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.

State space solution to 3D multilayered elastic soils based on order reduction method

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

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.

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.

Sliding Mode Control Design via Reduced Order Model Approach

This paper presents a design of continuous-time sliding mode control for the higher order systems via reduced order model. It is shown that a continuous-time sliding mode control designed for the reduced order model gives similar performance for thc higher order system. The method is illustrated by numerical examples. The paper also introduces a technique for design of a sliding surface such that the system satisfies a cost-optimality condition when on the sliding surface.

A single-manufacturer multi-retailer sustainable reworking model for green and environmental sensitive demand under discrete ordering cost reduction

This paper develops an economic production quantity(EPQ)model for a singlemanufacturer multi-retailer(SMMR)production and reworking system with green and environmental sensitive customer demand.The minimum cost of the manufacturer has obtained under carbon emissions(CE)policies and discrete ordering cost reduction.The model is used to optimize the total number of shipments,greening investment level,environmental measure,and lot size for productions and rework.This research work determines that the manufacturer’s and retailer’s profits will be increased after considering the environmental and green dependent demand of customers.Further,the development of green and environmental demand is proposed to minimize the CE and maximize the demand for the customers.In the existing literature,no discrete investment is developed for reducing the cost of ordering for the retailer/buyer.However,in this paper,we have introduced it.We provide numerical examples to explain the models and determine the significance of model parameters.

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.

市场主体登记秩序法益的刑法保护

市场主体登记制度兼具公私法属性,所蕴含的秩序法益存在一元论与二元论之争。市场主体登记秩序相对于个人法益而言具有独立性,秩序法益保护具有效率、自由和安全的多元价值。秩序法益具有复杂性和抽象性,存在与个人法益并存或单独存在的类型形态,有必要运用法益还原论予以还原。基于类型化思维,根据秩序法益能否还原、是否必须还原、是否已还原为个人法益的不同情况,判断其应否成为刑法保护的法益、是否将个人法益所受的实际侵害作为具体定罪标准。市场主体虚假登记主要涉及“两虚一逃”犯罪,在认缴登记制改革下,“两虚一逃”呈现出罪化趋势,但仍存在入罪的现实必要性;实践中应针对其所侵犯的秩序法益的不同类型形态予以刑事责任认定。

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.

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.

A Local Deep Learning Method for Solving High Order Partial Differential Equations

At present, deep learning based methods are being employed to resolvethe computational challenges of high-dimensional partial differential equations(PDEs). But the computation of the high order derivatives of neural networks iscostly, and high order derivatives lack robustness for training purposes. We proposea novel approach to solving PDEs with high order derivatives by simultaneously approximating the function value and derivatives. We introduce intermediate variablesto rewrite the PDEs into a system of low order differential equations as what is donein the local discontinuous Galerkin method. The intermediate variables and the solutions to the PDEs are simultaneously approximated by a multi-output deep neuralnetwork. By taking the residual of the system as a loss function, we can optimizethe network parameters to approximate the solution. The whole process relies onlow order derivatives. Numerous numerical examples are carried out to demonstrate that our local deep learning is efficient, robust, flexible, and is particularlywell-suited for high-dimensional PDEs with high order derivatives.

An Impedance-based Parameter Design Method for Active Damping of Load Converter Station in MTDC Distribution System

To achieve the efficient application of impedance analysis in the stability assessment and enhancement of multiterminal DC distribution systems, this paper proposes the DCside reduced-order impedance models with power control and AC voltage control, respectively, by taking the load converter station as the object. By using the DC-side current as the feedforward state, the active compensator applied to the load converter station with two control modes is also derived as well as the corresponding reduced-order impedance models. Combined with the reduced-order impedance models, a method based on damping factor sensitivity is further proposed to design the parameters of the derived active compensators. The verification results in the frequency domain and time domain demonstrate the accuracy of the reduced-order impedance and the effectiveness of the proposed compensator parameter design method.

Composite Control of Nonlinear Singularly Perturbed Systems via Approximate Feedback Linearization

This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.

Design and Verification of High-Speed VLSI Physical Design

With the rapid development of deep submicron (DSM) VLSI circuit designs, many issues such as time closure and power consumption are making the physical designs more and more challenging. In this review paper we provide readers with some recent progress of the VLSI physical designs. The recent developments of floorplanning and placement, interconnect effects, modeling and delay, buffer insertion and wire sizing, circuit order reduction, power grid analysis, parasitic extraction, and clock signal distribution are briefly reviewed.

ε-Dependent Controllability for Two Time-Scale Systems

This paper investigates the controllability of two time-scale systems using both the time-scale separation model and the slow-fast order reduction model. This work considers the effect of a singular perturbation parameter on the model transformations to improve the criterion precision. The Maclaurin expansion method and homotopy arithmetic are introduced to obtain t-dependent controllability criteria. Examples indicate that the s-dependent controllability criteria are more accurate and that the controllability of two time-scale systems does not change during model transformations with these more accurate forms.

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.