Design Theory and Similarity Mechanics

The research area design theory and similarity mechanics at the Institute of Aircraft Design deals with the digitization and automation of complex design tasks.

Design languages for design automation

Graph-based design languages map terms (i.e. the "vocabulary") and assembly knowledge (i.e. the "rules") into recombineable language building blocks and operations. In the information representation of a design language, the nodes of a graph serve as abstract placeholders (i.e. as models) for real objects or processes. Thus a graph representation ("design graph") is machine-processed in place of the product design. This machine processing expands and modifies the graph dynamically at runtime by so-called "model-to-model transformations" (M2M). The abstract product representation allows a simple modularization and scalability and allows the consistent integration of different disciplinary domain models (see figure below). The coupling of the framework to domain-specific software systems is essential in order to integrate the existing knowledge and subprocesses. The couplings are implemented as interfaces that generate domain-specific models in the target format (DSL) from the abstract graph representation ("model-to-text transformations" (M2T)). There are already interfaces for geometry (CAD), multi-body systems (MBS), finite elements (FEM), flow analysis (CFD), etc. (see figure below).

Design analysis and evaluation

Using Buckingham's Pi theorem it is possible to transform a physical relationship of n dimensioned variables into a dimensionless description with only m = n - g dimensionless variables. Where g stands for the number of basic variables used. This knowledge can also be transferred to drafts - which can also be described by dimensioned variables - and reinterpreted as evaluation.

Every minimal description in the sense of the Pi theorem is an evaluation.

Schema der Entwurfsanalyse und -bewertung

Digital factory

In addition to a multitude of boundary conditions, a product has a significant influence on the associated (digital) factory. The information already provided by a product created with graph-based design languages can be further processed automatically and used to generate suitable production sites. The aim is to be able to automatically design an optimal factory (in terms of costs, energy, time, etc.). This concerns the resources used as well as the manufacturing processes. In addition, the "Pi Group" is also concerned with the question of the optimal factory layout.

Image: ZAFH Project DiP

Automated cable routing and piping

An essential step in the design of complex products is cabling and piping. The "Pi-Group" researches algorithms for automated cable and pipe routing, as well as the physical simulation of cables and pipes for installation simulations and other applications.

Image: IILS mbH
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Projects

The Center for Applied Research "Digital Product Lifecycle" (DiP) transfers the extremely powerful approaches of hardware and software development (e.g. the Unified Modellig Language UML) and adapts them to wide areas of mechanical engineering and automotive engineering. The aim is to integrate the entire product life cycle with all relevant product, process and resource-related data into a digital overall model and to provide the necessary processes, methods, tools and libraries.

Digital modelling of the product life cycle of a car bonnet

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Homepage Digital Product Lifecycle

The overall IDEaliSM aim can be divided into three main-objectives:

  • An advanced integration framework for distributed multidisciplinary design and optimization enabling Competence Centres to offer and share engineering services and to collaborate in Distributed Development Teams.
  • An Engineering Language Workbench: a set of domain specific and high-level modelling languages, ontologies and data standards to enable flexible configuration of engineering workflows and services and enable straightforward integration into distributed the advanced integration framework.
  • A methodology for service-oriented development processes to redefine the product development process and information architecture to enable collaboration between service-oriented Competence Centers in Distributed Development Teams.

The resulting development framework will support European industries to enhance their level of integration and flexibility in product development to reduce the effort, cost and time-to-market in designing innovative aircraft and automotive structures and systems. As such, IDEaliSM fits well within the ‘Engineering Technology’ field identified in the ITEA2 research roadmap and the challenges within the Systems Engineering and Software Engineering domains.

Homepage Project IDEaliSM

Publications

All publications by year of publication

  1. 2025

    1. Heimbach, S., & Rudolph, S. (2025). Automatic Evaluation and Partitioning of Algorithms for Heterogeneous Systems. Proceedings of the 13th International Conference on Model-Based Software and Systems Engineering, 177–185. https://doi.org/10.5220/0013153700003896
    2. Schuchter, T., Saft, P., Stetter, R., Pfeil, M., Höpken, W., Till, M., & Rudolph, S. (2025). Application of artificial intelligence in model-based systems engineering of automated production systems. Procedia CIRP, 136, 61–66. https://doi.org/10.1016/j.procir.2025.08.013
    3. Borowski, J., & Rudolph, S. (2025). Automation and Optimization of the Design and Development Process for a Formula Student Racing Car Suspension. In J. Borowski & S. Rudolph (Eds.), SAE Technical Paper Series. SAE International400 Commonwealth Drive, Warrendale, PA, United States. https://doi.org/10.4271/2025-01-0270
    4. Neumaier, M., Anselment, M., & Rudolph, S. (2025). Validation of a Machine Learning Model for Certification Using Symbolic Regression and a Behaviour Envelope. Aerospace, 12, Article 5. https://doi.org/10.3390/aerospace12050412
    5. Braiger, J., Baur, J., Gugliuzza, J., Rudolph, S., Carosella, S., & Middendorf, P. (2025). Design Automation of Fibre Composite Parts via Graph-Based Design Languages. In D. Holder, F. Wulle, & J. Lind (Eds.), Advances in Automotive Production Technology -- Digital Product Development and Manufacturing (pp. 344–352). Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-88831-127
    6. Anselment, M., Neumaier, M., & Rudolph, S. (2025). Systematic tree search for symbolic regression: deterministically searching the space of dimensionally homogeneous models. CEAS Aeronautical Journal. https://doi.org/10.1007/s13272-025-00886-3
    7. Schuchter, T., Till, M., Stetter, R., & Rudolph, S. (2025). Digital Integrated Design and Assembly Planning Processes for Sports Vehicles Using the Example of a Skateboard. Vehicles, 7, Article 1. https://doi.org/10.3390/vehicles7010022

  2. 2024

    1. Neumaier, M., Schopper, C., Gundlach, T., Gast, C., Döring, D., & Rudolph, S. (2024). Automated packing and piping in an Airbus A320 main landing gear bay: an industrial development case study. CEAS Aeronautical Journal, 15, Article 4. https://doi.org/10.1007/s13272-024-00765-3
    2. Grüble, T., Stetter, R., Schuchter, T., Till, M., & Rudolph, S. (2024). Combined Geometric and Kinetic Data Model in Model-Based Systems Engineering of Robotic Cells. Procedia CIRP, 128, 156–161. https://doi.org/10.1016/j.procir.2024.03.005
    3. Saft, P., Pfeil, M., Stetter, R., Till, M., & Rudolph, S. (2024). Integration of geometry modelling and behavior simulation based on graph-based design languages and functional mockup units. Procedia CIRP, 128, 310–315. https://doi.org/10.1016/j.procir.2024.06.025
    4. Schumacher, S., Stetter, R., Till, M., Laviolette, N., Algret, B., & Rudolph, S. (2024). Simulation-Based Prediction of the Cold Start Behavior of Gerotor Pumps for Precise Design of Electric Oil Pumps. Applied Sciences, 14, Article 15. https://doi.org/10.3390/app14156723
    5. Neumaier, M., Kranemann, S., Kazmeier, B., & Rudolph, S. (2024). Automated pipe design in 3D using a multi-objective toolchain for efficient decision-making. Journal of Computational Design and Engineering, 11, Article 5. https://doi.org/10.1093/jcde/qwae070
    6. Rudolph, S. (2024). On Some Artificial Intelligence Methods in the V-Model of Model-Based Systems Engineering. Proceedings of the 12th International Conference on Model-Based Software and Systems Engineering, 386–393. https://doi.org/10.5220/0012639700003645

  3. 2023

    1. Margraf, A., Cui, H., Heimbach, S., Hähner, J., Geinitz, S., & Rudolph, S. (2023). Model-Driven Optimisation of Monitoring System Configurations for Batch Production. Proceedings of the 11th International Conference on Model-Based Software and Systems Engineering, 176–183. https://doi.org/10.5220/0011688900003402
    2. Grüble, T., Stetter, R., Schuchter, T., Till, M., & Rudolph, S. (2023). Graph-based Design Languages for the Development of a Robotic Cell with Compliant Grippers. Europe ISR 2023 - International Symposium on Robotics, Proceedings. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85184350585&partnerID=40&md5=66b913cac7ecb7d62784b0818df0661b
    3. Voss, C., Petzold, F., & Rudolph, S. (2023). Graph transformation in engineering design: an overview of the last decade. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 37. https://doi.org/10.1017/S089006042200018X

  4. 2022

    1. Neumaier, M., Kranemann, S., Kazmeier, B., & Rudolph, S. (2022). Automated Piping in an Airbus A320 Landing Gear Bay Using Graph-Based Design Languages. Aerospace, 9, Article 3. https://doi.org/10.3390/aerospace9030140
    2. Voss, C., Petzold, F., & Rudolph, S. (2022). Connecting Building Design with the Digital Factory by Design Languages to Explore Different Solutions. Journal of Integrated Design and Process Science, 24, Article 3–4. https://doi.org/10.3233/JID200019
    3. Elwert, M., Ramsaier, M., Eisenbart, B., Stetter, R., Till, M., & Rudolph, S. (2022). Digital Function Modeling in Graph-Based Design Languages. Applied Sciences, 12, Article 11. https://doi.org/10.3390/app12115301

  5. 2021

    1. Schopper, D., Kübler, K., Rudolph, S., & Riedel, O. (2021). EIPPM---The Executable Integrative Product-Production Model. Computers, 10, Article 6. https://doi.org/10.3390/computers10060072
    2. Holder, K., Schumacher, S., Friedrich, M., Till, M., Stetter, R., Fichter, W., & Rudolph, S. (2021). Digital Development Process for the Drive System of a Balanced Two-Wheel Scooter. Vehicles, 3, Article 1. https://doi.org/10.3390/vehicles3010003

  6. 2020

    1. Ramsaier, M., Breckle, T., Rudolph, S., & Schumacher, A. (2020). Automated evaluation of manufacturability and cost of steel tube constructions with graph-based design languages. Procedia CIRP, 88, 485–490. https://doi.org/10.1016/j.procir.2020.05.084
    2. Kübler, K., Schopper, D., Riedel, O., & Rudolph, S. (2020). Towards an Automated Product-Production System Design - Combining Simulation-based Engineering and Graph-based Design Languages. Procedia Manufacturing, 52, 258–265. https://doi.org/10.1016/j.promfg.2020.11.043
    3. Schopper, D., Tonhäuser, Claudia, & Rudolph, S. (2020, October). A User-friendly Assembly Planning Tool for Assembly Sequence Optimization.
    4. Borowski, J., Stetter, R., & Rudolph, S. (2020). Design, Dimensioning and Simulation of Inerters for the Reduction of Vehicle Wheel Vibrations---Case Studies. Vehicles, 2, Article 3. https://doi.org/10.3390/vehicles2030023

  7. 2019

    1. Zech, A., Stetter, R., Holder, K., Rudolph, S., & Till, M. (2019). Novel approach for a holistic and completely digital represented product development process by using graph-based design languages. Procedia CIRP, 79, 568–573. https://doi.org/10.1016/j.procir.2019.02.102
    2. Walter, B., Kaiser, D., & Rudolph, S. (2019). From Manual to Machine-executable Model-based Systems Engineering via Graph-based Design Languages. Proceedings of the 7th International Conference on Model-Driven Engineering and Software Development, 203–210. https://doi.org/10.5220/0007236702030210
    3. Walter, B., Martin, J., Schmidt, J., Dettki, H., & Rudolph, S. (2019). Executable State Machines Derived from Structured Textual Requirements - Connecting Requirements and Formal System Design. Proceedings of the 7th International Conference on Model-Driven Engineering and Software Development, 195–202. https://doi.org/10.5220/0007236601950202
    4. Holder, K., Rudolph, S., Stetter, R., & Salander, C. (2019). Automated requirements-driven design synthesis of gearboxes with graph-based design languages using state of the art tools. Forschung Im Ingenieurwesen, 83, Article 3. https://doi.org/10.1007/s10010-019-00322-z

  8. 2018

    1. Walter, B., Schilling, M., Piechotta, M., & Rudolph, S. (2018). Improving Test Execution Efficiency Through Clustering and Reordering of Independent Test Steps. 2018 IEEE 11th International Conference on Software Testing, Verification and Validation (ICST), 363–373. https://doi.org/10.1109/ICST.2018.00043
    2. Beisheim, N., Kiesel, M., & Rudolph, S. (2018). Digital Manufacturing and Virtual Commissioning of Intelligent Factories and Industry 4.0 Systems Using Graph-Based Design Languages. In Transdisciplinary Engineering Methods for Social Innovation of Industry 4.0. IOS Press. https://doi.org/10.3233/978-1-61499-898-3-93
    3. Wünsch, F., Ramsaier, M., Breckle, T., Stetter, R., Till, M., & Rudolph, S. (2018). EXECUTABLE COST-SENSITIVE PRODUCT DEVELOPMENT OF A SELF-BALANCING TWO-WHEEL SCOOTER WITH GRAPH-BASED DESIGN LANGUAGES. Proceedings of the DESIGN 2018 15th International Design Conference, 1769–1780. https://doi.org/10.21278/idc.2018.0409

  9. 2017

    1. Kiesel, M., Klimant, P., Beisheim, N., Rudolph, S., & Putz, M. (2017). Using Graph-based Design Languages to Enhance the Creation of Virtual Commissioning Models. Procedia CIRP, 60, 279–283. https://doi.org/10.1016/j.procir.2017.01.047
    2. Holder, K., Zech, A., Ramsaier, M., Stetter, R., Niedermeier, H.-P., Rudolph, S., & Till, M. (2017). Model-Based Requirements Management in Gear Systems Design Based On Graph-Based Design Languages. Applied Sciences, 7, Article 11. https://doi.org/10.3390/app7111112
    3. Vogel, S., & Rudolph, S. (2017). Automated Piping with Standardized Bends in Complex Systems Design. In G. Fanmuy, E. Goubault, D. Krob, & F. Stephan (Eds.), Complex Systems Design & Management (pp. 113–124). Springer International Publishing. https://doi.org/10.1007/978-3-319-49103-59
    4. Ramsaier, M., Spindler, C., Stetter, R., Rudolph, S., & Till, M. (2017). Digital Representation in Multicopter Design Along the Product Life-cycle. Procedia CIRP, 62, 559–564. https://doi.org/10.1016/j.procir.2016.06.008
    5. Walter, B., Hammes, J., Piechotta, M., & Rudolph, S. (2017). A Formalization Method to Process Structured Natural Language to Logic Expressions to Detect Redundant Specification and Test Statements. 2017 IEEE 25th International Requirements Engineering Conference (RE), 263–272. https://doi.org/10.1109/RE.2017.38

  10. 2016

    1. Gross, J., & Rudolph, S. (2016). Modeling graph-based satellite design languages. Aerospace Science and Technology, 49, 63–72. https://doi.org/10.1016/j.ast.2015.11.026
    2. Gross, J., & Rudolph, S. (2016). Rule-based spacecraft design space exploration and sensitivity analysis. Aerospace Science and Technology, 59, 162–171. https://doi.org/10.1016/j.ast.2016.10.007
    3. Gross, J., & Rudolph, S. (2016). Geometry and simulation modeling in design languages. Aerospace Science and Technology, 54, 183–191. https://doi.org/10.1016/j.ast.2016.03.003
    4. Schmidt, J., & Rudolph, S. (2016). Graph-Based Design Languages: A Lingua Franca for Product Design Including Abstract Geometry. IEEE Computer Graphics and Applications, 36, Article 5. https://doi.org/10.1109/MCG.2016.89

  11. 2014

    1. Schmidt, J., & Rudolph, S. (2014). Gaining system design knowledge by systematic design space exploration with graph based design languages. 390–393. https://doi.org/10.1063/1.4897755

  12. 2012

    1. Rudolph, S., Heisserman, J., & Culley, S. (2012). Design Computing and Cognition (DCC′10). Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 26, Article 2. https://doi.org/10.1017/S0890060412000017

  13. 2009

    1. Rudolph, S. (2009). Mathematical Foundations of Non-Classical Extensions of Similarity Theory. In G. M. L. Gladwell, R. Moreau, J. Engelbrecht, L. B. Freund, A. Kluwick, H. K. Moffatt, N. Olhoff, K. Tsutomu, D. van Campen, Z. Zheng, & F. M. Borodich (Eds.), IUTAM Symposium on Scaling in Solid Mechanics (Vol. 10, pp. 27–35). Springer Netherlands. https://doi.org/10.1007/978-1-4020-9033-2_3
    2. Böhnke, D., Reichwein, A., & Rudolph, S. (2009). Design Language for Airplane Geometries Using the Unified Modeling Language. Volume 5: 35th Design Automation Conference, Parts A and B, 661–670. https://doi.org/10.1115/DETC2009-87368
    3. Gross, J., Reichwein, A., Bock, D., Laufer, R., & Rudolph, S. (2009). An Executable Unified Product Model Based on UML to Support Satellite Design. AIAA SPACE 2009 Conference & Exposition. https://doi.org/10.2514/6.2009-6642

  14. 2008

    1. Kormeier, T., & Rudolph, S. (2008). On Pattern Recognition in Rule-Based Topology Modification. Volume 1: 34th Design Automation Conference, Parts A and B, 1185–1193. https://doi.org/10.1115/DETC2008-49394

  15. 2007

    1. Haq, M., & Rudolph, S. (2007). A design language for generic space-frame structure design. International Journal of Computer Applications in Technology, 30, Article 1/2. https://doi.org/10.1504/IJCAT.2007.015699

  16. 2006

    1. Rudolph, S. (2006). A SEMANTIC VALIDATION SCHEME FOR GRAPH-BASED ENGINEERING DESIGN GRAMMARS. In J. S. GERO (Ed.), Design Computing and Cognition ’06 (pp. 541–560). Springer Netherlands. https://doi.org/10.1007/978-1-4020-5131-928
    2. Kormeier, T., & Rudolph, S. (2006). Topological Synthesis of Shell Structures. Volume 1: 32nd Design Automation Conference, Parts A and B, 13–22. https://doi.org/10.1115/detc2006-99092
    3. Werner, J., & Rudolph, S. (2006). Material Flow Simulation Using Design Languages. Volume 4a: 18th International Conference on Design Theory and Methodology, 337–344. https://doi.org/10.1115/detc2006-99434

  17. 2005

    1. Schaefer, J., & Rudolph, S. (2005). Satellite design by design grammars. Aerospace Science and Technology, 9, Article 1. https://doi.org/10.1016/j.ast.2004.08.003
    2. Kormeier, T., & Rudolph, S. (2005). On Self-Similarity as a Design Paradigm. Volume 5a: 17th International Conference on Design Theory and Methodology, 507–516. https://doi.org/10.1115/detc2005-84167

  18. 2004

    1. Rudolph, S., & Bölling, M. (2004). Constraint-based conceptual design and automated sensitivity analysis for airship concept studies. Aerospace Science and Technology, 8, Article 4. https://doi.org/10.1016/j.ast.2004.03.001
    2. Alber, R., & Rudolph, S. (2004). On a Grammar-Based Design Language That Supports Automated Design Generation and Creativity. In J. C. Borg, P. J. Farrugia, & K. P. Camilleri (Eds.), Knowledge Intensive Design Technology (pp. 19–35). Springer US. https://doi.org/10.1007/978-0-387-35708-92
    3. Gläßel, H., Zimmermann, F., Brückner, S., Schöttle, U. M., & Rudolph, S. (2004). Adaptive neural control of the deployment procedure for tether-assisted re-entry. Aerospace Science and Technology, 8, Article 1. https://doi.org/10.1016/j.ast.2003.08.007

  19. 2003

    1. Melan, A., & Rudolph, S. (2003). Deriving dimensionless features for color object recognition in different color models. In I. Kadar (Ed.), Signal Processing, Sensor Fusion, and Target Recognition XII (pp. 562–573). SPIE. https://doi.org/10.1117/12.487055
    2. Brueckner, S., & Rudolph, S. (2003). Knowledge discovery in engineering dynamic system analysis. In B. V. Dasarathy (Ed.), Data Mining and Knowledge Discovery: Theory, Tools, and Technology V (pp. 185–192). SPIE. https://doi.org/10.1117/12.487158

  20. 2002

    1. Melan, A., & Rudolph, S. (2002). Dimensionless color features. In I. Kadar (Ed.), Signal Processing, Sensor Fusion, and Target Recognition XI (pp. 374–383). SPIE. https://doi.org/10.1117/12.477623
    2. Rudolph, S., & Brueckner, S. (2002). Interdependencies in data preprocessing, training methods, and neural network topology generation. In K. L. Priddy, P. E. Keller, & P. J. Angeline (Eds.), Applications and Science of Computational Intelligence V (pp. 98–107). SPIE. https://doi.org/10.1117/12.458702
    3. Brueckner, S., & Rudolph, S. (2002). Aspects of knowledge discovery in technical data. In B. V. Dasarathy (Ed.), Data Mining and Knowledge Discovery: Theory, Tools, and Technology IV (pp. 109–117). SPIE. https://doi.org/10.1117/12.460218
    4. Barrios, L. J., & Rudolph, S. (2002). Knowledge discovery process for scientific and engineering data. In B. V. Dasarathy (Ed.), Data Mining and Knowledge Discovery: Theory, Tools, and Technology IV (pp. 118–125). SPIE. https://doi.org/10.1117/12.460219

  21. 2001

    1. Till, M., & Rudolph, S. (2001). Optimized time-frequency distributions for acoustic signal classification. In H. H. Szu, D. L. Donoho, A. W. Lohmann, W. J. Campbell, & J. R. Buss (Eds.), Wavelet Applications VIII (pp. 81–91). SPIE. https://doi.org/10.1117/12.421187
    2. Melan, A., & Rudolph, S. (2001). Contrast-invariant dimensionless features. In I. Kadar (Ed.), Signal Processing, Sensor Fusion, and Target Recognition X (pp. 531–541). SPIE. https://doi.org/10.1117/12.436981
    3. Glaessel, H., Kloeppel, V., & Rudolph, S. (2001). Neural control of helicopter blade-vortex interaction noise. In A.-M. R. McGowan (Ed.), Smart Structures and Materials 2001: Industrial and Commercial Applications of Smart Structures Technologies (pp. 460–470). SPIE. https://doi.org/10.1117/12.429687
    4. Haecker, J., & Rudolph, S. (2001). Neural network topology design for nonlinear control. In K. L. Priddy, P. E. Keller, & P. J. Angeline (Eds.), Applications and Science of Computational Intelligence IV (pp. 214–223). SPIE. https://doi.org/10.1117/12.421173
    5. Brueckner, S., & Rudolph, S. (2001). Knowledge discovery in scientific data using hierarchical modeling in dimensional analysis. In B. V. Dasarathy (Ed.), Data Mining and Knowledge Discovery: Theory, Tools, and Technology III (pp. 208–217). SPIE. https://doi.org/10.1117/12.421075

  22. 2000

    1. Rudolph, S. (2000). Visualization and Comparison of Solution Paths With Artificial Metrics. Volume 2: 26th Design Automation Conference, 1051–1060. https://doi.org/10.1115/DETC2000/DAC-14487

  23. 1999

    1. Yusan, H., & Rudolph, S. (1999). A Study of Constraint Management Integration Into the Conceptual Design Phase. Volume 1: 25th Design Automation Conference, 157–167. https://doi.org/10.1115/DETC99/DAC-8680

  24. 1997

    1. Rudolph, S. (1997). On a Case-Based Reasoning Technique Based on Similarity Methods and its Use in Engineering Design. Volume 3: 9th International Design Theory and Methodology Conference. https://doi.org/10.1115/DETC97/DTM-4125

  25. 1996

    1. Rudolph, S. (1996). On a Mathematical Foundation of Axiomatic Design. Volume 4: 8th International Conference on Design Theory and Methodology. https://doi.org/10.1115/96-DETC/DTM-1530
    2. Rudolph, S. (1996). Upper and lower limits for `the principles of design’. Research in Engineering Design, 8, Article 4. https://doi.org/10.1007/BF01597227

Group members

This image showsStephan Rudolph

Stephan Rudolph

PD Dr.-Ing.

Head of research group "Design Theory and Similarity Mechanics"

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