Abstract
Typical process is a sample process which can reflect processes of a group of similar parts. As a kind of process knowledge it can be referred to for the process planning of new parts. In this paper a methodology of typical process discovery for body-in-white (BIW) parts, based on the distance (i.e. dissimilarity) between processes, is proposed. The process for BIW part is divided into assembly positioning, joining, and quality inspection operations, in accordance with the typical assembly; the assembly oriented typical process is extracted based on these three operations. The distances of assembly positioning, joining, and quality inspection are calculated respectively using different measuring methods. The distance between processes is calculated as the sum of the assembly positioning, joining, and quality inspection distances. Furthermore, the clustering algorithm is applied to form the process clusters according to the distances between processes. The mean variances of the distance between processes in the cluster are calculated. The process with the minimum mean variance in the cluster is selected as the typical process. Finally, a case study is used to show the procedure of the typical processes acquisition for BIW and validate the effectiveness of the proposed method.
Introduction
The assembly for the body-in-white (BIW) involves 300–500 parts and the BIW is built with high precision and at low cost [3]. In addition, the process planning for the BIW is a demanding job, especially for novice planners. The reuse of existing part processes can reduce repetitive design work, and avoid the process planning for similar BIW parts from scratch. Therefore, process knowledge discovery and reuse can significantly improve the efficiency and quality of this planning [6]. However, Knowledge discovery is the most time-consuming process and the bottleneck in constructing a knowledge-based system. Knowledge acquisition is a research focus. Case retrieval methodology, which is frequently used in the field of knowledge discovery and reuse, is also widely used in BIW process planning. For example, Zhou et al. [11] established a relationship between the assembly models in conceptual design and reusable design examples, and subsequently proposed a reusable BIW conceptual design method using case-based reasoning technique. Chen et al. [8] proposed a BIW assembly process design system which is based on the case retrieval methodology. A similar method was developed by Chen et al. [7] who established an object-oriented and extended case representation model for the BIW parts. However, the method of case retrieval has shortcomings. First, case retrieval is based mainly on the calculation of similarity between part features. The similarity depends mainly on the feature representation andfeature weights. However, feature representation and the weight vary from person to person, thereby leading to different results for the same case. Second, the case retrieval method requires a case library. In order to obtain satisfactory results, the case library must contain a sufficient number of similar cases. The construction of this library is, however, time-consuming. In addition, the case library must be continuously improved and complemented. As such, this paper proposes a typical process discovery methodology for the BIW process planning.
Typical process is a sample process which reflects processes of a group of similar parts. Therefore, when we formulate assembly processes for new parts, a typical process can be referred to, which can improve the efficiency of process planning greatly. This procedure is similar to the case retrieval method, which means a case retrieved from the case database is used for reference for a new case. Compared with the case retrieval method, the typical process method needs the relatively small typical process library and typical process can be accessed through keyword searches. These characteristics can improve the efficiency of searching for typical processes. This paper aims to develop a methodology for extracting BIW typical process from the process database. The proposed approaches provide a new alternative for the BIW process planning.
The remainder of the paper is organized as follows: the state of the art BIW assembly is introduced in Section 2. A discovery framework of typical processes is presented in Section 3. An approach for calculations of dissimilarity between BIW processes is developed in Section 4. A method of typical process acquisition based on the mean variance is proposed in Section 5. A case is presented to demonstrate the validity of the proposed method in Section 6. Some concluding remarks and future research are presented in Section 7.
Previous studies on the BIW assembly
The process planning activity of the BIW assembly constitutes a critical bridge between the development and design of a product and its final assembly and delivery to the customer. As such, the BIW assembly has been extensively investigated in an effort to improve the assembly quality and efficiency. For example, Liu and Hu [16] revealed that different joint types and combinations resulted in differing variations in the dimensional assembly; i.e., BIW assembly quality could be improved using various joint configurations and types. In addition, Lee and Saitou [1] used a genetic algorithm to optimize the assembly sequence, in order to minimize the assembly variation of the BIW. In other work, Shiu et al. [2] presented a tolerance allocation methodology for BIW and aerospace assembly processes. With this method, design requirements are used as constraints, the associated manufacturing costs are minimized, and the allowable tolerances associated with each characteristic of the process is maximized. Shi et al. [9] proposed a process navigation system, which integrates BIW assembly monitoring and error diagnosis. Furthermore, Yubing et al. [13] developed and applied an algorithm to predict the accumulation of variations in the BIW assembly; a subsequent compensation was used to reduce the unnecessary or surplus variation. Ceglarek and Szafarczyk [5] proposed a method for the systematic evaluation of a flexible adaptive assembly system, which could compensate for the variability in part dimensions stemming from upstream processes.
Artificial intelligence provides an efficient approach to the implementation of knowledge-based design automation systems, which may improve the efficiency of BIW assembly process designs. Ceglarek et al. [4] proposed a knowledge-based diagnostic method for the BIW assembly process. Using this method, assembly process faults can be rapidly detected and localized, based on in-line dimensional measurements. In addition, Zhao et al. [17] proposed the assembly information model for BIW, which can generate all feasible assembly sequences. Similarly, Chen et al. [8] developed an intelligent system for the BIW assembly process. Using this system, the joint types and assembly sequences, which result in the best dimensional accuracy, can be automatically generated. Raza and Harrison [14] introduced a Reconfigurable Assembly Systems, which is a knowledge-based system that is capable of designing, engineering, manufacturing new, and changing existing, processes as well as resources. Moreover, this system facilitates enterprises, which rapidly respond to changes in the dynamic global markets. Ko et al. [10] also proposed a method of developing an intelligent recommendation system for BIW assembly. This system shows the detailed part information during the selection of part. Papakostas et al. [15] formulated a knowledge-enabled approach to BIW assembly, which uses existing knowledge to generate the process plans considering the quality requirements and the assembly constraints.
Discovery framework of typical processes for BIW parts
The BIW is composed of 300–500 complex sheet metals and its assembly consists of two main procedures. First, different parts are joined to form components or sub-assemblies. Second, parts, components, and sub-assemblies are joined, to form the BIW, via the transmission devices, fixtures, equipment, and other positioning equipment [12]. This assembly must comply with strict quality requirements and assembly sequences. For example, parts are placed at the exact location and clamped. These parts are joined after the selection of appropriate joining methods and the quality of the assembly is then inspected. In accordance with the typical BIW assembly characteristics, the assembly process can be divided three major operations, i.e. assembly positioning, joining, and quality inspection operations.
To acquire the typical process from the process library the dissimilarities between processes needed to be calculated. In this paper, the distance is used to denote the dissimilarity. Its value ranges from 0 to 1. The distance between processes is calculated as the sum of the distance of the three major operations. First, the distance between assembly positioning operations is computed. The assembly positioning is classified into marking positioning, fixture positioning and mounting hole positioning. The distance between them is computed using the expert scoring method. Second, the distance between joining processes is computed. Several joining methods are employed in joining operations. The joining method is classified as welding, cementation, riveting and so on. It is coded and their distance is calculated by the Manhattan distance. Third, the distance between quality inspection operations is computed. The matrix for quality inspection operation is constructed and the distance between quality inspection operations is calculated by binary attribute distance. After the distances of three major operations are obtained, the total distance of process is gotten by adding operation distances according to their different weights. The hierarchical clustering algorithm is used to obtain the process dendrogram. The number of clusters can be gotten according to the inter-cluster threshold. The mean variances of the distance between processes in the cluster are calculated. Typical process for BIW parts can be extracted from every cluster based on the mean variance. The discovery framework of typical process for BIW parts is shown in Fig. 1 using the cluster analysis.
Typical process discovery framework for BIW parts.
Distance between assembly positioning operations
Three kinds of assembly positioning methods namely, marking, fixture, and mounting hole positioning methods, are used in assembly positioning operation. A kind of assembly positioning method is used in one positioning operation. Thus, the distance calculation between assembly positioning operations is the distance calculation between assembly positioning methods. The distance between two different assembly positioning methods cannot be directly computed, but is evaluated using an expert scoring method instead. In fact, the average distance of several expert scorings is taken as the distance between the assembly positioning methods. Table 1 shows the distances determined using the expert scoring method. The marking positioning, which is currently dominated by manual labor, is the traditional positioning method. It uses the marking device to sign the assembly positions. The positioning accuracy and efficiency of this method are relatively low. However, the fixture and mounting hole positionings are operated by automatic fixtures. The former is the most commonly used method in the BIW assembly, whereas the latter is employed only for specially shaped parts. In addition, their positioning accuracy and efficiency are relatively high. The similarity between these positioning methods results in only a small inter-method distance. The difference between the marking and fixture positioning methods as well as between the marking and mounting hole positioning methods is greater than that between the fixed and mounting hole positioning methods; the corresponding inter-method distances are therefore larger than that between their fixture and mounting hole counterparts.
Distance between assembly positioning methods
Distance between assembly positioning methods
There are several joining methods used in the joining operation for the BIW parts. Thus, the distance calculation between the joining operations is essentially the distance calculation between the joining methods used in joining operations. The joining methods are classified as welding, riveting, and cementation. In order to accurately calculate the distance between the different welding methods, the welding is classified as spot welding, laser welding, and CO2 protection welding. Some regions must, however, be polished after welding. In this work, polishing is classified as a joining method. In addition, a joining operation for one part may be composed of several joining methods.
The joining method is a category attribute, and hence the inter-method distance cannot be directly calculated. Therefore, a coding system is established for the joining method and the inter-method distance is then computed based on codes. The code of each joining method is composed of several digits. The accuracy of the determined difference and difficulty of establishing standard procedures for classification and coding both increase with increasing number of digits in the coding system. According to the characteristics and category of joining method for BIW, a four-digit coding system is selected. Spotwelding, laser welding, and CO2 protection welding all belong to welding. Their processes are similar; hence they have same first two codes. The similarity of process between welding and riveting is small, so riveting only has same first one code with welding. The processes of cementation and polishing have big difference with welding and riveting, so their first codes are different. The codes used for each joining method is shown in Table 2.
The codes of joining sub-operation
The codes of joining sub-operation
The distance between codes may be determined using the Manhattan distance. The distance between the lth joining methods in the ith and jth joining operations based on the code distance can be expressed as:
The distance calculation between joining methods need to follow the rules, i.e., if the digits in the first position of two codes differ, i.e., vil1 ≠ vjl1, then subsequent digits are considered to be different since they do not belong to the same category. The distance between these two joining methods is equal to 1. If the first digits of two codes are the same and the second digit of two codes is different, the second and subsequent digits are considered to be different, a series of operations are performed until the all digits in the code are compared. According to Equation (1) and the above rules, the distance of six types of joining methods is calculated and listedin Table 3.
The distances between joining sub-operations
A joining operation contains several joining methods. The distance of between the ith and jth joining operations can be expressed as:
The distance calculation of joining operation need to follow the rules, i.e., the distance of the most similar two joining methods from the two joining operations is first computed, then so is the distance of the second most similar two joining methods. A series of calculations are performed until all distances are computed.
The BIW manufacturing quality has a significant effect on the vehicle quality including the shape accuracy, dimensional accuracy, joint quality, sealing quality, and other aspects. Several quality inspection items need to be checked in the quality inspection operation for the BIW parts. The calculation of the distance between quality inspection operations is the calculation of the distances between quality inspection operation items checked in quality inspection operations. In order to calculate the distance between quality inspection items a distance formula of the binary attribute is adopted.
Distance between the binary attributes
A binary attribute contains two values, “no” and “yes”, which are represented as 0 and 1, and indicate the absence and presence, respectively, of the item. Table 4 [18] shows the attribute matching between objects i and j. In Table 4, x, y, r, and s are the respective number of both attributes, which have a value of 1, 0 in i and 1 in j, 1 in i and 0 in j, and 0. The total number of binary attributes is t and t = x + y + r + s.
The attribute matching table between objects i and j
The attribute matching table between objects i and j
In the BIW quality inspection items, items that must be tested are represented by 1; 0 represents the items which do not have to be tested. The two binary states are, however, not equally important; i.e., the positive matches are more important than the negative ones and therefore we are more concerned about the tested item than the non-tested one. The Jaccard coefficient is especially suitable for describing the difference between these asymmetrical attributes. Furthermore, the weight is assigned a value of 1 when both attributes have a value of 0. The distance between two asymmetrical attributes is expressed as [18]:
In general, if many parts are assembled then the m parts and their n quality inspection items (attributes) can be expressed as an m×n matrix, i.e.,
The quality inspection item is a binary attribute. The quality inspection items and its number both vary with the type of joining method; i.e., different joining methods require different quality inspection items. If a quality inspection item is selected, its value is 1 and 0 otherwise; i.e.,
The values 1 and 0 are not equally important. In fact, items having a value of 1 are more important than their counterparts, which have a value of 0. The quality inspection item is therefore an asymmetric binary variable. Thus, the distance between two quality inspection operations depends on the number of the same quality inspection items two quality inspection operations contain. Based on Equation (3), the distance between the i
th
and j
th
quality inspection operations can be expressed as:
The algorithms used to compute the distance of the assembly positioning, joining and quality inspection operations were discussed in the previous sections. The distance between processes is the total distance of the assembly positioning, joining and quality inspection operations. Each of the three factors has a different effect on the process. As such, each operation is assigned a distinct weight. The total distance between the processes is calculated from:
After the total distances between the processes are obtained, these processes are divided into several different groups. A typical process is extracted from each group and used as the typical process of the corresponding group.
Process clustering
Process clustering is used to classify processes into different clusters based on their distance between processes. A cluster is a collection of processes, and each process is more similar to the other processes in the same cluster than those in other clusters. Clustering must comply with certain distance guidelines. In addition, the distance is typically determined via the minimum distance, maximum distance, and average distance; therefore, we can obtain different hierarchical clustering results by using different distance criteria. For example, the minimum distance method uses the minimum distance between two processes, which belong to two different clusters, to represent the inter-cluster distance. However, this representation can lead to excessive processes in a single cluster and low levels of similarity between the processes. In contrast, the maximum distance method uses the maximum distance between two processes, which belong to two different clusters, to represent the inter-cluster distance. This approach, however, leads to insufficient, highly similar processes in a single cluster. Therefore, due to the drawbacks associated with the clustering effect of both the minimum and maximum distance methods, the average distance method is selected for determining the distance between clusters.
The average distance method uses the average distance between any two processes from two clusters. The average distance between cluster C
i
and C
j
is computed as:
The number of clusters reflects different levels of various clusters. For the same process samples, the distance between processes and the number of processes within a cluster, decrease with increasing numbers of clusters. Conversely, the distance between processes, and the number of processes within a cluster increase with decreasing numbers of clusters. The number of clusters is typically determined by two methods. The first method is to directly specify the number of clusters. The second method is to specify the inter-cluster threshold and then calculate the number of clusters. Furthermore, the number of clusters decreases with increasing inter-cluster threshold and vice versa. In this work, the inter-cluster threshold, which directly reflects the degree of similarity between the processes, is used to determine the number of clusters.
When the total distance of each process is obtained, the number of clusters can be computed based on the inter-cluster threshold. The mean variances of the distance between processes(i.e., the mean variances of process) in the cluster are calculated. The process with the minimum mean variance in the cluster is selected as the typical process. Each cluster has a typical process. For example, consider a cluster that consists of m processes, v1, v2, v3, ⋯ , vm-1, v
m
; the mean variance of process v
i
compared to other processes is calculated as:
In this section, a case is given to show the procedure of extracting typical processes. Process data of eight BIW parts are showed in Table 5. Every BIW parts process contains assembly positioning, joining, and quality inspection operations. There are three types of assembly positioning method, i.e., marking, fixture, and mounting hole positioning method. One kind of assembly positioning method is used in the assembly position operation for one BIW part. A joining operation contains several joining methods. There are six types of joining methods in total, i.e., cementation, CO2 protection welding, spot welding, laser welding, polish, and riveting. One to three types of joining methods are used in the joining operation for one BIW part. There are seven types of quality inspection items, i.e., joint location, joint quality, joint length, coating thickness, deformation, number of spot welding and number of riveting. Four to five types of quality inspection items are used in the quality inspection for one BIW part.
Process data for BIW parts
Process data for BIW parts
The number of joining methods for parts is different. In general, the joining operation includes three methods at most, one item at least in the Table 5. When there isn’t the corresponding item in the coding matrix the number 0 is fill up the vacancy. The coding matrix of joining operation is as follows according to the Table 2:
The distance matrix of joining operation is as follows according to Equation (2):
The distance matrix of assembly positioning is obtained according to Table 1.
Every BIW part needs to be tested after the joining operation. Different joining operation requires different inspection items and the number of quality inspection item is distinct. According to the content in Table 5, the correlation matrix of quality inspection operation is showed in Table 6. The first column is joint locations, the second column is joint lengths, the third column is joint defects, the fourth column is deformation in the joint, the fifth column is coating thickness, and the sixth column is the number of joints. Among them the joint quality refers to the various joint defects and the number of joint specially refers to the number of spotting welding and riveting.
Correlation matrix for quality inspection operation
Correlation matrix for quality inspection operation
The distances of every two quality inspection operations are computed and the distance matrix is as follows:
After the distance of assembly positioning, joining operations and quality inspection are obtained and the weight of various distances are assigned according to the degree of influence on the process, the total distance is calculated according to the Equation (7). The total distance matrix is as follows:
In the total distance matrix, the weight of joining operation is assigned to 0.6. The weights of assembly positioning operation and quality inspection operation are both assigned to 0.2. The weight of joining operation is significantly higher than the weights of assembly positioning operation and quality inspection operation, because the joining operation is the most important operation in BIW assembly which directly affects the assembly qualities of BIW.
Process can be clustered after the total distance of process is obtained. Eight part processes are clustered hierarchically according to the average distance method. Firstly, eight processes are divided into eight clusters. The two clusters whose distance is the minimum distance among eight processes are merged into a new cluster. The new cluster and the rest of clusters continue to be merged after the calculation of average distance among them. The above step is repeated until all clusters are merged into one cluster. The clustering result is showed in Fig. 2.
Process clustering based on average distance.
According to the inter-cluster threshold, the number of cluster can be obtained. In this case, when inter-cluster threshold α is equal to 0.6 eight part processes can be divided into two clusters, cluster 1 {1, 5, 7} and Cluster 2 {1, 3, 4, 6, 8}. According to Equation (9) the mean variances of process in cluster 1 are as follows:
The mean variance of process v7 is the least, so it is selected as the typical process of cluster 1.
According to Equation (9) the mean variances of process in cluster 2 are as follows:
The mean variance of process v3 is the least, so it is selected as the typical process of cluster 2.
The above clustering results reveal that cluster 1 exhibits smaller mean variances than those of cluster 2. Moreover, v7, the typical process of cluster 1, constitutes a more optimal process than its counterpart v3, which is in cluster 2. If process v3 does not fulfill the process requirements, then the inter-cluster threshold can be reduced. When the inter-cluster threshold α is assigned a value of 0.5, the eight part processes can be divided into three clusters, namely, cluster 1 {1, 5, 7}, cluster 2 {2, 3, 4}, and cluster 3 {6, 8}. The corresponding mean variances are listed in Table 7. In addition, with mean variances of 0.247, 338, and 0.040, processes v7, v3, and v6 or v8 are selected as the typical processes of clusters 1, 2, and 3, respectively. The minimum mean variances of clusters 2 and cluster 3 are significantly lower than the values obtained when α= 0.6. The inter-cluster threshold α affects both the numbers of clusters and the mean variance. Therefore, the threshold α plays a significant role in the acquisition of the typical processes.
The mean variance of the processes
This paper proposed a methodology for the typical process discovery of the BIW, based on the distances between processes. In accordance with the typical assembly process for the BIW, the process is divided into assembly positioning, connection, and quality inspection operations. Distance calculation algorithms of the three operations are proposed, based on the characteristics of said operations. Furthermore, an expert scoring method is used to compute the distance between the assembly positioning operations. Since the distance between connection operations cannot be computed directly, the Manhattan distance is used to calculate these distances, based on the four-digit coding employed for the joining operation. The quality inspection operation typically includes several items but the number of items varies. To ensure that the calculation results are scientifically sound and reasonable, a binary attribute formula is used to compute the distance between the quality inspection operations. The part processes are classified into several clusters, based on the total distance between the processes. The corresponding typical process is subsequently extracted from every cluster by means of the mean variance method. The proposed approach extracts typical processes for the BIW and realizes the reuse of process knowledge. In addition, the process we formulate through the typical process is more standardized than that formulated through the case retrieval. With the advance of the technology, some new joining methods have been applied in BIW assembly. Based on this study, the new joining methods and more digits coding system capturing more information can be considered as topics for further researches.
Footnotes
Acknowledgments
This work was supported by National Natural Science Foundation of China [51565058].