Advances of Model Order Reduction Research in Large-scale System Simulation

Model Order Reduction (MOR) plays more and more imp or tant role in complex system simulation, design and control recently. For example , for the large-size space structures, VLSI and MEMS (Micro-ElectroMechanical Systems) etc., in order to shorten the development cost, increase the system co ntrolling accuracy and reduce the complexity of controllers, the reduced order model must be constructed. Even in Virtual Reality (VR), the simulation and d isplay must be in real-time, the model order must be reduced too. The recent advances of MOR research are overviewed in the article. The MOR theor y and methods may be classified as Singular Value decomposition (SVD) based, the Krylov subspace based and others. The merits and demerits of the different meth ods are analyzed, and the existed problems are pointed out. Moreover, the applic ation’s fields are overviewed, and the potential applications are forecaste d. After the existed problems analyzed, the future work is described. There are som e problems in the traditional methods such as SVD and Krylov subspace, they are that it’s difficult to (1)guarantee the stability of the original system, (2) b e adaptive to nonlinear system, and (3) control the modeling accuracy. The f uture works may be solving the above problems on the foundation of the tradition al methods, and applying other methods such as wavelet or signal compression.

An Adaptive Substructure-Based Model Order Reduction Method for Nonlinear Seismic Analysis in OpenSees

Structural components may enter an initial-elastic state,a plastic-hardening state and a residual-elastic state during strong seismic excitations.In the residual-elastic state,structural components keep in an unloading/reloading stage that is dominated by a tangent stiffness,thus structural components remain residual deformations but behave in an elastic manner.It has a great potential to make model order reduction for such structural components using the tangent-stiffness-based vibration modes as a reduced order basis.In this paper,an adaptive substructure-based model order reduction method is developed to perform nonlinear seismic analysis for structures that have a priori unknown damage distribution.This method is able to generate time-varying substructures and make nonlinear model order reduction for substructures in the residual-elastic phase.The finite element program OpenSees has been extended to provide the adaptive substructure-based nonlinear seismic analysis.At the low level of OpenSees framework,a new abstract layer is created to represent the time-varying substructures and implement the modeling process of substructures.At the high level of OpenSees framework,a new transient analysis class is created to implement the solving process of substructure-based governing equations.Compared with the conventional time step integration method,the adaptive substructure-based model order reduction method can yield comparative results with a higher computational efficiency.

Model Order Reduction for Coupled Dynamic Characterization of Torsional Micromirrors

Numerical solutions could not perform rapid system-level simulation of the behavior of micro-electro-mechanical systems（MEMS） and analytic solutions for the describing partial differential equations are only available for simple geometries.Model order reduction（MOR） can extract approximate low-order model from the original large scale system.Conventional model order reduction algorithm is based on first-order system model,however,most structure mechanical MEMS systems are naturally second-order in time.For the purpose of solving the above problem,a direct second-order system model order reduction approach based on Krylov subspace projection for the coupled dynamic study of electrostatic torsional micromirrors is presented.The block Arnoldi process is applied to create the orthonormal vectors to construct the projection matrix,which enables the extraction of the low order model from the discretized system assembled through finite element analysis.The transfer functions of the reduced order model and the original model are expanded to demonstrate the moment-matching property of the second-order model reduction algorithm.The torsion and bending effect are included in the finite element model,and the squeeze film damping effect is considered as well.An empirical method considering relative error convergence is adopted to obtain the optimal choice of the order for the reduced model.A comparison research between the full model and the reduced model is carried out.The modeling accuracy and computation efficiency of the presented second-order model reduction method are confirmed by the comparison research results.The research provides references for MOR of MEMS.

AN ACCELERATED WAVEFORM RELAXATION APPROACH BASED ON MODEL ORDER REDUCTION FOR LARGE COUPLING SYSTEMS

In this paper, we present an accelerated simulation approach on waveform relaxation using Krylov subspace for a large time-dependent system composed of some subsystems. This approach first allows these subsystems to be decoupled by waveform relaxation. Then the Arnoldi procedure based on Krylov subspace is provided to accelerate the simulation of the decoupled subsystems independently. For the new approach, the convergent conditions on waveform relaxation are derived. The robust behavior is also successfully illustrated via numerical examples.

Recent Advance in Non-Krylov Subspace Model Order Reduction of Interconnect Circuits

Model order reduction of interconnect circuits is an important technique to reduce the circuit complexity and improve the efficiency of post-layout verification process in the nanometer VLSI design. Existing works using the Krylov subspace method are very efficient, but the resulting models are less compact and lack global accuracy. Also, existing methods cannot handle interconnect circuits with large input and output ports. Recent advances in reduction techniques using non-Krylov subspace techniques such as truncated balanced realization （TBR） hold some promise to solve these problems. In this paper, we first review the classic TBR-based reduction methods and then present the recent developments in fast TBR-based reduction and techniques such as PMTBR, SBPOR, and ETBR methods. These newly proposed methods try to avoid the expensive computing steps in traditional TBR methods at some cost to accuracy to boost efficiency and scalability, which is critical to reduce large interconnect parasitics modeled as RLCK circuits. The ETBR method can also reduce circuits with massive ports by considering the input signals. We show the pros and cons of each method and compare them on a set of large interconnect circuits, and finally point to some new research directions for this area.

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

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 realtime 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.

Fast Model-based Design of High Performance Permanent Magnet Machine for Next Generation Electric Propulsion for Urban Aerial Vehicle Application

Model order reduction(MOR)is considered as a good alternative to reduce the computational scale for electro-magnetic problems.The aim of this work is to introduce the use of dynamic mode decomposition(DMD)as a promising tool for MOR to analyze its effectiveness in creating a fast model-based design platform for the permanent magnet motor design for ur-ban aerial vehicles(UAVs).Using a singular value decomposition(SVD)based DMD,the design process is constructed and verified against different scenarios.

RLC Equivalent Circuit Synthesis Method for Structure-Preserved Reduced-Order Model of Interconnect in VLSI

This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalent circuitscan be synthesized, both the structures of input and output incidence matrices and theblock structure of the circuit matrices should be preserved in the reduced-order models.Block structure preserving MOR methods have been well established. In this paper,we propose an embeddable Input-Output structure Preserving Order Reduction(IOPOR) technique to further preserve the structures of input and output incidencematrices. By combining block structure preserving MOR methods and IOPOR technique,we develop an RLC equivalent circuit synthesis method RLCSYN (RLC SYNthesis).Inline diagonalization and regularization techniques are specifically proposedto enhance the robustness of inductance synthesis. The pure RLC model, high modelingaccuracy, passivity guaranteed property and SPICE simulation robustness makeRLCSYN more applicable in interconnect analysis, either for digital IC design ormixedsignal IC simulation.

Robust control of isopropyl benzene production process using H_(∞) loop shaping control scheme

This paper discusses robust control strategy for isopropyl benzene production process using the method of loop shaping H_(∞) technology.This cumene production process is a part of phenol plant in HOCL,Kochi.H_(∞) control of the propylene concentration is done here.The H_(∞) controller is derived from the linearised model of the reactor.The optimal H_(∞) controller is obtained by simplifying two algebraic Riccati equations.The proposed PID-like H_(∞) controller provides a single tuning parameter which makes the controller design more accurate.The proposed controller has been compared with other robust controllers like H_(2) and LQR.The H_(∞) controller is found to be superior in a wide frequency range and has a feature of low distortion and good regulating performance.The reactor model has been developed in COMSOL Multiphysics with the parameters obtained from HOCL plant,Kochi.The model extracted is reduced using model order reduction for the controller design.

LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

In recent years,the Active Flutter Suppression(AFS)employing Linear ParameterVarying(LPV)framework has become a hot spot in the research field.Nevertheless,the flutter suppression technique is facing two severe challenges.On the one hand,due to the fatal risk of flight test near critical airspeed,it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data.On the other hand,saturation of the actuator may degrade the closed-loop performance,which was often neglected in the past work.To tackle these two problems,a new active controller design procedure is proposed to suppress flutter in this paper.Firstly,with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates(SMILE)technique,a set of high-fidelity Linear Time-Invariant(LTI)models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system.And then,the unstable aeroelastic dynamics beyond critical airspeed are‘predicted’by extrapolating the resulting LPV model.Secondly,based on the control-oriented LPV model,an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation.Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored,the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter(BFF)when encountering the actuator saturation.However,the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system whenencountering serious actuator saturation.

Equivalent Pi-Network Model of Lossy and Dispersive Coupled Transmission Lines

An equivalent circuit representation is presented for a set of coupled transmission lines. An ap- proximation of the hyperbolic secant function allows a simple derivation of a staged model that accounts for the complex frequency dependent parameters. The model converts the T-ladder network into a i-r-network with controlled sources. The equivalent circuit based approach presented here is not only intriguing but also enhances the computed accuracy and efficiency. Numerical simulations verify the accuracy of this approach for both time and frequency domain responses.

A Static Condensation Reduced Basis Element Approach for the Reynolds Lubrication Equation

In this paper,we propose a Static Condensation Reduced Basis Element(SCRBE)approach for the Reynolds Lubrication Equation(RLE).The SCRBEmethod is a computational tool that allows to efficiently analyze parametrized structures which can be decomposed into a large number of similar components.Here,we extend the methodology to allow for a more general domain decomposition,a typical example being a checkerboard-pattern assembled from similar components.To this end,we extend the formulation and associated a posteriori error bound procedure.Our motivation comes from the analysis of the pressure distribution in plain journal bearings governed by the RLE.However,the SCRBE approach presented is not limited to bearings and the RLE,but directly extends to other component-based systems.We show numerical results for plain bearings to demonstrate the validity of the proposed approach.