DARPA<\/a> in 2017 to describe methods for automatically explaining AI models. These approaches either aim to explain the model as a whole or replace it with a more comprehensible surrogate model [10]. XAI techniques are increasingly being applied in the Industry 4.0 domain [11, 12].<\/p>\n\n\n\nArchitecture of AI-based digital twins<\/h2>\n\n\n\n The core element of the AI-based digital twin is a novel, self-learning engineering model. It begins with a product and production model that represents function, behavior, and product geometry. Graph-based design languages, such as the Unified Modeling Language [13, 14] and the Design Cockpit 43 [15] (Figure 1, top), are employed. This approach integrates semantic modeling into the product and production models, enabling the ontological classification of terms and entities within the broader domain context and mapping their relationships and interdependencies.<\/p>\n\n\n\n
In contrast to traditional product and production models, the semantically rich model not only acts as an expressive input for artificial intelligence and machine learning processes but also serves as a repository for the knowledge gained through AI regarding cause-and-effect relationships and influencing factors (Figure 1, right). The semantically rich model, as a vital component of the architecture, is technically implemented as a knowledge graph, modeled using the Web Ontology Language (OWL) and stored in the graph-based database GraphDB (Figure 1, middle). This knowledge graph functions as the central knowledge base for all information relevant to or generated for AI-based digital twins.<\/p>\n\n\n\n
This framework is well-suited for the integrated, life cycle spanning representation of cross-domain product and process data across areas such as function, behavior, structure, and geometry. By utilizing sensors and actuators (for example, integrated through a production planning and control system), performance and execution data from the production process are collected and semantically annotated, linking them to the product and production model. AI techniques from the field of machine learning are then applied to analyze this data using the semantic model, generating insights into causal relationships and process patterns in the form of AI models.<\/p>\n\n\n\n
These insights are then integrated into the overall model as part of a self-learning digital twin and serve as input for simulating production processes. Utilizing techniques from eXplainable AI (XAI), an automatic explanation and description of the AI models is generated, such as characterizing influential features or applying layer wise relevance propagation. The simulation of system behavior, along with the explanation of the underlying AI models, forms the interface of the digital twins for the end user, such as a production manager or employee.<\/p>\n\n\n\n
A key concept of the proposed approach is the decomposition of the overall system into Functional Mockup Units (FMUs) [14, 16], each of which has its own dynamics and behavior. The overall system behavior is then derived from the interaction of all FMUs, which are linked through output\/input relationships.<\/p>\n\n\n\n
This decomposition is already modeled in Design Cockpit 43. A central aspect of the present architecture is the dynamic modeling of the behavior of individual FMUs, not solely through fixed rules or mathematical equations (i.e., classical behavior models), but by automatically learning it from execution and performance data using machine learning (ML) methods. For the FMUs defined in Design Cockpit 43, corresponding ML models can be trained and stored in the knowledge graph for further use.<\/p>\n\n\n\n
All relevant aspects of the product and production models, i.e., the FMU definitions and the product and production geometries, as well as the ML models and explanations in addition to the classic simulation and behavioral models, are transferred to the co-simulation based on INTO-CPS (Integrated Tool Chain for Model-based Design of Cyber-Physical Systems) [16]. When simulating system behavior, it is possible to use different ML models to calculate the FMU output or to provide explanations for the output calculated based on the ML model. Figure 1 shows the overall architecture of the digital twin with all components and their interaction.<\/p>\n\n\n\nFigure\u00a01: Architecture of the AI-based digital twin.<\/em><\/figcaption><\/figure>\n\n\n\nValidation using a FESTO laboratory system<\/h2>\n\n\n\n In this study, a FESTO laboratory system is utilized as a specific application for the exemplary implementation and validation. Figure 2 (top) illustrates the various modules of the FESTO laboratory system. Following the co-simulation concept outlined earlier, the system modules are first decomposed into individual Functional Mockup Units (FMUs), and their output-input interactions are defined (Figure 2).<\/p>\n\n\n\nFigure\u00a02: FESTO laboratory system with Functional Mockup Units (FMUs).<\/em><\/figcaption><\/figure>\n\n\n\nValidation is demonstrated using the Functional Mockup Unit (FMU) component slide in the \u201ctesting\u201d module as a case study. To validate the concept of the ML-based, self-learning digital twin, relevant input parameters for the successful sliding process were defined for the FMU component slide, including factors such as air pressure in the slide, component weight, and the curvature of the component’s underside. The output of the FMU is the time required for the sliding process and the success of the process itself.<\/p>\n\n\n\n
To validate the approach, all components of the architecture for the component slide application were implemented prototypically. Execution data was generated through test runs, system behavior was learned from this data, and ultimately, the system behavior was simulated in the co-simulation framework as part of the digital twin.<\/p>\n\n\n\n
Figure 3 (left) shows a surrogate model (i.e. a substitute model for explaining arbitrary black box models such as artificial neural networks) in the form of a decision tree, which represents the learned system behavior of the component slide based on the execution data created.<\/p>\n\n\n\n
Figure 3 (right) illustrates a section of the graphical simulation of the digital twin with the FMU component slide. The decision tree serves as the basis for simulating the system\u2019s behavior, which can thus be predicted and simulated for different input parameters.<\/p>\n\n\n\nFigure\u00a03: Decision tree and graphical simulation for the functional mockup unit component slide.<\/em><\/figcaption><\/figure>\n\n\n\nThe FESTO laboratory system replicates an entire production process, comprising numerous production steps and processing operations. This makes it particularly well-suited for validating the co-simulation concept, where the overall process is decomposed into sub-units known as Functional Mockup Units (FMUs). Additionally, each module of the system is managed and monitored by a programmable logic controller (PLC). The generated execution and performance data are therefore representative of real-world systems.<\/p>\n\n\n\n
The proposed co-simulation approach enables not only the detailed modeling of individual FMUs\u2014either through mathematical\/physical models or AI-based approaches\u2014but also the representation of complex concurrent processes. However, it should be noted that, in the scope of this validation, FMUs were only linked sequentially. The modeling of complex, concurrent interactions between FMUs using AI was not within the focus of this study.<\/p>\n\n\n\n
A novel approach to AI-based, self-learning digital twins<\/h2>\n\n\n\n This AI-driven approach replaces traditional physical or mathematical simulations of Functional Mockup Units (FMUs) with machine learning models, eliminating the need for extensive parameter determination. By incorporating techniques from eXplainable AI (XAI), the methodology enhances the interpretability and explainability of ML models. The introduction of a semantically rich model as a core architectural component extends conventional product and production data models, enabling the structured representation of knowledge and relationships.<\/p>\n\n\n\n
This model serves both as an input for AI-driven analysis and as a repository for the insights generated through ML and XAI methods. The proposed approach was prototypically implemented and validated using a FESTO laboratory system. Selected system stations were modeled, analyzed, and simulated as Functional Mockup Units (FMUs), enabling the verification of both individual components and the overall architecture. This validation demonstrated the feasibility of AI-based self-learning digital twins and confirmed the functionality of the co-simulation framework.<\/p>\n\n\n\n
The next steps in the ongoing research include the integration of additional eXplainable AI (XAI) techniques, with a particular focus on natural language descriptions of machine learning models using large language models (LLMs) and retrieval-augmented generation (RAG) [17]. Furthermore, the overall approach will be tested on a real production plant to assess its scalability and practical applicability. Another promising direction involves leveraging synthetic simulation data generated from process models in Design Cockpit 43 to further enhance model training and validation.<\/p>\n\n\n\n
This article was written as part of the project \u201cKIDZ – AI-based digital twin\u201d, funded by the Carl Zeiss Foundation in the funding program \u201cAI breakthroughs\u201d.<\/em><\/p>\n
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