Reduced-order Computational Model Research Articles

Real-Time Prediction of Probabilistic Crack Growth with a Helicopter Component Digital Twin

To deploy the airframe digital twin or to conduct probabilistic evaluations of the remaining life of a structural component, a (near) real-time crack-growth simulation method is critical. In this paper, a reduced-order simulation approach is developed to achieve this goal by leveraging two methods. On the one hand, the symmetric Galerkin boundary element method–finite element method (SGBEM-FEM) coupling method is combined with parametric modeling to generate the database of computed stress intensity factors for cracks with various sizes/shapes in a complex structural component, by which hundreds of samples are automatically simulated within a day. On the other hand, machine learning methods are applied to establish the relation between crack sizes/shapes and crack-front stress intensity factors. By combining the reduced-order computational model with load inputs and fatigue growth laws, a real-time prediction of probabilistic crack growth in complex structures with minimum computational burden is realized. In an example of a round-robin helicopter component, even though the fatigue crack growth is simulated cycle by cycle, the simulation is faster than real-time (as compared with the physical test). The proposed approach is a key simulation technology toward realizing the digital twin of complex structures, which further requires fusion of model predictions with flight/inspection/monitoring data.

Multi-frequency model reduction for uncertainty quantification in computational vibroacoutics

This work is devoted to the vibroacoustics of complex systems over a broad-frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. On one hand, the global displacements are associated with the main stiff part and on the other hand, the local displacements are associated with the preponderant vibrations of the flexible subparts. Such complex structures induce interweaving of these two types of displacements, which introduce an overlap of the usual three frequency bands (low-, medium- and high-frequency bands (LF, MF, and HF). A reduced-order computational vibroacoustic model is constructed by using a classical modal analysis with the elastic and acoustic modes. Nevertheless, the dimension of such reduced-order model (ROM) is still important when there is an overlap for each one of the three frequency bands. A multi-frequency reduced-order model is then constructed for the structure over the LF, MF, and HF bands. The strategy is based on a multilevel projection consisting in introducing three reduced-order bases that are obtained by using a spatial filtering methodology. To filter out the local displacements in the structure, a set of global shape functions is introduced. In addition, a classical ROM using acoustic modes is carried out for the acoustic cavity. Then, the coupling between the multilevel ROM and the acoustic ROM is presented. A nonparametric probabilistic modeling is then proposed to take into account the model uncertainties induced by modeling errors that increase with the frequency. The proposed approach is applied to a large-scale computational vibroacoustic model of a car.

Robust Three-Dimensional Acoustic Performance Probabilistic Model for Nacelle Liners

This paper is devoted to the robust optimization of nacelle liners (acoustic treatments). The full computational aeroacoustic model is based on the convected Helmholtz equation in presence of a nonhomogeneous flow velocity field, which is computed by solving the potential Euler equations. Uncertainties are taken into account in order to increase the robustness of the predictions. A reduced-order computational aeroacoustic model is constructed in order to implement the nonparametric probabilistic model of uncertainties induced by the modeling errors in the aeroacoustic model and in the liner model. In addition, the uncertainties on the acoustic excitation induced by the fan are taken into account using the parametric probabilistic approach. The developed methodology is applied to a three-dimensional nacelle intake and allows for computing the confidence regions of the random far-field radiated pressure in terms of random sound pressure level, which are compared with experiments for one flight condition, one frequency, and for two types of liners.

Multi-Frequency Model Reduction for Uncertainty Quantification in Computational Vibroacoustics of Automobiles

<div class="section abstract"><div class="htmlview paragraph">This paper deals with the vibroacoustics of complex systems over a broad frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. The vibroacoustics model is represented by the usual global-displacements elastic modes associated with the main part, and by local elastic modes, associated with the preponderant vibrations of the flexible sub-parts. The main difficulty of the vibroacoustics analysis of complex system is the interweaving of the global displacements with the local displacements, which introduces an overlap of the usual three frequency domains (LF, MF and HF). A reduced-order computational vibroacoustic model constructed with a classical modal analysis is introduced. Nevertheless, the dimension of such reduced-order model (ROM) is still high when the frequency band of analysis overlaps for each frequency domain. A multi-level reduced-order model for the structure is constructed over the LF, MF, and HF bands. The strategy is based on a multi-level projection consisting in introducing three reduced-order bases that are obtained by using a filtering methodology of local displacements. To filter out the local displacements we introduce a set of global shape functions. In addition, a classical ROM using acoustic modes is implemented for the acoustic cavity. Then, the coupling between the multi-level reduced order model and the acoustic reduced-order model is presented. A nonparametric probabilistic modeling is then proposed to take into account the model uncertainties induced by modeling errors that increase with the frequency. The proposed approach is applied to a car.</div></div>

Diagnostic performance of virtual fractional flow reserve derived from routine coronary angiography using segmentation free reduced order (1-dimensional) flow modelling

Fractional flow reserve (FFR) improves assessment of the physiological significance of coronary lesions compared with conventional angiography. However, it is an invasive investigation. We tested the performance of a virtual FFR (1D-vFFR) using routine angiographic images and a rapidly performed reduced order computational model. Quantitative coronary angiography (QCA) was performed in 102 with coronary lesions assessed by invasive FFR. A 1D-vFFR for each lesion was created using reduced order (one-dimensional) computational flow modelling derived from conventional angiographic images and patient specific estimates of coronary flow. The diagnostic accuracy of 1D-vFFR and QCA derived stenosis was compared against the gold standard of invasive FFR using area under the receiver operator characteristic curve (AUC). QCA revealed the mean coronary stenosis diameter was 44% ± 12% and lesion length 13 ± 7 mm. Following angiography calculation of the 1DvFFR took less than one minute. Coronary stenosis (QCA) had a significant but weak correlation with FFR (r = -0.2, p = 0.04) and poor diagnostic performance to identify lesions with FFR <0.80 (AUC 0.39, p = 0.09), (sensitivity - 58% and specificity - 26% at a QCA stenosis of 50%). In contrast, 1D-vFFR had a better correlation with FFR (r = 0.32, p = 0.01) and significantly better diagnostic performance (AUC 0.67, p = 0.007), (sensitivity - 92% and specificity - 29% at a 1D-vFFR of 0.7). 1D-vFFR improves the determination of functionally significant coronary lesions compared with conventional angiography without requiring a pressure-wire or hyperaemia induction. It is fast enough to influence immediate clinical decision-making but requires further clinical evaluation.

Revisiting the experiment of a free-surface resonance of a liquid in a vibration tank using a nonlinear fluid–structure computational model

Using an advanced nonlinear fluid–structure reduced-order computational model, this work revisits and explains a resonance of the free surface of water contained in a thin elastic cylindrical tank, which was experimentally exhibited by Lindholm, 1962 and Abramson, 1966. The proposed simulation model allows the experimental setup to be reproduced. The structure undergoes large displacements and large deformations (geometrical nonlinear effects of the structure) that play an important role on the liquid vibrations. The experimental setup is simulated using a large-scale numerical model of the elastic cylindrical tank partially filled with water that is considered as a compressible fluid and that takes into account surface tension and sloshing effects. The results show that for a frequency external excitation in the frequency band [500,2,500]Hz of the fluid–structure system, unexpected high-amplitude sloshing vibrations are observed in the frequency band [0,150]Hz. The observed phenomenon, which cannot be reproduced with a linear fluid–structure model, is explained by the transfer of the vibrational energy from the frequency band of excitation into a low-frequency band (and then exciting the first sloshing modes) by a non-direct coupling mechanism between the structural modes and the sloshing modes.

Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures

Three-dimensional (3D), lattice-based micro- and nano-architected materials can possess desirable mechanical properties that are unattainable by homogeneous materials. Manufacturing these so-called structural metamaterials at the nano- and microscales typically results in non-slender architectures (e.g., struts with a high radius-to-length ratio r∕l), for which simple analytical and computational tools are inapplicable since they fail to capture the effects of nodes at strut junctions. We report a detailed analysis that quantifies the effect of nodes on the effective Young’s modulus (E∗) of lattice architectures with different unit cell geometries through (i) simple analytical constructions, (ii) reduced-order computational models, and (iii) experiments at the milli- and micrometer scales. The computational models of variable-node lattice architectures match the effective stiffness obtained from experiments and incur computational cost that are three orders-of-magnitude lower than alternative, conventional methods. We highlight a difference in the contribution of nodes to rigid versus non-rigid architectures and propose an extension to the classical stiffness scaling laws of the form E∗∝C1(r∕l)α+C2(r∕l)β, which holds for slender and non-slender beam-based architectures, where constants C1 and C2 change with lattice geometry. We find the optimal scaling exponents for rigid architectures to be α=2 and β=4, and α=4 and β=6 for non-rigid architectures. These analytical, computational, and experimental results quantify the specific contribution of nodes to the effective stiffness of beam-based architectures and highlight the necessity of incorporating their effects into calculations of the structural stiffness. This work provides new, efficient tools that accurately capture the mechanics and physics of strut junctions in 3D beam-based architected materials.

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

Within the framework of the state-of-the-art, this paper presents a summary of some common research works carried out by the authors concerning computational methods for the prediction of the responses in the frequency domain of general linear dissipative vibroacoustics (structural-acoustic) systems for liquid and gas in the low-frequency (LF) and medium-frequency (MF) domains, including uncertainty quantification (UQ) that plays an important role in the MF domain. The system under consideration consists of a deformable dissipative structure, coupled with an internal dissipative acoustic fluid including a wall acoustic impedance, and surrounded by an infinite acoustic fluid. The system is submitted to given internal and external acoustic sources and to prescribed mechanical forces. An efficient reduced-order computational model (ROM) is constructed using a finite element discretization (FEM) for the structure and the internal acoustic fluid. The external acoustic fluid is treated using a symmetric boundary element method (BEM) in the frequency domain. All the required modeling aspects required for the analysis in the MF domain have been introduced, in particular the frequency-dependent damping phenomena and model uncertainties. An industrial application to a complex computational vibroacoustic model of an automobile is presented.

Uncertainty Quantification for an Elasto-acoustic Nonlinear Reduced-Order Computational Model.

The present research concerns the numerical analysis of an uncertain coupled fluid-structure dynamical system, for which the geometrical nonlinearities of the structure induced by the large deformations and the large displacements are taken into account. The structure is coupled with an internal cavity filled with a linear inviscid compressible fluid. The formulation is carried out in terms of displacements and pressure unknowns. The modal basis is made up of the structural modes of the structure and the acoustic modes of the fluid. A nonlinear-reduced order model is then numerically constructed in order to reduce the size of the problem. The uncertainties are then implemented by using the nonparametric probabilistic framework. Note that a peculiar attention that allows the uncertainties on the nonlinear part to be coherently taken into account by preventing the presence of a too large number of random variables used for generating the stochastic model is made. A numerical application is presented.

Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity

Abstract This paper deals with a novel formulation of a nonlinear reduced-order computational model for analyzing the nonlinear vibrations of a linear viscoelastic structure with weak nonlinear geometrical effects, coupled with a linear acoustic liquid with sloshing and capillarity on the free surface. The model proposed is derived from the one used in fluid-structure interaction for linear systems, for which the analysis of the acoustic-sloshing-capillarity phenomena is efficient thanks to the use of a projection on the linear modes of the linear acoustic liquid and on the sloshing modes with capillarity. Concerning the construction of the vector basis for the structure, it is proposed to use a POD approach for the viscoelastic structure with weak nonlinear geometrical effects and taking into account the added mass induced by the liquid. The methodology for constructing the vector bases of the admissible sets and for obtaining the nonlinear ROM are detailed. The computational nonlinear ROM that is presented can directly be used for analyzing the vibrations of such fluid-structure systems using commercial finite element softwares for computing the vector bases and the projections.

A coupled discrete element-finite difference model of selective laser sintering

Selective laser sintering (SLS) is an additive manufacturing technology whereby one can 3D print parts out of a powdered material. However, in order to produce defect free parts of sufficient strength, the process parameters (laser power, scan speed, powder layer thickness, etc.) must be carefully optimized depending on material, part geometry, and desired final part characteristics. Computational methods are very useful in the quick optimization of such parameters without the need to run numerous costly experiments. Most published models of this process involve continuum-based techniques, which require the homogenization of the powder bed and thus do not capture the stochastic nature of this process. Thus, the aim of this research is to produce a reduced order computational model of the SLS process which combines the essential physics with fast computation times. In this work the authors propose a coupled discrete element-finite difference model of this process. The powder particles are modeled as discrete, thermally and mechanically interacting spheres. The solid, underneath substrate is modeled via the finite difference method. The model is validated against experimental results in the literature and three-dimensional simulations are presented.

Uncertainty quantification in computational linear structural dynamics for viscoelastic composite structures

This paper deals with the analysis of a stochastic reduced-order computational model in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties. The computational framework proposed is based on a recent theoretical work that allows for constructing the stochastic reduced-order model using the nonparametric probabilistic approach. In the frequency domain, the generalized damping matrix and the generalized stiffness matrix of the stochastic computational reduced-order model are random matrices. Due to the causality of the dynamical system, these two frequency-dependent random matrices are statistically dependent and are linked by a compatibility equation induced by the causality of the system, involving a Hilbert transform. The computational aspects related to the nonparametric stochastic modeling of the reduced stiffness matrix and the reduced damping matrix that are frequency-dependent random matrices are presented. A dedicated numerical approach is developed for obtaining an efficient computation of the Cauchy principal value integrals involved in those equations for which an integration over a broad frequency domain is required. A computational analysis of the propagation of uncertainties is conducted for a composite viscoelastic structure in the frequency range. It is shown that the uncertainties on the damping matrix have a strong influence on the observed statistical dispersion of the stiffness matrix.

Multilevel reduced-order computational model in structural dynamics for the low- and medium-frequency ranges

This work deals with the dynamical analysis of complex structures composed of several structural levels and characterized by the presence of numerous local elastic modes intertwined with global modes, in the medium-frequency range as well as in the low-frequency range. For constructing the ROM, a family of global-displacements eigenvectors are calculated and are used instead of the classical elastic modes. Since it is also of importance to adapt the physical models (damping, level of uncertainties, etc.) to each one of the structural levels, a multilevel ROM is proposed. A validation is performed for an automobile complex structure.

A global/local probabilistic approach for reduced-order modeling adapted to the low- and mid-frequency structural dynamics

Abstract The research presented here is devoted to the construction of a probabilistic reduced-order computational model adapted to the low- and mid-frequency structural dynamics. The methodology presented here is based on a global/local separation of the space of admissible displacements by solving two separated eigenvalue problems in which the kinetic energy is modified. This paper presents a general framework for constructing the modified kinetic energy by introducing classes of kinematic reductions. The global/local separation allows the construction of a probabilistic model of uncertainties for which the fluctuations of the global displacements and the fluctuations of the local displacements can be controlled separately.

Enhancing physiologic simulations using supervised learning on coarse mesh solutions.

Computational modelling of physical and biochemical processes has emerged as a means of evaluating medical devices, offering new insights that explain current performance, inform future designs and even enable personalized use. Yet resource limitations force one to compromise with reduced order computational models and idealized assumptions that yield either qualitative descriptions or approximate, quantitative solutions to problems of interest. Considering endovascular drug delivery as an exemplary scenario, we used a supervised machine learning framework to process data generated from low fidelity coarse meshes and predict high fidelity solutions on refined mesh configurations. We considered two models simulating drug delivery to the arterial wall: (i) two-dimensional drug-coated balloons and (ii) three-dimensional drug-eluting stents. Simulations were performed on computational mesh configurations of increasing density. Supervised learners based on Gaussian process modelling were constructed from combinations of coarse mesh setting solutions of drug concentrations and nearest neighbourhood distance information as inputs, and higher fidelity mesh solutions as outputs. These learners were then used as computationally inexpensive surrogates to extend predictions using low fidelity information to higher levels of mesh refinement. The cross-validated, supervised learner-based predictions improved fidelity as compared with computational simulations performed at coarse level meshes—a result consistent across all outputs and computational models considered. Supervised learning on coarse mesh solutions can augment traditional physics-based modelling of complex physiologic phenomena. By obtaining efficient solutions at a fraction of the computational cost, this framework has the potential to transform how modelling approaches can be applied in the evaluation of medical technologies and their real-time administration in an increasingly personalized fashion.

Nonlinear data-driven computational models for response prediction and change detection

Summary Data are used from three relatively large-scale experimental soil-foundation-superstructure interaction (SFSI) systems to develop reduced-order computational models for response prediction and change-detection relevant to structural health monitoring and computational mechanics. The three systems under consideration consist of identical superstructures with: (i) fixed base; (ii) box foundation; and (iii) pile foundation. The three SFSI systems were developed and experimentally tested at Tongji University. In the first part of the study, a computational time-marching prediction framework is proposed by incorporating trained neural network(s) within an ordinary differential equation solver and dynamically predicting the response (i.e., displacement and velocity) of the SFSI systems to various earthquake excitations. Two approaches are investigated: global approach and subsystem approach. Both approaches are tested and validated with linear and nonlinear systems, and their respective pros and cons are discussed. In the second part of the study, the trained neural networks from the global approach are further used for change-detection in the SFSI systems. The detected changes in the systems are then quantified through a measure of a normalized error index. Challenges related to the physical interpretation of the quantified changes in the SFSI systems are addressed and discussed. It is shown that the general procedures adopted in this paper provide a robust nonlinear model that is reliable for computational studies, as well as furnishing a robust tool for detecting and quantifying inherent change in the system. Copyright © 2014 John Wiley & Sons, Ltd.

Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation

The paper presents a complete experimental validation of an advanced computational methodology adapted to the nonlinear post-buckling analysis of geometrically nonlinear structures in presence of uncertainty. A mean nonlinear reduced-order computational model is first obtained using an adapted projection basis. The stochastic nonlinear computational model is then constructed as a function of a scalar dispersion parameter, which has to be identified with respect to the nonlinear static experimental response of a very thin cylindrical shell submitted to a static shear load. The identified stochastic computational model is finally used for predicting the nonlinear dynamical post-buckling behavior of the structure submitted to a stochastic ground motion.

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

Stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics

This paper is devoted to the construction of a stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics. We are particularly interested in automotive vehicles which are made up of stiff parts and flexible components. This type of structure is characterized by the fact that it exhibits, in the low frequency range, not only the classical global elastic modes but also numerous local elastic modes which cannot easily be separated from the global elastic modes. To solve this difficult problem, an innovative method has recently been proposed for constructing a reduced order computational dynamical model adapted to this particular situation for the low frequency range. Then a new adapted generalized eigenvalue problem is introduced and allows a global vector basis to be constructed for the global displacements space. This method requires to decompose the domain of the structure into sub-domains. Such a decomposition is carried out using the Fast Marching Method. This global vector basis is then used to construct the reduced order computational model. Since there are model uncertainties induced by modeling errors in the computational model, the nonparametric probabilistic approach of uncertainties is used and implemented in the reduced order computational model. The methodology is applied to a complex computational model of an automotive vehicle.

Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

A reduced-order model is constructed to predict, for the low-frequency range, the dynamical responses in the stiff parts of an automobile constituted of stiff and flexible parts. The vehicle has then many elastic modes in this range due to the presence of many flexible parts and equipment. A nonusual reduced-order model is introduced. The family of the elastic modes is not used and is replaced by an adapted vector basis of the admissible space of global displacements. Such a construction requires a decomposition of the domain of the structure in subdomains in order to control the spatial wave length of the global displacements. The fast marching method is used to carry out the subdomain decomposition. A probabilistic model of uncertainties is introduced. The parameters controlling the level of uncertainties are estimated solving a statistical inverse problem. The methodology is validated with a large computational model of an automobile.