Documents published in Scipedia

• Adaptivity and uncertainty of multi-fidelity surrogate models for shape optimization

  J. Wackers, H. Pehlivan Solak, R. Pellegrini, A. Serani

  WCCM2024.

  
  

  Abstract

  Engineering design optimization based on expensive simulation is increasingly performed with surrogate models [1], i.e. approximate models fitted through a small dataset of simulation results. To build surrogates within the lowest possible computational budget, modern approaches use multi-fidelity data (combinations of cheap low-fidelity and expensive high-fidelity simulation results) and adaptive sampling strategies, which add simulation points one by one where they are most likely to discover the optimum [2]. Uncertainty estimation of the surrogate model is crucial for efficient adaptive sampling, since it guides the choice of new sampling points. Thus, underestimation of the uncertainty may lead to sampling in suboptimal regions, missing the true optimum. Existing surrogate models such as Gaussian process regression [3] and Stochastic Radial Basis Functions (SRBF) [4], provide uncertainty estimations, which are often used. Nevertheless, uncertainty estimation is so important for a successful surrogate model, that a more thorough investigation seems warranted. This is the main objective of this paper. This paper studies three issues with uncertainty estimation, in the context of multifidelity SRBF. First, most existing techniques rely on knowledge about the global behavior of the data, such as spatial correlations. However, the number of training points can be too small to reconstruct this global information from the data. We argue that in this situation, user-provided estimation of the function behavior is a better choice (section 3). Furthermore, the dataset may contain noise, i.e. random errors without spatial correlation (section 4). Surrogate models can filter out this noise, usually by modeling it as belonging to a normal distribution with zero mean, but this introduces two separate uncertainties: the optimum amount of noise filtering is unknown, and for a small dataset the local mean of the noisy data may not correspond to the true simulation response. Finally, in multi-fidelity models, the low-fidelity data are corrected by high-fidelity results, which could reduce the amount of uncertainty they introduce.

  Abstract
  Engineering design optimization based on expensive simulation is increasingly performed with surrogate models [1], i.e. approximate models fitted through a small dataset of [...]

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• A PROBABILISTIC GRAPHICAL MODEL APPROACH TO INTERPRET, VERIFY, AND DECOUPLE MULTI-PHYSICS SYSTEMS

  T. Price-Broncucia, S. Amorese, R. Baptista, R. Morrison

  WCCM2024.

  
  

  Abstract

  Multi-physics scientific codes, like those used in weather prediction and spacecraft simulation, often involve the coupling of many subdomain models. The resulting models are generally expensive to run. These costs, along with the model’s complexity, make downstream tasks like model calibration and uncertainty quantification especially difficult. In this work, we simplify structure in multi-physics models by learning an undirected graphical model corresponding to the system state variables, where the edges in the learned graph represent conditional dependence between variables. Depending on the application of interest, the resulting graph may (1) reveal the probabilistic structure of the joint distribution; (2) identify the most important coupling variables (those that must be shared between subdomain models), and those which may be safely neglected; (3) identify candidate variables for first-pass verification tasks; or (4) decouple parts of a model, while maintaining accuracy in the model predictions. We illustrate these possibilities through two multi-physics numerical models, the Multiple Prediction Across Scales-Atmosphere (MPAS-A) code base and a fire detection satellite model

  Abstract
  Multi-physics scientific codes, like those used in weather prediction and spacecraft simulation, often involve the coupling of many subdomain models. The resulting models [...]

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• A mesoscopic domain decomposition approach composed with preconditioned conjugate gradient for modeling concrete

  Y. Xu, Z. Lin

  WCCM2024.

  
  

  Abstract

  Concrete structure is widely used in civil engineering. Numerical Simulation in mesoscale could provide a powerful analysis tool, which is based on the Total Finite Element Tearing and Interconnecting (TFETI) method. However, the unneglectable computational resource consumption limited the implementation of the meso-modeling method in engineering. This study investigated an efficient solution for concrete structure simulation, which was programmed using Python. A cantilever beam model with dimensions of 100mm × 50mm was simulated and studied. Then, a comparison with the ABAQUS model was given to demonstrate the accuracy and efficiency of the TFETI. Furthermore, a reliability analysis of a 300mm × 300mm concrete sample under the axial compression was performed. The results showed that the TFETI method achieved the same level of accuracy as ABAQUS. Moreover, the TFETI model solving required less computational source for the same number of elements as the one on the ABAQUS. In the reliability analysis of the axially loaded model, TFETI demonstrated superior solution speed. In conclusion, the TFETI exhibits excellent solution efficiency in finite element analysis of concrete structures, offering valuable insights and references for computational analysis of large-dimension civil engineering structures.

  Abstract
  Concrete structure is widely used in civil engineering. Numerical Simulation in mesoscale could provide a powerful analysis tool, which is based on the Total Finite Element [...]

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• A kinematically-exact reduced-order rod model for elastoplastic failure in thin-walled members

  M. Pires Kassab, E. Campello, A. Ibrahimbegovic

  WCCM2024.

  
  

  Abstract

  This work profits from a weakly coupled multiscale approach to derive a 7-DOF kinematically-exact reduced-order rod model for thin-walled members (starting from [1]) with a plastic hardening constitutive equation (based on [2]-[3]) that emulates the coupling between local buckling effects and hardening plasticity at material level. The model is implemented in an in-house finite element program for flexible thin structures and shall be validated against reference solutions. The novelty as compared to [2]-[3] is the extension to the fully 3D context, including torsion-warping degrees-of-freedom and arbitrary (plastic) failure mode capabilities, allowing for the modelling of complex structural problems involving thin-walled rod members. Although kinematically-exact rod models are able to detect critical loads and represent postcritical configurations in many common scenarios, issues are bound to emerge when local effects (such as buckling of web and/or flanges) are relevant, especially when they are coupled with plastic deformations. For rod models, the combination of those factors can be satisfactorily represented in a phenomenological way by embedding them on a stress-resultant/crosssectional strains hardening plastic model, instead of enriching the model´s kinematics and related material law. One can employ weakly coupled multiscale modelling to generate constitutive relationships among the different strain and stress in a pre-processing stage. Information about plasticity, loss of geometrical stiffness and local buckling are passed to the macro-scale rod model without increasing the amount of global degrees-of-freedom. Incremental steps of the numerical solution are solved with the split operator, whereby local variables are solved in an element-wise fashion and thus not introduced in the global system. Quadratic convergence of the overall solution procedure is achieved. The coupling among geometrical and hardening effects limits the load bearing capacity of the structural members and determinates the failure load.

  Abstract
  This work profits from a weakly coupled multiscale approach to derive a 7-DOF kinematically-exact reduced-order rod model for thin-walled members (starting from [1]) with [...]

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• A finite deformation micropolar peridynamic theory and its application to metamaterials

  . Sajal, P. Roy

  WCCM2024.

  
  

  Abstract

  Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent propagation of elastic waves in certain range of frequency called bandgap. The microstructure of these materials affects the overall response of the structures. Microstructures may undergo significant rotations and their rotary inertia needs to be considered along with deformation. As the metamaterials in the study involve cracks, we develop a finite deformation micropolar peridynamics (PD) theory. The proposed PD micropolar theory is validated by comparing the results obtained from the boundary element solutions of plate with a hole. The response of metamaterials with periodic arrangement of holes and cracks is studied under static and dynamic loads and the results are compared with the nonpolar PD theory.

  Abstract
  Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent [...]

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• Generative model to predict the deformation field of CFRP laminates with geometric deviations in wing assembly

  Y. Liu, Y. Zhao, Q. Lin, W. Pan

  WCCM2024.

  
  

  Abstract

  Thin-walled structure of CFRP laminates is widely utilized in the assembly of aircraft wings. The deformation field generated during the assembly process can impact the assembly performance of the structure, thereby influencing the product quality and operational performance of the wings. The geometric deviations on the critical mating surfaces of the laminate and physical parameters are key factors influencing the deformation fields during the assembly process. Analyzing the mapping relationship between fusion assembly data and deformation field plays a crucial role for assessing the assembly results. The traditional analysis methods only consider the impact of simple directional deviations on assembly results and do not comprehensively account for the multi-source input. This paper proposes a multi-source assembly input -deformation analysis framework for CFRP bolted joints in aircraft wing assembly. Taking the parameters representing the geometric deviations and physical parameters as input and deformation field as output, a conditional generative model is employed to learn the influence pattern of the geometric deviations on the deformation field. The framework establishes a prediction model from the deviation field to the deformation field and introduces specific accuracy metrics. Corresponding simulations demonstrate that the proposed method can predict assembly deformation field more efficiently than traditional numerical methods.

  Abstract
  Thin-walled structure of CFRP laminates is widely utilized in the assembly of aircraft wings. The deformation field generated during the assembly process can impact the assembly [...]

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• A fast prediction method for bearing strength of aircraft composite bolted structures considering initial assembly deviation

  Q. Lin, Y. Zhao, Y. Liu, W. Pan

  WCCM2024.

  
  

  Abstract

  Bearing limitation is a key performance indicator for composite bolted joints. Assembly process parameters such as washer structural parameters, interfacial friction coefficients and tightening process parameters have a significant effect on the bearing limitation. In the actual production process, there are inevitably deviations between the assembly process parameters and their design values. The accumulation of assembly process deviations leads to an obvious dispersion of the bearing limitation, which makes it difficult for composite bolted joints to be reliably in service. In this paper, the dispersion of assembly process parameters is experimentally tested to quantitatively characterize its uncertainty. Then, based on the high fidelity finite element analysis method, a data set of bearing limitation under different assembly process parameters is prepared. A data-driven algorithm is used to establish a fast prediction model for bearing limitation. The fast prediction model is used to realize the uncertainty analysis and the reliability evaluation for the bearing limitation. The established analysis method and the obtained conclusions can provide a reference for the reliability design and analysis of composite bolted joints.

  Abstract
  Bearing limitation is a key performance indicator for composite bolted joints. Assembly process parameters such as washer structural parameters, interfacial friction coefficients [...]

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• Hybrid quantum algorithm for the Lattice-Boltzmann method

  D. Wawrzyniak, J. Winter, S. Schmidt, T. Indinger

  WCCM2024.

  
  

  Abstract

  We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity.

  Abstract
  We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision [...]

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• On the iterative solution of saddle point problems using a symmetric positive definite preconditioner

  P. Devloo, G. Avancini, M. Meneghel

  WCCM2024.

  
  

  Abstract

  Saddle point problems frequently appear in many mathematical and engineering applications. Most systems of partial differential equations with constraints give rise to saddle point linear systems. Typical examples include mixed finite element formulations to solve fluid flows and/or elasticity problems under full incompressibility. The inversion of saddle point problems is challenging due to inherent numerical instability in the direct inversion methods. Many direct and iterative methods have been proposed to overcome this challenges, such as the Schur complement and the Uzawa’s method. In the context of mixed finite element for incompressible flows using stable H(div)-L2 spaces for velocity and pressure, we propose an iterative method that can effectively solve a saddle point problem iteratively by summing a small compressibility to the original matrix. The preconditioning matrix is symmetric positive definite, which allows the usage of Cholesky decomposition and/or CG-like iterative solvers to compute the incremental solution for the velocities unknowns. A procedure to compute the average pressure of each element of the incompressible problem is developed using the unbalanced fluxes caused by the compressibility perturbation. The average is updated during the iterative process as a function of the velocity increment at each iteration.

  Abstract
  Saddle point problems frequently appear in many mathematical and engineering applications. Most systems of partial differential equations with constraints give rise to saddle [...]

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• Effect of the capillary force on the repose angle of granular materials

  W. Ziye, T. Yong

  WCCM2024.

  
  

  Abstract

  The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the properties of granular media, leading to an increase in the repose angle. This change is mainly attributed to the capillary force resulting from the liquid bridge when the small amount of water was introduced. The capillary force as an attractive force increases the interaction between particles and becomes a dominant factor affecting the angle of repose because it is usually stronger than gravity. In this paper, a new discrete element method (DEM) model was developed in which the capillary force was calculated by the liquid bridge model based on toroidal approximation. The developed DEM model linked the microscopic liquid bridge volume to the macroscopic water content and it also considered the effect of liquid bridge breakage and formation on capillary force. The numerical model was first validated by comparing the experimental and numerical results. Then, the effects of surface tension, volume of the liquid bridge, and the contact angle are studied numerically. Finally, the empirical equation between water content and angle of repose is given under the present simulation conditions. This work will provide a deep understanding for the effect of capillary on the angle of repose.

  Abstract
  The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the [...]

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