Data-Driven Decision-Making: Leveraging Digital Twins for Reprocessing in the Circular Factory

Introduction

Modern manufacturing systems are increasingly complex, particularly in non-linear, interdependent production lines. This complexity raises the likelihood of downtime and maintenance, challenges that redundancy measures or stricter quality standards cannot fully mitigate. Circular factories (CFs), which aim to promote sustainability by reprocessing components, face additional challenges due to the variable quality of returned inputs [1]. Addressing these issues requires advanced frameworks capable of managing uncertainty and optimizing decision-making in dynamic environments. DDDM in manufacturing involves the continuous acquisition, processing, and analysis of data to optimize strategies across a product’s lifecycle, from design to end-of-life decisions.

Within the CF [2], DDDM enables resource optimization, extended product lifespans, and sustainable practices by integrating machine learning to develop functional and reliability models that guide predictive and prescriptive decisions [3]. The FBM provides actionable insights to assess a product’s operational performance based on its current condition. Using the relations between the embodiment and the functional behavior of a product, the FBM links the two domains and allows for the evaluation of used products. The operational performance can be derived [4] and expressed as a metric by comparing the functional behavior with the product’s requirements. To gain insights into the performance over time, the System Reliability Model (SRM) complements this metric by addressing potential failure modes, including fatigue, corrosion, and wear, estimating the impact of failures, and predicting the product’s performance under various conditions [5]. Together, these models enable monitoring and predicting product health and support DDDM in the CF. DTs serve as the core of this data integration process. A DT is a virtual representation of a physical asset [1], continuously updated with real-time product data throughout the processes within the CF. Data from the FBM and SRM is integrated and dynamically updated to inform reprocessing decisions. DTs ensure that data-driven insights provided by product conditions guide decisions.

Background

DTs, FBMs, and SRMs form the foundation of modern manufacturing systems. They are particularly relevant in the context of CF, which faces significant challenges due to the variability in the quality of returned parts. DTs represent physical systems virtually and enable real-time, bidirectional data flow between physical and digital domains. Their characteristics have been defined across various authoritative implementations [6, 7, 8, 9, 10]. DTs have evolved significantly [11], driven by advancements in high-performance computing [12], Moore’s Law [13], IoT technologies [14], chip design [15], and deep learning [16]. These advancements have expanded DT applications from predictive maintenance to real-time system simulations, enabling complex decision-making scenarios. The issue of R-strategies lies in their optimal choice [17]. To make informed decisions about reprocessing strategies, it is essential to have quantitative knowledge about the relations between a product’s embodiment and functional behavior [3]. Understanding these embodiment-function relations (EFRs) provides insight into the product‘s current condition and creates a cornerstone for targeted and effective reprocessing. In the vision of the CF, this step is carried out by the FBM. Behavior investigation is carried out using behavioral models [18] of physical systems. They include qualitative approaches such as Characteristics Properties Modeling [19] and quantitative approaches like experimental studies or numerical simulations [20]. Behavioral models investigate how the product’s functional behavior is derived from its embodiment [4]. However, the inversion of this investigation, needed for reprocessing decisions in the CF, requires implicit expert knowledge. In the CF, the FBM integrates this implicit expert knowledge to form real-time computational models, enabling bidirectional evaluation of the EFRs. Therefore, the FBM helps to assess product functionality based on the current condition but does not include degradation over time. SRMs address this gap by focusing on the performance of systems and components over time. Reliability is the probability of a system or component performing its required function at varying performance levels over a specified period under stated conditions [5]. Tools like Ishikawa diagrams [21] and Design Structure Matrices [22] identify key failure causes and subsystem interactions, while Reliability Block Diagrams (RBDs) [23] provide a graphical representation of the system’s reliability.

Furthermore, probabilistic approaches, such as Bayesian inference [24] and Markov models [25], are used to evaluate gradual degradation and multi-state system reliability. This allows for more nuanced assessments of components that may not fail outright but experience performance declines. Multi-state system reliability models (MSSRMs) are effective for systems where performance degradation occurs gradually or in multiple modes and represent a special case of SRMs [26, 27]. Although DTs, FBMs, and SRMs are powerful individually, current methodologies cannot dynamically synchronize functional and reliability data. This limitation restricts their applicability in CFs, where real-time decision-making is essential. To address this gap, the paper proposes a unified framework that integrates DTs, FBMs, and SRMs to enhance strategies for component reprocessing.

Framework

The proposed framework integrates DTs, FBMs, and SRMs into a unified framework to enable precise DDDM in CFs. By dynamically synchronizing functional and reliability data within the DTs, the framework supports real-time decisions on component reprocessing. Angle grinder is used as the case study, as seen in Figure 1, to support the vision of the perpetual innovative product for reprocessing products in CFs.

Figure 1

A vision of the “perpetual innovative product” for reprocessing products in CFs using an angle grinder as a case study

Digital Twin (DT) as the Decision Core

The DT serves as the central component of the framework, providing a platform for real-time data aggregation, synchronization, and simulation. DTs enable hierarchical decision-making by dynamically updating system states and evaluating whether components require disassembly or a refit for reprocessing, as illustrated in Figure 2. Compared to linear production factories where there is more uniformity, the CF needs a more flexible DT because of the high variability of the products. When a product enters the CF, an instance is created in the DT and dynamically updated accordingly for new measurements and remanufacturing. This process makes the DT instance-specific in the CF context. For example, decisions regarding an angle grinder, such as determining if it retains 95 percent of its performance, rely on iterative updates from the DT [1]. In the case of decision-making on the bevel gear, for example, these updates are invoked by measurements of its parameters, such as circular pitch, shaft angle, and elasticity, represented as distributions that are refined throughout the CF. DTs in the context of the CFs also simulate recombination scenarios to assess the cross-generational compatibility of components, which is also part of CF DTs being instance-specific. They integrate real-time data from FBMs and SRMs, enabling reprocessing decisions such as disassembling, remanufacturing, or reusing parts. By synchronizing these inputs, DTs lay the foundation for precise and efficient decision-making in CFs, optimizing resource use while maintaining high-reliability standards.

Figure 2

Hierarchical disassembly of an angle grinder, using the data from the FBMs, the SRMs and other different stations in the CF, and replicating it digitally in the DT – Features are stored as probability distributions

Functional Behavior and System Reliability Models as Decision Inputs

Functional Behavior Model (FBM)

The functional behavior based on its current condition must be considered to decide how a used product should be reprocessed in a CF. This is done by the FBM, which expands behavioral models to evaluate the EFRs in both directions automatically. The FBM is developed in a controlled laboratory environment before the runtime of the CF. To incorporate the previously described implicit expert knowledge into the FBM, comprehensive system insights are created by using qualitative product models. The main emphasis of these models is to identify relevant EFRs and their interactions in the system. Afterward, this qualitative knowledge is embedded in a quantitative approach, such as a physics-informed neural network. As a result, the quantified EFRs and their interactions are not pure black box models inside the FBM, but conclusions can be drawn between the two domains.

Furthermore, the approach enables the combination of specific key performance indicators (KPIs) in the form of a performance metric to evaluate functional behavior. In the CF, the FBM supports the inspection of used products entering the CF and guides their disassembly and reprocessing. Figure 3 shows the different inputs of the FBM and their corresponding domains.

Figure 3

Inputs of the functional behavior model (FBM) spanning the domains of design

Functional tests at the inspection station provide information about the current performance. If the functional requirements of the target condition are fulfilled, the system or subsystem is fit to be reused. If not, further disassembly and measurements are required. To guide this iterative disassembly, the FBM identifies structural areas of interest. These areas include the subsystems or components that are most likely to cause degradation in performance. For example, the gearbox‘s condition is most likely to cause a change in the vibration emissions of an angle grinder. After each step, geometric measurements are carried out to verify the assumptions. This way, a minimal degree of disassembly can be achieved. The FBM also defines how the structural parameters must be adjusted to meet the functional requirements. This is possible due to the bidirectional assessment of the EFRs and references in the form of historical data. The derived Instance-Specific Tolerance Scheme (ITS) is shown in Figure 3. The exemplary three-dimensional space’s boundaries represent the target condition’s functional requirements. Everything inside exceeds the requirements, and everything outside falls short. Based on the geometric measurements and their corresponding uncertainty, the instances of used products are mapped as points or areas in the ITS. As indicated by the different colors, an initial statement regarding the end-of-life strategies and manufacturing processes can be derived. The FBM, therefore, facilitates runtime decisions during the inspection of used products and links functional evaluation to longterm dependability by providing a performance metric.

System Reliability Model (SRM)

To reprocess products in the CF, it is essential to know about the individual systems and subsystems’ performance over time. The SBM complements the FBM by predicting the instance-specific reliability of components, subsystems, and systems under various conditions. The SRM used in this framework uses MSSRM, which provides a nuanced evaluation of performance degradation over time. The SRM development consists of two distinct phases Figure 4. In the first phase, the SRM is built and trained using lifetime test data and knowledge about the functional behavior of the FBM. This process occurs in a controlled laboratory environment, as described by Leitenberger et al. [25]. First, it defines the system’s reliability structure by identifying key failure modes using Ishikawa diagrams, RBD, and Design Structure Matrices as described above. Next, it collects data through sensors and test-bench simulations, capturing operational loads and material behavior. The SRM is then parameterized with historical load curves and a system performance metric, enabling predictive capabilities. Bayesian approaches and Markov models are applied to analyze state transitions and handle model uncertainties.

Figure 4

Workflow of the Instance-specific SRM within the CF

4SRM within the CF

Once the SRM is developed and validated, it is implemented and applied directly on the shop floor of the CF and integrated into the DT. The data incorporated in the DT, combined with the FBM, which records the current state of the angle grinder, serves as input for the SRM during deployment. The SRM must account for the impact of varying reprocessing strategies on multi-state system and subsystem reliability, as different recombination or remanufacturing approaches for components affect their instance-specific functional behavior over time. Consequently, a key output of the SRM is the multi-state system and subsystem reliability prediction under diverse reprocessing strategies, as exemplified by three different strategies in Figure 4. The blue cube in Figure 4 part (d) is the ITS based on the current condition described by the FBM. As performance degrades over time, it is necessary to establish tolerance boundaries, as seen in Figure 4 (d), as the red cube, to ensure the tool continues to meet the required functional behavior throughout its lifecycle. This reliability-related ITS, aligned with the functional requirements defined by the FBM, is another critical output of the SRM. Figure 4, part (d) by the green dot, symbolizes an exemplary instance of fulfilling the requirements. Both outputs, the instance-specific reliability prediction, and the reliability-related ITS, inform the R-strategies for optimizing component reuse while maintaining functionality.

Model integration for decision-making

The decision-making process relies on the reliability-related ITS, which integrates FBM and SRM outputs within the DT to guide remanufacturing decisions. The process begins at the inspection station by evaluating whether components meet baseline functional requirements. If not, the FBM guides the disassembly and geometrical measurements on the subsystem and component levels. Therefore, the FBM guarantees that the SRM receives all relevant information to assess performance over time. All the gathered data is passed to the DT, feeding the DT representation in Figure 5. The DT dynamically updates component attributes using Bayesian techniques by combining prior knowledge and real-time evidence [24].

Figure 5

Framework of the DDDM in the CF leveraging DT and the integration of FBM and SRM for the R-strategies

Furthermore, the FBM determines the system’s performance based on its current condition and passes it on to the SRM. This performance can be expressed both in the form of a performance metric focusing on the behavior or in the form of an ITS, concentrating on the structure. An initial statement regarding the possible end-of-life strategies can be derived based on the comparison between the current performance and its target condition. Depending on the possible combinations and reprocessing strategies, the SRM predicts the instance-specific system reliability. The varying performance predictions enable the DT to dynamically decide on further reprocessing within the CF. Compared to the FBM, a reliability-related ITS further refined the manufacturing tolerances to incorporate the degradation over time. This ensures that decisions regarding reuse, repair, or disassembly are based on precise, data-driven insights.

Bayesian fusion methods on Gaussian Mixture Models (GMMs), which can represent complex uncertainties inherent to the products in the CFs, further refine these insights, enabling accurate decisions on component compatibility (Eq. 1). Where P(a) represents the prior knowledge about the attributes, P(a|I) is the likelihood function of the evidence, derived from measurements. The normalization factor P(a) is negligible as it adds no information to I. Bayesian fusion updates prior knowledge by combining it with the likelihood function as new evidence is being updated in the DT. After this update, the ITS is used as a benchmark for decision-making regarding the actual posterior knowledge in the DT. Figure 5 illustrates how FBMs and SRMs interact within the DT to ensure reprocessed components meet functional and reliability standards.

(1) P ( I ) = P ( I ) P ( I ) P ( a )

Discussion

The proposed DDDM framework leverages DT technology, particularly instance-specific handling, to address the challenges of reprocessing used returned products with uncertainties, ensuring that each product‘s unique condition is thoroughly considered. By integrating FBMs and SRMs, the framework enables precise, data-driven recombination decisions aligned with market standards. The DT aggregates real-time data, supports scenario simulations, and optimizes resource utilization in CFs. The FBM evaluates the functional state of components, facilitating targeted disassembly and adjustments to meet performance metrics. It combines implicit expert knowledge with measurable parameters, and its bidirectional approach between EFRs and historical data allows iterative refinement of parameters, driving the development of ITS. The SRM complements this by providing predictive insights into system and subsystem reliability under varying conditions, with reliability-related ITS further refining decision-making by balancing structural tolerances against degradation over time. Additionally, Bayesian fusion techniques enhance the framework’s ability to address uncertainties, enabling the DT to update prior knowledge dynamically and improve decision accuracy, ensuring alignment with evolving performance and reliability conditions.

However, the framework faces several challenges and limitations. Experimental validation is lacking, which limits the demonstration of its real-world effectiveness. The methodology for setting ITS boundaries in the FBM and SRM remains unclear, as does selecting appropriate reliability metrics to evaluate performance for diverse components and recombination strategies. DT implementation is further constrained by the high data acquisition costs and computational demands for real-time integration, posing scalability and broader adoption challenges. Additionally, the focus on the three core components, FBM, SRM, and DT, overlooks other critical aspects of CFs, such as inspection processes, material considerations, manufacturing stations, and factory planning, which are essential for a fully integrated circular factory.

Future work should focus on experimental validation to establish the framework’s practical effectiveness and refine methodologies for defining ITS boundaries and selecting reliability metrics for performance evaluation. Expanding the framework to incorporate additional elements of CFs, such as inspection and material handling processes, could enable a more comprehensive and holistic approach to sustainable manufacturing.

Conclusion

This paper addresses the challenge of reprocessing returned products with unknown conditions within a CF, driven by the need for sustainable resource use aligning with circular economy principles. The proposed framework integrates FBM, SRM, and DT by leveraging DT to enable DDDM across product generations. The FBM quantifies performance metrics, while the SRM predicts reliability and informs tolerance schemes, both dynamically interacting with the DT to guide reprocessing decisions on component disassembly, reuse, repair, or recombination. The DT is a central data hub, aggregating various data to support scenario evaluations. The results demonstrated through an angle grinder case study highlight the framework‘s ability to ensure functionality and reliability standards for primary market applications and reduce waste. Despite its strengths, it faces challenges such as high-quality data acquisition, computational demands, and the need for experimental validation. Future work should address these limitations and explore integrating additional factory elements to enable a more comprehensive and scalable approach.