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Traditional three-dimensional numerical methods require a long time for transient computational fluid dynamics simulation on oil-filling process of hydrodynamic braking. The purpose of this paper is to investigate reconstruction and prediction methods for the pressure field on blade surfaces to explore an accurate and rapid numerical method to solve transient internal flow in a hydrodynamic retarder.

Dynamic braking performance for the oil-filling process was simulated and validated using experimental results. With the proper orthogonal decomposition (POD) method, the dominant modes of transient pressure distribution on blades were extracted using their spatio-temporal structural features from the knowledge of computed flow data. Pressure field on blades was reconstructed. Based on the approximate model (AM), transient pressure field on blades was predicted in combination with POD. The causes of reconstruction and prediction error were, respectively, analyzed.

Results show that reconstruction with only a few dominant POD modes could represent all flow samples with high accuracy. POD method demonstrates an efficient simplification for accurate prediction of the instantaneous variation of pressure field in a hydrodynamic retarder, especially at the stage of high oil-filling rate.

The paper presents a novel numerical method, which combines POD and AM approaches for rapid and accurate prediction of braking characteristics during the oil-filling period, based on the knowledge of computed flow data.

This paper presents the application in circuit simulation of a method for model reduction of nonlinear systems that has recently been developed for chemical systems. The technique is an extension of the well‐known balanced truncation method that has been applied extensively in the reduction of linear systems. The technique involves the formation of controllability and observability gramians either by simulated results or by measurement data. The empirical gramians are subsequently employed to determine a subspace of the full state‐space that contains the most significant dynamics of the system. A Galerkin projection is used to project the system onto the subspace to form a lower‐dimensional nonlinear model. The method is applied to a nonlinear resistor network which is a standard example for exemplifying the effectiveness of a nonlinear reduction strategy.

The purpose of this paper is to present the embedding of linear and nonlinear order reduction methods in a theoretical framework for handling hierarchically interconnected dynamical systems.

Based on the component connection modeling (CCM), a modified framework called mCCM for describing interconnected dynamic systems especially with hierarchical structures is introduced and used for order reduction purposes. The balanced truncation method for linear systems and the trajectory piecewise linear reduction scheme are used for the order reduction of systems described within the mCCM framework.

It is shown that order reduction methods can be embedded into the context of interconnected dynamical systems with the benefit of having a further degree of freedom in form of the hierarchical level, on which the order reduction is performed.

The aspect of hierarchy within system descriptions is exploited for order reduction purposes. This distinguishes the presented approach from common methods, which already start with single large-scale systems without explicitly considering hierarchical structures.

Nonlinear dynamical systems may, under certain conditions, be represented by a bilinear system. The paper is concerned with the construction of the controllability and observability gramians for the corresponding bilinear system. Such gramians form the core of model reduction schemes involving balancing.

The paper examines certain properties of the bilinear system and identifies parameters that capture important information relating to the behaviour of the system.

Novel approaches for the determination of approximate constant gramians for use in balancing‐type model reduction techniques are presented. Numerical examples are given which indicate the efficacy of the proposed formulations.

The systems under consideration are restricted to the so‐called weakly nonlinear systems, i.e. those without strong nonlinearities where the essential type of behaviour of the system is determined by its linear part.

The suggested methods lead to an improvement in the accuracy of model reduction. Model reduction is a vital aspect of modern system simulation.

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design of radio‐frequency integrated circuits.

The paper presents an efficient modeling technique for the fluxset magnetic field sensor. Using separate numerical solutions for the electric and magnetic fields, an equivalent SPICE circuit is extracted in the postprocessing phase. The main contribution of the paper is the technique used to model the distributed capacitive effects in insulation between coils, by concentrating them in an “Extended II scheme”, an infinite circuit which is optimally reduced to a finite one. The results are in qualitative agreement with the experimental ones.

Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues.

Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system.

The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

The paper is concerned with interpolatory proper orthogonal decomposition (IPOD) methods for nonlinear transmission line circuits. This paper aims to examine several factors that must be considered when applying such model reduction techniques to this kind of circuit.

Two types of POD will be implemented. In each case, the choice of the order of the reduced model and the order of the interpolation space shall be considered. The stability of the models shall be explored.

The results indicate that the order for the reduced model to obtain accurate results depends on the chosen method when considering nonlinear transmission lines. The results also indicate that the structure of the nonlinear transmission line is crucial for determining the stability of the reduced models.

The work compares two IPOD methods and discusses the issues involved in achieving an accurate and stable reduced-order model for a nonlinear transmission line.

This paper aims to develop an efficient evaluation method to more intuitively and effectively investigate the influence of the wing fuel mass variations because of fuel burn on transonic aeroelasticity.

The proposed efficient aeroelastic evaluation method is developed by extending the standard computational fluid dynamics (CFD)-based proper orthogonal decomposition (POD)/reduced order model (ROM).

The results of this paper show that the proposed aeroelastic efficient evaluation method can accurately and efficiently predict the aeroelastic response and flutter boundary when the wing fuel mass vary because of fuel burn. It also shows that the wing fuel mass variations have a significant effect on transonic aeroelasticity; the flutter speed increases as the wing fuel mass decreases. Without rebuilding an expensive, time-consuming CFD-based POD/ROM for each wing fuel mass variation, the computational cost of the proposed method is reduced obviously. It also shows that the computational efficiency improvement grows linearly with the number of model cases.

The paper presents a potentially powerful tool to more intuitively and effectively investigate the influence of the wing fuel mass variation on transonic aeroelasticity, and the results form a theoretical and methodological basis for further research.

The proposed evaluation method makes it a reality to apply the efficient standard CFD-based POD/ROM to investigate the influence of the wing fuel mass variation because of fuel burn on transonic aeroelasticity. The proposed efficient aeroelastic evaluation method, therefore, is ideally suited to deal with the investigation of the influence of wing fuel mass variations on transonic aeroelasticity and may have the potential to reduce the overall cost of aircraft design.

The concepts of the “equal-equivalents” permit the definition of one-dimensional and multidimensional inequalities, of individual “welfare” (the same function for all individuals) and, as a result, of classical inequality properties and of the optimal allocation in “macrojustice” (optimum income taxation and transfers, amounting in particular to equal liberty of choice in different domains).

The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X.

By applying the principle of hierarchical identification and the Hermitian/skew‐Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift‐splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation.

The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms.

So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew‐Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation.