Reduced Order Modeling for Real-Time Stent Deformation Simulations of Transcatheter Aortic Valve Prostheses.

Computational modeling can be a critical tool to predict deployment behavior for transcatheter aortic valve replacement (TAVR) in patients with aortic stenosis. However, due to the mechanical complexity of the aortic valve and the multiphysics nature of the problem, described by partial differential equations (PDEs), traditional finite element (FE) modeling of TAVR deployment is computationally expensive. In this preliminary study, a PDEs-based reduced order modeling (ROM) framework is introduced for rapidly simulating structural deformation of the Medtronic Evolut R valve stent frame. Using fifteen probing points from an Evolut model with parametrized loads enforced, 105 FE simulations were performed in the so-called offline phase, creating a snapshot library. The library was used in the online phase of the ROM for a new set of applied loads via the proper orthogonal decomposition-Galerkin (POD-Galerkin) approach. Simulations of small radial deformations of the Evolut stent frame were performed and compared to full order model (FOM) solutions. Linear elastic and hyperelastic constitutive models in steady and unsteady regimes were implemented within the ROM. Since the original POD-Galerkin method is formulated for linear problems, specific methods for the nonlinear terms in the hyperelastic case were employed, namely, the Discrete Empirical Interpolation Method. The ROM solutions were in strong agreement with the FOM in all numerical experiments, with a speed-up of at least 92% in CPU Time. This framework serves as a first step toward real-time predictive models for TAVR deployment simulations.

Reduced order modeling and model order reduction for continuum manipulators: an overview.

Soft robot's natural dynamics calls for the development of tailored modeling techniques for control. However, the high-dimensional configuration space of the geometrically exact modeling approaches for soft robots, i.e., Cosserat rod and Finite Element Methods (FEM), has been identified as a key obstacle in controller design. To address this challenge, Reduced Order Modeling (ROM), i.e., the approximation of the full-order models, and Model Order Reduction (MOR), i.e., reducing the state space dimension of a high fidelity FEM-based model, are enjoying extensive research. Although both techniques serve a similar purpose and their terms have been used interchangeably in the literature, they are different in their assumptions and implementation. This review paper provides the first in-depth survey of ROM and MOR techniques in the continuum and soft robotics landscape to aid Soft Robotics researchers in selecting computationally efficient models for their specific tasks.

Real-time simulation of the transplanted tooth using model order reduction.

The biomechanics of transplanted teeth remain poorly understood due to a lack of models. In this context, finite element (FE) analysis has been used to evaluate the influence of occlusal morphology and root form on the biomechanical behavior of the transplanted tooth, but the construction of a FE model is extremely time-consuming. Model order reduction (MOR) techniques have been used in the medical field to reduce computing time, and the present study aimed to develop a reduced model of a transplanted tooth using the higher-order proper generalized decomposition method. The FE model of a previous study was used to learn von Mises root stress, and axial and lateral forces were used to simulate different occlusions between 75 and 175N. The error of the reduced model varied between 0.1% and 5.9% according to the subdomain, and was the highest for the highest lateral forces. The time for the FE simulation varied between 2.3 and 7.2 h. In comparison, the reduced model was built in 17s and interpolation of new results took approximately 2.10-2s. The use of MOR reduced the time for delivering the root stresses by a mean 5.9 h. The biomechanical behavior of a transplanted tooth simulated by FE models was accurately captured with a significant decrease of computing time. Future studies could include using jaw tracking devices for clinical use and the development of more realistic real-time simulations of tooth autotransplantation surgery.

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls.

Nowadays, the shipbuilding industry is facing a radical change toward solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation, and by reducing the metal raw materials used during the manufacturing. This work focuses on the last aspect by presenting a complete structural optimization pipeline for modern passenger ship hulls which exploits advanced model order reduction techniques to reduce the dimensionality of both input parameters and outputs of interest. We introduce a novel approach which incorporates parameter space reduction through active subspaces into the proper orthogonal decomposition with interpolation method. This is done in a multi-fidelity setting. We test the whole framework on a simplified model of a midship section and on the full model of a passenger ship, controlled by 20 and 16 parameters, respectively. We present a comprehensive error analysis and show the capabilities and usefulness of the methods especially during the preliminary design phase, finding new unconsidered designs while handling high dimensional parameterizations.

Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment.

An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla-Hughes-McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 104 and 1 × 105, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.

Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach.

In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.

Parametric Damage Mechanics Empowering Structural Health Monitoring of 3D Woven Composites.

This paper presents a data-driven structural health monitoring (SHM) method by the use of so-called reduced-order models relying on an offline training/online use for unidirectional fiber and matrix failure detection in a 3D woven composite plate. During the offline phase (or learning) a dataset of possible damage localization, fiber and matrix failure ratios is generated through high-fidelity simulations (ABAQUS software). Then, a reduced model in a lower-dimensional approximation subspace based on the so-called sparse proper generalized decomposition (sPGD) is constructed. The parametrized approach of the sPGD method reduces the computational burden associated with a high-fidelity solver and allows a faster evaluation of all possible failure configurations. However, during the testing phase, it turns out that classical sPGD fails to capture the influence of the damage localization on the solution. To alleviate the just-referred difficulties, the present work proposes an adaptive sPGD. First, a change of variable is carried out to place all the damage areas on the same reference region, where an adapted interpolation can be done. During the online use, an optimization algorithm is employed with numerical experiments to evaluate the damage localization and damage ratio which allow us to define the health state of the structure.

Modeling and Vibration Control of Sandwich Composite Plates.

A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton's principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.

Inverse Identification of a Constitutive Model for High-Speed Forming Simulation: An Application to Electromagnetic Metal Forming.

Forming simulation requires a constitutive model whose parameters are typically determined with tensile tests assumed static. However, this conventional approach is impractical for high-speed forming simulation characterized by high strain rates inducing transient effects. To identify constitutive parameters in relation to high-speed forming simulation, we formulated the problem of constitutive modeling as inverse parameter estimation addressed by regularized nonlinear least squares. Regarding the proposed inverse constitutive modeling, we adopted the L-curve method for proper regularization and model order reduction for rapid simulation. For demonstration, we corroborated the proposed strategy by identifying the modified Johnson-Cook model in the context of a free bulge test with electromagnetic metal forming simulation. The L-curve method allowed us to systematically choose a regularization parameter, and model order reduction brought enormous computational savings. After identifying constitutive parameters, we successfully verified and validated the reduced and original simulation models, respectively, with a manufactured workpiece. In addition, we validated the numerically identified constitutive model with a dynamic material test using a split Hopkinson pressure bar. Overall, we showed that inverse constitutive modeling for high-speed forming simulation can be effectively tackled by regularized nonlinear least squares with the help of an L-curve and a reduced-order model.

Operator compression with deep neural networks.

This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales. Based on the existing methods that compress such a multiscale operator to a finite-dimensional sparse surrogate model on a given target scale, we propose to directly approximate the coefficient-to-surrogate map with a neural network. We emulate local assembly structures of the surrogates and thus only require a moderately sized network that can be trained efficiently in an offline phase. This enables large compression ratios and the online computation of a surrogate based on simple forward passes through the network is substantially accelerated compared to classical numerical upscaling approaches. We apply the abstract framework to a family of prototypical second-order elliptic heterogeneous diffusion operators as a demonstrating example.

An Efficient, Memory-Saving Approach for the Loewner Framework.

The Loewner framework is one of the most successful data-driven model order reduction techniques. If N is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices L ∈ C N × N and S ∈ C N × N can be defined by solely relying on information encoded in the considered data set and they play a crucial role in the computation of the sought rational model approximation.In particular, the singular value decomposition of a linear combination of S and L provides the tools needed to construct accurate models which fulfill important approximation properties with respect to the original data set. However, for highly-sampled data sets, the dense nature of L and S leads to numerical difficulties, namely the failure to allocate these matrices in certain memory-limited environments or excessive computational costs. Even though they do not possess any sparsity pattern, the Loewner and shifted Loewner matrices are extremely structured and, in this paper, we show how to fully exploit their Cauchy-like structure to reduce the cost of computing accurate rational models while avoiding the explicit allocation of L and S . In particular, the use of the hierarchically semiseparable format allows us to remarkably lower both the computational cost and the memory requirements of the Loewner framework obtaining a novel scheme whose costs scale with N log N .

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands.

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

A framework for simplification of quantitative systems pharmacology models in clinical pharmacology.

Quantitative systems pharmacology (QSP) is a relatively new discipline within modelling and simulation that has gained wide attention over the past few years. The application of QSP models spans drug-target identification and validation, through all drug development phases as well as clinical applications. Due to their detailed mechanistic nature, QSP models are capable of extrapolating knowledge to predict outcomes in scenarios that have not been tested experimentally, making them an important resource in experimental and clinical pharmacology. However, these models are complicated to work with due to their size and inherent complexity. This makes many applications of QSP models for simulation, parameter estimation and trial design computationally intractable. A number of techniques have been developed to simplify QSP models into smaller models that are more amenable to further analyses while retaining their accurate predictive capabilities. Different simplification techniques have different strengths and weaknesses and hence different utilities. Understanding the utilities of different methods is essential for selection of the best method for a particular situation. In this paper, we have created an overall framework for model simplification techniques that allows a natural categorisation of methods based on their utility. We provide a brief description of the concept underpinning the different methods and example applications. A summary of the utilities of methods is intended to provide a guide to modellers in their model endeavours to simplify these complicated models.

Harris hawks optimization algorithm for model order reduction of interconnected wind turbines.

This paper illustrates the investigation of higher-scale interconnected wind turbine to realize its analytical design and simulation performance in terms of reduced order model. The present research is aimed to visualize the efficacy of the propounded harris hawks optimization (HHO) approach for different reduced order transfer functions with reference to model order reduction studies. Compared to the higher-scale model, the applied methodology aims to obtain better results in terms of steadiness and computational effort. Moreover, to realize a higher-dimensional power system, the implementation of the HHO may proffer more effectiveness and robustness as opposed to the state-of-the-art optimization techniques. The applied methodology aims to obtain better results in terms of stability and computational effort. Furthermore, to realize a higher dimensional system, implementation of the HHO may offer more effectiveness and robustness as opposed to the state-of-the-art optimization techniques.

On the parameter combinations that matter and on those that do not: data-driven studies of parameter (non)identifiability.

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.

Low-Computational-Cost Hybrid FEM-Analytical Induction Machine Model for the Diagnosis of Rotor Eccentricity, Based on Sparse Identification Techniques and Trigonometric Interpolation.

Since it is not efficient to physically study many machine failures, models of faulty induction machines (IMs) have attracted a rising interest. These models must be accurate enough to include fault effects and must be computed with relatively low resources to reproduce different fault scenarios. Moreover, they should run in real time to develop online condition-monitoring (CM) systems. Hybrid finite element method (FEM)-analytical models have been recently proposed for fault diagnosis purposes since they keep good accuracy, which is widely accepted, and they can run in real-time simulators. However, these models still require the full simulation of the FEM model to compute the parameters of the analytical model for each faulty scenario with its corresponding computing needs. To address these drawbacks (large computing power and memory resources requirements) this paper proposes sparse identification techniques in combination with the trigonometric interpolation polynomial for the computation of IM model parameters. The proposed model keeps accuracy similar to a FEM model at a much lower computational effort, which could contribute to the development and to the testing of condition-monitoring systems. This approach has been applied to develop an IM model under static eccentricity conditions, but this may extend to other fault types.

A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems: Application to Deformable Capsules Flowing in Microchannels.

An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic channel and vary systematically the governing parameter, namely the capillary number, ratio of the viscous to elastic forces, and the confinement ratio, ratio of the capsule to tube size. The resulting space-time-parameter problem is solved using two global POD reduced bases, determined in the offline stage for the space and parameter variables, respectively. A suitable low-order spatial reduced basis is then computed in the online stage for any new parameter instance. The time evolution of the capsule dynamics is achieved by identifying the nonlinear low-order manifold of the reduced variables; for that, a point cloud of reduced data is computed and a diffuse approximation method is used. Numerical comparisons between the full-order fluid-structure interaction model and the reduced-order one confirm both accuracy and stability of the reduction technique over the whole admissible parameter domain. We believe that such an approach can be applied to a broad range of coupled problems especially involving quasistatic models of structural mechanics.

Efficient design optimization of a miniaturized thermoelectric generator for electrically active implants based on parametric model order reduction.

This research focuses on the design of a miniaturized thermoelectric generator (TEG) for electrically active implants. Its design optimization is performed using the finite element method. A simplified TEG model is obtained by replacing the thermocouple array with a single representative thermopile, which considers the number and fill factor of the thermocouples as parameters. Instead of rebuilding the geometry of a detailed model with multiple thermocouples, the simplified model adapts the material properties of its representative thermopile, facilitating design optimization. We extend the model by integrating the simplified TEG together with a housing inside a human tissue model for thermoelectric analysis. For computation efficiency and applicability of model order reduction (MOR), a thermal model is derived from the thermoelectric one, with the Peltier effect being considered through an effective thermal conductivity. Through parametric MOR, two parametric reduced-order models are generated from the full-scale thermoelectric and thermal model, respectively. Furthermore, we demonstrate the design optimization of TEG both in full-scale and reduced-order model for maximal power output and sufficient voltage output.

Model order reduction of flow based on a modular geometrical approximation of blood vessels.

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

Reduction of quantitative systems pharmacology models using artificial neural networks.

Quantitative systems pharmacology models are often highly complex and not amenable to further simulation and/or estimation analyses. Model-order reduction can be used to derive a mechanistically sound yet simpler model of the desired input-output relationship. In this study, we explore the use of artificial neural networks for approximating an input-output relationship within highly dimensional systems models. We illustrate this approach using a model of blood coagulation. The model consists of two components linked together through a highly dimensional discontinuous interface, which creates a difficulty for model reduction techniques. The proposed approach enables the development of an efficient approximation to complex models with the desired level of accuracy. The technique is applicable to a wide variety of models and provides substantial speed boost for use of such models in simulation and control purposes.