Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A Bayesian learning approach for dynamic parameter identification and its applications in industrial robotic systems","authors":"Xing-ao Li ,&nbsp;Dequan Zhang ,&nbsp;Xinyu Jia ,&nbsp;Xu Han ,&nbsp;Guosong Ning ,&nbsp;Qing Li","doi":"10.1016/j.cma.2025.117951","DOIUrl":"10.1016/j.cma.2025.117951","url":null,"abstract":"<div><div>Accurate dynamic modeling is essential for implementing model-based control strategies to enhance the performance of industrial robots. However, conventional dynamic parameter identification methods suffer from several limitations, such as insufficient accuracy, lack of physical feasibility assurance, and inadequate utilization of prior information. More importantly, the existing methods fail to quantify the uncertainties in dynamic parameters and their effects on the performance effectively. To address these challenges, this study proposes a novel Bayesian learning framework for dynamic parameter identification and torque prediction in industrial robots. This framework integrates the inverse dynamic model (IDM) into Bayesian inference, leveraging its linear characteristics to derive an analytical representation of dynamic parameters that inherently accounts for uncertainty information. On this basis, the key factors influencing the mean and standard deviation of the dynamic parameters are analyzed. By extrapolating the uncertainty information obtained, the method generates reliable uncertainty bounds for robotic joint torques. Moreover, incorporating reasonable prior information enhances identification accuracy while ensuring the physical feasibility of dynamic parameters. To evaluate the effectiveness of the proposed approach, three industrial robot analysis examples are presented. The first two are used to demonstrate the feasibility and performances of the proposed method, while the third, an in-house experimental study on HSR-JR612 robot, further validates its accuracy in parameter identification and the uncertainty-bound prediction for the joint torques. These results underscore the engineering applicability of the proposed framework in industrial robotic systems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117951"},"PeriodicalIF":6.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupling of data-driven and model-driven computing within non-matching meshes","authors":"Xiaowei Bai ,&nbsp;Jie Yang ,&nbsp;Qun Huang ,&nbsp;Wei Huang ,&nbsp;Huicui Li ,&nbsp;Noureddine Damil ,&nbsp;Heng Hu","doi":"10.1016/j.cma.2025.117959","DOIUrl":"10.1016/j.cma.2025.117959","url":null,"abstract":"<div><div>This work aims to couple distance-minimizing data-driven computing with model-driven computing (standard constitutive model-based simulations), allowing for non-matching interfaces between computational regions meshed with both full and reduced finite elements. Specifically, data-driven (DD) computing is employed for regions where the material constitutive models are difficult to determine, whilst model-driven (MD) computing is applied to the remaining regions to take advantage of its computational efficiency. To connect non-matching interfaces, a penalty-based technique is utilized to ensure the continuity of displacements and the accurate transfer of interaction forces across these interfaces. In this manner, the proposed method becomes more versatile and practical for engineering applications, enabling separate modeling of data-driven and model-driven regions with different mesh refinements or types of elements (e.g., coarse and fine meshes, full and reduced finite elements) based on their specific needs. Several examples are provided to illustrate the effectiveness and robustness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117959"},"PeriodicalIF":6.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"AEK-MFIS: An adaptive ensemble of Kriging models based on multi-fidelity simulations and importance sampling for small failure probabilities","authors":"Wei Zhang ,&nbsp;Zhonglai Wang ,&nbsp;Haoyu Wang ,&nbsp;Zhangwei Li ,&nbsp;Yunfei Wang ,&nbsp;Ziyi Zhao","doi":"10.1016/j.cma.2025.117952","DOIUrl":"10.1016/j.cma.2025.117952","url":null,"abstract":"<div><div>The reliability analysis methods based on the surrogate model significantly reduce the number of true performance function calls. However, existing reliability analysis methods ignore Low-Fidelity (LF) information in the assessment of reliability analysis, which consequently leads to the difficulty in efficiently and accurately estimating the small failure probabilities with time-consuming High-Fidelity (HF) finite element simulation. To address this challenge, a novel reliability analysis named AEK-MFIS is presented in this paper, which aims at reducing the times of HF simulation calls while providing the accurate estimation result for small failure probabilities. The proposed AEK-MFIS comprises the following strategies: (1) based on the Kalman Filter (KF) and Multi-Fidelity (MF) Kriging model, a novel ensemble of Kriging (EK) models is introduced to fuse information from different fidelities; (2) to select the best points in a more accurate and efficient way, a novel active learning function named Global Error-based Active Learning Function (GEALF) is presented; (3) a new stopping criterion is constructed based on the EK prediction, which aims at avoiding the pre-mature or late-mature for evaluating the small failure probabilities. Six examples involving two numerical and four engineering examples are introduced to elaborate and validate the effectiveness of the proposed method for estimating the small failure probabilities.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117952"},"PeriodicalIF":6.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A graph neural network surrogate model for multi-objective fluid-acoustic shape optimization","authors":"Farnoosh Hadizadeh ,&nbsp;Wrik Mallik ,&nbsp;Rajeev K. Jaiman","doi":"10.1016/j.cma.2025.117921","DOIUrl":"10.1016/j.cma.2025.117921","url":null,"abstract":"<div><div>This study presents a graph neural network (GNN)-based surrogate modeling approach for multi-objective fluid-acoustic shape optimization. The proposed GNN model transforms mesh-based simulations into a computational graph, enabling steady-state prediction of pressure and velocity fields around varying geometries subjected to different operating conditions. We employ signed distance functions to implicitly encode geometries on unstructured nodes represented by the graph neural network. By integrating these functions with computational mesh information into the GNN architecture, our approach effectively captures geometric variations and learns their influence on flow behavior. The trained graph neural network achieves high prediction accuracy for aerodynamic quantities, with median relative errors of 0.5%–1% for pressure and velocity fields across 200 test cases. The predicted flow field is utilized to extract fluid force coefficients and boundary layer velocity profiles, which are then integrated into an acoustic prediction model to estimate far-field noise. This enables the direct integration of the coupled fluid-acoustic analysis in the multi-objective shape optimization algorithm, where the airfoil geometry is optimized to simultaneously minimize trailing-edge noise and maximize aerodynamic performance. Results show that the optimized airfoil achieves a 13.9% reduction in overall sound pressure level (15.82 dBA) while increasing lift by 7.2% under fixed operating conditions. Optimization was also performed under a different set of operating conditions to assess the model’s robustness and demonstrate its effectiveness across varying flow conditions. In addition to its adaptability, our GNN-based surrogate model, integrated with the shape optimization algorithm, exhibits a computational speed-up of three orders of magnitude compared to full-order online optimization applications while maintaining high accuracy. This work demonstrates the potential of GNNs as an efficient data-driven approach for fluid-acoustic shape optimization via adaptive morphing of structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117921"},"PeriodicalIF":6.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants","authors":"N. Sukumar ,&nbsp;Amit Acharya","doi":"10.1016/j.cma.2025.117909","DOIUrl":"10.1016/j.cma.2025.117909","url":null,"abstract":"<div><div>Many partial differential equations (PDEs) such as Navier–Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently, a variational principle based on the dual (Lagrange multiplier) field was proposed. The essential idea in this approach is to treat the given PDEs as constraints, and to invoke an arbitrarily chosen auxiliary potential with strong convexity properties to be optimized. On requiring the vanishing of the gradient of the Lagrangian with respect to the primal variables, a mapping from the dual to the primal fields is obtained. This leads to requiring a convex dual functional to be minimized subject to Dirichlet boundary conditions on dual variables, with the guarantee that even PDEs that do not possess a variational structure in primal form can be solved via a variational principle. The vanishing of the first variation of the dual functional is, up to Dirichlet boundary conditions on dual fields, the weak form of the primal PDE problem with the dual-to-primal change of variables incorporated. We derive the dual weak form for the linear, one-dimensional, transient convection–diffusion equation. A Galerkin discretization is used to obtain the discrete equations, with the trial and test functions in one dimension chosen as linear combination of either shallow neural networks with Rectified Power Unit (RePU) activation functions or B-spline basis functions; the corresponding stiffness matrix is symmetric. For transient problems, a space–time Galerkin implementation is used with tensor-product B-splines as approximating functions. Numerical results are presented for the steady-state and transient convection–diffusion equations and transient heat conduction. The proposed method delivers sound accuracy for ODEs and PDEs and rates of convergence are established in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> seminorm for the steady-state convection–diffusion problem.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117909"},"PeriodicalIF":6.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture","authors":"C.G. Krishnanunni ,&nbsp;Tan Bui-Thanh","doi":"10.1016/j.cma.2025.117938","DOIUrl":"10.1016/j.cma.2025.117938","url":null,"abstract":"<div><div>This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a <span><math><mrow><mi>ɛ</mi><mo>−</mo><mi>δ</mi><mo>−</mo></mrow></math></span> stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a <span><math><mrow><mi>ɛ</mi><mo>−</mo><mi>δ</mi></mrow></math></span> stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. We also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117938"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3D XFEM for fluid-driven fracturing of layered anisotropic rock","authors":"XiuYuan Chen,&nbsp;Hao Yu,&nbsp;YiLun Zhong,&nbsp;Quan Wang,&nbsp;HengAn Wu","doi":"10.1016/j.cma.2025.117963","DOIUrl":"10.1016/j.cma.2025.117963","url":null,"abstract":"<div><div>We propose a novel planar 3D extended finite element method (XFEM) for fluid-driven fracturing of layered rocks, where the material properties and fracture toughness are anisotropic. The crack tip singular functions vary along the curved fracture front, which stems from differing crack tip asymptotes caused by variations in local material properties. These functions in three-dimensional anisotropic space are first established. A coordinate transformation for the stress matrix is defined by the normal to curved fracture front at each quadrature point, and the global elastic stiffness matrix is transformed to calculate its local form. The characteristic equation, obtained by extracting the plane strain components from the local elastic stiffness matrix, is solved to compute the tip enrichment functions of the corresponding quadrature points. Additionally, a hybrid explicit-implicit method is developed for fracture propagation and geometric description with rock anisotropy. In this approach, the explicit Irwin's criterion is regularized by inverting the varying crack tip asymptotes at different fracture front nodes, which provides the anisotropic propagation distances and injection time constraint during each propagation step. The apparent Young's modulus is introduced in the criterion to capture the variations of local material properties with propagation angle. The fracture surface is represented implicitly by two level set functions, which are calculated from the fracture description updated through the Irwin's criterion. This hybrid method avoids solving complex advection-type equations and improves the computational efficiency of nodal enrichment without iterating through fracture elements repeatedly. The proposed method is validated against the analytical solutions and various numerical cases with non-self-similar propagation behavior and strong fracture toughness anisotropy. This work provides a powerful approach for modeling the complex propagation behavior of 3D hydraulic fracture (HF) in tight formation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117963"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamically-Informed Iterative Neural Operators for heterogeneous elastic localization","authors":"Conlain Kelly,&nbsp;Surya R. Kalidindi","doi":"10.1016/j.cma.2025.117939","DOIUrl":"10.1016/j.cma.2025.117939","url":null,"abstract":"<div><div>Engineering problems frequently require solution of governing equations with spatially-varying, discontinuous coefficients. Mapping large ensembles of coefficient fields to solutions can become a major computational bottleneck using traditional numerical solvers, even for linear elliptic problems. Machine learning surrogates such as neural operators often struggle to fit these maps due to sharp transitions and high contrast in the coefficient fields. Furthermore, in design applications any available training data is by definition less informative due to distribution shifts between known and novel designs. In this work, we focus on a canonical problem in computational mechanics: prediction of local elastic deformation fields over heterogeneous material structures subjected to periodic boundary conditions. We construct a hybrid approximation for the coefficient-to-solution map using a Thermodynamically-informed Iterative Neural Operator (TherINO). Rather than using coefficient fields as direct inputs and iterating over a learned latent space, we employ thermodynamic encodings – drawn from the constitutive equations – and iterate over the solution space itself. Through an extensive series of case studies, we elucidate the advantages of these design choices in terms of efficiency, accuracy, and flexibility. We also analyze the model’s stability and extrapolation properties on out-of-distribution coefficient fields and demonstrate an improved speed–accuracy tradeoff for predicting elastic quantities of interest.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117939"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Space–time Isogeometric Analysis of cardiac electrophysiology","authors":"Paola F. Antonietti ,&nbsp;Luca Dedè ,&nbsp;Gabriele Loli ,&nbsp;Monica Montardini ,&nbsp;Giancarlo Sangalli ,&nbsp;Paolo Tesini","doi":"10.1016/j.cma.2025.117957","DOIUrl":"10.1016/j.cma.2025.117957","url":null,"abstract":"<div><div>This work proposes a stabilized space–time method for the monodomain equation coupled with the Rogers–McCulloch ionic model, which is widely used to simulate electrophysiological wave propagation in the cardiac tissue. By extending the Spline Upwind method and exploiting low-rank matrix approximations, as well as preconditioned solvers, we achieve both significant computational efficiency and accuracy. In particular, we develop a formulation that is both simple and highly effective, designed to minimize spurious oscillations and ensuring computational efficiency. We rigorously validate the method’s performance through a series of numerical experiments, showing its robustness and reliability in diverse scenarios.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117957"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A physics-informed 3D surrogate model for elastic fields in polycrystals","authors":"Lucas Monteiro Fernandes ,&nbsp;Samy Blusseau ,&nbsp;Philipp Rieder ,&nbsp;Matthias Neumann ,&nbsp;Volker Schmidt ,&nbsp;Henry Proudhon ,&nbsp;François Willot","doi":"10.1016/j.cma.2025.117944","DOIUrl":"10.1016/j.cma.2025.117944","url":null,"abstract":"<div><div>We develop a physics-informed neural network pipeline for solving linear elastic micromechanics in three dimensions, on a statistical volume element (SVE) of a polycrystalline material with periodic geometry. The presented approach combines a convolutional neural network containing residual connections with physics-informed non-trainable layers. The latter are introduced to enforce the strain field admissibility and the constitutive law in a way consistent with so-called fast Fourier transform (FFT) algorithms. More precisely, differential operators are discretized by finite differences in accordance with the Green operator used in FFT computations and treated as convolutions with fixed kernels. The deterministic relationship between crystalline orientations and stiffness tensors is transferred to the network by an additional non-trainable layer. A loss function dependent on the divergence of the predicted stress field allows for updating the neural network’s parameters without further supervision from ground truth data. The surrogate model is trained on untextured synthetic polycrystalline SVEs with periodic boundary conditions, realized from a stochastic 3D microstructure model based on random tessellations. Once trained, the network is able to predict the periodic part of the displacement field from the crystalline orientation field (represented as unit quaternions) of an SVE. The proposed self-supervised pipeline is compared to a similar one trained with a data-driven loss function instead. Further, the accuracy of both models is analyzed by applying them to microstructures larger than the training inputs, as well as to SVEs generated by the stochastic 3D microstructure model, utilizing various different parameters. We find that the self-supervised pipeline yields more accurate predictions than the data-driven one, at the expense of a longer training. Finally, we discuss how the trained surrogate model can be used to solve certain inverse problems on polycrystalline domains by gradient descent.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117944"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}