented as follows. Figure 4 shows the framework of the proposed modular disassembly design method.

Case study
The proposed methods are applied to the protective device of CNC horizontal boring machine tool TGK46100, which is displayed in Figure 5. The main part information is shown in Table 3.
With Eqs. (1)-(6), the comprehensive incidence matrix can be constructed as  In order to analyze the connection relationship and constraint relationship among the modules, the disassembly multi-constrained graph is described in Figure 6. By considering the relevant disassembly information, basic disassembly information list is constructed, which is shown in Table 5.     Figure 6 Disassembly multi-constrained graph of protective device  The set of disassembly schemes is F={F1, F2, F3, F4} and the set of evaluation indicators is P={P1, P2, P3, P4, P5, P6}. The comprehensive weight of evaluation indicators, which are determined by EWM and AHP, is shown in Table 7. The weighted standardized decision matrix is constructed as Table 8. The positive and negative ideal solutions of disassembly schemes can be obtained as Table 9.  w   After dimensionless processing for the Euclidean distance and the grey correlation value, the relative closeness degree can be obtained as Table 10. As a result, we conclude that F2 is the optimal disassembly scheme. Last but not least, it is necessary to compare proposed method to other well-known methods. Ant colony algorithm (ACA) and artificial bee colony algorithm (ABCA) are also popular swarm intelligence algorithm. Thus, they are comparable to the improved PSOA. Besides, fuzzy comprehensive evaluation (FCE) and intuitionistic fuzzy evaluation (IFE) are used as benchmark methods to evaluate the modified TOPSIS. The comparison results are shown in the Table 11. It can be found that the ranking results of different methods are identical, which reflects the validity of the proposed method.