A multisource data‐driven approach for carbon footprint analysis of remanufacturing systems

The remanufacturing industry is experiencing significant growth, resulting in a substantial increase in its carbon footprint. Unfortunately, this issue is not receiving adequate attention at present. Moreover, existing methods for analyzing carbon footprints in remanufacturing systems are inefficient and inaccurate due to the complex relationship between carbon emissions and the dynamic nature of the systems. In this paper, we propose a multisource data‐driven approach for carbon footprint analysis of remanufacturing systems. First, we examine the relationship between carbon emissions and the uncertainty surrounding end‐of‐life (EOL) product components, as well as the corresponding resource recovery strategies, such as reuse, recycle, and remanufacture. This analysis allows us to define the carbon footprint boundary of remanufacturing systems. Next, we establish a carbon footprint model for recycling strategies using recycling data. Additionally, we propose a carbon footprint model for remanufacture strategies by utilizing the back propagation neural network based on particle swarm optimization algorithm and data from the materials flow, energy flow, and waste flow of these strategies. By combining these models, we can accurately calculate the carbon footprint of remanufacturing systems. To demonstrate the effectiveness of our approach, we present a case study on the remanufacturing of an EOL automobile engine. This case study showcases how our methodology can be utilized as a valuable tool for analyzing carbon footprints and identifying strategies to reduce carbon emissions in remanufacturing systems.

attention with its excellent performance of resources saving and carbon emission reduction. 4Remanufacturing is a series of reprocessing approaches to return endof-life (EOL) products to as-good-as-new ones, it can reduce costs by 50%, save energy by 60%, save materials by 70%, and reduce emissions by 80% compared with the traditional manufacturing. 5With these advantages, the remanufacturing industry has become a breakthrough of industry sustainable development strategy in many countries, the size and capacity of which has grown dramatically in recent years.For instance, in China, the remanufacturing industry has reached 200 billion RMB in 2020, and the size may have double growth in the next 5 years. 6With the continued rising volume of the remanufacturing industry, it has consumed and will continuously consume more resources and energy, as well as carbon emissions.Therefore, the carbon footprint of the remanufacturing industry needs to be revisited.
The carbon footprint is a term to measure the total amount of carbon emissions from a lifecycle perspective. 7imilar to manufacturing systems, the carbon footprint of remanufacturing systems could also be defined as the sum of carbon emissions caused by material consumption, energy consumption, and waste disposal. 8However, due to the uncertain resource recovery strategies, the carbon footprint of remanufacturing systems is more complex than that of manufacturing systems.Specifically, the EOL product is composed of many components with uncertain conditions, that is, wear and fatigue, when it is input to remanufacturing systems, it requires appropriate resource recovery strategies, namely, reuse, recycle, and remanufacture. 9Since energy consumption, material consumption, and waste recycling are quite different in these strategies, it led to the carbon footprint of remanufacturing systems having significant variations with manufacturing systems.In general, there are almost no carbon emissions in the reuse strategy, only waste disposal carbon emissions are generated in the recycle strategy, and energy consumption carbon emissions, material consumption carbon emissions, and waste disposal carbon emissions all exist in the remanufacture strategy. 10It is claimed that the carbon footprint of remanufacturing systems is highly relevant to the components recovery strategies of EOL products and cannot only consider the carbon emissions of a certain component machining process, like, manufacturing systems.Therefore, the carbon footprint boundary of remanufacturing systems is broader than manufacturing systems, and it is closely related to the components recovery strategies of EOL products.
In addition, for a remanufacture strategy that generates the most carbon emissions, the carbon footprint is dynamically correlated with remanufacturing conditions, it makes the impact factors of carbon footprint numerous and difficult to obtain. 11,12Some of the existing approaches for carbon footprint analysis are based on the principles of lifecycle assessment (LCA) and using statistical methods to calculate the carbon emissions. 13These methods are difficult to apply in remanufacturing systems due to the diverse impact factors.Other carbon footprint analysis approaches focus on the establishment of a carbon emission model from energy consumption, material consumption, and waste recycling, these mechanism-based methods hardly describe the dynamic natures of carbon emissions and may lead to inefficient or inaccurate analysis results.
To this end, this paper presents a definition of the carbon footprint boundary of remanufacturing systems according to the resource recovery strategies of EOL products, and proposes a multisource data-driven approach for carbon footprint analysis of remanufacturing systems.The remainder of this paper is organized as follows.Section 2 reviews the current works on carbon footprint.Section 3 defines the carbon footprint boundary of remanufacturing systems.Section 4 elaborates on the overall framework and details of the proposed method.Section 5 verifies the feasibility of the proposed method in a case study.Section 6 summarizes the conclusions and future works.

| LITERATURE REVIEW
The carbon footprint of the remanufacturing industry is a hotspot at home and abroad.Compared with the original manufacturing, remanufacturing eliminates the processes of forging, casting, stamping, and so forth, and the surface treatment, surfacing, mechanical processing, and other processes are involved in remanufacturing systems, 14 it makes that many studies on carbon footprint analysis of manufacturing systems can be used to the remanufacturing systems.Li et al. 15 defined a carbon emission generalized boundary by analyzing the sources of carbon emissions of the machining system and proposed a quantitative method of the carbon emission from energy consumption, material consumption, and waste recycling.Tridech and Cheng 16 studied the characteristics of carbon emissions and established a theoretical model for low carbon manufacturing.Tan 17 established a carbon emission model of manufacturing processes considering processing time, costs, resource consumption, and environmental impacts.Tseng and Hung 18 studied the relationship between carbon emissions and resource utilization at workshop and extended process chain levels and established a strategic decision-making model for a sustainable supply chain.Wiedmann 19 used an input-output method to quantitative the carbon emissions of remanufacturing processes.The above studies mainly focus on the carbon footprint analysis at the system level, which may provide valuable references for the carbon footprint boundary of remanufacturing systems in this paper.
As mentioned above, the resource recovery strategies have a huge impact on the carbon footprint of remanufacturing systems.The remanufacturability evaluation is considered as an essential basis for the decision-making of these strategies, it can be assessed by using numerical metrics, such as computeraided design information. 20San 21 pointed out that there were many factors that need to be considered when the remanufacturability of used mobile phones was evaluated and found that the innovation rate and obsolescence were the main factors of remanufacturability.Karaulova and Bashkite 22 assessed the remanufacturability of used industrial equipment with LCA data and proposed a resource recovery strategy decision-making approach based on the TRIZ matrix.Du 23 proposed an integrated method to evaluate the remanufacturability of used machine tools from three aspects including technological, economic, and environmental feasibility, and established an analytic hierarchy process (AHP)-based model to determine the resource recovery strategies.Omwando et al. 24 studied the four factors of EOL products and presented a bilevel fuzzy method to determine the resource recovery strategies.These studies illustrate the basis for the decision-making of resource recovery strategies, which can provide a good indication of the kind of multisource data needed for this study.
When the resource recovery strategies of EOL product are determined, the carbon emission of these strategies should be quantified to analyze the carbon footprint of remanufacturing systems.For instance, Rahimifard et al. 25 designed a web-based information system to calculate the carbon emissions of recycling and disposal strategies.Liao et al. 26 studied the carbon emission nature of reuse and remanufacture strategies and established an environmental benefits assessment model for remanufacturing systems.The above studies provide evidence for the carbon footprint analysis of resource recovery strategies.However, due to the complex relationship between carbon emissions and material consumption, energy consumption, and waste disposal of remanufacture strategy, the above studies are difficult to provide an accurate analysis of the carbon footprint.On the basis of this, Zhou and Liu 27 studied the energy consumption of remanufacturing systems and established an energy consumption model for the remanufacturing tasks.Guo et al. 28 studied the energy consumption characteristics in remanufacturing systems and the reasons for energy consumption uncertainty and proposed a graphical evaluation and review technology-based energy consumption model for parts remanufacturing.Liao et al. 29 studied the carbon emissions nature of resource recovery strategies and established a definite relation between quality loss and environmental efficiency of remanufacturing systems with Monte Carlo simulation.Zheng et al. 30 studied the material consumption of advanced restoring technologies in remanufacturing systems, such as brush electroplating, arc spraying, and laser cladding.He et al. 31 established a carbon footprint estimation model for the EOL products based on the unascertained mathematics theory.He et al. 32 combined the carbon footprint model with the unascertained number model at the raw materials acquisition stage.Zhang et al. 33 established a carbon emission calculation model for used engineering machinery parts based on fuzzy-extension AHP.Qin et al. 34 studied the energy consumption nature of additive manufacturing with multisource data from product design, material condition, and working environment.These studies analyzed the impact elements of carbon footprint caused by material consumption, energy consumption, and waste disposal, and may provide support for the carbon footprint model establishment of remanufacture systems in this paper.
In addition, most of the existing methods for carbon footprint analysis focus on the principles of LCA, to establish the "bottom-up" or "top-down" model to analyze the carbon footprint of a product or system. 35,36These methods are used to describe the carbon footprint of urban, household, or industrial dimensions, [37][38][39][40][41] and often employ statistical approaches to analyze the carbon footprint.These approaches are hard to illustrate the coupling relationships between carbon footprint and energy consumption, materials consumption, and waste recycling, and are difficult to apply directly in remanufacturing systems.
3][44][45] It gives a novel idea for data-driven carbon footprint analysis of remanufacturing systems.

| CARBON FOOTPRINT BOUNDARY OF REMANUFACTURING SYSTEMS
The purpose of remanufacturing systems is to transform the EOL products into remanufactured, reused, or recycled components with appropriate resource recovery strategies.It will inevitably produce material consumption, energy consumption, and waste disposal, which cause carbon emissions.To define the carbon footprint boundary of remanufacturing systems, the carbon emission source of recovery strategies should be studied first according to the composition of EOL product.
The EOL product is composed of many components with uncertainty, some with minimal failure degree can be reused directly in the reuse strategy, some with significant failure degree can only be recycled in the recycle strategy and others need to be remanufactured in remanufacture strategy before they can be used.Therefore, the carbon footprint can be described with Equation (1).
where CF represents the carbon footprint of remanufacturing systems.CF reu , CF rec , and CF rem are the carbon footprint of reuse, recycle, and remanufacturing strategies, respectively.The EOL product is composed of reused components, remanufactured components, and recycled components.As mentioned above, there are almost no carbon emissions in the reuse strategy, and only waste disposal carbon emissions in the recycle strategy.On the other hand, the remanufacture strategy involves energy carbon emissions, material carbon emissions, and waste carbon emissions.As a result, there are distinct differences in the energy flow, material flow, and waste flow among these strategies, which in turn lead to significant variations in their respective carbon footprints.Therefore, Equation (1) can be further expanded as Equation (2).

  (
) where m and n are the numbers of recycled and remanufactured components of the EOL product, respectively.It is noted that the waste carbon footprint is caused by the energy consumption and carbon emissions from the recycling process, it can be calculated with the quality of the recycled components in the recycling strategy and the waste material (such as waste cutting fluid, chips, etc.) in remanufactured strategy, and the carbon footprint factors related to the material type.Therefore, the C F rec w i and C F rem w j can be shown in Equation (3).
where The energy carbon footprint can be obtained with the energy consumption and carbon footprint factors corresponding to the energy type.Considering the remanufacturing processes, such as grinding, polishing, and drilling, electricity is the most common energy type in remanufacturing systems.In this paper, C F rem e j -can be calculated with the mass of electricity energy consumption and the carbon footprint factors of electricity energy, as shown in Equation ( 4).
where E elec j represents electricity energy consumption of the jth remanufactured component.f elec represents the carbon footprint factors of electricity energy.
In the remanufacture strategy, the part of components is removed as chips and the auxiliary materials (such as cutting fluid, cutting tools, etc.) are consumed to transform the remaining essence of components into remanufactured components.Therefore, the material carbon footprint can be calculated with the mass of component and auxiliary materials consumption and the corresponding carbon footprint factors, as shown in Equation (5).
where M rem raw j and M rem aux j represent the mass of the jth component and auxiliary material consumption in its remanufacturing process, respectively.f rem raw j and f rem aux j represent the carbon footprint factors of the corresponding component and auxiliary material.
When the carbon footprint of remanufactured and recycled components of EOL products is calculated with the above approach, the carbon footprint of remanufacturing systems can be calculated as the sum of these results.Therefore, according to the formulas (2)-( 5), the carbon footprint of remanufacturing systems can be shown in Equation (6).
On the basis of the analysis above, the carbon footprint boundary of remanufacturing systems can be shown in Figure 1.

| CARBON FOOTPRINT OF REMANUFACTURING SYSTEMS
In this paper, a multisource data-driven approach is proposed to analyze the carbon footprint of remanufacturing systems.First, the multisource data from EOL products, remanufacturing systems, and carbon footprint database are collected and preprocessed.Then, considering the composition of EOL products and the resource recovery strategies, a multisource data-driven carbon footprint model of recycled components and a particle swarm optimization (PSO)-back propagation (BP) model for energy carbon footprint, material carbon footprint and waste carbon footprint of remanufactured components are established, respectively.Finally, the carbon footprint of this remanufacturing system can be described as the sum of them.The overall framework of the proposed approach is shown in Figure 2.

| Multisource data collecting and preprocessing
The multisource data are defined as the data collected from different resource recovery strategies and related carbon footprint database in this paper, such as failure data from EOL products, waste data from recycle strategy and material data, energy data, and waste data from remanufacture strategies, and the standard coal equivalent data from carbon footprint factors database.The failure data are used to determine resource recovery strategies for the components of EOL product, and the specific decision-making approach can be found in the following literature. 46,47he waste data from the recycle strategy are employed to calculate the quality of the recycled components of the EOL product, and the material data, energy data, and waste data from the remanufacture strategy are used to calculate the amount of material consumption, energy consumption, and waste emissions of the remanufactured components of the EOL product.Then, the standard coal equivalent data could be used to transform these values into carbon emissions.To capture the above multisource data, the IoT and various smart sensors are used to collect the failure Carbon footprint boundary of a remanufacturing system.EOL, end-of-life.data, material data, energy data, and waste data.The standard coal equivalent data can be obtained from the product lifecycle database, such as the China Products Carbon Footprint Factors Database. 48To clearly describe this issue, the multisource data, as well as its usage are listed in Table 1.
It is noted that the above-collected data are often the raw data from resource recovery strategies, and need to be preprocessed and features extracted to make the data suitable for the proposed model.In particular, the null or redundancy data should be removed to ensure the high quality of data. 49hen the raw data are preprocessed, the driving factor should be identified to explore the factors affecting carbon footprint of remanufacturing systems.
Owing to the dynamic nature of carbon emissions, and small amount and unknown distribution law of data, it is difficult to use the traditional method to identify the driving factors. 50To address this issue, the gray relation analysis (GRA) is adopted.In comparison to other correlation analysis methods, GRA offers several advantages in terms of data processing, correlation measurement, and noise reduction. 51,52First, GRA can analyze data even in the presence of missing or incomplete information, making it suitable for addressing small sample sizes, nonlinear relationships, nonstationarity, and uncertain problems.Second, the method utilizes gray relation coefficients to measure the correlation between factors, which reveals the intrinsic relationship by comparing the similarities in trend developments.This provides a more accurate reflection of the interactions between factors.Additionally, GRA establishes models and applies noise reduction techniques to the original data, thereby reducing the impact of random fluctuations and insignificant variations on the analysis results.This helps improve the credibility of the factors and minimize noise interference.Finally, GRA is a simple and intuitive method that is easy to understand and apply.It does not require rigorous hypothesis testing of the data and is suitable for analyzing various problems.GRA provides intuitive correlation rankings and visualizations, which facilitate decision-makers in quickly understanding the driving factors.The following are the specific steps.
(1) Establish the feature sequence and behavior sequences of the remanufacturing systems, and transformed them with the initial value operator.
The transformed sequences are listed in Equation (7).
Overall framework of the proposed approach.BP, back propagation; EOL, end-of-life; PSO, particle swarm optimization.∈ where ρ is the resolution coefficient to describe the relevance of these factors, the general value is 0.5.Δ i 0 , Δ min and Δ max represent the sequence difference, minimum difference, and maximum difference of these two series, respectively, which can be calculated with Equation (9).
The γ p is used to illustrate the relevance between the factors and the carbon footprint.For instance, if  γ 0.6 ρ when ρ = 0.5, it indicates that the factor is closely related to the system.And then, all factors could be sorted according to it.

| Model establishment with PSO-BP
After conducting GRA, the driving factors of carbon footprint under the remanufacture strategy were identified, including raw material consumption, auxiliary material consumption, energy consumption, and so forth.Then, PSO-BP is proposed to calculate the carbon footprint.As a classical feed-forward neural network, the BP neural network possesses favorable characteristics such as self-learning, self-organization, adaptability, and strong fault tolerance due to its structural properties.This allows for a certain degree of input sample errors, resulting in a reliable simulation effect for multisource data samples. 53However, the traditional BP neural network suffers from drawbacks such as a susceptibility to local extreme values and slow or nonconvergent convergence speeds.To T A B L E 1 Multisource data of the proposed approach.

Failure mode
The failure expressions of EOL product, for example, wear, abrasion, pitting, and so forth

Failure degree
The value of failure modes of EOL product

Raw material properties
The type of raw material Material flow Raw material and auxiliary material consumption

Raw materials volume
The value of raw material consumption

Auxiliary material properties
The type of auxiliary material

Auxiliary materials volume
The value of auxiliary material consumption

Waste properties
The type of waste emissions Waste flow Waste emissions

Treatment method
The disposal methods of waste

Waste volume
The value of waste disposal

Machining power
The power of remanufacturing equipment Energy flow Energy consumption

Machining time
The duration of the remanufacturing process

Carbon footprint factors
The carbon equivalent coefficients for materials and energy sources during preparation and processing

Carbon footprint database
Converting material, energy consumption, and waste disposal into carbon equivalents Abbreviation: EOL, end-of-life.
address this issue, researchers have used genetic algorithms (GAs) to optimize the BP neural network 54 and improve convergence speed.In comparison, the PSO algorithm is simpler to calculate and requires less parameter adjustment.Utilizing PSO to optimize the initial weights and thresholds of BP not only avoids falling into local extreme values but also improves convergence speed. 55Accordingly, PSO-BP is selected for calculating the final carbon footprint in this study.
The algorithm flow of the model is depicted in Figure 3, and the specific steps are outlined as follows.
(1) Normalization of multisource data.Due to the fact that these driving factors affecting carbon footprint are multidimensional, parameters from each dimension have different scales and units.It would affect the results of data analysis.Therefore, data normalization is needed to remove the scales and units of different dimensional data.Specifically, each parameter is linearly transformed using the conversion function in Equation ( 11), mapping them to the range of [0, 1].
new min max min (11)   where x new is the normalization result, x is the sample value, x min is the minimum value in it, and x max is the maximum value in it.(2) Determine the structure of BP neural network.The framework of a BP neural network consists of input layer, output layer, and hidden layer, both of which have only one layer, while the hidden layer can be single or multiple.The advantage of multiple hidden layers is that it can reduce the training error and improve the computational accuracy, but it would lead to model training time consumption, so we adopt single hidden layer in this paper, and the number of nodes in the hidden layer is determined by the empirical equation, which can be calculated with Equation (12).
where m denotes the nodes number of hidden layer, n denotes the nodes number of input layer, l denotes the Flowchart of PSO-BP neural network.BP, back propagation; PSO, particle swarm optimization.
YAN ET AL.
| 4453 nodes number of output layer, and α denotes a constant within 1-10.(3) Initialize the BP neural network.The purpose of initialization is first to configure the network parameters, which include the number of iterations, the learning rate, and the target error.The second is to determine the connection weights W between the input, output and hidden layer neurons and the threshold for initializing the hidden layer.(4) Initialize related parameters of particle swarm.
Initialize the individual particle position and velocity, and calculate the individual fitness value to get the current optimal fitness value of the population as the parameter of the next iteration calculation.( 5) Determine the fitness function.The particle fitness function is constructed using the error of BP neural network, which can be calculated with the mathematical expression as shown in Equation ( 13): where n denotes the number of samples, T i denotes the desired output of sample, and O i denotes the actual output.( 6) Determine the individual and global optimum and optimize the PSO algorithm.Determine the optimal position and fitness value of individual particle and population.Adjust the optimal position of the particles according to the fitness values, and update the particle population with these optimal positions.(7) When the iterations reach the maximum iteration number or the error meets the minimum error, the optimal solution of the PSO algorithm is employed as the initial weight and threshold of the BP neural network.Otherwise return to ( 4). ( 8) The BP neural network is trained and tested with the normalized feature data.If the error is output the result, otherwise go to (2).

| Model validation
To evaluate the efficiency and accuracy of the PSO-BP neural network, a model validation method is also proposed in this paper, and the root-mean-square error (RMSE) is selected as evaluation indicators.The specific formula is shown in Equation (14).
where f x ( ) i is the measured value of the ith group, and y i is the actual value of the ith group.The RMSE can be used to explain the regression performance and accuracy of the PSO-BP model, respectively.
The mean absolute percentage error (MAPE) and the coefficient of determination (R 2 ) are selected to further validate the superiority of the PSO-BP model over other models, as shown in Equation (15).
where y i is the actual value, y ˆi is the predictive value, y ¯i is the mean of the actual value, and N is the sample size.

| CASE STUDY
To substantiate the feasibility of the aforementioned model and methodology, a carbon footprint analysis methodology is performed on an EOL automobile engine remanufacturing system.Recognized as a pivotal component in automobiles, the engine holds significant value for remanufacturing purposes.The main constituents of this EOL automobile engine include the cylinder block, gear, camshaft, feed valve, cylinder head, cylinder liner, crankshaft, connecting rod, and piston ring.However, these components often exhibit uncertain quality conditions, necessitating the adoption of specific resource recovery strategies.Consequently, the carbon footprint boundary of this automobile engine remanufacturing system becomes ambiguous.Furthermore, the carbon emissions associated with the remanufacture strategy for these components are intricately linked to the energy flow, material flow, and waste flow during the remanufacturing processes.Thus, defining and quantifying the carbon footprint of the automobile engine remanufacturing system pose significant challenges.

| Definition of carbon footprint boundary
On the basis of the failure mode data and failure degree data of the EOL automobile engine, the specific resource recovery strategies for these components can be determined by using the remanufacturability assessment methods. 56,57Then, using the two EOL automobile engines consisting of components with different failure characteristics as example, the specific resource recovery strategies for these components are listed in Table 2.
According to the analysis of Section 3, the carbon footprint boundary of these two remanufacturing systems can be illustrated in Figures 4 and 5.

| Results for carbon footprint analysis
To show the generality and to avoid duplicate descriptions of the proposed method, the EOL automobile engine remanufacturing system 2 is chosen to analyze its carbon footprint in this paper.The details are as follows.
First, the raw data are collected from the data source of energy flow, material flow and waste flow of remanufacture strategy and recycle strategy, respectively, and the driving factors for carbon footprint of these data are identified with the proposed GRA method.On the basis of this, the data of raw material consumption, auxiliary material consumption, energy consumption, waste material disposal and waste liquid disposal are determined as the main driving factors in this case study.The main multisource data for carbon footprint analysis of EOL automobile engine remanufacturing system 2 is listed in Table 3.
Then, the carbon footprint of recycle strategy and remanufacture strategy can be analyzed with the approaches mentioned in Sections 3 and 4, and the results are described as follows.
The gear and piston ring components are treated with recycle strategy, the carbon footprint of them is calculated with Equation (3), the results are listed in Table 4.
A PSO-BP neural network is established to calculate the carbon footprint of the remaining components that are treated with remanufacture strategy.The input layer consists of five nodes corresponding to the five driving factors: raw material consumption, auxiliary material consumption, energy consumption, waste material disposal, and waste liquid disposal.The output layer comprises a single node representing the carbon footprint of each component.The number of nodes in the hidden layer can be determined using Equation (12).
To construct the PSO-BP neural network, the parameters of the BP neural network are set, and the | 4455 relevant parameters of the PSO algorithm are initialized as outlined in Table 5.
After the model was established with the data in Table 5, the carbon footprint of the remaining components was calculated with the multisource data given in the text.And the results are shown in Figures 6-8.

| Discussion
By means of the results from this paper, some of discoveries are enlightening for the carbon footprint of remanufacturing systems.
The carbon footprint of remanufacturing should be given enough attention due to the rapid development of remanufacturing industry.Aiming with this purpose, the carbon footprint boundary of remanufacturing systems should be recognized first.Comparing with the previous research on carbon footprint of manufacturing systems (i.e., Li et al. 58 and Zhang 59 ), this paper focuses on the differences between remanufacturing systems and manufacturing systems, proposes a definition of carbon footprint boundary through the remanufacturability of EOL products and carbon emission nature of corresponding resource recovery strategies of remanufacturing systems.From Figures 4 and 5, the special carbon footprint boundary shows that the proposed definition enables integrated consideration of the failure characteristics of components, and can fully describe the carbon footprint of the remanufactured system for EOL products.
From Figures 6 to 8, the carbon emission performance of each component of EOL automobile engine can be visualized, and the energy carbon footprint, material carbon | 4457 footprint and waste carbon footprint of crankshaft.It shows that the most energy consumption and material consumption are occurred in the remanufacturing processes of crankshaft, and may offer a focus for reducing carbon emissions of the remanufacturing systems.
In addition, the calculated values of CF rem-e , CF rem-m , and CF rem-w for each component in remanufacture strategy are quite close to their actual values, it shows that the proposed multisource data-driven approach can reflect the carbon emission performance of remanufacturing systems.To further illustrate the advantages of this method, the RMSE method is employed to analyze the errors of these two values, and the results are listed in Table 6.
According to the results, the errors between the actual values and calculated values are all in an acceptable range.The largest error value is 17.92%, which is generated from the waste carbon footprint of cylinder block.It is due to the complex remanufacturing process of this component, some errors occur in the incomplete data collection in terms of emissions or data feature extraction, which will provide a feasible direction for the improvement of this algorithm.
To verify the superiority of the proposed PSO-BP neural network, other common intelligent models, such as standard BP and GA-BP neural networks, are selected for analyzing carbon footprint of remanufacturing systems.The comparison results are shown in Figure 9.
As can be seen from Figure 9, the three models can all calculate the carbon footprint of the remaining components are treated with remanufacture strategy, but the predictive value of PSO-BP is closer to the actual value.To further validate the performance of the three models, two evaluation indicators: MAPE and R 2 are calculated using Equation ( 12), the calculation results are shown in Table 7.
The two metrics can express the calculation accuracy and convergence speed of each model more intuitively.Generally, the smaller the MAPE, the closer to 1 of R 2 , the higher the prediction accuracy of the model, and the faster the convergence speed.It can be seen from Table 7 that the performance of PSO-BP is better than the other two intelligent models, indicating that this model is more suitable for the calculation of carbon footprint of remanufacturing systems.
Through the above analysis, some advantages of the proposed approach can be summarized, as follows: (1) The carbon footprint boundary definition of remanufacturing systems correlates the uncertainty of the EOL products with carbon emission nature of corresponding resource recovery strategies of remanufacturing systems, it will provide a strong theoretical support for the carbon footprint analysis of  | 4459 remanufacturing systems.(2) The multisource data-driven approach for carbon footprint analysis of remanufacture strategy based on PSO-BP network can prevent the difficulties of carbon emission mechanism modeling and have superior accuracy, it ensures a methodological support for evaluating the carbon emission performance of remanufacturing systems.(3) This methodology provides a systematic analysis of the carbon footprint of remanufacturing systems, and it can be utilized as an effective tool to not only analyze the carbon footprint but also explore possible strategies of reducing carbon emissions for remanufacturing systems.

| CONCLUSIONS
In this paper, a multisource data-driven approach has been presented to analyze the carbon footprint of remanufacturing systems.First, the carbon emission nature and boundary of remanufacturing systems is defined considering the different resource recovery strategies of EOL product.Then, a GRA and PSO-BP algorithm is employed to explore the factors and calculate carbon footprint of remanufactured components.Finally, an EOL automobile engine remanufacturing system case study is verified by comparing the calculated value with the actual value of carbon footprint.The results show that proposed multisource data-driven model can be utilized as an effective tool to analyze the carbon footprint of EOL products.
The main limitation of this paper is that the multisource data mentioned in the paper are all structured data, but in the remanufacturing engineering practice, there is still a large amount of unstructured data, for which the algorithm proposed in this paper may no longer be applicable.Therefore, in the future work, we will fully consider the multimodal characteristics of EOL product lifecycle data and seek for more suitable algorithms to realize a more accurate analysis of the carbon footprint of remanufacturing systems.

C F rec w i -
represents the waste carbon footprint of the ith recycled component in the recycling strategy.C F rem e j -, C F rem m j -, and C F rem w j are the energy carbon footprint, materials carbon footprint, and waste carbon footprint of the jth remanufactured component in the remanufacturing strategy, respectively.

-
represent the quality of the ith recycled component and the jth waste material in remanufactured strategy.f rec w i -and f rem w j -represent the carbon footprint factors of the type of the ith recycled components and the jth waste material in the remanufactured strategy.

F
I G U R E 4 Carbon footprint boundary of EOL automobile engine remanufacturing system 1.CF, carbon footprint; EOL, end-of-life.F I G U R E 5 Carbon footprint boundary of EOL automobile engine remanufacturing system 2. CF, carbon footprint; EOL, end-of-life.

F
I G U R E 6 Carbon footprint of energy consumption in remanufacture strategy.F I G U R E 7 Carbon footprint of consumption in remanufacture strategy.

F
I G U R E 8 Carbon footprint of waste disposal in remanufacture strategy.T A B L E 6 Error analysis for PSO-BP.
T A B L E 2 Resource recovery strategies for the components.
T A B L E 3 Multidata for carbon footprint of EOL automobile engine remanufacturing system 2. Carbon footprint of recycle strategy.Parameter setting of models.
Remanufactured components Actual values (kg CO 2 ) Calculated values (kg CO 2 ) RMSE CF rem-e CF rem-m CF rem-w CF rem-e CF rem-m CF rem-w CF rem-e CF rem-m CF rem-w Abbreviations: BP, back propagation; PSO, particle swarm optimization.YAN ET AL.