Showing papers on "Model order reduction published in 2022"

A Real-time Cutting Model Based on Finite Element and Order Reduction

Abstract: Telemedicine plays an important role in Corona Virus Disease 2019 (COVID-19). The virtual surgery simulation system, as a key component in telemedicine, requires to compute in real-time. Therefore, this paper proposes a real-time cutting model based on finite element and order reduction method, which improves the computational speed and ensure the real-time performance. The proposed model uses the finite element model to construct a deformation model of the virtual lung. Meanwhile, a model order reduction method combining proper orthogonal decomposition and Galerkin projection is employed to reduce the amount of deformation computation. In addition, the cutting path is formed according to the collision intersection position of the surgical instrument and the lesion area of the virtual lung. Then, the Bezier curve is adopted to draw the incision outline after the virtual lung has been cut. Finally, the simulation system is set up on the PHANTOM OMNI force haptic feedback device to realize the cutting simulation of the virtual lung. Experimental results show that the proposed model can enhance the real-time performance of telemedicine, reduce the complexity of the cutting simulation and make the incision smoother and more natural. © 2022 CRL Publishing. All rights reserved.

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

Abstract: A robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we propose a method to systematically address the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either over-conservative or heuristic and possibly unreliable methods.

Deep-HyROMnet: A Deep Learning-Based Operator Approximation for Hyper-Reduction of Nonlinear Parametrized PDEs

Abstract: Abstract To speed-up the solution of parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as surrogate models obtained through machine learning techniques. Thanks to its physics-based structure, ensured by the use of a Galerkin projection of the full order model (FOM) onto a linear low-dimensional subspace, the Galerkin-RB method yields approximations that fulfill the differential problem at hand. However, to make the assembling of the ROM independent of the FOM dimension, intrusive and expensive hyper-reduction techniques, such as the discrete empirical interpolation method (DEIM), are usually required, thus making this strategy less feasible for problems characterized by (high-order polynomial or nonpolynomial) nonlinearities. To overcome this bottleneck, we propose a novel strategy for learning nonlinear ROM operators using deep neural networks (DNNs). The resulting hyper-reduced order model enhanced by DNNs, to which we refer to as Deep-HyROMnet, is then a physics-based model, still relying on the RB method approach, however employing a DNN architecture to approximate reduced residual vectors and Jacobian matrices once a Galerkin projection has been performed. Numerical results dealing with fast simulations in nonlinear structural mechanics show that Deep-HyROMnets are orders of magnitude faster than POD-Galerkin-DEIM ROMs, still ensuring the same level of accuracy.

Parallel Higher Order DGTD and FETD for Transient Electromagnetic-Circuital-Thermal Co-Simulation

Abstract: A hybrid higher order discontinuous Galerkin time-domain (DGTD) method and finite-element time-domain (FETD) method with parallel technique is proposed for electromagnetic (EM)–circuital–thermal co-simulation in this article. For electromagnetic simulation, DGTD method with higher order hierarchical vector basis functions is used to solve Maxwell equation. Circuit simulation is carried out by modified nodal analysis method. For thermal simulation, FETD method with higher order interpolation scalar basis functions is adopted to solve heat conduction equation. To implement electromagnetic–circuital–thermal co-simulation, the electromagnetic and circuital equations are strongly coupled through voltages, currents, and electric fields at the lumped ports first. Then the electromagnetic and thermal equations are weakly coupled with electromagnetic loss and temperature-dependent medium parameters. Finally, large-scale parallel technique is used to accelerate the process of multiphysics simulation. Numerical results are given to validate the correctness and capability of the proposed electromagnetic–circuital–thermal co-simulation method.

Fast data-driven model reduction for nonlinear dynamical systems

Abstract: Abstract We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable ) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.

Topology optimization of MEMS resonators with target eigenfrequencies and modes

Abstract: In this paper we present a density based topology optimization approach to the synthesis of industrially relevant MEMS resonators. The methodology addresses general resonators employing suspended proof masses or plates, where the first structural vibration modes are typically of interest and have to match specific target eigenfrequencies . As a significant practical example we consider MEMS gyroscope applications, where target drive and sense eigenfrequencies are prescribed, as well as an adequate distance of spurious modes from the operational frequency range. The 3D dynamics of the structure are analysed through Mindlin shell finite elements and a numerically efficient design procedure is obtained through the use of model order reduction techniques based on the combination of multi-point constraints, static approximations and static reduction. Manufacturability of the optimized designs is ensured by imposing a minimum length scale to the geometric features defining the layout. Using deterministic, gradient-based mathematical programming, the method is applied to the design of both single mass and tuning fork MEMS resonators. It is demonstrated that the proposed methodology is capable of meeting the target frequencies and corresponding modes fulfilling common industrial requirements.

POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations

Abstract: Abstract In the present paper we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable, e.g., in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

Stability Preserving Model Reduction Technique for 1-D and 2-D Systems With Error Bounds

Abstract: 2-D state-space models are hard to deal with due to the complex structure; furthermore, simulation, analysis, design, and control will become more complicated when its order increases. In this brief, the decomposition of the 2-D model into two 1-D models are obtained by minimal rank-decomposition condition then the model reduction is performed on these two 1-D models. The proposed technique applies to both 1-D and 2-D systems. Furthermore, the proposed technique provides the reduced-order model’s stability, and an a priori error bound expression for the 1-D and 2-D systems. Numerical examples are presented along with comparisons among existing and the proposed techniques that illustrate the proposed technique’s efficacy.

Improved Nonlinear Analysis of a Propeller Blade Based on Hyper-Reduction

Abstract: In this study, an improved nonlinear-analysis framework capable of predicting geometric nonlinearity and high-speed rotation in rotating structures was developed. A nonlinear time-transient simulation requires large computations owing to an iterative solution algorithm. To reduce the anticipated computational cost, a proper orthogonal decomposition (POD)-based reduced-order modeling (ROM) combined with hyper-reduction is applied. To efficiently perform computations during the online stage, three hyper-reduction techniques were employed to approximate the nonlinear finite-element matrices: discrete empirical interpolation method (DEIM), Gauss–Newton with approximated tensors (GNAT), and energy-conserving sampling and weighting (ECSW). The present frameworks are applied to the time-transient simulation of a propeller, including parametric variations. Compared with the DEIM method, the GNAT and ECSW methods exhibited better enhancement of the accuracy and robustness of the reduced-order representation. Additionally, the computational efficiency of the ECSW method was improved significantly compared with that of other POD-based ROM approaches.

Nonlinear Model Order Reduction of Induction Motors Using Parameterized Cauer Ladder Network Method

Abstract: In this study, we established the nonlinear model order reduction (MOR) of induction motors by parameterizing a multi-port Cauer ladder network (CLN). Appropriate parameters were selected to incorporate nonlinear magnetic characteristics. The parameterized multi-port CLN was applied to the transient analysis of a rotating induction motor. The proposed method reproduced the finite-element analysis results with various driving frequencies and slips. The parameterized multi-port CLN can effectively reduce the computation time for analyses requiring a large number of time steps.

An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics

Abstract: In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven nature and its modularity allow an easy integration into existing pipelines. We describe a complete optimization framework with automated geometrical parameterization, reduction of the dimension of the parameter space, and non-intrusive model order reduction such as dynamic mode decomposition and proper orthogonal decomposition with interpolation. Moreover several industrial examples are illustrated.

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

Abstract: 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.

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Abstract: This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the full model is approximated on local reduced spaces that are adapted in time using dynamical low-rank approximation techniques. The reduced dynamics is prescribed by approximating the symplectic projection of the Hamiltonian vector field in the tangent space to the local reduced space. This ensures that the canonical symplectic structure of the Hamiltonian dynamics is preserved during the reduction. In addition, accurate approximations with low-rank reduced solutions are obtained by allowing the dimension of the reduced space to change during the time evolution. Whenever the quality of the reduced solution, assessed via an error indicator, is not satisfactory, the reduced basis is augmented in the parameter direction that is worst approximated by the current basis. Extensive numerical tests involving wave interactions, nonlinear transport problems, and the Vlasov equation demonstrate the superior stability properties and considerable runtime speedups of the proposed method as compared to global and traditional reduced basis approaches.

Static condensation of peridynamic heat conduction model

Abstract: A model order reduction methodology for reducing the order of the peridynamic transient heat model is proposed. This methodology is based on the static condensation procedure. To set the development of the model reduction procedure on a sound mathematical setting, a nonlocal vector calculus was employed in the formulation of the heat transport problem. The model order reduction framework proposed in this study provides a technique to reduce the dimensionality of a peridynamic transport model while still maintaining accurate prediction of the model response. Moreover, the methodology can be adaptively applied to accommodate different resolution requirements for different sections of the model. Using numerical experiments, the proposed methodology is shown to be capable of accurately reproducing results of the full peridynamic transient heat transport problem.