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The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

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.

To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems.

The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21^a model is studied with the proposed reduced-order method.

For the TEAM 21^a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model.

The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.

The purpose of this paper is to analyze the stability of aeroelastic systems using a novel reduced order aeroelastic model.

The proposed aeroelastic model is a reduced-order model constructed based on the aerodynamic model identification using the generalized aerodynamic force response and the unsteady boundary element method in various excitation frequency values. Due to the low computational cost and acceptable accuracy of the boundary element method, this method is selected to determine the unsteady time response of the aerodynamic model. Regarding the structural model, the elastic mode shapes of the shell are used.

Three case studies are investigated by the proposed model. In the first place, a typical two-dimensional section is introduced as a means of verification by approximating the Theodorsen function. As the second test case, the flutter speed of Advisory Group for Aerospace Research and Development 445.6 wing with 45° sweep angle is determined and compared with the experimental test results in the literature. Finally, a complete aircraft is considered to demonstrate the capability of the proposed model in handling complex configurations.

The paper introduces an algorithm to construct an aeroelastic model applicable to any unsteady aerodynamic model including experimental models and modal structural models in the implicit and reduced order form. In other words, the main advantage of the proposed method, further to its simplicity and low computational effort, which can be used as a means of real-time aeroelastic simulation, is its ability to provide aerodynamic and structural models in implicit and reduced order forms.

The paper aims to develop an efficient data-driven modeling approach for the hydroelastic analysis of a semi-circular pipe conveying fluid with elastic end supports. Besides the structural displacement-dependent unsteady fluid force, the steady one related to structural initial configuration and the variable structural parameters (i.e. the variable support stiffness) are considered in the modeling.

The steady fluid force is treated as a pipe preload, and the elastically supported pipe-fluid model is dealt with as a prestressed hydroelastic system with variable parameters. To avoid repeated numerical simulations caused by parameter variation, structural and hydrodynamic reduced-order models (ROMs) instead of conventional computational structural dynamics (CSD) and computational fluid dynamics (CFD) solvers are utilized to produce data for the update of the structural, hydrodynamic and hydroelastic state-space equations. Radial basis function neural network (RBFNN), autoregressive with exogenous input (ARX) model as well as proper orthogonal decomposition (POD) algorithm are applied to modeling these two ROMs, and a hybrid framework is proposed to incorporate them.

The proposed approach is validated by comparing its predictions with theoretical solutions. When the steady fluid force is absent, the predictions agree well with the “inextensible theory”. The pipe always loses its stability via out-of-plane divergence first, regardless of the support stiffness. However, when steady fluid force is considered, the pipe remains stable throughout as flow speed increases, consistent with the “extensible theory”. These results not only verify the accuracy of the present modeling method but also indicate that the steady fluid force, rather than the extensibility of the pipe, is the leading factor for the differences between the in- and extensible theories.

The steady fluid force and the variable structural parameters are considered in the data-driven modeling of a hydroelastic system. Since there are no special restrictions on structural configuration, steady flow pattern and variable structural parameters, the proposed approach has strong portability and great potential application for other hydroelastic problems.

The aim of the paper is to investigate the impacts of simplifications of a reduced-order simulation model of squirrel cage induction machines (SCIMs) by numerical experiments.

Design of setups to isolate the main influences on the results of the reduced-order model of SCIMs. Results of time-stepping finite element calculations are used as benchmark.

Whereas neglecting eddy current effects and the assumption of a sinusoidal rotor current distribution leads to acceptable deviations in regular inverter operation, the sampling and interpolation of the machine parameters in a two-axis coordinate system considerably deteriorate the model accuracy. Using a polar coordinate system for this purpose is expected to significantly improve the model quality.

Preparing the ground for a successful, both fast and accurate simulation model of SCIMs as parts of electrified drivetrains.

In this paper, an effective method to calculate the reduced-order model (ROM) of high-order linear time-invariant system is elaborated; this is done by evaluating time moments of the original high-order model (HOM).

The developed method has been applied to a hydraulic actuator of antiroll bar mechanism dedicated to heavy vehicle semi-active suspension. And as the actuator is a large-scale system; and that in this case, the only control applied is a classical control and with trial and error procedure (like PID), the use of an order reduction method is necessary. Hence, the actuator that has an eighth-order transfer function with uncontrollable states has been approximated by fully controllable second-order model, which is suitable for feedback controllers (RST, LQR […]). The RST control is applied to control the roll angle of the actuator and simulations are carried out to show the effectiveness of the procedure.

It is clear that RST shows good tracking as compared to PID. For further work, the given RST controller has a discrete character and can be easily implemented on the real process and then as a further simulation, one can use another controller such as fractional adaptive controller.

In the recent years, the technological need of modeling order, thus the complexity of the systems, directed the researchers toward the reduction of order of these systems, not only to facilitate the analysis but also to find a suitable approximation of the high-order systems while keeping the same important characteristics as closely as possible. Several methods are available but they fail to give stable transfer functions or important characteristics of the original system.

The purpose of this paper is to enable fast finite element (FE) analysis of electromagnetic structures with multiple geometric design variables.

The proposed methodology combines multi‐variable model‐order reduction with mesh perturbation techniques and polynomial interpolation of parameter‐dependent FE matrices.

The resulting reduced‐order models are of comparable accuracy as but much smaller size than the original FE systems and preserve important system properties such as reciprocity.

The method is limited to mesh variations that are obtained from a nominal discretization by continuous deformation. Topological changes in the mesh are not permissible.

In contrast to the underlying FE models, the resulting reduced‐order systems are very cheap to analyze. Possible applications include parametric libraries, design optimization, and real‐time control.

The paper extends the scope of moment‐matching order‐reduction techniques to a class of non‐polynomial systems arising from FE models with geometric parameters.

This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.

A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.

The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.

Only linear magnetic materials are considered in the present formulation.

The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.

The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

To provide an efficient and accurate model for interconnect networks characterised by frequency‐domain scattering or admittance parameters. The parameters are derived from measurements or rigorous full‐wave simulation.

Initially, Hilbert transform relationships are enforced to ensure causality. A reverse Fourier series representation of the discrete data is then converted to the z‐domain and from this a state‐space formulation is determined. This enables the application of a judiciously chosen model reduction algorithm to obtain an efficient time‐domain representation of the network.

Sample results from both simulated and measured data indicate the efficacy of the proposed modelling strategy. For successful implementation of the strategy, it is necessary to employ the Hilbert transform to ensure that a causal impulse response is obtained.

The method is applicable to the interconnect networks for which the analytical models cannot be obtained due to the complexity and inhomogeneity of the geometries involved.

The work combines in a novel manner aspects from several existing techniques proposed for network simulation and model reduction. The end result is a highly efficient causal, stable and passive representation of the network in question for implementation in a time‐domain circuit simulator.