Research on identification of key processes in machining process based on PageRank algorithm

Aiming at the difficulty of quantitatively evaluating the critical processes in the manufacturing process of complex mechanical products, a critical process identification method based on the PageRank algorithm is proposed with the goal of identifying key processes in the machining process. Based on the complex network theory, the error transfer network model of the machining process is established in this paper. Adopting the actual machining process as the data set of the complex network, the weights of the machining feature nodes are calculated by the PageRank ranking algorithm, and the nodes are ranked according to the weight values to assess the influence and importance of the nodes in the network model. Finally, taking the connecting rod machining process of a medium-speed marine diesel engine as an example, the results show that the method can quickly and effectively identify the key processes in the machining process.


Introduction
In the manufacturing process of mechanical products, the focus of processing quality control lies in the manufacturing process itself. 1 The machining process node is the basic unit that constitutes the entire machining process, and the formation of the final quality of the product is the result of the joint action of multiple machining processes. 2Therefore, the control of the processing characteristics of each process has become the focus of controlling processing quality.However, the machining process of complex mechanical products often has complexity, and a complete production process usually consists of dozens of processes.In the production process, quality control of the entire machining process is often achieved through supervision, testing, and control of a few key processes.Consequently, the effective identification of key processes has become a significant issue in ensuring the effectiveness of processing quality control.
In recent years, scholars at home and abroad have carried out more studies on the identification of key processes and quality features in mechanical product processing.Currently, qualitative analysis methods are commonly used to identify key processes in machining processes.Thorton et al. 3,4 classified the importance of key characteristics based on process data.Yang et al., 5 due to the concept of tolerance control, calculated key process control points using the Analytic Hierarchy Process.This type of these methods is a qualitative analysis method in which experts determine the key processes in the part machining processes based on experience.When confronted with complex mechanical products, miscarriage and misjudgment of critical processes can easily occur. 6Some researchers also analyzed the criticality of the machining process from the perspective of the production process.Wang et al. 7 analyzed the key processes of the cold roll production process with the process quality loss function as the evaluation index.Francisco et al. proposed the concepts of key sets and key clouds to identify key tasks in the management process; Kim et al. 8 proposed a twostep method for key process identification -global key process identification based on overall quality analysis as well as localized key process identification based on regression coefficient matrix and clustering algorithm.These methods mainly evaluate the operating status of multiple processes themselves.And manufacturing processes are considered and analyzed poorly from a systematic perspective.At the same time, the complexity of these identification methods greatly reduces their applicability in actual production.Li et al. 9 proposed a multi-objective whale optimization method to identify the quality characteristics of unbalanced product quality data sets.This method took the feature dimension and G-mean as the target to construct a multi-objective optimization problem.The solution of the model reduces the feature dimension and improves the accuracy of various quality results.Ma and Mao 10 used the entropy weight method, Mahalanobis distance and Taguchi experiment principle combination algorithm to identify the key features of product quality data.This method successively carried out three rounds of filtering and screening by calculating the entropy weight of each quality index, the Mahalanobis distance between samples, and the signal-to-noise ratio and range of quality characteristics in Taguchi experiment.Finally, the key quality characteristic indicators of this dataset are determined.Wang and Nu 11 proposed a recognition method of quality characteristics based on Filter theory.This method filters quality characteristics based on Lasso algorithm to remove irrelevant and redundant quality characteristics, and uses the classification accuracy of support vector machine as the final evaluation criterion.
In this research work, in view of the difficulty in identifying quantitatively the key processes of complex mechanical products in the machining processes, the author proposes a method of identification of key processes in the machining processes based on the PageRank algorithm from the perspective of actual processing technology.Based on the complex network theory, a network model is established to describe the relationship between the processing quality of parts and the working condition elements in the machining processes. 12By introducing the PageRank algorithm to analyze each node in the process error transmission network, the weight of the processing feature nodes is obtained, and the node influence degree is sorted to identify the key processes in the machining processes.Finally, the effectiveness and applicability of the proposed method are verified through an actual example.

Process network modeling based on complex network theory
The complex network theory is an effective method for analyzing the coupling relationship in complex systems.4][15][16][17][18] It can be used to analyze the rule of error generation, accumulation, and transmission in the process of multi-machining processes.To establish the processing network, it is necessary to extract and process the process information according to the process information and process characteristics of the parts so as to abstracting the nodes of the process error transmission network of parts and the transitive relation between nodes. 19

Machining process network node and edge relationship definition
Node definition (a) Machining feature (MF) is the basic unit of part processing, which represents the geometric shape and topological relationship of the workpiece surface.A complex mechanical part usually contains multiple different machining features.As a description of the precision of the machining characteristics, the quality features can be regarded as the attribute of the machining features.A machining feature typically contains one or more quality features.In the process of machining complex machine parts, the state of machining features is constantly changing, which is essentially the evolution process of quality features.(b) Quality feature (QF) is defined as a set of quality information that includes parameters such as nominal requirements, tolerances, and actual errors.All quality features can be divided into two main types: autocorrelated quality features and correlated quality features.

Edge relationship definition. (a) Evolutionary relationship (ER):
The realization of the final quality requirements of a machining feature usually requires more than one machining stage.For example, the machining of a hole feature usually includes three stages (bore the hole A1, enlarge the hole A2, and ream the hole A3).As a result, the orientation of the edges is defined as the evolutionary relationship A1!A2!A3.(b) Location relationship (LR): In the machining process of multiple processes, the implementation of the location reference is an indispensable part of the part machining, for example, there are three machining features B1, C1, and D1 perpendicular to each other.If the machining features C1 and D1 are the location reference of the machining B1, the edge relationship between them is the location relationship C1!B1 and D1!B1.(c) Processing relationship (PR): According to the requirements of different machining accuracy and types, different machining features in different machining stages usually adopt different machining elements.The relationship between edges between such nodes is defined as a processing relationship, for example, MT!MF represents a certain type of machine tool processing a certain processing feature.(d) Attribute relationship (AR): A processing feature usually contains one or more quality features as well as the edge relationship between this machining feature and its affiliated quality features is defined as an attribute relationship, namely MF!QF.
For the convenience of network modeling, Table 1 provides the coding rules for processing process network nodes.

Construction of the processing process network model
For the machining process network model of the machine element, its composition includes network nodes and connecting edges between different nodes.The model can be defined as , in which W = W 1 , W 2 , :::, W l f g represents the set of machining element nodes during the part machining process; M = M 1 , M 2 , :::, M m f g represents a set of machining feature nodes for parts; Q = Q 1 , Q 2 , :::, Q n f g represents the set of quality feature nodes output by machining features and E = E 1 , E 2 , :::, E k f gdescribing the transitive relation between nodes represents the set of directed edges in the machining process network.
According to the above definition of edge relationship of the machining process network, the transitive relation between different machining feature nodes mainly depends on the evolution relationship and location relationship.The transitive relation between machining feature nodes and quality feature nodes depends on the attribute relationship and the transitive relation between machining element nodes and machining feature nodes depends on processing relationship.Figure 1 is a schematic diagram of the machining process sub-network model, in which ER, LR, PR, and AR respectively represent the evolution relationship, Based on each established machining process subnetwork, the sub-networks are merged in the order of machining features to ultimately form a complete machining process network model for the part.

A node importance evaluation method based on PageRank algorithm
To realize the analysis of the processing network of the machine element, it is usually necessary to introduce topological relationship evaluation indicators to study the topological relationship of nodes and networks in the network.However, the commonly used topological relationship indicators can only describe the overall performance of the network and the degree of association between nodes, and cannot obtain the criticality of each node.In the processing technology of machine element, not every node has the same criticality.Therefore, in order to more accurately sort the nodes in the processing technology network of parts, that is, find the key process, the weight of each node needs to be calculated.
Define the criticality of a node as the sum of the node weights that point to that node.Therefore, it is necessary to obtain the weight of each node before conducting key ranking.However, in actual machining processes, it is difficult to simply obtain the weight of each node through machining processes.
PageRank algorithm 21,22 is a classical algorithm used to rank web pages in search engines.The algorithm is used to calculate the authority value of Web pages, and then rank Web pages according to the size of the authority value.Simply put, the core idea of PageRank algorithm is: if a web page is linked to by many other web pages, it means that this web page is important and recognized by many web pages, that is, the authority value will be relatively high; If a page with a high authority value links to another page, the authority value of the linked page will be increased accordingly.That is, in the PageRank algorithm, the PR value represents the authority value of each Web page, which depends not only on the number of linked web pages, but also on the quality and importance of the web pages pointing to this web page.
The PageRank algorithm can efficiently identify the most influential nodes in the network, so this article introduces the PageRank algorithm to identify key processes in the machining process.
The PageRank algorithm assumes that the weight of each node is same.Based on the initial weight of each node, the weight of each node after the first iteration is calculated.Then, based on the weight of the node obtained from the first iteration, the weight of the node for the second iteration is calculated, and so on until the weight of the node converges to a stable value, which is called the PageRank value of the node.The larger the PageRank value, the larger the weight of the node.
The iteration rules of the PageRank algorithm are represented as: In the formula: B i is the matrix of PageRank values of the network nodes after the i-th iteration.The initial PageRank values B 0 of nodes are all set to 1/N .N is the number of nodes in the network, and a mn in the matrix A represents the number of edges from the m-th network node to the n-th network node in the network.The process of iterative PageRank calculation is shown in Algorithm 1.

Case study
To demonstrate the practicality and applicability of this method, taking the actual machining process of a certain type of medium-speed marine diesel engine connecting rod as an example, the PageRank algorithm is used to identify key processes in the machining process.Compared with common engine connecting rods, medium-speed marine diesel engine connecting rods are of large size, heavy weight, multiple models, low production capacity, complex production processes, and difficult to effectively ensure machining quality.By identifying the key processes of connecting rods for medium-speed marine diesel engines, quality control of the key processes is strengthened to ensure processing quality.The connecting rod parameters of a mediumspeed marine diesel engine are shown in Table 2.
Figure 2 shows the connecting rod diagram of a medium-speed marine diesel engine.
To better describe the transitive relation between the connecting rod machining process and the output quality, each process of the connecting rod is decomposed into multiple machining features, and each machining feature corresponds to its unique quality features.The machining features of the connecting rod and its corresponding main quality features are shown in Table 3.
Based on the above methods and the machining process content in the table, a diesel engine connecting rod machining process network as shown in Figure 3 is established, where the size of the network node represents the size of the PageRank value, that is, the larger the network node, the higher its importance.
Table 4 shows the node feature PR values of the connecting rod machining process network obtained according to the iterative convergence of the PageRank algorithm.
According to the analysis results of the connecting rod machining process network, the machining feature nodes with larger PageRank values are defined as the key machining features of the connecting rod machining process.The visualization results of the connecting rod machining process network show that the darker the color and the larger the node, the larger the PageRank value of the points.It can be seen that the machining feature nodes MF030A, MF055A, MF065B, MF070B, and MF095A have a larger PageRank value, such as the connecting rod machining process localized sub-network shown in Figure 4.By clustering the key machining process with the process number, the corresponding process numbers for key machining features can be obtained respectively, which are 030, 055, 065, 070, and 095.The above processes correspond to the content of the upper and lower part of the connecting rod milling, semi-finish boring of the size of the head hole, machining of the large end cap bolt holes, fine boring of the size of the head hole and honing the size  of the head hole.Referring to crafts people's experience, the results of the analysis in line with the actual processing of the connecting rod of the medium-speed marine diesel engines.

Summary
This research proposes a key process identification method for machining processes based on the PageRank algorithm, starting from the establishment of a machining process network model and the evaluation of the importance of network nodes.The main conclusions are as follows: (1) The theory of complex network can be applied to establish an error transmission network model in the machining process.It can also realize the visualization of machining process to facilitate the analysis of key processes; (2) The PageRank ranking algorithm can be applied to the processing technology network to calculate the weights of nodes in the network model and sort the weight values of nodes to obtain key processes; (3) The example analysis of a connecting rod machining process for a medium-speed marine diesel engine shows that this method can quickly and effectively identify key processes in the machining process, verifying the feasibility and applicability of this method.
In summary, this article considers the relationship between machining features, machining elements, and quality features in the manufacturing process as well as conducts weight calculation and visual analysis on the recognition of key machining features in the manufacturing process, achieving the recognition of key processes.The accuracy, effectiveness, and feasibility of the method proposed in this paper have been verified through case analysis and visual simulation, which can provide a reference for the study of key processes in the manufacturing process of complex mechanical products.However, due to the fact that the PageRank algorithm used for weight assignment in this article is a static algorithm, precise judgment of error changes in dynamic machining cannot be achieved.Therefore, it is worth further research to determine the weight of the dynamic changes of processing technology.

Figure 1 .
Figure 1.Schematic diagram of processing process subnetwork model.

NFigure 2 .
Figure 2. Connecting rods for medium speed marine diesel engines: (a) 3D model of semi-finished products and (b) on-site physical image.

Table 1 .
Encoding rules for network nodes.
location relationship, processing relationship, and attribute relationship.

Table 2 .
Table of connecting rod parameters for a medium-speed marine diesel engine.

Table 3 .
Corresponding table of connecting rod machining features and quality features.

Table 4 .
PR values of each node feature.