Showing papers on "Model order reduction published in 2018"

Fast, Generic, and Reliable Control and Simulation of Soft Robots Using Model Order Reduction

Abstract: Obtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a finite element model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft-robot model. To keep the computational efficiency, hyperreduction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity, etc.) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FEMs of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FEMs and provides a generic way to control soft robots.

High-Fidelity Model Order Reduction for Microgrids Stability Assessment

Abstract: Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for large-scale power systems. In particular, the network dynamics, despite its fast nature, appears to have major influence on stability of slower modes. While detailed models are available, they are both computationally expensive and not transparent enough to provide an insight into the instability mechanisms and factors. In this paper, a computationally efficient and accurate reduced-order model is proposed for modeling inverter-based microgrids. The developed model has a structure similar to quasi-stationary model and at the same time properly accounts for the effects of network dynamics. The main factors affecting microgrid stability are analyzed using the developed reduced-order model and shown to be unique for microgrids, having no direct analogy in large-scale power systems. Particularly, it has been discovered that the stability limits for the conventional droop-based system are determined by the ratio of inverter rating to network capacity, leading to a smaller stability region for microgrids with shorter lines. Finally, the results are verified with different models based on both frequency and time domain analyses.

Reduced-Order Models for Representing Converters in Power System Studies

Abstract: A reduced-order model that preserves physical meaning is important for generating insight in large-scale power system studies. The conventional model-order reduction for a multiple-timescale system is based on discarding states with fast (short timescale) dynamics. It has been successfully applied to synchronous machines, but is inaccurate when applied to power converters because the timescales of fast and slow states are not sufficiently separated. In the method proposed here, several fast states are at first discarded but a representation of their interaction with the slow states is added back. Recognizing that the fast states of many converters are linear allows well-developed linear system theories to be used to implement this concept. All the information of the original system relevant to system-wide dynamics, including nonlinearity, is preserved, which facilitates judgments on system stability and insight into control design. The method is tested on a converter-supplied mini power system and the comparison of analytical and experiment results confirms high preciseness in a broad range of conditions.

$\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems

Abstract: We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volte...

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Abstract: Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

Model Order Reduction a Key Technology for Digital Twins

Abstract: An increasing number of disruptive innovations with high economic and social impact shape our digitalizing world. Speed and extending scope of these developments are limited by available tools and paradigms to master exploding complexities. Simulation technologies are key enablers of digitalization. They enable digital twins mirroring products and systems into the digital world. Digital twins require a paradigm shift. Instead of expert centric tools, engineering and operation require autonomous assist systems continuously interacting with its physical and digital environment through background simulations. Model order reduction (MOR) is a key technology to transfer highly detailed and complex simulation models to other domains and life cycle phases. Reducing the degree of freedom, i.e., increasing the speed of model execution while maintaining required accuracies and predictability, opens up new applications. Within this contribution, we address the advantages of model order reduction for model-based system engineering and real-time thermal control of electric motors.

A Manifold Learning Approach for Integrated Computational Materials Engineering

Abstract: Image-based simulation is becoming an appealing technique to homogenize properties of real microstructures of heterogeneous materials. However fast computation techniques are needed to take decisions in a limited time-scale. Techniques based on standard computational homogenization are seriously compromised by the real-time constraint. The combination of model reduction techniques and high performance computing contribute to alleviate such a constraint but the amount of computation remains excessive in many cases. In this paper we consider an alternative route that makes use of techniques traditionally considered for machine learning purposes in order to extract the manifold in which data and fields can be interpolated accurately and in real-time and with minimum amount of online computation. Locallly Linear Embedding is considered in this work for the real-time thermal homogenization of heterogeneous microstructures.

Combined Parameter and Model Reduction of Cardiovascular Problems by Means of Active Subspaces and POD-Galerkin Methods

Abstract: In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid. A parametric description of the admissible deformations, based on radial basis functions interpolation, is introduced. Since the parameter space may be very large, the first step in the combined reduction technique is to look for active subspaces in order to reduce the parameter space dimension. Then, we rely on model order reduction methods over the lower dimensional parameter subspace, based on a POD-Galerkin approach, to further reduce the required computational effort and enhance computational efficiency.

Cauer Ladder Network Representation of Eddy-Current Fields for Model Order Reduction Using Finite-Element Method

Abstract: A novel model order reduction method for efficient analysis of linear eddy-current problems is proposed in which the quasi-static electromagnetic fields are expressed by a weighted sum of a sequence of static electric- and magnetic-field modes. The modes are calculated sequentially by static electric and static magnetic computations using the conventional finite-element method, and the time-dependent weights are the voltages and currents of an equivalent Cauer ladder network of the problem. In this paper, the formulation of the method and a numerical test problem are presented, and the accuracy and enormous efficiency of the method are demonstrated by solving a 3-D nonlinear inductor model with a voltage excitation by a dc–dc converter, linearized around the dc current using frozen differential permeability.

A Geometric Approach to Dynamical Model Order Reduction

Abstract: Any model order reduced dynamical system that evolves a modal decomposition to approximate the discretized solution of a stochastic PDE can be related to a vector field tangent to the manifold of f...

Nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact

Abstract: In this paper, the nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact are investigated. A novel framework is proposed, in which the sophisticated geometrical structure is considered by finite solid element method and efficient model order reduction is applied to the model. The validity and efficiency of the reduced-order model are verified through critical speed and eigen problems. Its stable and unstable solutions are calculated by means of the assembly technique and the multiple harmonic balance method combined with the alternating frequency/time domain technique (MHB–AFT). The accurate frequency amplitudes are obtained accordingly for each harmonic component. The stabilities of the solutions are checked by the Floquet theory. Through the numerical computations, some complex nonlinear phenomena, such as combined frequency vibration, hysteresis, and resonant peak shifting, are discovered when the rub-impact occurs. The results also show that the control parameters of mass eccentricity, rub-impact stiffness, and rotational speed ratio make significant but different influences on the dynamical characteristics of the system. Therefore, a key innovation of this paper is the marriage of a hybrid modeling method—accurate modeling technique combined with model order reduction and solution method—highly efficient semi-analytic method of MHB–AFT. The proposed framework is benefit for parametric study and provides a better understanding of the nonlinear dynamical behaviors of the real complicated dual-rotor aero-engine with rub-impact.

Clustering approach to model order reduction of power networks with distributed controllers

Abstract: This paper considers the network structure preserving model reduction of power networks with distributed controllers. The studied system and controller are modeled as second-order and first-order ordinary differential equations, which are coupled to a closed-loop model for analyzing the dissimilarities of the power units. By transfer functions, we characterize the behavior of each node (generator or load) in the power network and define a novel notion of dissimilarity between two nodes by the $\mathcal {H}_{2}$ -norm of the transfer function deviation. Then, the reduction methodology is developed based on separately clustering the generators and loads according to their behavior dissimilarities. The characteristic matrix of the resulting clustering is adopted for the Galerkin projection to derive explicit reduced-order power models and controllers. Finally, we illustrate the proposed method by the IEEE 30-bus system example.

Advances in reduced order methods for parametric industrial problems in computational fluid dynamics

Abstract: Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

Randomized Local Model Order Reduction

Abstract: In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solut...

Gradient-Based Multiobjective Optimization with Uncertainties

Abstract: In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.

A Reduced-Order Electrochemical Model of Li-Ion Batteries for Control and Estimation Applications

Abstract: In this paper, a reduced-order electrochemical model of lithium-ion batteries is developed for control and estimation applications through analytical model order reduction based on a Galerkin projection method. The governing diffusion partial differential equations in the liquid and solid phases are approximated into low-order systems of ordinary differential equations while the physical meaning of all model parameters is preserved, allowing one to perform state and parameter estimation. The selection of basis functions for the Galerkin projection method and model order truncation is carefully determined based on analysis both in the frequency and time domains. With the reduced-order diffusion models in the liquid and solid phases, an extended single particle model incorporating the electrolyte dynamics is developed. The model is then validated against the experimental data gathered from two batteries with different chemistries (lithium nickel manganese cobalt oxide/graphite and lithium iron phosphate oxide/graphite) at different input conditions. Results show that the reduced-order model agrees very well with experimental data at various conditions. Meanwhile, it can be simulated thousands of times faster than the real time, making it suitable for long-term-life simulation, control, and estimation applications.

Balanced truncation model order reduction in limited time intervals for large systems

Abstract: In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on the efficient numerical realization of this model reduction approach in case of large system dimensions. We discuss numerical methods to deal with the resulting matrix exponential functions and Lyapunov equations which are solved for low-rank approximations. Our main tool for this purpose are rational Krylov subspace methods. We also discuss the eigenvalue decay and numerical rank of the solutions of the Lyapunov equations. These results, and also numerical experiments, will show that depending on the final time horizon, the numerical rank of the Lyapunov solutions in time-limited balanced truncation can be smaller compared to standard balanced truncation. In numerical experiments we test the approaches for computing low-rank factors of the involved Lyapunov solutions and illustrate that time-limited balanced truncation can generate reduced order models having a higher accuracy in the considered time region.

A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Abstract: We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead.

Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework

Abstract: The Loewner framework for model reduction is extended to the class of linear switched systems. One advantage of this framework is that it introduces a trade-off between accuracy and complexity. Moreover, through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system. Hence, another advantage of the framework is that it does not require the initial system matrices. More exactly, the data used in this framework consists in frequency domain samples of input-output mappings of the original system. The definition of generalized transfer functions for linear switched systems resembles the one for bilinear systems. A key role is played by the coupling matrices, which ensure the transition from one active mode to another.

POD reduced-order modeling for evolution equations utilizing arbitrary finite element discretizations

Abstract: The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing proper orthogonal decomposition (POD-MOR) for nonlinear parabolic evolution problems. We consider snapshots which live in different finite element spaces, which means in a fully discrete setting that the snapshots are vectors of different length. From a numerical point of view, this leads to the problem that the usual POD procedure which utilizes a singular value decomposition of the snapshot matrix, cannot be carried out. In order to overcome this problem, we here construct the POD model/basis using the eigensystem of the correlation matrix (snapshot Gramian), which is motivated from a continuous perspective and is set up explicitly, e.g., without the necessity of interpolating snapshots into a common finite element space. It is an advantage of this approach that the assembly of the matrix only requires the evaluation of inner products of snapshots in a common Hilbert space. This allows a great flexibility concerning the spatial discretization of the snapshots. The analysis for the error between the resulting POD solution and the true solution reveals that the accuracy of the reduced-order solution can be estimated by the spatial and temporal discretization error as well as the POD error. Finally, to illustrate the feasibility of our approach, we present a test case of the Cahn–Hilliard system utilizing h-adapted hierarchical meshes and two settings of a linear heat equation using nested and non-nested grids.

Simulation-Based Classification; a Model-Order-Reduction Approach for Structural Health Monitoring

Abstract: We present a model-order-reduction approach to simulation-based classification, with particular application to structural health monitoring. The approach exploits (1) synthetic results obtained by repeated solution of a parametrized mathematical model for different values of the parameters, (2) machine-learning algorithms to generate a classifier that monitors the damage state of the system, and (3) a reduced basis method to reduce the computational burden associated with the model evaluations. Furthermore, we propose a mathematical formulation which integrates the partial differential equation model within the classification framework and clarifies the influence of model error on classification performance. We illustrate our approach and we demonstrate its effectiveness through the vehicle of a particular physical companion experiment, a harmonically excited microtruss.

Semi-analytic contact technique in a non-linear parametric model order reduction method for gear simulations

Abstract: In this work we present a novel method for the solution of gear contact problems in flexible multi-body. These problems are characterized by significant variation in the location and size of the contact area, typically requiring a high number of degrees of freedom to correctly capture deformation and stress fields. Therefore fully dynamic simulation is computationally prohibitive. To overcome these limitations, we exploit a combined analytic-numerical contact model within a parametric model order reduction (PMOR) scheme. The reduction space consists of a truncated set of eigenvectors augmented with a parameter dependent set of residual static shape vectors. Each static shape is computed by interpolating among a set of displacement modes of the interacting bodies, obtained from a series of precomputed static contact analyses. During the contact analyses, an analytic model based on the Hertz theory describes the teeth local deformation. We implement the proposed method in an in-house code and we apply it to spur and helical gears dynamic contact analyses. We compare the results with classical PMOR schemes highlighting how the combined use of the semi-analytic contact model allows to decrease further the model complexity as well as the computational burden, for both static and dynamic cases. Finally, we validate the methodology by means of a comparison with experimental data found in literature, showing that the numerical method is able to capture quantitatively the static transmission error measurements in case of both helical and spur geared transmission for different torque levels.

Energy preserving model order reduction of the nonlinear Schrödinger equation

Abstract: An energy preserving reduced order model is developed for two dimensional nonlinear Schrodinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of Hamiltonian ordinary differential equations are integrated in time by the energy preserving average vector field (AVF) method. The mass and energy preserving reduced order model (ROM) is constructed by proper orthogonal decomposition (POD) Galerkin projection. The nonlinearities are computed for the ROM efficiently by discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD). Preservation of the semi-discrete energy and mass are shown for the full order model (FOM) and for the ROM which ensures the long term stability of the solutions. Numerical simulations illustrate the preservation of the energy and mass in the reduced order model for the two dimensional NLSE with and without the external potential. The POD-DMD makes a remarkable improvement in computational speed-up over the POD-DEIM. Both methods approximate accurately the FOM, whereas POD-DEIM is more accurate than the POD-DMD.