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Robust and Explainable 3D Mode Shape Recognition Using Region-Aware Graph Neural Networks
Tong Duy Son, Marc Brughmans, Andrey Hense, Kohta Sugiura, Sebastian Ciceo, Paolo di Carlo, Theo Geluk
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Summary
The paper proposes a 'Canonical Engineering Graph Representation' and a region-aware graph learning framework to solve the problem of robust and explainable 3D mode shape recognition in automotive NVH (Noise, Vibration, and Harshness) development. Unlike traditional methods that rely on geometry-dependent finite element (FE) meshes, this approach transforms heterogeneous FE models and experimental measurements into a common semantic graph where nodes represent persistent structural regions (e.g., roof rails, pillars, side sills) and edges represent engineering-informed relationships. This decoupling of engineering semantics from numerical discretization allows for high cross-vehicle transferability and provides physically interpretable explanations by relating predictions directly to structural regions. The framework uses graph attention learning and region-aware pooling to achieve high classification accuracy even under severe label scarcity.
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Relation Signals (4)
Structural Regions → arenodesof → Canonical Engineering Graph Representation
confidence 100% · nodes represent semantically meaningful structural regions connected through engineering-informed relationships.
Graph Attention Network → captures → Structural Interactions
confidence 100% · Graph attention learning captures structural interactions between these regions...
Canonical Engineering Graph Representation → transforms → FE Mesh
confidence 100% · Rather than learning directly from vehicle-specific FE meshes, heterogeneous FE models and experimental measurements are transformed into a common graph...
Canonical Engineering Graph Representation → enables → Cross-vehicle Transferability
confidence 95% · The resulting representation decouples engineering knowledge from numerical discretization, allowing transfer across different vehicle programs...
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Abstract
Abstract:Mode shape recognition is a fundamental task in automotive NVH development, yet it remains dependent on manual visual inspection by experienced engineers. Existing approaches based on engineering heuristics, Modal Assurance Criterion (MAC), or geometry-dependent AI representations often exhibit limited robustness across different vehicle architectures, finite element (FE) meshes, and experimental measurement layouts, restricting their industrial applicability. This paper presents a Canonical Engineering Graph Representation and region-aware graph learning framework for robust and explainable 3D mode shape recognition. Rather than learning directly from vehicle-specific FE meshes, heterogeneous FE models and experimental measurements are transformed into a common graph whose nodes represent semantically meaningful structural regions connected through engineering-informed relationships. Geometry-independent regional descriptors are combined with graph attention learning and region-aware pooling to capture structural interactions while preserving engineering semantics and enabling physically interpretable predictions. The resulting representation decouples engineering knowledge from numerical discretization, allowing transfer across different vehicle programs without requiring identical mesh topology or sensor configurations. The proposed framework is validated using FE and experimental datasets from four vehicle programs under severe label scarcity. Results demonstrate high classification accuracy, cross-vehicle transferability, and physically meaningful explanations by directly relating predictions to engineering-defined structural regions used in NVH analysis. Beyond mode shape recognition, the proposed Canonical Engineering Graph Representation provides a reusable engineering abstraction for trustworthy and transferable AI across heterogeneous simulation and experimental workflows.
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- Source: https://arxiv.org/abs/2607.01522v1
- Canonical: https://arxiv.org/abs/2607.01522v1
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Robust and Explainable 3D Mode Shape Recognition Using Region-Aware Graph Neural Networks Tong Duy Son 1 , Marc Brughmans 1 , Andrey Hense 1,2 , Kohta Sugiura 3 , Sebastian Ciceo 1 , Paolo di Carlo 1 , Theo Geluk 1 1 Siemens Digital Industries Software, Interleuvenlaan 68, 3001 Leuven, Belgium e-mail: son.tong@siemens.com 2 KU Leuven, Campus Diepenbeek, Department of Mechanical Engineering Wetenschapspark 27, B-3590, Diepenbeek, Belgium 3 Siemens Digital Industries Software, 3-1-9 Shin-Yokohama, Yokohama 222-0033, Japan Abstract Body-in-White (BiW) mode shape recognition is a fundamental task in automotive noise, vibration, and harshness (NVH) development, yet it remains dependent on manual visual inspection by experienced engineers. Existing approaches based on engineering heuristics, Modal Assurance Criterion (MAC), or geometry-dependent AI representations often exhibit limited robustness across different vehicle architec- tures, finite element (FE) meshes, and experimental measurement layouts, restricting their applicability in industrial development. This paper presents a canonical engineering graph representation and region-aware graph learning framework for robust and explainable 3D mode shape recognition. Rather than learning directly from vehicle-specific FE meshes, heterogeneous FE models and experimental measurements are transformed into a common graph whose nodes represent semantically meaningful structural regions connected through engineering-informed relationships. Geometry-independent regional descriptors are combined with graph attention learning and region-aware pooling to capture structural interactions while preserving engineering semantics and enabling physically interpretable predictions.The resulting representation decouples engineering knowledge from numerical discretization, allowing learning to transfer across different vehicle programs without requiring identical mesh topology or sensor configurations. The proposed framework is validated using FE and experimental datasets from four vehicle programs under severe label scarcity. Experimental results demonstrate high classification accuracy, cross-vehicle transfer- ability, and physically meaningful explanations by directly relating model predictions to engineering-defined structural regions used in NVH analysis. Beyond mode shape recognition, the proposed Canonical Engi- neering Graph Representation establishes a reusable engineering abstraction that can support trustworthy and transferable AI across heterogeneous simulation and experimental workflows. 1 Introduction Automotive product development relies heavily on simulation-driven engineering, where computer-aided en- gineering (CAE) and computational fluid dynamics (CFD) are used to evaluate structural, vibro-acoustic, and aerodynamic performance before physical prototypes are finalized. In structural development, finite element (FE) models are widely used to analyze body stiffness, modal behaviour, and noise, vibration, and harshness arXiv:2607.01522v1 [eess.SY] 1 Jul 2026 Full VehicleTrim BodyFE Body-in-WhiteTest Body Data Transferable Across simulation variants and test data Generalizable Usable across historical data and workflows Explainable Results reflect engineering intuition Data Generation Guide additional simulations and labels Classification: Mode Shape Recognition (torsion, bending, pumping, local modes...) ✓From single dataset to large scale variations ✓Fast, Scalable Figure 1: Overview of the proposed Canonical Engineering Graph Representation and region-aware graph learning framework for explainable and transferable Body-in-White mode shape classification. (NVH), while aerodynamic simulations are used to predict drag, pressure distribution, wall shear stress, and flow behaviour around the vehicle [1, 2]. These analyses play a central role in engineering decisions related to body design, structural refinement, aerodynamic efficiency, and overall vehicle performance. Modern vehicle development generates a large volume of digital engineering artifacts throughout the de- sign, simulation, testing, and validation process. These include 3D CAD models, Body-in-White (BiW) and trimmed-body representations, finite element models, CFD meshes, and experimental testing measurements. In practice, these engineering assets are distributed across different software tools, vehicle programs, simula- tion variants, sensor layouts, and development teams. Consequently, valuable engineering knowledge often remains fragmented across heterogeneous engineering representations, making it difficult to reuse historical engineering data and develop AI methods that operate consistently throughout the engineering workflow. Recent advances in artificial intelligence (AI) have created new opportunities to accelerate engineering work- flows by reducing repetitive expert effort and supporting engineering decision making. In structural dynam- ics, AI has been applied to structural interpretation, mode assessment, cross-variant comparison, and data- driven modelling of NVH behaviours [3, 4]. In particular, automatic mode shape classification has attracted increasing interest because engineers routinely inspect hundreds of vibration modes throughout vehicle de- velopment. Despite decades of progress in simulation technology, manual interpretation of modal deforma- tion patterns remains time consuming, subjective, and difficult to scale across multiple vehicle programs and design iterations. Graph neural networks (GNNs) have recently emerged as a promising learning paradigm for 3D engineering AI because they preserve structural relationships while operating on irregular engineering data. Compared with image- or voxel-based representations, graph representations explicitly model structural connectivity and physical interactions, making them particularly well suited to finite element models and other 3D engi- neering simulation models. Existing graph-based methods have demonstrated promising performance across structural mechanics, surrogate modelling, and physics-based simulation [5]. Nevertheless, most existing approaches remain closely coupled to geometry-dependent representations, making their performance sensi- tive to mesh discretization, node layouts, and sensor configurations. As a result, transferring learned models across different vehicle architectures or between simulation and experimental data remains a challenging problem. From an engineering perspective, this limitation reflects a more fundamental challenge. Engineers rarely interpret structural behaviour at the level of individual finite element nodes. Instead, modal assessment is naturally performed using persistent structural entities such as roof rails, pillars, side sills, floor structures, and cross members. While numerical discretizations may vary substantially across vehicle programs, these engineering concepts remain significantly consistent. This observation suggests that transferable engineering AI should learn from engineering semantics rather than geometry-dependent numerical representations. For practical deployment in industrial NVH workflows, four challenges remain particularly important: 1. Transferability: AI models should generalize across different vehicle programs, historical datasets, finite element discretizations, and experimental sensor layouts without requiring extensive vehicle- specific retraining. 2. Limited labelled data: obtaining expert-reviewed mode labels is expensive, making it difficult to construct large annotated datasets. 3. Explainability: predictions should be physically interpretable and consistent with the engineering reasoning used during modal assessment, allowing engineers to understand the structural mechanisms behind each prediction. 4. Industrial practicality: AI methods should integrate throughout the engineering development work- flow by enabling consistent reasoning across heterogeneous engineering representations, including simulation models, experimental measurements, test data, and successive vehicle programs, while re- maining robust under limited annotations. Despite encouraging progress, current graph learning pipelines remain largely vehicle specific because they learn directly from geometry-dependent finite element meshes rather than engineering concepts. Conse- quently, model predictions often provide limited physical insight and are difficult to reuse across different vehicle programs, simulation variants, or experimental measurements. More importantly, relatively little attention has been devoted to developing reusable engineering representations that preserve engineering se- mantics across heterogeneous datasets. To address these challenges, this paper proposes a region-aware graph learning framework built upon a Canonical Engineering Graph Representation for robust and explainable BiW mode shape recognition. Rather than learning directly from geometry-dependent finite element meshes, the proposed approach first constructs a graph representation that transforms heterogeneous engineering models into a common semantic graph composed of engineering-defined structural regions connected through physically meaningful relation- ships. Regional displacement responses are aggregated into geometry-independent node features, enabling structurally consistent representations across different vehicle architectures and sensor layouts. Graph atten- tion learning captures structural interactions between these regions, while a region-aware pooling strategy in- corporates engineering-informed structural descriptors to improve discrimination between physically similar mode families. By separating engineering semantics from numerical discretization, the proposed framework enables transferable graph learning while naturally supporting engineering-oriented interpretation of model predictions. The proposed framework is validated using BiW simulation and experimental datasets from multiple vehi- cle programs. The results demonstrate robust classification performance despite severe label scarcity while maintaining strong transferability across different vehicle architectures, mesh discretizations, and sensor layouts. Furthermore, the semantic graph representation enables physically meaningful explanations by re- lating model predictions directly to structural regions commonly used during engineering review. Although this work focuses on hierarchical mode shape recognition, the proposed canonical engineering graph pro- vides a reusable engineering representation that can support trustworthy and scalable Engineering AI across automotive development workflows. The main contributions of this work are summarized as follows: 1. We propose a canonical engineering graph representation that transforms heterogeneous BiW mod- els into a common semantic space independent of mesh topology and sensor configuration, enabling robust learning across different vehicle architectures, finite element discretizations, and experimental measurement configurations. 2. We develop a region-aware graph learning framework that combines graph attention learning with engineering-informed regional descriptors for explainable hierarchical mode shape classification. 3. We demonstrate robust cross-vehicle transfer using both finite element and experimental datasets under severe label scarcity while providing physically interpretable predictions that can be directly related to meaningful structural regions used in engineering practice. The remainder of this paper is organized as follows. Section 2 reviews related work on CAE mode shape classification and graph learning. Section 3 presents the proposed framework. Section 4 describes the dataset generation. Section 5 presents the experimental results. Finally, Section 6 concludes the paper and discusses future works. 2 Related Work This section reviews previous research most relevant to automatic mode shape recognition and graph rep- resentations for 3D engineering structures. Rather than providing a broad survey of engineering AI, the discussion focuses on developments that directly motivate the proposed Canonical Engineering Graph Rep- resentation and region-aware graph learning framework for explainable Body- in-White (BiW) mode shape classification. 2.1 Automated Mode Shape Recognition Automatic recognition of structural vibration mode shapes has long been an important objective in auto- motive CAE. During vehicle development, engineers routinely inspect finite element (FE) modal results to identify characteristic deformation mechanisms, including torsional, bending, pumping, and local structural modes. These modal characteristics provide essential insight into body stiffness, structural dynamics, and noise, vibration, and harshness (NVH) performance while supporting design optimisation across successive vehicle programs [1, 4]. Despite decades of development in simulation technology, mode classification remains heavily dependent on manual engineering interpretation. Engineers visually compare modal deformation patterns and assign engineering labels based on structural experience. Although reliable, this process is time consuming, subjec- tive, and increasingly difficult to scale when hundreds of vibration modes must be reviewed across multiple design iterations and vehicle variants. Early efforts to automate this task relied primarily on engineering heuristics, Modal Assurance Criterion (MAC), modal parameter estimation, and manually designed structural descriptors extracted from simula- tion results [1]. Classical machine learning methods subsequently improved automation by learning from handcrafted features, but their performance remained closely tied to vehicle-specific preprocessing and fea- ture engineering. More recently, graph-based learning methods have emerged as a promising alternative for structure-aware mode shape recognition, with [3] demonstrating that graph convolutional networks can suc- cessfully classify structural mode shapes directly from engineering representations, highlighting the potential of graph learning for industrial NVH applications. However, several limitations remain. Most existing graph-based approaches are coupled to individual vehicle models, limiting transfer across different vehicle architectures and mesh discretisations. Furthermore, clas- sification accuracy alone provides limited engineering value without interpretable predictions, and compara- tively little attention has been given to developing reusable representations that enable systematic knowledge transfer across vehicle programs. 2.2 Graph Representations and Learning for Engineering Structures Graph neural networks (GNNs) have emerged as an effective learning paradigm for engineering applications because they naturally represent irregular spatial relationships while preserving structural connectivity. Com- pared with regular grids or images, graph representations allow engineering entities to be modelled together with their physical interactions, making them well suited to finite element models, computational meshes, and other simulation-derived engineering data. Several alternative representations have been explored for three-dimensional engineering problems. Voxel and grid-based methods are compatible with convolutional neural networks but often require fine spatial discretisation to preserve geometric fidelity, resulting in high computational and memory costs for large engineering models. Point-based approaches, including PointNet and PointNet++, avoid explicit mesh- ing and have demonstrated strong performance on geometric recognition tasks, but they do not explicitly model structural connectivity or engineering relationships [6]. Graph representations, by contrast, explicitly preserve adjacency, connectivity, and physical interactions through node-edge relationships, making them particularly suitable for structural mechanics and physics-based engineering problems. Recent advances have further extended graph learning through attention mechanisms, graph transformers, physics-informed learning, and mesh-based surrogate modelling, demonstrating promising performance for structural analysis, computational mechanics, and engineering simulation [5, 7, 8, 9]. The success of these methods has established graph learning as an important computational framework for Engineering AI. However, their effectiveness depends not only on the learning architecture but also on how engineering systems are represented as graphs. Different graph construction strategies encode different struc- tural relationships, physical priors, and engineering knowledge, which can significantly influence prediction performance, generalisation capability, transferability, and interpretability. Most existing approaches construct graphs directly from computational meshes, finite element discretisa- tions, or geometric neighbourhoods. Consequently, the graph topology largely reflects numerical discreti- sation rather than the engineering concepts used during product development. Variations in mesh topology, node numbering, element density, or measurement layouts therefore often require adapting the graph repre- sentation, limiting knowledge reuse across different vehicle programs, simulation variants, and experimental measurements. From an engineering perspective, however, structural behaviour is rarely interpreted at the level of individual finite element nodes. Instead, engineers reason using persistent structural entities such as roof rails, pillars, side sills, floor structures, cross members, and longitudinal load paths. These engineering concepts remain largely consistent across different vehicle programs even when the underlying numerical discretisations differ substantially. This observation suggests that transferable Engineering AI should learn from engineering semantics rather than geometry-dependent numerical representations. Existing studies therefore demonstrate the effectiveness of graph learning for engineering applications while leaving the design of reusable engineering representations largely unexplored [2]. This gap motivates the Canonical Engineering Graph Representation proposed in this work, which represents heterogeneous engi- neering models using persistent engineering regions and physically meaningful structural relationships rather than vehicle-specific numerical discretisations. 2.3 Research Gap and Motivation The preceding literature review highlights three remaining challenges that motivate the present work. First, existing graph learning methods generally operate on geometry-dependent representations that remain sensitive to mesh topology, vehicle-specific discretisations, and sensor layouts. This limits their ability to transfer across different vehicle programs without substantial retraining. Second, although recent GNNs achieve encouraging classification performance, their learned representations are typically difficult to inter- pret from an engineering perspective. Attention maps or node importance scores alone do not necessarily correspond to the structural entities that engineers use during modal assessment and design review. Third, Restricted | © Siemens 2025 | Siemens Digital Industries Software Figure 2: Graph construction from wireframe. most current studies focus primarily on improving predictive performance, while comparatively little atten- tion has been devoted to developing reusable engineering representations that preserve engineering semantics across simulation models, experimental measurements, and successive vehicle generations. As a result, his- torical engineering knowledge cannot be readily reused and is often relearned independently for each vehicle program instead of being accumulated within a common engineering representation. These observations motivate the region-aware graph framework proposed in this paper. Rather than learning directly from geometry-dependent finite element meshes, the proposed approach constructs a Canonical Engineering Graph Representation whose nodes represent persistent engineering-defined structural regions and whose edges encode physically meaningful structural relationships. By separating engineering semantics from numerical discretisation, the proposed representation provides a common foundation for transferable graph learning, engineering-oriented interpretation, and knowledge reuse across heterogeneous engineering datasets. The central hypothesis of this work is that transferable learning across heterogeneous engineering datasets is enabled not primarily by increasingly sophisticated graph neural network architectures, but by learning on a canonical engineering graph representation that preserves engineering semantics while remaining indepen- dent of mesh discretisation. 3 Proposed Region-Aware Graph Framework The proposed framework introduces a Canonical Engineering Graph Representation that maps heteroge- neous engineering models into a common semantic graph whose nodes represent persistent structural regions and whose edges encode physically meaningful relationships. By decoupling engineering semantics from numerical discretisation, this representation provides a transferable foundation for graph learning across different vehicle programs, mesh topologies, and experimental configurations. This design is motivated by an observation from industrial NVH development. Although BiW models differ substantially across vehicle programs in mesh resolution, modelling strategy, assembly configuration, and sensor layout, engineers interpret vibration behaviour through persistent structural entities such as roof rails, A/B/C-pillars, side sills, floor structures, cross members, and rear body components. These entities remain largely consistent across multiple vehicle programs even when the underlying numerical models change significantly. A representation is considered canonical in this work if engineering entities performing equivalent struc- tural functions are mapped to the same graph entities regardless of vehicle geometry, mesh topology, node numbering, or experimental measurement configuration. Knowledge is therefore transferred at the level of engineering concepts rather than numerical mesh entities. Based on this philosophy, the framework is designed according to three engineering objectives. Figure 3: Canonical BiW regional decomposition used for engineering-aware feature fusion and aggregation. Engineering semantics. Nodes and edges correspond to recognisable structural regions and physically meaningful relationships rather than arbitrary finite element nodes or mesh connectivity. Transferable representations. The framework remains applicable across different vehicle programs, finite element discretisations, assembly variants, and experimental measurements without requiring fundamentally different graph constructions. Engineering interpretability. Beyond accurate prediction, industrial deployment requires that engineers understand which structural regions contribute to a classification and whether these regions correspond to physically meaningful deformation mechanisms. Guided by these objectives, the framework consists of four stages: 1. Canonical Engineering Graph Representation: heterogeneous engineering models are transformed into a common semantic graph whose nodes represent engineering-defined structural regions and whose edges encode engineering-informed structural relationships. 2. Graph representation learning: a graph attention network propagates information between engineer- ing regions through message passing on the canonical graph, learning structural interactions associated with each vibration mode. 3. Engineering-aware prediction: learned graph embeddings are fused with engineering-informed re- gional descriptors for hierarchical mode shape classification. 4. Engineering interpretation and knowledge reuse: graph-level predictions are mapped back to engineering- defined structural regions to support explainable model interpretation, cross-vehicle transfer, and reuse of learned engineering knowledge. Figure 1 summarises the complete workflow. The following subsections describe the Canonical Engineering Graph Representation, the region-aware graph learning framework, and the resulting engineering properties for explainability and transferability. 3.1 Canonical Engineering Graph Representation The Canonical Engineering Graph Representation is formalized as a mapping from a heterogeneous engi- neering model to a semantic graph. Starting from a finite element model or experimental wireframe, the structural skeleton of the vehicle is extracted and partitioned into persistent BiW regions, including front rails, side sills, roof rails, A/B/C-pillars, floor structures, cross members, and rear body components, which Figure 4: Region-aware aggregation of a vehicle wireframe model with 119 nodes onto the canonical engi- neering graph. correspond to the longitudinal load paths, pillars, and lateral members described in the engineering review process. Unlike finite element nodes, these engineering regions remain consistent across vehicle architec- tures and modelling strategies, making them suitable as transferable graph entities. Each vehicle is then represented as the attributed graph G = (V, E, X, R), whereV denotes the set of engineering-defined structural regions (rather than individual finite element nodes or measurement sensors), E represents engineering-informed structural relationships between regions, X contains regional node features, and R stores edge attributes describing pairwise structural interactions. Each node summarises the collective dynamic behaviour of one engineering region, enabling finite element models with different mesh densities, topologies, and numbering schemes to be represented using a common semantic graph structure. Four categories of structural relationships are considered as graph edges: structural adjacency between neigh- bouring body regions, left-right symmetry, longitudinal load-path coupling, and vertical roof-floor coupling. These relationships reflect how structural deformation propagates throughout the vehicle body and provide stronger engineering priors than purely distance-based graph construction. For each engineering region, displacement responses from the original finite element model are aggregated to compute geometry-independent regional descriptors. The node feature vector comprises the following quantities: mean displacement magnitude, RMS displacement magnitude, dominant displacement direction, signed vertical response, and regional deformation energy. These features characterise the modal behaviour of each engineering region independently of the underlying mesh discretisation. Edge attributes provide complementary relational information describing the interaction between neighbour- ing structural regions, including edge type, relative deformation energy, phase agreement, and structural coupling characteristics. Together, node and edge attributes allow the graph to capture both local structural behaviour and global deformation mechanisms while preserving explicit engineering semantics. The resulting representation possesses three fundamental properties. First, it is geometry independent, allowing different finite element meshes and experimental sensor layouts to be mapped onto a common semantic graph structure. Second, it is engineering interpretable, since every graph entity corresponds directly to recognisable structural members used during NVH engineering review. Third, it is knowledge transferable, because learning is performed on persistent engineering concepts rather than numerical mesh entities. Once engineering models have been transformed into this common representation, different graph learning algorithms can operate on the same engineering abstraction across simulation models, experimental measurements, and multiple vehicle programs. 3.2 Region-Aware Graph Learning Given the Canonical Engineering Graph Representation defined above, the objective of the learning frame- work is to infer structural mode categories from regional dynamic responses while preserving engineering interpretability. The goal is not to introduce a new graph neural network architecture, but to enable graph learning on a representation whose nodes and edges already carry engineering meaning. Each mode shape is represented as one graph sample. Node attributes describe regional dynamic responses, while edges encode engineering-defined structural relationships. The graph is processed using a multi-layer graph attention network (GAT), which propagates information between neighbouring engineering regions through message passing. For graph layer l, the hidden representation of node i is updated as h (l+1) i = σ X j∈N(i) ∪ i α (l) ij W (l) h (l) j , where h (l) i denotes the node embedding at layer l, W (l) is a learnable linear transformation matrix, and σ(·) denotes a nonlinear activation function. The self-loop term j = i is included so that each region retains its own embedding during aggregation. Attention coefficients α (l) ij are computed by applying a shared attention function to the concatenated features of each node pair, with the resulting scores normalized across all neighbours using a softmax function. Attention allows the network to assign different importance to neighbouring structural regions depending on the current deformation pattern. After several graph attention layers, each node embedding captures both local regional response and structural context within the BiW graph. A conventional graph classifier would aggregate node embeddings through uniform global pooling to ob- tain a graph-level representation. However, this does not explicitly exploit engineering knowledge about characteristic deformation mechanisms. Bending, torsion, and pumping modes, for example, are often dis- tinguished by relative responses of roof, floor, side structures, and longitudinal members rather than by a uniform average over all regions. To address this limitation, the proposed framework introduces an engineering-aware feature fusion strat- egy. In addition to the learned graph embedding, analytical descriptors are computed directly from the canonical engineering regions. These descriptors summarise deformation characteristics used during manual modal assessment, including floor and roof energy fractions, longitudinal member responses, and vertical deformation uniformity. Because they are computed at the region level, these descriptors remain invariant to mesh density and node numbering. Let z GNN denote the global graph embedding obtained by mean pooling over all engineering region embed- dings at the final graph attention layer L, and let z eng denote the vector of engineering-informed regional descriptors. The final graph representation is formed by concatenation, z = Concat(z GNN , z eng ), combining learned structural interactions with explicit engineering priors. This fusion is particularly useful for distinguishing physically similar mode families where purely learned graph embeddings may not capture subtle but important engineering differences. The fused representation z is passed to a hierarchical prediction network that follows the reasoning process used during NVH engineering review. The classifier first predicts the dominant structural mechanism at Level 1, such as torsion, bending, or pumping, and then refines the prediction to the corresponding Level 2 subtype. This hierarchical formulation improves robustness under limited labelled data and reflects the way engineers typically perform modal assessment. The complete network is trained end-to-end using a multi-task objective, L = L L1 + λL L2 with λ > 0, where L L1 and L L2 denote cross-entropy losses for Level 1 and Level 2 classification respectively, and λ is a weighting hyperparameter balancing the two tasks. The engineering-aware feature fusion ensures that region-level descriptors provide complementary physical priors that remain consistent across different mesh discretisations and vehicle layouts. 3.3 Engineering Interpretability and Transferability A key objective of the proposed framework is not only accurate mode shape classification, but also the pro- duction of representations that remain meaningful throughout the engineering review process. Because all learning is performed on the Canonical Engineering Graph Representation, every prediction can be inter- preted, transferred, and reused within the same semantic engineering representation. The following para- graphs discuss these engineering properties in turn. Interpretability. Every node in the canonical graph G corresponds to a persistent engineering region rather than an individual finite element node. Consequently, learned embeddings, attention coefficients α (l) ij , engi- neering descriptors, and regional feature importance can be related directly to recognisable structural com- ponents such as roof rails, pillars, floor structures, side sills, and rear body members. This enables engineers to verify whether a predicted mode class is supported by physically meaningful deformation mechanisms, providing a transparent basis for engineering validation beyond classification accuracy. Transferability. Conventional graph learning approaches typically depend on vehicle-specific mesh topol- ogy, node numbering, or sensor placement. The proposed framework instead performs learning on the canonical graph that abstracts away from numerical discretisation. As long as different BiW models can be mapped through Φ to the same semantic regional decomposition, the learned representation remains ap- plicable despite differences in mesh density, finite element topology, or experimental measurement layout. Transferability therefore depends primarily on preserving engineering semantics rather than maintaining identical numerical discretisations. Knowledge reuse. The fused representation z combines data-driven graph learning with structural fea- tures that engineers already use during modal assessment. Rather than replacing engineering knowledge, this hybrid representation preserves physical consistency while allowing the model to accumulate structural understanding across vehicle programs. Because different vehicle programs share the same canonical rep- resentation, engineering knowledge learned from one program can be reused and progressively refined for subsequent programs rather than being relearned from scratch. Industrial deployment. From an industrial perspective, the proposed framework establishes a reusable engineering representation that can be integrated throughout the engineering development workflow rather than acting as a task-specific classifier tied to a single vehicle model. Once a BiW model has been mapped through Φ, the same canonical graph provides a reusable foundation for different vehicle programs, simu- lation variants, experimental measurements, and related engineering learning tasks without redesigning the underlying representation. Although the present work focuses on hierarchical BiW mode shape classification, the underlying design philosophy is more general. Engineering problems characterised by persistent engineering entities and phys- ically meaningful relationships can be represented using a similar canonical mapping. The proposed frame- work therefore provides a practical step towards reusable, explainable, and transferable graph learning for industrial engineering AI. Labelingthe Baseline Body-in-White Modes C123 based automated wireframe creation Page 1 FULL MODE SETTARGET MODE SET LABELING Automatic Wireframe GEOMETRY MODEL Nastran Output File 42 modes (0-100Hz) Target Modes Target Labels Import BIW FE model Automatic identification of structural skeleton Automatic creation of 1D beam elements Create RBE3 connections Conversion to PLOTEL and set creation Figure 5: Overview of the engineering wireframe generation, physics-guided data augmentation, automatic mode shape labeling, and graph construction pipeline. 4 Dataset Generation and labeling The proposed framework operates on the Canonical Engineering Graph Representation introduced in Section 3 rather than directly on detailed FE meshes. Consequently, the objective of the dataset preparation process is not only to generate labelled vibration modes, but also to construct engineering-consistent structural rep- resentations that can be mapped onto the same canonical graph across heterogeneous vehicle programs. The complete data generation pipeline consists of three stages: engineering wireframe generation from FE models and experimental measurements, physics-guided data augmentation with automatic label transfer, and construction of a heterogeneous multi-vehicle benchmark comprising FE models and experimental mea- surements from four vehicle programs. Figure 5 provides an overview of the complete workflow. 4.1 Automated Wireframe Creation Rather than constructing graphs directly from detailed FE meshes, the proposed framework first extracts an engineering wireframe representation for each BiW model. The objective is not simply to reduce model complexity, but to construct a structural abstraction that better reflects the engineering load paths used during modal assessment while remaining compatible with both simulation and experimental measurements. The wireframe represents the principal load-carrying members of the vehicle, including roof rails, pillars, side sills, floor structures, cross members, longitudinal rails, and rear body members. Local panels, brackets, and secondary sheet-metal components are intentionally excluded, since their dominant contribution is lim- ited to localized deformation and provides relatively little information for global mode shape classification. Starting from the imported FE shell model, the structural skeleton is identified automatically and one- dimensional beam elements are generated along the centre lines of the principal body members. RBE3 interpolation elements are subsequently introduced to connect the beam elements to the surrounding shell mesh without introducing artificial structural stiffness. Finally, the beam network is converted into PLOTEL elements and organized into engineering sets, producing a lightweight structural wireframe that remains consistent across different vehicle variants and assembly configurations. The wireframe serves as the intermediate structural representation from which the Canonical Engineering Graph Representation described in Section 3 is constructed. Table 1: Summary of the heterogeneous multi-vehicle dataset. OEM1 node and label counts are reported before augmentation; following the physics-guided augmentation procedure, OEM1 contributes 310 labelled mode shapes for model training. VehicleSourceNodesLabelled Modes OEM1Simulation11910 OEM2Simulation1949 OEM3Testing585 OEM4Testing612 4.2 Physics-guided Data Augmentation and Automatic labeling Expert-reviewed mode shape labels are typically scarce in industrial NVH development because modal interpretation requires experienced CAE engineers. To alleviate this limitation, a physics-guided concept modelling strategy is adopted to expand the available training data while preserving physically meaningful structural behaviour. The augmentation procedure is based on a reduced modal representation of the vehicle body, providing an accurate yet computationally efficient description of structural dynamics in the modal domain [10, 11]. Controlled stiffness modifications are introduced through concept beam models generated using commercial engineering software. By systematically varying these structural modifications, physically consistent mode shape variants are created without requiring repeated full-scale FE analyses. Starting from only 10 expert- reviewed modes, the proposed augmentation procedure generates 30 structural variants per mode, resulting in 310 labelled mode shapes available for model training. A key advantage of this augmentation strategy is that the underlying engineering wireframe remains un- changed throughout the generation process. Consequently, one-to-one correspondence between structural entities is preserved, allowing expert-reviewed labels to be transferred automatically using the Modal Assur- ance Criterion (MAC). This avoids repeated manual review of every generated mode while enabling efficient construction of a substantially larger labelled dataset. It should be emphasized that MAC-based label transfer is only applicable within this controlled augmentation framework, where structural correspondence is explicitly maintained. Across different vehicle programs, changes in mesh topology, vehicle geometry, and experimental measurement layouts prevent direct MAC- based matching. This limitation constitutes one of the primary motivations for introducing the Canonical Engineering Graph Representation proposed in this work. Mode labeling is restricted to the frequency range of 0–100 Hz, which contains the dominant global BiW vibration modes considered in the present study. The selected frequency interval can be adapted for other engineering applications without changing the underlying graph representation. 4.3 Multi-Vehicle Benchmark Dataset The final benchmark comprises four heterogeneous BiW vehicle programs, including two finite element models and two experimental datasets. Although these vehicle programs differ substantially in body geom- etry, structural topology, node density, and measurement configuration, they can all be transformed into the same Canonical Engineering Graph Representation prior to learning. Table 1 summarizes the characteristics of the multi-vehicle dataset. The reference vehicle (OEM1) con- tributes 310 labelled mode shapes, including the physics-guided augmented samples described above. Three additional vehicle programs contribute 9, 2, and 5 manually reviewed mode shapes, respectively. This dis- tribution reflects typical industrial development, where mature vehicle programs possess extensive historical annotations, whereas newly introduced vehicle platforms initially contain only a small number of expert- reviewed vibration modes. FE Model: BIW OEM1 (119 nodes) FE Model: BIW OEM2 (194 nodes) Test Data: BIW OEM3 (58 nodes) Test Data: BIW OEM4 (61 nodes) Figure 6: Characteristics of the proposed benchmark dataset. (a) Engineering wireframes extracted from the four vehicle programs used in this study, illustrating differences in geometry, topology, and measurement density across finite element and experimental datasets. (b) Distribution of manually reviewed mode labels across vehicle programs and vibration mode classes. Figure 6(a) illustrates the variation in graph size across vehicle programs, while Figure 6(b) shows the dis- tribution of labelled samples across vehicle platforms and mode classes. The benchmark therefore captures three challenges frequently encountered in industrial engineering AI: heterogeneous engineering representa- tions, limited labelled data, and mixed simulation-to-test learning. Training and evaluation follow a stratified split into training, validation, and test subsets while preserving ve- hicle diversity throughout the dataset. More importantly, all vehicle programs are transformed into the same Canonical Engineering Graph Representation before learning. Consequently, the subsequent experiments evaluate not only classification accuracy, but also the ability of the proposed engineering representation to transfer structural knowledge across heterogeneous finite element models and experimental measurements under realistic industrial conditions. 5 Experimental Results The experimental evaluation aims to validate the three engineering objectives introduced in Section 3. Specif- ically, the experiments investigate whether the proposed Canonical Engineering Graph Representation en- ables 1. accurate hierarchical mode shape classification under realistic industrial data constraints; 2. physically meaningful engineering interpretation of the learned representations; and 3. transferable learning across heterogeneous vehicle programs, finite element models, and experimental measurements. All vehicle programs are first transformed into the same Canonical Engineering Graph Representation before graph learning. Unless otherwise stated, the graph encoder, training strategy, and region-aware pooling follow the methodology described in Section 3. 5.1 Quantitative Evaluation Table 2 summarizes the quantitative evaluation under two training strategies. A model trained exclusively on the reference vehicle achieves high within-vehicle performance but generalizes poorly to unseen vehicle pro- grams (90.8% Level-1 and 81.6% Level-2 accuracy) because of differences in geometry, mesh discretization, and structural layouts. This observation highlights the limitations of learning directly from vehicle-specific engineering representations. In contrast, when all vehicle programs are transformed into the proposed Canonical Engineering Graph Representation, the multi-vehicle framework achieves 100% Level-1 accuracy, 98.7% Level-2 accuracy, and 99.2% combined hierarchical accuracy on the held-out test set (Table 2). Only one of the 76 test samples is misclassified, and the prediction remains within the same higher-level pumping family, indicating that the learned representation preserves the dominant structural deformation mechanism even for ambiguous mode subtypes. The confusion matrix in Figure 7 further shows that nearly all errors occur between physically similar mode families, while torsional and bending modes are consistently separated. Compared with reference-vehicle- only training, the proposed framework improves Level-2 classification accuracy by 17.1 percentage points. More importantly, this improvement cannot be explained solely by the graph neural network architecture. Instead, it results from the combination of the Canonical Engineering Graph Representation, engineering- informed regional descriptors, and multi-vehicle representation learning. These results support the central hypothesis of this work that transferable engineering AI depends primarily on engineering representations rather than geometry-dependent mesh discretizations. Table 2: Held-out test performance under different training strategies. Training strategyL1 Acc. (%) L2 Acc. (%) Comb. (%) Reference-vehicle-only training90.881.685.3 Multi-vehicle training100.098.799.2 5.2 Engineering Interpretability Accurate prediction alone is insufficient for practical deployment in automotive NVH engineering. Engi- neers must also understand whether model predictions are supported by physically meaningful structural behaviour. Unlike conventional graph learning approaches operating directly on finite element nodes, the proposed framework performs explanation on the Canonical Engineering Graph Representation, allowing attribution to be visualized directly on recognizable engineering regions. Representative examples are shown in Figure 8. Torsional modes primarily activate pillar-side sill con- nections and longitudinal load paths, whereas bending modes emphasize vertically coupled roof and floor structures. Pumping modes highlight either floor or roof regions depending on the dominant deformation mechanism. These activation patterns agree well with established engineering interpretation of BiW modal behaviour, demonstrating that the learned representation captures meaningful structural concepts rather than vehicle-specific numerical artefacts. From an engineering perspective, this capability provides considerably greater practical value than con- ventional black-box classifiers. Rather than returning only a predicted label, the framework identifies the structural regions that support the decision, allowing engineers to verify whether the prediction is consistent with expected deformation mechanisms during manual modal review. 5.3 Cross-Vehicle Generalization and Transferability The principal objective of the proposed framework is not merely to maximize classification accuracy on a single vehicle program, but to enable engineering knowledge transfer across heterogeneous engineering datasets. This represents a significantly more challenging problem because each vehicle differs in body geometry, finite element topology, node density, and experimental measurement configuration. As illustrated in Figure 6, all four vehicle programs can be transformed into the same Canonical Engineer- ing Graph Representation despite their substantial structural differences. Consequently, graph learning is performed within a common engineering representation rather than on vehicle-specific numerical models. Figure 7: Confusion matrix for fine-grained mode classification on the held-out multi-vehicle test set. The transfer experiments demonstrate that the proposed representation successfully preserves engineering semantics across both FE models and experimental measurements. Despite using only 9, 2, and 5 manually reviewed mode shapes from the three target vehicle programs, the framework effectively transfers knowledge from the reference vehicle while maintaining high classification accuracy. This suggests that the learned representation captures persistent engineering concepts rather than vehicle-specific mesh characteristics. From an industrial perspective, this substantially reduces the effort required to deploy AI models to new vehicle programs. Instead of constructing a large labelled dataset for every new vehicle, engineers can initialize the framework using only a small number of representative mode shapes while reusing engineering knowledge accumulated from previous development programs. Overall, the experimental results demonstrate that the proposed Canonical Engineering Graph Representa- tion satisfies the three engineering objectives introduced in Section 3. It provides accurate hierarchical mode shape classification under severe label scarcity, maintains engineering interpretability throughout the learn- ing process, and enables structural knowledge to transfer across heterogeneous finite element models and experimental measurements. These findings provide encouraging evidence that transferable engineering AI depends primarily on engineering representations rather than on the numerical discretization of individual simulation models. Restricted | © Siemens 2026 | Siemens Digital Industries SoftwarePage 1 Feature Importance Figure 8: Representative attribution maps illustrating how predictions are associated with physically mean- ingful engineering regions. 6 Conclusion This paper presented a Canonical Engineering Graph Representation for explainable and transferable engi- neering AI, demonstrated through the application of hierarchical Body-in-White (BiW) mode shape classifi- cation. Rather than learning directly from geometry-dependent finite element meshes, the proposed frame- work transforms heterogeneous simulation and experimental data into a common engineering representation composed of persistent engineering regions and physically meaningful structural relationships. By separat- ing engineering semantics from numerical discretization, the proposed representation enables graph learning to operate on engineering concepts rather than vehicle-specific mesh topology. Experimental evaluation on four heterogeneous vehicle programs demonstrates that the proposed representa- tion supports accurate hierarchical mode shape classification despite limited labeled data and substantial dif- ferences in vehicle geometry, finite element topology, and experimental measurement layouts. The learned representations remain physically interpretable by mapping model predictions directly to engineering re- gions commonly used during NVH assessment, while successful cross-vehicle transfer indicates that the framework captures persistent structural concepts rather than vehicle-specific numerical characteristics. The principal contribution of this work is therefore the proposed engineering representation rather than the graph neural network architecture. The results suggest that transferable engineering AI depends primarily on engineering representations rather than geometry-dependent numerical models. The Canonical Engineer- ing Graph Representation provides a common engineering abstraction through which historical engineering knowledge can be accumulated, reused, and transferred across successive vehicle programs and heteroge- neous engineering datasets. Although this study focuses on BiW mode shape classification, the proposed representation is intentionally formulated as a reusable engineering foundation rather than a task-specific solution. Engineering problems that can be described through persistent functional regions and physically meaningful relationships—including structural dynamics, model correlation, simulation-to- test analysis, and other CAE workflows—may benefit from the same underlying representation. Future work will investigate automatic construction of Canonical Engineering Graph Representations, self- supervised and few-shot representation learning, active data generation for reducing expert labeling effort, and application to additional simulation-driven engineering domains. More broadly, Canonical Engineering Graph Representations are envisioned as an important step towards trustworthy, explainable, and reusable engineering AI capable of integrating heterogeneous engineering knowledge throughout the development workflows. Acknowledgment This work is supported by the Flanders Innovation and Entrepreneurship (VLAIO) project Simulation And TestIng Solutions For TrustworthY Data-centric AI (SATISFY.AI). References [1] D. J. Ewins, Modal Testing: Theory, Practice and Application.London: Research Studies Press, 2000. [2] T. D. Son, K. Sugiura, M. Brughmans, A. Hense, Z. Liu, A. Veeraraghavan, A. Bhave, J. Masters, P. di Carlo, and T. 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