A Product Evolution Rules Based Method for Retired Mechanical Product Demand Acquisition

Abstract

Accurate acquisition of retired mechanical products demand (RMPD) is the basis for realizing effective utilization of remanufacturing service data and improving the feasibility of remanufacturing schemes. Some studies have explored product demands, making product demands an important support for product design and development. However, these studies are obtained through the transformation of customer and market demand information, and few studies are studied from a product perspective. However, remanufacturing services for retired mechanical products (RMP) must consider the impact of the failure characteristics. Consequently, based on the generalized growth of RMP driven by the failure characteristics, the concept of RMPD is proposed in this paper. Then, the improved ant colony algorithm is proposed to mine the generalized growth evolution law of RMP from the empirical data of remanufacturing services, and the RMPD is deduced based on the mapping relationship between the product and its attributes. Finally, the feasibility and applicability of the proposed method are verified by obtaining the demand for retired rolls. In detail, the results show that the proposed method can obtain the RMPD accurately and efficiently, and the performance of the method can be continuously optimized with the accumulation of empirical data.

1. Introduction

The product renewal and iteration in the process of manufacturing transformation and upgrading have caused a sharp increase in retired mechanical products (RMP). As one of the main modes of green manufacturing, remanufacturing is an effective way to achieve the development and utilization of the residual value of RMP. However, due to the influence of the failure characteristics, the design decision of remanufacturing schemes can produce the multi-granularity growth mode [1]. It is mainly reflected in the objective evolution law of product property, function, and performance in a favorable direction. The retired mechanical product demand (RMPD), which is determined by the failure characteristics of RMP, is the key to determining the feasibility of remanufacturing schemes. Therefore, the research on RMPD can not only better understand the impact of failure characteristics on the generalized growth mode of RMP, but also provide support for more accurate and efficient development of remanufacturing schemes. It is of great significance to realize the full utilization of RMP and reduce the waste of resources.

Product demand is the bridge connecting market, customer, and product development and is the design goal of each link in the product development process. Therefore, the acquisition and analysis of product demand is the basis of product design and development. In the existing research, the comprehensive demand for product function, quality, and sales is generally transformed by the information mapping between customers, markets, and products. For example, in the field of product functional demand, related research calculated the importance of functional demands through the analytic network process and quality function deployment (ANP-QFD), established models based on the correlation relationship and autocorrelation between customer requirements and functional demands and introduced the fuzzy theory for optimization to achieve the purpose of transforming customer requirements into functional demands [2,3]. In the field of product quality demand, some studies focus on the qualitative and quantitative relationship between online review rating and sentiment and product demand and establish aggregated multinomial choice model to achieve a deep understanding of the customer’s perception of product quality [4]. In the field of product market demand, relevant research is aimed at the relationship between market demand and product design in the complex and dynamic market environment to predict the initial demand for new products in the early stage [5,6]. Different from the function of the above product demand, the remanufacturing service for RMP should be designed and produced based on RMPD, which is the evolution law of product property, function, and performance under the generalized growth mode of RMP driven by failure characteristics. However, there are few studies finding design and production decision information from the characteristics of the product itself. Therefore, knowing how to obtain RMPD based on product evolution rules is of great significance for efficient and accurate generalized growth decisions and remanufacturing scheme design.

The remanufacturing service of RMP consists of customer-oriented service production and RMP-oriented production service [7]. This paper takes the RMP-oriented productive service as the research background and studies the acquisition method of RMPD based on product evolution rules. Firstly, based on the systematic description of the generalized growth mode of RMP, the concept of RMPD is proposed, and it is clarified that this study is based on the empirical data of remanufacturing services. Then, based on the definition of RMPD, the demand acquisition method is explored, and the acquisition process of RMPD is divided into two stages: mining the evolution rules of RMP and obtaining the reasoning of product attribute mapping. Finally, this paper takes the remanufacturing of the rolling mill roll system, the core equipment in the metallurgical industry, as an example to mine the generalized growth evolution rules of the retired rolls through the remanufacturing service empirical data and obtain the product demand of the retired rolls by reasoning.

The highlight of this paper mainly includes the following points:

• The generalized growth and evolution mode of RMP is revealed. Based on the experience of technicians in the production process of making decisions on the remanufacturing method of RMP, the generalized growth evolution mode of RMP is analyzed, which is used as the basis for obtaining RMPD;
• The concept of RMPD is put forward. Different from the relevant research on product demand, the research on RMPD is based on the evolution law of product property, function, and performance under the generalized growth mode determined by the failure characteristics, rather than the transformation from customer and market demand;
• The traditional rule mining method is improved to obtain RMPD efficiently and accurately. Based on the traditional rule mining method, the advantages and applicability of the method are verified by a case study, which can provide effective support for the improvement and expansion of the enterprise’s remanufacturing service.

The remainder of the paper is structured as follows: Section 2 provides an overview of related research on product demand and product evolution and their inspiration for this study. In Section 3, the generalized growth mode of RMP is systematically described, and the definition of RMPD is proposed. Section 4 introduces, in detail, the mining method of generalized growth and evolution rules of RMP and the process of obtaining RMPD based on evolution rules reasoning. Section 5 verifies and discusses the feasibility and applicability of the acquisition method of RMPD based on the remanufacturing empirical data of typical metallurgical equipment rolling mill rolls. Section 6 gives the conclusion of this study and points out the direction of future research.

2. Related works

2.1. Product Demand

Existing research has endowed product demands with rich connotations in the fields of product design, manufacturing, management, and other fields, making product demands the design goal of each link in the product development process [8]. Therefore, knowing how to accurately obtain product demand information and effectively guide product design and development is a hot issue.

In the related research of product demand, the main mode to obtain product demand is to transform customer requirements information into technical characteristics of the product based on the mapping relationship between product demands and customer requirements [9]. For example, Liu and Lu [10] proposed a systematic functional design framework to manage the design coupling between customer requirements and functional demands by investigating customer domains and exploring functional domains, thereby mapping customer requirements to functional demands in an adaptive way. Bin He et al. [11] proposed an information conversion method from the functional domain to the physical domain, which realizes the conversion from fuzzy sustainable functional demands to design parameters based on the multi-level customer requirement information description for products. Jeong et al. [12] proposed a requirement discovery process based on QFD, which derives the key functions of the system from user requirements in order to check the validity of user requirements and ensure the consistency and integrity of functional demands. In addition, there are some studies to predict product demand through data analysis [13]. For example, Schöggl et al. [14] evaluated environmental, economic, and social assessments during the early design and development phase of a product, defining the sustainability-related improvement demands to be completed by engineers. Lai et al. [15] mined the design requirements of product features, performance levels, and quantities based on massive dynamic network data, and applied them to product design, product improvement, and market analysis to help companies effectively optimize the design process and reduce product production costs. Majd Kharfan et al. [16] used machine learning techniques to identify important predictors to help retailers make better demand forecasts.

Formalized product demand information provides an important basis for product design and manufacturing, inventory, and supply chain management. In the complex product design and development stage, mapping the customer’s technical functional requirements and subjective preferences into detailed product attributes and design parameters into the product design can provide an important basis for the product’s principle scheme and structural design [17,18]. In the process of product manufacturing, by accurately describing product performance demands and mapping them to engineering features to resolve parameter conflicts in the manufacturing process, the purpose of optimizing the manufacturing process plan can be achieved [19]. van Steenbergen and Mes [20] predict the demand for new products before the launch of products based on historical sales data and product characteristics, which can provide effective support for enterprises’ business decisions such as procurement and inventory control. Therefore, the comparison of the impact of product demand factors on the product market based on historical sales data and the accurate prediction of product demand can provide a basis for the formulation of reasonable product sales strategies and improve product inventory and supply chain management performance [21,22].

The above research on product demand is mainly based on the analysis and prediction of customer and market demand data, and the obtained product demand information can effectively guide product design, production, sales, etc., which has certain reference significance for customer and market demand research of remanufacturing services. However, the difference is that the remanufacturing service for RMP must consider the influence of its complex failure characteristics. Therefore, knowing how to obtain RMPD based on the failure characteristics is of great significance to the feasibility of its remanufacturing scheme decision.

2.2. Product Evolution

Product evolution is the evolution of a product in order to adapt to a changing product environment such as new technologies [23], new customers, and market demands. This evolution often improves product performance and structure through redesign and obtains new products with better performance and higher reliability, thereby enhancing the market competitiveness of new products.

The evolution of products can be analyzed from multiple levels such as category, structure, and performance. Product category evolution is a continuous evolution based on the cumulative changes of model features of new products. Kivi et al. [24] proposed a planning and forecasting technique to reveal the product category evolution process and the diffusion of new product features. However, typical product evolution is reflected in product structure evolution. Zhang et al. [25] proposed four structural evolution operation modes: combination evolution method, decomposition evolution method, substitution evolution method, and material change evolution method, and described product structure evolution from the requirements of product environmental performance. Li et al. [26] analyzed the complexity, importance, and robustness of product structure, revealed the evolution characteristics of product structure based on a time-varying network model, and provided designers with product development direction. Park and Kremer [27] characterized the topological structure of product evolution by identifying the basic topological characteristics and patterns of each generational product, revealing the intrinsic evolution mechanism of product structure, and effectively applying it to predict and simulate the continuous evolution of product structure. In addition, some studies focus on the evolution of product clusters, representing the product cluster structure as a network that describes the relationship between the components in the product cluster structure. In the context of considering customer requirements and product reliability, determining the parts that need to be improved can provide customers with more competitive product configuration schemes in the future market [28,29].

In the market competition environment, enterprises need to make continuous technological improvements to products to meet the market demand. Therefore, it is very important to predict the possible product evolution mode for enterprises to innovative product development. Oh et al. [30] proposed a systematic method based on link prediction to predict the evolution trend of products and assist enterprises in making product strategic planning or identifying the development of new functions. Based on the information from the previous generation of products, Biswas et al. [31] established a prediction model for the dynamic evolution of product clusters, identified key technical features from dynamic factors such as technology, market, and customers, and predicted products with the best performance. Li et al. [32] deduced the dynamic customer requirement-driven product evolution mechanism by using the data accumulated in the process of product evolution and established a dynamic product design evolution model based on the Bayesian network to deduce the product function evolution mode.

The above-related research on product evolution is the exploration of the characteristics and methods of product evolution driven by market and customer requirements. These studies have laid a theoretical foundation for the research on the evolution mode of RMP. However, since the failure characteristics of RMP determine their generalized growth mode, their failure characteristics are the driving factors that need special consideration in product evolution. Therefore, this paper will study the evolution mode of RMP under complex failure characteristics as the basis for obtaining RMPD.

3. RMPD Based on Generalized Growth

3.1. Generalized Growth Evolution Model Driven by Failure Characteristics

The complex failure characteristics are the main influencing factors for generalized growth decisions and remanufacturing scheme designs of RMP. The variety of failure forms and the difference in failure degree make the generalized growth mode of RMP more flexible. Therefore, under different failure characteristics, RMP should follow different growth patterns and evolve into recycled products with different properties, performances, and functions. As shown in Figure 1, in the generalized growth evolution mode of RMP, each node represents the product’s property, performance, function, and other attributes, where ${\mathrm{P}}_{\mathrm{i}}$ is a product set composed of a subset of product attribute sets. RMP have corresponding failure characteristics, that is, failure form S and failure degree D. RMP with certain failure characteristics ${\{\mathrm{S},\mathrm{D}\}}_{\mathrm{x}}$ can be remanufactured into different recycled products. For example, under the drive of failure characteristics ${\{\mathrm{S},\mathrm{D}\}}_0$, RMP can evolve into product ${\mathrm{P}}_0$ with original attributes through remanufacturing; under the drive of failure characteristics ${\{\mathrm{S},\mathrm{D}\}}_1$, RMP can have two evolution modes: one way is to reconfigure the original product attributes and restore the RMP to original product ${\mathrm{P}}_0$; another way is to change the product attributes and make RMP evolve into other types of recycled product ${\mathrm{P}}_1$ with new product attributes. Similarly, the multi-granularity generalized growth evolution mode can be formed under complex failure characteristics.

3.2. RMPD Based on Evolutionary Rule

The multi-granularity generalized growth evolution model of RMP determines that the evolution of RMP follows the objective development law of the effective utilization of residual value. Therefore, RMPD can be defined as: the objective evolution law of product property, performance, and function develop in a favorable direction determined by the product evolution process driven by failure characteristics.

Therefore, the potential evolutionary rules in the product generalized growth mode are the important basis for obtaining RMPD. As shown in Figure 2, the failure characteristics ${\{\mathrm{S},\mathrm{D}\}}_{\mathrm{x}}$, original products ${\mathrm{P}}_{\mathrm{i}}^0$, recycled products ${\mathrm{P}}_{\mathrm{i}}^{\prime }$, and product attributes $p_{\mathrm{i}}^{\mathrm{n}}$ reflect that the change of product attributes in the same direction is the result of the generalized growth evolution of RMP. Therefore, in order to obtain RMPD, we must first obtain the potential generalized growth evolution law of RMP in the process of remanufacturing.

4. RMPD Acquisition Method Based on Product Evolution Rules

RMPD is the objective law of product property, performance, and function in the process of product evolution. Excavating the law of product evolution is the basis of demand acquisition. This process is shown in Figure 3.

Step 1: Building generalized growth drivers and product evolution factors.

The failure characteristics of RMP are the direct driving factors of the generalized growth evolution of RMP. Therefore, it is necessary to conduct qualitative and quantitative analysis on the specific failure characteristics of RMP, which can be defined as:

$${\mathrm{F}}_x={\left\{\mathrm{S},\mathrm{D}\right\}}_x$$

Under the influence of different failure characteristics, RMP have multi-granularity growth evolution modes, which are mainly embodied as product evolution factors composed of product property, function, performance, and other attributes, and can be defined as:

$${\mathrm{P}}_{\mathrm{i}}=\left\{p_1,p_2,\cdots , p_{\mathrm{i}},\cdots \right\}$$

Step 2: Define the rules of multi-granularity evolution for RMP.

According to Figure 1, the generalized growth mode of RMP can be divided into horizontal and vertical evolution rules. In the horizontal direction, the recycled product is a new product on the basis of inheriting the attributes of the original product. In the vertical direction, recycled products need to realize new product functions and upgrade the original products. Therefore, the evolution rule can be defined as:

Horizontal rules: if ${\left\{\mathrm{S},\mathrm{D}\right\}}_x$ ⊕ $\left\{p_1\right\}$ or ${\left\{\mathrm{S},\mathrm{D}\right\}}_x$ ⊕ $\left\{p_1,p_2\right\}$ or … or ${\left\{\mathrm{S},\mathrm{D}\right\}}_x$ ⊕ $\left\{p_1,p_2,\cdots ,p_{\mathrm{i}},\cdots \right\}$, then ${{\mathrm{P}}_0}^{\prime }=${$p_0^1,p_0^2$, $p_0^3$, …, $p_0^{\mathrm{n}}$, …} or … or ${{\mathrm{P}}_{\mathrm{i}}}^{\prime }$={$p_{\mathrm{i}}^1,p_{\mathrm{i}}^2$, $p_{\mathrm{i}}^3$, …, $p_{\mathrm{i}}^{\mathrm{n}},\dots$}.

Vertical rules: if ${\left\{\mathrm{S},\mathrm{D}\right\}}_{\mathrm{x}}$ ⊕ $\left\{p^1,p^2,\dots ,p^{\mathrm{n}}\right\},$ then ${{\mathrm{P}}_{\mathrm{i}}}^{\prime }=${$p_{\mathrm{i}}^1,p_{\mathrm{i}}^2,$ $p_{\mathrm{i}}^3$, …, $p_{\mathrm{i}}^{\mathrm{n}}$, …}.

Step 3: Discover potential evolution rules of RMP.

In this paper, the AP-ACO algorithm will be used to mine the evolution rules of the above RMP from the existing empirical data accumulated in remanufacturing services. The algorithm is detailed in Section 4.1.

Step 4: Reasoning RMPD based on evolution rules.

Original products and recycled products have their specific product attribute characteristics, which have a unique mapping relationship with product type and model, etc. Therefore, on the basis of the product evolution rules, the evolution rules of product property, performance, and function can be deduced, that is, the RMPD.

4.1. Mining Evolution Rule of RMP

(1)

Data preprocessing

The mining of generalized growth evolution rules of RMP is based on decision-making empirical data in the remanufacturing service. In order to facilitate data mining, it is necessary to standardize and improve the key information of existing data, and then transform it into a data form easy to be identified and calculated by computer. Here the remanufacturing services transactional dataset is converted to a binary dataset by Equation (1), where item $\mathrm{i}$ is 1 when it is included in transaction $\mathrm{j}$ and 0 when it is not. Such a data form can speed up database traversal.

$$\mathrm{M}\left(\mathrm{i},\mathrm{j}\right)=\{\begin{array}{c}1, \mathrm{i}\in \mathrm{j}\\ 0, \mathrm{i}\notin \mathrm{j}\end{array}$$

(1)

(2)

Determination of initial pheromone concentration based on Apriori algorithm

The initial pheromone concentration is the most critical parameter affecting the performance of the ant colony algorithm. In order to avoid blindness and improve the efficiency of the algorithm, the initial pheromone concentration of the ant colony algorithm is determined by the iterative process of the Apriori algorithm [33]. Firstly, the support degree and confidence degree of two measures of association rules are defined. Support is the proportion of the occurrence times of data elements in the data set, as shown in Equation (2). Confidence is the probability of the appearance of another data element after the appearance of one data element, as shown in Equation (3).

$$\mathrm{support}(\mathrm{X},\mathrm{Y})=\mathrm{P}(\mathrm{XY})=\frac{\mathrm{num}\left(\mathrm{XY}\right)}{\mathrm{num}\left(\mathrm{All}\right)}$$

(2)

$$\mathrm{confidence}(\mathrm{X},\mathrm{Y})=\mathrm{P}(\mathrm{X}\leftarrow \mathrm{Y})=\frac{\mathrm{P}\left(\mathrm{XY}\right)}{\mathrm{P}\left(\mathrm{Y}\right)}$$

(3)

Then, the frequent itemsets are obtained. The itemset of binary data after data preprocessing is regarded as a particle, and all data are scanned and counted to produce a set of candidate items. Then the candidate itemsets are filtered according to the minimum support, and the candidate itemsets generate frequent itemsets.

Finally, the frequent item matrix is constructed. Any two elements in the matrix will form a candidate binomial set, and the support degree of all candidate binomial sets will be calculated. The support degree is the weight of the co-occurrence elements of binomial sets, and the reciprocal of the support degree is the pheromone concentration between the elements of the ant colony algorithm.

(3)

Mining frequent itemsets based on the ant colony algorithm

After the initial pheromone is obtained by the Apriori algorithm, the ant colony algorithm can be used to mine the maximum frequent itemsets in association rules. Similar to the ant colony algorithm’s search for optimal paths, Tabu, and Allowed tables are set to store data items. Initially, ants are randomly placed on different data items as starting points, and data items are added to the set ${\mathrm{f}}_{\mathrm{k}}$ of selected data items and Tabu tables. Then, by means of Equation (4), the probabilistic transfer function values of all the remaining optional data items are calculated, and the next item is selected accordingly.

$${\mathrm{P}}_{\mathrm{j}}^{\mathrm{k}}\left(\mathrm{t}\right)=\{\begin{array}{c}\frac{{\mathsf{\tau }}_{\mathrm{j}}{\left(\mathrm{t}\right)}^{\mathsf{\alpha }}{\mathsf{\eta }}_{\mathrm{j}}{\left(\mathrm{t}\right)}^{\mathsf{\beta }}}{{\sum }_{\mathrm{j}}{\mathsf{\tau }}_{\mathrm{j}}{\left(\mathrm{t}\right)}^{\mathsf{\alpha }}{\mathsf{\eta }}_{\mathrm{j}}{\left(\mathrm{t}\right)}^{\mathsf{\beta }}}, \mathrm{j}\in {\mathrm{Allowed}}_{\mathrm{k}} \\ 0 , \mathrm{j}\in {\mathrm{Tabu}}_{\mathrm{k}} \end{array}$$

(4)

In the equation, ${\mathsf{\tau }}_{\mathrm{j}}\left(\mathrm{t}\right)$ is the pheromone concentration at time t; ${\mathsf{\eta }}_{\mathrm{j}}\left(\mathrm{t}\right)$ is a heuristic function.

The data item corresponding to the maximum value of ${\mathrm{P}}_{\mathrm{j}}^{\mathrm{k}}\left(\mathrm{t}\right)$ is selected to add ${\mathrm{f}}_{\mathrm{k}}$ to determine whether ${\mathrm{f}}_{\mathrm{k}}$ is a frequent item set. If the local pheromone concentration is updated according to Equation (5) and added to the Tabu table, it should be deleted from the Allowed table and the next search should be started.

$${\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)=\left(1-\mathsf{\epsilon }\right)·{\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)+\mathsf{\epsilon }·\Delta {\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)$$

(5)

$$\Delta {\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)={\sum }_{\mathrm{k}=1}^{\mathrm{m}}\Delta {\mathsf{\tau }}_{\mathrm{ij}}{\left(\mathrm{t}\right)}^{\mathrm{k}}\cdots$$

(6)

$$\Delta {\mathsf{\tau }}_{\mathrm{ij}}{\left(\mathrm{t}\right)}^{\mathrm{k}}=\{\begin{array}{c}\mathrm{Q}, \mathrm{P}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t} \mathrm{i}, \mathrm{j} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} {\mathrm{f}}_{\mathrm{k}} \mathrm{s}\mathrm{e}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{n}\mathrm{t} \mathrm{k} \\ 0, \mathrm{O}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\end{array}$$

(7)

If ${\mathrm{f}}_{\mathrm{k}}$ is not a frequent item sets after joining, it should be deleted from ${\mathrm{f}}_{\mathrm{k}}$ and it should be decided whether to continue the search based on Equation (8).

$$\mathrm{stop}(\mathrm{k})=\{\begin{array}{c}1, \mathrm{p}>{\mathrm{p}}_0\\ 0, \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r} \end{array}$$

(8)

In the equation, p is the random number on [0, 1]. ${\mathrm{p}}_0$ is a fixed value between [0, 1]. If $\mathrm{stop}(\mathrm{k})=1$, searching should be stopped. If $\mathrm{stop}(\mathrm{k})=0$, the item set is placed in the Tabu table and deleted from the Allowed table, then the search continues. After all ants have completed a single traversal, the maximum frequent itemsets that they traversed are recorded.

Before the start of the next iteration, according to the positive feedback of the ant colony algorithm, after the ant colony finishes a search, pheromone updates are made on the edges formed by the most frequent item focus points in this iteration. The following are the ways:

$${\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}+1\right)=\left(1-\mathsf{\rho }\right)·{\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)+\mathsf{\rho }·\Delta {\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)$$

(9)

$$\Delta {\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}\right)=\{\begin{array}{c}\frac{\mathrm{Q}}{{\mathrm{L}}_{\mathrm{best}}}, \mathrm{I}\mathrm{f} \mathrm{i}, \mathrm{j} \mathrm{i}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{a} \mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{i}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{s}\mathrm{e}\mathrm{t}\\ 0 , \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\end{array}$$

(10)

(4)

Obtain product evolution rules

The frequent itemsets obtained by the ant colony algorithm are used as input data of the Apriori algorithm, in which the non-empty subsets of all frequent item sets are used as itemsets to calculate the confidence of all frequent itemsets. If the confidence of the frequent itemset is greater than the minimum confidence set, the frequent itemset is output, that is, the obtained product evolution rules.

The above (1)–(4) is the acquisition process of the evolution rules of RMP, and its pseudo codes are shown in Algorithm 1.

Algorithm 1: Pseudo codes of AP-ACO algorithm

Initialize: minsup, minconf, NC_max, m, $\mathsf{\alpha }$, $\mathsf{\beta },\mathsf{\rho }$

F1 = find_frequent_1-itemsets(D)

f(itemi, itemj) = CheckSup(dataset, {i, j}), $\forall \mathrm{i},\mathrm{j}\in$ F1

Creat frequent matrix named TSP, it consists of f(itemi, itemj)

Start:  m = random(TSP)m < n

for(k = 0, k < m, k++){

j = next_item(k);

add j to Tabu

if (fqset ⊂ path && j $\in$ fqset)

add fqset to Fk

else  add j to forbid}

if(i,j ⊂ Fbest) updata ${\mathsf{\tau }}_{\mathrm{ij}}\left(\mathrm{t}+1\right)$

if(reached NC_max)

goto Exit

else  goto Start

Exit: for each Li$\complement$Lk

if(support(Fk)/support(Fi) ≥ minconf)

Print Fi→(Fk–Fi)

4.2. RMPD Information Extraction

Horizontal positioning analysis:

There is a maximum attribute feature set $\left\{p_{\mathrm{i}}^1,p_{\mathrm{i}}^2,p_{\mathrm{i}}^3,\dots ,p_{\mathrm{i}}^{\mathrm{n}}\right\}$ for each category of products, and the same category of products all belong to the configuration combination subset of these product attribute features. Therefore, by changing the combination of various attributes and characteristics, it can be refined into a variety of recycled products of the same type. Based on the product’s maximum attribute feature set, the product attributes are removed, exchanged, scaled, and other operations to generate more recycled products with attribute combinations.

Vertical positioning analysis:

The new category of recycled products is based on the redesign of RMP, that is, the inheriting, upgrading, and innovative design of the original product attributes. The three mechanisms supporting product evolution mainly include the inheritance function, renewal function, and improvement function, which provide more feasible product evolution space for the multi-granularity generalized growth of RMP.

Through product type and attribute mapping, RMPD is inferred based on product evolution rules, which are used to guide the generalized growth decision and remanufacturing scheme design of RMP.

5. Case Study

Inspired by the key research and development project of 2021 Technology Innovation Development Project of Enterprises Supported by Hubei Province (High-tech Enterprises): Research and Development of Key Technologies for Intelligent Processing of Machine Parts Remanufacturing Based on Full Information of Multi-source Failure Detection (2021BAB002), this paper collected a large amount of empirical data on remanufacturing service decision of metallurgical equipment and its parts were collected through field investigation. Among them, the rolling mill is typical metallurgical equipment, and its main consumable component is the mill roll. The use of mill roll directly affects the cost and economic benefits of metallurgical equipment. Therefore, recording the product demand of mining retired mill rolls based on the remanufacturing service of enterprises can provide a more flexible way for the remanufacturing of retired mill rolls, thus effectively improving the utilization rate of mill rolls and reducing production costs.

5.1. Data Processing

Mill roll is the core component that directly or indirectly exerts a force on the rolled piece during the rolling process and causes the rolled piece to produce plastic deformation. The mill rolls commonly used in the metallurgical industry can be divided into two categories: cold mill rolls and hot mill rolls. According to the structure and function of the rolling mill, it can be divided into the roll system composed of work roll (WR), middle roll (MR), and support roll (SR). Based on the existing research on roller performance [34], this paper mainly studies the evolution law of roll material, surface hardness, and geometric properties (roll diameter and roll length). Mill roll parameters of some mainstream rolling mills in the market have been collected through field research, and some data are shown in

Table 1. Mill roll parameters of rolling mill.

No.	Model	Roll System	Material	Min_Roll Diameter (mm)	Max_ Roll Diameter (mm)	Roll Length (mm)	Surface Hardness (HRC)
1	20-high rolling mill	WR	9Cr2Mo	58	73.5	1450	62–64
2		MR(#1)	9Cr2Mo	96	105	1450	58–62
3		MR(#2)	9Cr2Mo	170	173	1450	58–62
4		SR	9Cr2Mo	297	300	1450	68–74
5	finishing mill	WR	9Cr2Mo	215	240	1050	95–100
6		MR	9Cr2Mo	300	330	1200	95–100
7		SR	forged steel	800	850	1000	68–74
8	18-high rolling mill	WR	12%Cr	120	150	1250	60–62
9		MR	5H12/MC5	330	355	1200	60–62
10		SR	forged steel	1110	1200	1000	68–74
11	1580 hot rolled	VR(#1)	9Cr2Mo	900	1000	430	75–80
12		WR(#1)	9Cr2Mo	1230	1350	1580	42–48
13		WR(#2)	9Cr2Mo	1060	1160	1580	75–80
14		SR(#1)	forged steel	1330	1480	1560	42–48
15		SR(#2)	forged steel	1450	1600	1560	69–75
16	1880 hot rolled	WR(#1)	9Cr2Mo	1200	1350	1880	75–80
17		VR(#1)	9Cr2Mo	1100	1200	440	42–48
18		WR(#2)	9Cr2Mo	1100	1250	1880	75–80
19		VR(#2)	9Cr2Mo	570	630	350	42–48
20		SR	forged steel	1450	1600	1860	65–71
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

.

In metallurgical production, the mill rolls are easy to be damaged in different forms and degrees because of the influence of dynamic and static load, wear, and temperature change. Through the analysis of the test data of retired rolls, it can be seen that several typical roll failure forms are common in the actual production activities of rolls, including cracking, peeling, pitting, sticking, tightening, and breaking, as shown in Figure 4. In the production process, excessive local pressure of the roll or rapid cold and heat of the roll will cause cracking (Figure 4a). The cracking roll will produce a peeling phenomenon when the crack expands during continuous use (Figure 4b). When impurities enter the mill, they cause pits of different shapes on the roller surface (Figure 4c). When the local pressure is too large, fragments and broken edges will cause sticking (Figure 4d) or tightening (Figure 4e). Roll breaking occurs when there are defects inside the roll or when the temperature stress is too large (Figure 4f).

The primary task of roll recycling and remanufacturing is to detect the failure of retired rolls and evaluate the failure degree according to different failure forms. In the actual testing process, some failure forms are easy to quantify, while others are difficult to quantify. Therefore, in order to facilitate data processing, the failure degree is graded by the designer according to the actual failure degree, as shown in

Table 2. Roll failure attribute division table of rolling mill.

Failure Form	Failure Level
	1	2	3	4	5
Cracking	no	≤1 mm	1~3 mm	3~5 mm	≥5 mm
Peeling	≤1 cm2	1~5 cm2	5~10 cm2	≥10 cm2	…
Pitting	≤1 mm	1~3 mm	3~5 mm	≥5 mm	…
Sticking	≤1 cm2	1~5 cm2	5~10 cm2	≥10 cm2	…
Tightening	≤1 mm	1~3 mm	3~5 mm	≥5 mm	…
Breaking	no	slight	obvious	…	…

. By dividing the failure degree of different failure forms, the failure characteristics of retired rolls can be described in a standard way, which is beneficial to data mining.

The failure characteristic is an important basis for the decision of the generalized growth mode of the retired rolls. However, the current growth pattern of retired rolls is a decision made by technicians with production experience based on failure status assessment. The accumulated decision-making empirical data lays a data foundation for the mining of roll evolution rules. In order to facilitate the mining of roll evolution law, the existing retired roll remanufacturing decision-making empirical data is first sorted and coded, and the coding rules are shown in

Table 3. Coding methods of evolution rules (i, j, k, l, m, n = 1, 2, 3, 4, 5; x is the product number).

Retired Product	Failure Characteristic						Recycled Product
Retired roll	Cracking	Peeling	Pitting	Sticking	Tightening	Breaking	Recycled roll
$P_x^0$	$F_1^i$	$F_2^j$	$F_3^k$	$F_4^l$	$F_5^m$	$F_6^n$	$P_x^{\prime }$

. Among them, the rule antecedent of the generalized growth evolution rule is the model and failure characteristics of the retired roll, and the rule consequence is the product model of the recycled product of the retired roll after remanufacturing. The data are integrated according to the coding rules in the table as the input of the evolutionary rule mining algorithm.

5.2. Mining of Roll Growth Evolution Rules Driven by Failure Characteristics

This section uses the product evolution rule mining algorithm proposed in Section 4 to mine potential roll evolution rules from remanufacturing service decision-making data. Firstly, the experimental environment was configured. The algorithm was implemented based on Intel Core I7 2.6 GHz Window10 and MatLab 2019Ra. Then, the parameters during the execution of the algorithm were set to the following: min_sup = 0.45, min_conf = 0.75, pop_size = 100, max_inter = 50, and α = 1, β = 5 for experiments.

The evolution rules of retired rolls are obtained through the evolution rule mining algorithm, as shown in

Table 4. Generalized growth evolution rules of retired rolls.

No.	Rule			Support	Confidence
1	$P_{16}^0$	$—F_4^4$	→  $P_{13}^{\prime }$	0.83	0.97
2	$P_7^0$	$—F_1^2$, $F_4^1$	→   $P_4^{\prime }$	0.81	0.97
3	$P_{10}^0$	$—F_3^5$,$F_4^2$	→   $P_5^{\prime }$	0.80	0.97
4	$P_{10}^0$	$—F_1^1$,$F_3^1$	→   $P_7^{\prime }$	0.80	0.97
5	$P_{15}^0$	$—F_1^4$,$F_6^2$	→   $P_{14}^{\prime }$	0.78	0.97
6	$P_4^0$	$—F_1^1$,$F_2^2$,$F_3^1$	→   $P_{25}^{\prime }$	0.75	0.97
7	$P_{11}^0$	$—F_2^3$,$F_3^2$	→   $P_{19}^{\prime }$	0.72	0.83
8	$P_{27}^x$	$—F_4^2$,$F_5^1$	→   $P_{11}^{\prime }$	0.72	0.80
9	$P_9^0$	$—F_1^1$,$F_3^1$, $F_6^3$	→   $P_6^{\prime }$	0.70	0.80
⋮	⋮			⋮	⋮

. In the table, different types of retired rolls can be remanufactured into different types of recycled products under the corresponding failure characteristics. For example, (rule1) 1880 hot rolling roll #1 with a sticking level of 4 can become 1580 hot rolling roll #2 after remanufacturing; (rule6) the support roll of 20-high rolling roll with cracking level of 1, peeling level of 2, and pitting level of 1 can be used as the middle roll of the 12-high rolling mill after remanufacturing, etc. In addition, the same product can also evolve into different types of recycled products under different failure characteristics. For example, (rule3 and rule4) 1580 hot rolling support rolls can be used as finishing mill work rolls after remanufacturing when the failure characteristics are level 5 pitting degree and level 2 sticking degree. When the failure characteristic is at a level 1 cracking degree and level 1 pitting degree, it can be used as the support roll of an 18-high rolling mill after remanufacturing. This evolution relationship reflects the objective law of generalized growth evolution of retired roll under corresponding failure characteristics. The potential generalized growth evolution law of retired roll in these empirical data is an important basis for obtaining the demand for retired rolls.

5.3. Demand Acquisition of Retired Roll Products Based on Failure Characteristics

The product demand of retired roll is the objective law that the property, performance, and function of retired roll develop in a favorable direction. Therefore, based on the mapping relationship between the roll and its product features, the evolution rule of the product attributes of the corresponding retired roll can be obtained through the inference of the above evolution rule of retired roll, that is, the product demand information of retired roll, as shown in

Table 5. Demand information of retired roll products.

No.	Rule
1	$P_{16}^0${9Cr2Mo;Ø1200/1350–1880;HRC:75–80}	→$P_4^{\prime }$ {9Cr2Mo;Ø1060/1160–1580;HRC:75–80}
2	$P_7^0$ {9Cr2Mo;Ø800/850–1000;HRC:68–74}	→$P_4^{\prime }$ {9Cr2Mo;Ø1060/1160–1580;HRC:75–80}
3	$P_{10}^0${forged steel;Ø1110/1200–1000;HRC:68–74}	→$P_5^{\prime }$ {9Cr2Mo;Ø215/240–1050;HRC:95–100}
4	$P_{10}^0${forged steel;Ø1110/1200–1000;HRC:68–74}	→$P_7^{\prime }$ {9Cr2Mo;Ø800/850–1000;HRC:68–74}
5	$P_{15}^0${forged steel;Ø1450/1600–1560;HRC:69–75}	→$P_{14}^{\prime }$ {forged steel;Ø1330/1480–1560;HRC:42–48}
6	$P_4^0$ {9Cr2Mo;Ø1060/1160–1580;HRC:75–80}	→$P_{25}^{\prime }$ {9Cr2Mo;Ø215/225–1450;HRC:58–62}
7	$P_{11}^0${9Cr2Mo;Ø900/1000–430;HRC:75–80}	→$P_{19}^{\prime }$ {9Cr2Mo;Ø570/630–350;HRC:42–48}
8	$P_{27}^0$ {9Cr2Mo;Ø1100/1200–440;HRC:42–48}	→$P_{11}^{\prime }$ {9Cr2Mo;Ø900/1000–430;HRC:75–80}
9	$P_9^0$ {5H12/MC5;Ø330/355–1200;HRC:60–62}	→$P_6^{\prime }$ {9Cr2Mo;Ø300/330–1200;HRC:95–100}
⋮	⋮

.

The above product demands for retired rolls can effectively assist designers in redesign and remanufacturing decisions. As can be seen from the table, the remanufacturing method of retired rolls is in line with the product evolution model described above, that is, the product demand that evolves to the same type of product. For example, the material is 9Cr2Mo, the specification is Ø1200/1350–1880, HRC: 75–80 1880 hot rolling roll #1 becomes the same type of recycled product as 1580 hot rolling roll #2 after remanufacturing. On the premise that its material and surface hardness remain unchanged, its specifications evolve into Ø1060/1160–1580. For example, the 20-high rolling mill support roll with the material of 9Cr2Mo and the specification of Ø297/300–1450 and HRC: 68–74 is remanufactured into the 12-high rolling mill middle roll. On the premise that the material remains unchanged, the specification becomes Ø215/225–1450, HRC: 58–62. The product demand for retired rolls shows that the remanufacturing method has a certain flexibility, but it is also limited by the roll material, which is also in line with the actual work requirements of the roll.

5.4. Analysis and Discussion

The purpose of this study is to accurately obtain RMPD from product characteristics to support remanufacturing services, which can be understood as a predictive problem. Therefore, the accuracy of the forecast results reflects the quality level of the obtained RMPD. At the same time, on the basis of referring to the existing research methods of prediction problems, this paper gives the optimization method in this paper. This section will compare several research methods for such problems such as Apriori [35], FP-growth [36], and BPS-ACO [37], to verify the feasibility and adaptability of the proposed methods.

Firstly, this paper takes the hit rate as the evaluation index to verify the accuracy of RMPD [37]. A certain number of data is randomly selected from the empirical data as samples, and the accuracy of the demand information can be obtained by comparing the attributes of RMP and recycled products in the product demand information obtained by the method in this paper with the sample data, as shown in

Table 6. Demand quality of retired mechanical products.

Sample	5	10	15	20	25	30	35
Hit rate	1.00	1.00	0.80	0.90	1.00	1.00	0.90

. From the results under different sample data, it can be seen that the method in this paper has high accuracy and relatively stable prediction for RMPD. Therefore, the quality of RMPD obtained based on the method in this paper can be maintained at a high level, and this demand information has important guiding significance for the remanufacturing design and scheme decisions of RMP.

Secondly, in order to verify that the proposed method has better performance in solving such problems, we draw on several typical methods in related studies for comparative analysis. In the process of the case study, it is found that the setting of minimum support has an important impact on the performance of the method, so we compare the number of mining rules and operation efficiency of various algorithm mining rules for the change of minimum support, as shown in Figure 5.

It can be seen from Figure 5a that the number of mining rules of various algorithms decreases with the increase of the minimum support. When the minimum support is high, the number of rules is small and the data are difficult to use effectively, so the minimum support should be set reasonably in practical applications. Although the influence trend of minimum support on various algorithms is similar, the AP-ACO algorithm has a small change trend than other methods, which makes the setting of the minimum support less difficult.

In addition, according to the influence of minimum support on algorithm operation efficiency in Figure 5b, when the minimum support is large, the algorithm only needs to traverse the data with high support, and the amount of data traversed is small, so the algorithm operation efficiency is high, which corresponds to the phenomenon of a small number of mining rules in Figure 5a. At the same time, it is not difficult to find that among the various methods, the operating efficiency of the AP-ACO algorithm is least affected by the minimum support. In this case, when the minimum support is 0.45, 3892 rules are obtained within 76 s, which ensures that the data are efficiently and fully utilized. In contrast, the proposed method has a more stable running state.

The above comparison results show that the method used in this paper can effectively obtain the RMPD by adjusting parameters. However, in practical applications, the influence of the number of data items and transactions on the performance of the algorithm determines whether the algorithm is applicable. Therefore, we compare the impact of the number of items and transactions on the efficiency of each algorithm, and the results are shown in Figure 6.

When the number of items increases, the amount of data to be traversed by the algorithm increases. Therefore, as shown in Figure 6a, the run time of the algorithm generally increases. However, it can be seen that the AP-ACO algorithm has the smallest change compared with other algorithms, so the proposed method can maintain good mining efficiency under the commonly used number of items setting. In the practical production and service activities, the operation efficiency of the method will not change significantly with the increase in the number of projects in the enterprise business, which is conducive to the expansion of the enterprise business. At the same time, with the accumulation of enterprise service data, the number of transactions continues to increase. Although the increase in data volume is conducive to the accuracy of data mining results, it will also increase the computational pressure of the algorithm. Therefore, the running time of the algorithm in Figure 6b increases with the increase in the number of transactions. However, the method in this paper still has certain advantages. Therefore, the method in this paper can effectively adapt to the update of enterprise production service data, which is helpful to improve the quality of product demand.

In summary, the methods proposed in this paper can accurately obtain RMPD. At the same time, among some methods to solve similar problems, the proposed method can adapt to the changes of relevant parameters and application backgrounds and has certain advantages and applicability.

6. Conclusions and Future Work

Since the remanufacturing service for RMP should consider the influence of the failure characteristics, it is necessary to explore the evolution law of product property, performance, functions, and other characteristics from RMP to guide the remanufacturing scheme decision and service resource allocation. However, existing research lacks methods to mine demand information from the perspective of products. Therefore, this paper proposes a method to obtain RMPD based on the improved ant colony algorithm to mine the evolution law of products, which has made certain contributions to theoretical method research and practical application.

In terms of theoretical methods, this paper innovatively puts forward the concept of RMPD. Different from the traditional product demand, which is transformed by the mapping of customer and market demand information, RMPD is the demand information of product property, performance, functions, and other characteristics excavated from RMP. In addition, a corresponding acquisition method is proposed for RMPD, which is transformed into a prediction problem based on the failure characteristics, and the improved ant colony algorithm is used to mine the evolution law of the property, performance, functions, and other characteristics of RMP, and RMPD is deduced.

In terms of practical application, this paper verifies and compares the proposed method based on the project experience data. The results show that the product demand information of the retired roll obtained in this paper can provide effective guidance for the decision of the remanufacturing scheme. At the same time, through the comparison of a variety of typical methods of similar problems, it can be seen that the method proposed in this paper can ensure that the demand information obtained has high accuracy, and maintains relative superiority and applicability in the practical application of remanufacturing enterprises.

However, the remanufacturing service for RMP is a process of human-machine-thing collaborative participation. For demand-driven service remanufacturing, the research on its driving factors should consider both the factors of customers and the factors of RMP. Therefore, in future research, we should study how to obtain customer demand, and how to realize the multi-source demand information composed of customer demand and RMPD to guide the remanufacturing scheme decision-making and service resource allocation and strive to make full use of the surplus value of RMP through demand-driven remanufacturing services.