System Reduction Method Research Articles

Interpolatory Model Order Reduction Method for Second Order Systems

AbstractIn this paper, we propose a structure‐preserving model reduction method for second‐order systems based on H2 optimal interpolation. In the iterative process of the proposed method, an algorithm is presented for selecting interpolation points in order to control the dimension of the reduced system. Result about error analysis of the interpolation points selection algorithm is obtained and the property of the new model reduction method is also given. Finally, three numerical examples are performed to illustrate the effectiveness of the new method.

Interface reduction methods for mechanical systems with elastohydrodynamic lubricated revolute joints

In this contribution, three different reduction methods for elastic structures with lubricated interfaces are presented and compared with each other. While for the first two methods, classical reduction strategies from component mode synthesis are applied, for the third method, a dual reduction basis is used, consisting of vibration modes of the free floating structure, attachment modes and residual modes. Within this new dual approach, it is shown how the residual modes can be obtained by applying pressure distributions of analytical solutions of the hydrodynamic equations. The described methods are compared for two classical simulation example—for a one-sided elastohydrodynamic lubricated joint of a slider–crank mechanism in a floating frame of reference formulation as well as for an elastic rotor in a flexible journal bearing.

Splitting problem for WKB asymptotics in a nonresonant case and the reduction method for linear systems

As applied to the problem of asymptotic integration of linear systems of ordinary differential equations, we propose a reduction of order method that allows one to effectively construct solutions indistinguishable in the growth/decrease rate at infinity. In the case of a third-order equation, we use the developed approach to answer Bellman’s problem on splitting WKB asymptotics of subdominant solutions that decrease at the same rate. For a family of Wigner–von Neumann type potentials, the method allows one to formulate a selection rule for nonresonance values of the parameters (for which the corresponding second-order equation has a Jost solution).

Structure-Preserving-Based Model-Order Reduction of Parameterized Interconnect Systems

In recent years, the continued miniaturization of VLSI circuits leads to the need for more efficient simulation of large-scale linear dynamical systems with ever-increasing state-space dimension. The linear dynamical systems in VLSI circuit simulation are RC or RCL models of the VLSI circuit’s interconnected system. Model-order reduction is an important technique to reduce such a high complexity. Along the technology scaling, the indetermination in the manufacturing process causes variations in the critical dimensions and interlevel dielectric thickness of interconnects, which could make the system performance unpredictable and produce a significant parametric yield loss. An efficient exploitation of these design activities results in a parameterized model-order reduction technique able to reduce large systems of equations with respect to all of the variable parameters of the circuit, (i.e., resistance, capacitance, and inductance). For this purpose, we propose a novel parameterized model-order reduction method for interconnect variation systems, which is based on an efficient and reliable combination of invariable structure-preserving model-order reduction (SPMOR) methods and variable parameter retaining schemes. It is referred to as a parameterized interconnect model-order reduction via structure-preserving algorithm. The SPMOR model yields the same form of the original state equation and preserves the passivity of the parameterized RC and RLC networks, like the well-known passive reduced-order interconnect algorithm for nonparameterized RC and RLC networks. The most important benefit it entails is the ability to preserve the probability characteristic of the original interconnect systems. Pertinent numerical examples are proposed to validate the proposed SPMOR approach.

AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

LTI system order reduction approach based on asymptotical equivalence and the Co-operation of biology-related algorithms

A novel order reduction method for linear time invariant systems is described. The method is based on reducing the initial problem to an optimization one, using the proposed model representation, and solving the problem with an efficient optimization algorithm. The proposed method of determining the model allows all the parameters of the model with lower order to be identified and by definition, provides the model with the required steady-state. As a powerful optimization tool, the meta-heuristic Co-Operation of Biology-Related Algorithms was used. Experimental results proved that the proposed approach outperforms other approaches and that the reduced order model achieves a high level of accuracy.

Frequency-limited -controller order reduction for linear parameter-varying systems

ABSTRACTIn this paper, a controller order reduction method for linear parameter-varying systems is presented. The proposed method is based on the frequency-weighted balanced truncation technique, which has the advantage to reduce the order in a specific frequency range. The approach is discussed and is proved to preserve the closed-loop stability with a guaranteed upper error bound. Effectiveness and performance of the obtained reduced-order controller are investigated by applying it to an automotive semi-active suspension control. The obtained simulation results show that objectives such as the road handling and the passenger comfort realised with the reduced-order controller are kept in the same performance level as with the full-order controller. Moreover, a comparison with an other-order reduction method is shown and confirms the advantage of the developed method.

A Structured Model Reduction Method for Linear Interconnected Systems

This paper develops a model reduction method for a large-scale interconnected system that consists oflinear dynamic components. In the model reduction, we aim to preserve physical characteristics of each component. To this end, we formulate a structured model reduction problem that reduces the model order of components while preserving the feedback structure. Although there are a few conventional methods for such structured model reduction to preserve stability, they do not explicitly consider performance of the reduced-order feedback system. One of the difficulties in the problem with performance guarantee comes from nonlinearity of a feedback system to each component. The problem is essentially in a class of nonlinear optimization problems, and therefore it cannot be efficiently solved even in numerical computation. In this paper, application of an equivalent transformation and a proper approximation reduces this nonlinear problem to a problem of the weighted linear model reduction. Then, by using the weighted balanced truncation technique, we construct a reduced-order model with preserving the feedback structure to ensure small modeling error. Finally, we verify the effectiveness of the proposed method through numerical experiments.

Comparison of two model order reduction methods for elastic multibody systems with moving loads

In this paper, two different model order reduction approaches for elastic multibody systems with moving loads are considered. The first approach is based on a parametric formulation of the input an...

Frequency interval balanced truncation of discrete-time bilinear systems

This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework ...

Laguerre functions approximation for model reduction of second order time-delay systems

This paper presents a Laguerre-based model reduction method for time-delay systems, which naturally retains the second-order-structure of original systems. We expand time-delay systems under the Laguerre function basis and show that Laguerre coefficients satisfy a special linear system and therefore can be calculated iteratively. Then reduced models are produced using projection methods, where projection matrices are defined in terms of the derived Laguerre coefficients, while properties on the preservation of Laguerre coefficients are proved elegantly based on the linear system corresponding to Laguerre coefficients. We also discuss the practical implementation of the approach. A high order Arnoldi procedure with memory saving is provided which leads to an efficient execution of our approach in practice. Numerical examples are simulated to illustrate the feasibility and efficiency of our approach.

An Efficient Bayesian PAPR Reduction Method for OFDM-Based Massive MIMO Systems

We consider the problem of peak-to-average power ratio (PAPR) reduction in orthogonal frequency-division multiplexing (OFDM) based massive multiple-input multiple-output (MIMO) downlink systems. Specifically, given a set of symbol vectors to be transmitted to $K$ users, the problem is to find an OFDM-modulated signal that has a low PAPR and meanwhile enables multiuser interference (MUI) cancelation. Unlike previous works that tackled the problem using convex optimization, we take a Bayesian approach and develop an efficient PAPR reduction method by exploiting the redundant degrees of freedom of the transmit array. The sought-after signal is treated as a random vector with a hierarchical truncated Gaussian mixture prior, which has the potential to encourage a low PAPR signal with most of its samples concentrated on the boundaries. A variational expectation-maximization (EM) strategy is developed to obtain estimates of the hyperparameters associated with the prior model, along with the signal. In addition, the generalized approximate message passing (GAMP) is embedded into the variational EM framework, which results in a significant reduction in computational complexity of the proposed algorithm. Simulation results show our proposed algorithm achieves a substantial performance improvement over existing methods in terms of both the PAPR reduction and computational complexity.

Implicit Lagrange–Routh equations and Dirac reduction

In this paper, we make a generalization of Routh’s reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange–Routh equations can be obtained from the Hamilton–Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange–Routh equations can be described in the context of dynamical systems associated to Dirac structures, in which we fully utilize a symmetry reduction procedure for implicit Hamiltonian systems with symmetry.

Finite-frequency model reduction of continuous-time switched linear systems with average dwell time

ABSTRACTThis paper deals with the model reduction problem of continuous-time switched linear systems with finite-frequency input signals. The objective of the paper is to propose a finite-frequency model reduction method for such systems. A finite-frequency performance index is first defined in frequency domain, and then a finite-frequency performance analysis condition is derived by Parseval’s theorem. Combined with the average dwell time approach, sufficient conditions for the existence of exponentially stable reduced-order models are derived. An algorithm is proposed to construct the desired reduced-order models. The effectiveness of the proposed method is illustrated by a numerical example.

Boundary condition handling approaches for the model reduction of a vehicle frame

In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, ‘constraint first’ is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.

Block-Sparse Impulsive Noise Reduction in OFDM Systems—A Novel Iterative Bayesian Approach

Using a novel block iterative Bayesian algorithm (Block-IBA), this paper presents a new impulsive noise reduction method for OFDM systems. The method utilizes the guard band null subcarriers and data subcarriers for the impulsive noise estimation and cancellation. Unlike some other general OFDM transceivers which use time-domain interleaving (TDI) to cancel impulsive noise, we design a specific receiver for bursty impulsive noise channels that removes the delay due to TDI and saves memory space. The Block-IBA first estimates the variance and the transition matrix of Markov chain model for the impulsive noise. It then iteratively estimates the amplitudes and positions of the block-sparse impulsive noise using the steepest-ascent based expectation-maximization (EM), and optimally selects the nonzero elements of the block-sparse impulsive noise by adaptive thresholding. Numerical experiments show that the proposed receiver outperforms existing receivers under the block-sparse impulsive noise environment.

A novel method for optimal model simplification of large scale linear discrete-time systems

An accurate and stability preserving model order reduction method for large scale linear discrete-time systems is presented in this paper. The denominator coefficients of the reduced order model are obtained by least squares matching of time-moment proportional's and Markov parameters of the original system and reduced order model about (z − 1), while the numerator coefficients are determined by minimising the integral square error (ISE) between the unit step responses of the original system and its reduced order approximate. Instead of evaluating ISE from time responses of the system and its approximate, a matrix formula is developed in this paper. Three examples are provided to show the efficacy of the proposed method.

Piezoelectric beam with distributed control ports: a power-preserving discretization using weak formulation.

A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with piezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws.

Center Manifold of Fractional Dynamical System

Dimension reduction of dynamical system is a significant issue for technical applications, as regards both finite dimensional system and infinite dimensional systems emerging from either science or engineering. Center manifold method is one of the main reduction methods for ordinary differential systems (ODSs). Does there exists a similar method for fractional ODSs (FODSs)? In other words, does there exists a method for reducing the high-dimensional FODS into a lower-dimensional FODS? In this study, we establish a local fractional center manifold for a finite dimensional FODS. Several examples are given to illustrate the theoretical analysis.

H2 order-reduction for bilinear systems based on Grassmann manifold

In this paper, we focus on optimal H2 model reduction methods for bilinear systems. The optimal H2 model reduction problem can be viewed as a minimization problem on Grassmann manifold. By utilizing the geometry of Grassmann manifold, a gradient descent model reduction algorithm and a conjugate gradient model reduction algorithm based on Grassmann manifold are given. These two algorithms can simulate well the behavior of the original system and the order-reduced systems generated by our algorithms can satisfy the minimal stability requirement. Numerical examples are given to illustrate the effectiveness of our methods.