Computer Methods in Applied Mechanics and Engineering最新文献

A graph neural network surrogate model for multi-objective fluid-acoustic shape optimization

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-02 DOI: 10.1016/j.cma.2025.117921

Farnoosh Hadizadeh , Wrik Mallik , Rajeev K. Jaiman

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.

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引用次数: 0

Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-02 DOI: 10.1016/j.cma.2025.117909

N. Sukumar , Amit Acharya

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

L^{2}

norm and

H^{1}

seminorm for the steady-state convection–diffusion problem.

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引用次数: 0

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-01 DOI: 10.1016/j.cma.2025.117938

C.G. Krishnanunni , Tan Bui-Thanh

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

ɛ - δ -

stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a

ɛ - δ

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.

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引用次数: 0

3D XFEM for fluid-driven fracturing of layered anisotropic rock

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-01 DOI: 10.1016/j.cma.2025.117963

XiuYuan Chen, Hao Yu, YiLun Zhong, Quan Wang, HengAn Wu

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.

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引用次数: 0

Thermodynamically-Informed Iterative Neural Operators for heterogeneous elastic localization

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-01 DOI: 10.1016/j.cma.2025.117939

Conlain Kelly, Surya R. Kalidindi

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.

{"title":"Thermodynamically-Informed Iterative Neural Operators for heterogeneous elastic localization","authors":"Conlain Kelly, 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}

引用次数: 0

Space–time Isogeometric Analysis of cardiac electrophysiology

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-01 DOI: 10.1016/j.cma.2025.117957

Paola F. Antonietti , Luca Dedè , Gabriele Loli , Monica Montardini , Giancarlo Sangalli , Paolo Tesini

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.

引用次数: 0

A physics-informed 3D surrogate model for elastic fields in polycrystals

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-04-01 DOI: 10.1016/j.cma.2025.117944

Lucas Monteiro Fernandes , Samy Blusseau , Philipp Rieder , Matthias Neumann , Volker Schmidt , Henry Proudhon , François Willot

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.

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引用次数: 0

Neural networks meet phase-field: A hybrid fracture model

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-30 DOI: 10.1016/j.cma.2025.117937

Franz Dammaß , Karl A. Kalina , Markus Kästner

We present a hybrid phase-field model of fracture at finite deformation and its application to quasi-incompressible, hyperelastic rubber. The key idea is to combine the predictive capability of the well-established phase-field approach to fracture with a physics-augmented neural network (PANN) that serves as a flexible, high-fidelity model of the response of the bulk material. To this end, recently developed neural network approaches are developed further to better meet specific requirements of the phase-field framework. In particular, a novel architecture for a hyperelastic PANN is presented, that enables a decoupled description of the volumetric and the isochoric response based on a corresponding additive decomposition of the Helmholtz free energy. This is of particular interest when modelling fracture of soft quasi-incompressible solids with the phase-field approach, where a weakening of the incompressibility constraint in fracturing material is required. In addition, such an additive decomposition of the free energy is a prerequisite for the application of several split methods, i.e. decompositions of free energy into degraded and non-degraded portions, which can improve model behaviour under multiaxial stress states. For the formulation of the hybrid model, we define a pseudo-potential, in which the phase-field ansatz for fracture dissipation is combined with a polyconvex PANN model of the isochoric response. The PANN is formulated in polyconvex isochoric invariants. As a result, it can be shown that the PANN fulfils all desirable properties of hyperelastic potentials by construction. In particular, it is proven to be zero and take a global minimum for the undeformed state, which does also hold in case of deviations away from incompressibility. Moreover, a classical mixed displacement-pressure formulation of incompressibility based on the perturbed Lagrangian approach is included. Thereby, a relaxation of the incompressibility constraint in fracturing material is applied. This weakening of incompressibility is shown in to be essential in order to prevent numerical issues in the simulation, which would otherwise arise from the presence of zones showing both negligible isochoric stiffness and very high resistance against volume changes. The model is implemented in the finite element framework FEniCSx and studied by means of several examples. To this end, training and validation of the PANN are performed based on experimental data from the literature, and the hybrid fracture model is then verified against results of fracture experiments.

{"title":"Neural networks meet phase-field: A hybrid fracture model","authors":"Franz Dammaß , Karl A. Kalina , Markus Kästner","doi":"10.1016/j.cma.2025.117937","DOIUrl":"10.1016/j.cma.2025.117937","url":null,"abstract":"<div><div>We present a hybrid phase-field model of fracture at finite deformation and its application to quasi-incompressible, hyperelastic rubber. The key idea is to combine the predictive capability of the well-established phase-field approach to fracture with a physics-augmented neural network (PANN) that serves as a flexible, high-fidelity model of the response of the bulk material. To this end, recently developed neural network approaches are developed further to better meet specific requirements of the phase-field framework. In particular, a novel architecture for a hyperelastic PANN is presented, that enables a decoupled description of the volumetric and the isochoric response based on a corresponding additive decomposition of the Helmholtz free energy. This is of particular interest when modelling fracture of soft quasi-incompressible solids with the phase-field approach, where a weakening of the incompressibility constraint in fracturing material is required. In addition, such an additive decomposition of the free energy is a prerequisite for the application of several <em>split methods</em>, i.e. decompositions of free energy into degraded and non-degraded portions, which can improve model behaviour under multiaxial stress states. For the formulation of the hybrid model, we define a pseudo-potential, in which the phase-field ansatz for fracture dissipation is combined with a polyconvex PANN model of the isochoric response. The PANN is formulated in polyconvex isochoric invariants. As a result, it can be shown that the PANN fulfils all desirable properties of hyperelastic potentials by construction. In particular, it is proven to be zero and take a global minimum for the undeformed state, which does also hold in case of deviations away from incompressibility. Moreover, a classical mixed displacement-pressure formulation of incompressibility based on the perturbed Lagrangian approach is included. Thereby, a relaxation of the incompressibility constraint in fracturing material is applied. This weakening of incompressibility is shown in to be essential in order to prevent numerical issues in the simulation, which would otherwise arise from the presence of zones showing both negligible isochoric stiffness and very high resistance against volume changes. The model is implemented in the finite element framework <em>FEniCSx</em> and studied by means of several examples. To this end, training and validation of the PANN are performed based on experimental data from the literature, and the hybrid fracture model is then verified against results of fracture experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117937"},"PeriodicalIF":6.9,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734853","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}

引用次数: 0

PIGODE: A novel model for efficient surrogate modeling in complex geometric structures

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-29 DOI: 10.1016/j.cma.2025.117930

Chengyu Lu , Zhaoxi Hong , Xiuju Song , Zhixin Liu , Bingtao Hu , Yixiong Feng , Jianrong Tan

Physics-Informed Neural Network (PINN), as a novel neural network model, is known for its strong interpretability and generalization capabilities, making it widely used in surrogate models and various engineering scenarios. While traditional PINN has achieved good results in simple geometric scenarios, there is limited research on its application to complex geometric structures. Additionally, PINN integrates boundary conditions into the loss function, requiring retraining model when boundary conditions change. To address these issues, we propose a new Physics-Informed Graph Ordinary Differential Equation (PIGODE) model for constructing surrogate models in complex geometric structures. The Peridynamic Differential Operator (PDDO) is extended to a PIGODE which is defined on graph data structure, and a PDDO-based message passing layer is developed to replace automatic differentiation (AD). This method precomputes Peridynamic weights, thereby avoiding additional computational overhead during model training. Furthermore, boundary conditions are embedded into the model input to address the need for dynamically modifying boundary conditions in surrogate models. Through comparative studies with existing PINN solvers, we validate the effectiveness of the proposed model, demonstrating its superior performance on complex geometric structures. Additionally, this model is applied to practical engineering scenarios, specifically constructing a temperature field surrogate model for the conical picks of a tunnel boring machine. The research results indicate that the proposed PIGODE model not only enhances the interpretability and efficiency of surrogate models but also extends their applicability to complex geometric structures in engineering.

{"title":"PIGODE: A novel model for efficient surrogate modeling in complex geometric structures","authors":"Chengyu Lu , Zhaoxi Hong , Xiuju Song , Zhixin Liu , Bingtao Hu , Yixiong Feng , Jianrong Tan","doi":"10.1016/j.cma.2025.117930","DOIUrl":"10.1016/j.cma.2025.117930","url":null,"abstract":"<div><div>Physics-Informed Neural Network (PINN), as a novel neural network model, is known for its strong interpretability and generalization capabilities, making it widely used in surrogate models and various engineering scenarios. While traditional PINN has achieved good results in simple geometric scenarios, there is limited research on its application to complex geometric structures. Additionally, PINN integrates boundary conditions into the loss function, requiring retraining model when boundary conditions change. To address these issues, we propose a new Physics-Informed Graph Ordinary Differential Equation (PIGODE) model for constructing surrogate models in complex geometric structures. The Peridynamic Differential Operator (PDDO) is extended to a PIGODE which is defined on graph data structure, and a PDDO-based message passing layer is developed to replace automatic differentiation (AD). This method precomputes Peridynamic weights, thereby avoiding additional computational overhead during model training. Furthermore, boundary conditions are embedded into the model input to address the need for dynamically modifying boundary conditions in surrogate models. Through comparative studies with existing PINN solvers, we validate the effectiveness of the proposed model, demonstrating its superior performance on complex geometric structures. Additionally, this model is applied to practical engineering scenarios, specifically constructing a temperature field surrogate model for the conical picks of a tunnel boring machine. The research results indicate that the proposed PIGODE model not only enhances the interpretability and efficiency of surrogate models but also extends their applicability to complex geometric structures in engineering.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117930"},"PeriodicalIF":6.9,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734852","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}

引用次数: 0

A new paradigm for hybrid reliability-based design optimization: From β-circle to β-cylinder

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-29 DOI: 10.1016/j.cma.2025.117954

Peng Hao, Zehao Cui, Bingyi Du, Hao Yang, Yue Zhang

A new paradigm for hybrid reliability-based design optimization (HRBDO) is proposed. The key innovation lies in expanding the traditional β-circle into a β-cylinder along the interval dimensions, integrating both random and interval dimensional information. Building upon this theoretical foundation, a novel interval-based dimensional expansion β-cylinder active learning (IBAL) method is proposed, transforming the complex double-loop reliability calculation into an efficient single-loop process. The method employs Kriging models to replace expensive physical responses. Unlike traditional sampling techniques, the IBAL method focuses exclusively on predicted means and deviations on the β-cylinder to guide the Kriging models of performance functions, efficiently identifying the Most Probable Point (MPP). This approach effectively addresses challenges including interval dimensions nonlinearity, multiple extreme points, and multiple MPPs. In HRBDO, the method incorporates an active constraint screening (ACS) mechanism and an MPP objective function isosurface active learning (MIAL) method to enhance computational efficiency and avoid convergence to local optima. The effectiveness of the proposed method is validated through four mathematical examples and one engineering case study.

{"title":"A new paradigm for hybrid reliability-based design optimization: From β-circle to β-cylinder","authors":"Peng Hao, Zehao Cui, Bingyi Du, Hao Yang, Yue Zhang","doi":"10.1016/j.cma.2025.117954","DOIUrl":"10.1016/j.cma.2025.117954","url":null,"abstract":"<div><div>A new paradigm for hybrid reliability-based design optimization (HRBDO) is proposed. The key innovation lies in expanding the traditional <em>β</em>-circle into a <em>β</em>-cylinder along the interval dimensions, integrating both random and interval dimensional information. Building upon this theoretical foundation, a novel interval-based dimensional expansion <em>β</em>-cylinder active learning (IBAL) method is proposed, transforming the complex double-loop reliability calculation into an efficient single-loop process. The method employs Kriging models to replace expensive physical responses. Unlike traditional sampling techniques, the IBAL method focuses exclusively on predicted means and deviations on the <em>β</em>-cylinder to guide the Kriging models of performance functions, efficiently identifying the Most Probable Point (MPP). This approach effectively addresses challenges including interval dimensions nonlinearity, multiple extreme points, and multiple MPPs. In HRBDO, the method incorporates an active constraint screening (ACS) mechanism and an MPP objective function isosurface active learning (MIAL) method to enhance computational efficiency and avoid convergence to local optima. The effectiveness of the proposed method is validated through four mathematical examples and one engineering case study.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117954"},"PeriodicalIF":6.9,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725542","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}

引用次数: 0