A Reduced-Order Modeling of Multi-Port RC Networks by Means of Graph Partitioning

A modified reduced-order method for RC networks which takes a division-and-conquest strategy is presented.The whole network is partitioned into a set of sub-networks at first,then each of them is reduced by Krylov subspace techniques,and finally all the reduced sub-networks are incorporated together.With some accuracy,this method can reduce the number of both nodes and components of the circuit comparing to the traditional methods which usually only offer a reduced net with less nodes.This can markedly accelerate the sparse-matrix-based simulators whose performance is dominated by the entity of the matrix or the number of components of the circuits.

IGBT Temperature Field Monitoring Based on Reduced-order Model

With the rapid development of the world economy,IGBT has been widely used in motor drive and electric energy conversion.In order to timely detect the fatigue damage of IGBT,it is necessary to monitor the junction temperature of IGBT.In order to realize the fast calculation of IGBT junction temperature,a finite element method of IGBT temperature field reduction is proposed in this paper.Firstly,the finite element calculation process of IGBT temperature field is introduced and the linear equations of finite element calculation of temperature field are derived.Temperature field data of different working conditions are obtained by finite element simulation to form the sample space.Then the covariance matrix of the sample space is constructed,whose proper orthogonal decomposition and modal extraction are carried out.Reasonable basis vector space is selected to complete the low dimensional expression of temperature vector inside and outside the sample space.Finally,the reduced-order model of temperature field finite element is obtained and solved.The results of the reduced order model are compared with those of the finite element method,and the performance of the reduced-order model is evaluated from two aspects of accuracy and rapidity.

A reduced-order model for fast predicting ionized flows of hypersonic vehicles along flight trajectory

An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.

Matched Volterra reduced-order model for an airfoil undergoing periodic translation

This paper is devoted to application of the Reduced-Order Model(ROM)based on Volterra series to prediction of lift and drag forces due to airfoil periodic translation in transonic flow region.When there is large amplitude oscillation of the relative Mach number,as appeared in helicopter rotor movement in forward flight,the conventional Volterra ROM is found to be unsatisfactory.To cover such applications,a matched Volterra ROM,inspired from previous multistep nonlinear indicial response method based on Duhamel integration,is thus considered,in which the step motions are defined inside a number of equal intervals with both positive and negative step motions to match the airfoil forward and backward movement,and the kernel functions are constructed independently at each interval.It shows that,at least for the translation movement considered,this matched Volterra ROM greatly improves the accuracy of prediction.Moreover,the matched Volterra ROM,with the total number of step motions and thus the computational cost close to those of the conventional Volterra ROM method,has the additional advantage that the same set of kernels can match various translation motions with different starting conditions so the kernels can be predesigned without knowing the specific motion of airfoil.

Reduced-order modeling and vibration transfer analysis of a fluid-delivering branch pipeline that consider fluid–solid interactions

The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline(FDBP)are essential for analyzing vibration coupling effects and implementing vibration reduction optimization.Therefore,this study proposes a reduced-order dynamic modeling method suitable for FDBPs and then analyzes the vibration transfer characteristics.For the modeling method,the finite element method and absorbing transfer matrix method(ATMM)are integrated,considering the fluid–structure coupling effect and fluid disturbances.The dual-domain dynamic substructure method is developed to perform the reduced-order modeling of FDBP,and ATMM is adopted to reduce the matrix order when solving fluid disturbances.Furthermore,the modeling method is validated by experiments on an H-shaped branch pipeline.Finally,transient and steady-state vibration transfer analyses of FDBP are performed,and the effects of branch locations on natural characteristics and vibration transfer behavior are analyzed.Results show that transient vibration transfer represents the transfer and conversion of the kinematic,strain,and damping energies,while steady-state vibration transfer characteristics are related to the vibration mode.In addition,multiple-order mode exchanges are triggered when branch locations vary in frequency-shift regions,and the mode-exchange regions are also the transformation ones for vibration transfer patterns.

Reduced-order Modeling and Dynamic Stability Analysis of MTDC Systems in DC Voltage Control Timescale

An equivalent source-load MTDC system including DC voltage control units,power control units and interconnected DC lines is considered in this paper,which can be regarded as a generic structure of low-voltage DC microgrids,mediumvoltage DC distribution systems or HVDC transmission systems with a common DC bus.A reduced-order model is proposed with a circuit structure of a resistor,inductor and capacitor in parallel for dynamic stability analysis of the system in DC voltage control timescale.The relationship between control parameters and physical parameters of the equivalent circuit can be found,which provides an intuitive insight into the physical meaning of control parameters.Employing this model,a second-order characteristic equation is further derived to investigate system dynamic stability mechanisms in an analytical approach.As a result,the system oscillation frequency and damping are characterized in a straight forward manner,and the role of electrical and control parameters and different system-level control strategies in system dynamic stability in DC voltage control timescale is defined.The effectiveness of the proposed reduced-order model and the correctness of the theoretical analysis are verified by simulation based on PSCAD/EMTDC and an experiment based on a hardware low-voltage MTDC system platform.

Identification of reduced-order model for an aeroelastic system from flutter test data

Recently, flutter active control using linear parameter varying（LPV） framework has attracted a lot of attention. LPV control synthesis usually generates controllers that are at least of the same order as the aeroelastic models. Therefore, the reduced-order model is required by synthesis for avoidance of large computation cost and high-order controller. This paper proposes a new procedure for generation of accurate reduced-order linear time-invariant（LTI） models by using system identification from flutter testing data. The proposed approach is in two steps. The well-known poly-reference least squares complex frequency（p-LSCF） algorithm is firstly employed for modal parameter identification from frequency response measurement. After parameter identification,the dominant physical modes are determined by clear stabilization diagrams and clustering technique. In the second step, with prior knowledge of physical poles, the improved frequencydomain maximum likelihood（ML） estimator is presented for building accurate reduced-order model. Before ML estimation, an improved subspace identification considering the poles constraint is also proposed for initializing the iterative procedure. Finally, the performance of the proposed procedure is validated by real flight flutter test data.

Comparative study of reduced-order modeling method for the cavitating flow over a hydrofoil

As a high-dimensional complex nonlinear dynamic system,the analysis of the essence of flow has always been a difficult problem,especially in the flow including phase change.In recent years,it has become a feasible method to reduce the dimension of flow structure by reduced-order modeling(ROM)methods.In this paper,through the cavitation numerical simulation of NACA0015 hydrofoil,two ROM methods are used to reduce and restore three different cavitation respectively-proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD).The applicability of two methods in cavitation is discussed and reasons are analyzed.The results show that for stable cavitation,POD,DMD methods can accurately restore the flow field of a few modes with high energy.For unstable cavitation,only POD method can restore real flow field well.This situation is mainly due to the fact that POD,DMD method are applicable to different energy ratios,and different main mode selection criterion of DMD will lead to different main mode.ROM can greatly simplify the complexity of flow.Selecting a reasonable ROM can improve the accuracy of a small amount of database,and provide a basis for intelligent prediction of flow analysis.

Reduced-order modelling of urban wind environment and gaseous pollutants dispersion in an urban-scale street canyon

Hazardous chemical gases will spread rapidly after leakage.For emergency response to that,people need to obtain the information of wind and pollutant in time.However,it takes a lot of time to calculate the flow in large-scale urban areas by numerical simulation.Therefore,reduced-order model(ROM)is developed to improve the efficiency.In this paper,we propose a model based on proper orthogonal decomposition(POD)and radial basis function(RBF)interpolation.We validate the model by calculating the wind field and the pollutant propagation process in a 144 square kilometer area of Beijing.The results show that ROM can reduce CPU times by more than 99%at the cost of only 0.1%information loss,comparing with the traditional approach of computational fluid dynamics(CFD).

Non-intrusive reduced-order model for predicting transonic flow with varying geometries

A Non-Intrusive Reduced-Order Model(NIROM)based on Proper Orthogonal Decomposition(POD)has been proposed for predicting the flow fields of transonic airfoils with geometry parameters.To provide a better reduced-order subspace to approximate the real flow field,a domain decomposition method has been used to separate the hard-to-predict regions from the full field and POD has been adopted in the regions individually.An Artificial Neural Network(ANN)has replaced the Radial Basis Function(RBF)to interpolate the coefficients of the POD modes,aiming at improving the approximation accuracy of the NIROM for non-samples.When predicting the flow fields of transonic airfoils,the proposed NIROM has demonstrated a high performance.

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

Adding-Point Strategy for Reduced-Order Hypersonic Aerothermodynamics Modeling Based on Fuzzy Clustering

Reduced order models（ROMs） based on the snapshots on the CFD high-fidelity simulations have been paid great attention recently due to their capability of capturing the features of the complex geometries and flow configurations. To improve the efficiency and precision of the ROMs, it is indispensable to add extra sampling points to the initial snapshots, since the number of sampling points to achieve an adequately accurate ROM is generally unknown in prior, but a large number of initial sampling points reduces the parsimony of the ROMs. A fuzzy-clustering-based adding-point strategy is proposed and the fuzzy clustering acts an indicator of the region in which the precision of ROMs is relatively low. The proposed method is applied to construct the ROMs for the benchmark mathematical examples and a numerical example of hypersonic aerothermodynamics prediction for a typical control surface. The proposed method can achieve a 34.5% improvement on the efficiency than the estimated mean squared error prediction algorithm and shows same-level prediction accuracy.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data

Recently,the methodology of deep learning is used to improve the calculation accuracy of the Reynolds-averaged Navier-Stokes (RANS) model.In this paper,a neural network is designed to predict the Reynolds stress of a channel flow of different Reynolds numbers.The rationality and the high efficiency of the neural network is validated by comparing with the results of the direct numerical simulation (DNS),the large eddy simulation (LES),and the deep neural network (DNN) of other studies.To further enhance the prediction accuracy,three methods are developed by using several algorithms and simplified models in the neural network.In the method 1.the regularization is introduced and it is found that the oscillation and the overfitting of the results are eflectively prevented.In the method 2,y^+ is embedded in the input variable while the combination of the invariants is simplified in the method 3.From the predicted results,it can be seen that by using the first two methods,the errors are reduced.Moreover,the method 3 shows considerable advantages in the DNS trend and the smoothness of a curve.Consequently,it is concluded that the DNNs can predict effectively the anisotropic Reynolds stress and is a promising technique of the computational fluid dynamics.

A Reduced-Order Model for Structural Wave Control and the Concept of Degree of Controllability

This paper introduces the concept and criteria of controllability and degree of controllability for structural wave control, and advances a new approach to structural reduced-order model, which is similar to the constrained substructural method in dynamics, and is also the extension of the method of aggregation raised by Aoki. It has physical meaning and is easy to realize.

Reduced-order modeling of train-curved-slab-track dynamics with the effects of fastening failures

Fastening failures have frequently been found on China high-speed railway curved tracks in recent years.Thus the influence of fastening failures on high-speed train-track interaction in curved track needs to be analyzed.A train-curved slab track interaction model is built,in which the real shape of the curved rail is considered and modeled with reduced beam model(RBM)and curved beam theory,and the slabs are modeled with four-nodes Kirchhoff-Love plate elements.The present model is validated at first with different traditional models.Then the influence of fastening failure in curved slab track on train-track interaction dynamics is studied.A different number of failed fastenings is assumed to occur at the curved track,and different types of fastening failure including the fatigue fracture of the clip structure and failure of the rail pad are considered.Based on the calculation results,the fatigue fracture of the clip structure has little influence on train-track interaction dynamics.But when rail pad failure happens and its equivalent vertical stiffness and damping are less than one-tenth of its original,the fastening failure seriously affects the high-speed train operation safety,and it must be prevented.

Comparative analysis of empirical and deep learning models for ionospheric sporadic E layer prediction

Sporadic E(Es)layers in the ionosphere are characterized by intense plasma irregularities in the E region at altitudes of 90-130 km.Because they can significantly influence radio communications and navigation systems,accurate forecasting of Es layers is crucial for ensuring the precision and dependability of navigation satellite systems.In this study,we present Es predictions made by an empirical model and by a deep learning model,and analyze their differences comprehensively by comparing the model predictions to satellite RO measurements and ground-based ionosonde observations.The deep learning model exhibited significantly better performance,as indicated by its high coefficient of correlation(r=0.87)with RO observations and predictions,than did the empirical model(r=0.53).This study highlights the importance of integrating artificial intelligence technology into ionosphere modelling generally,and into predicting Es layer occurrences and characteristics,in particular.

Reduced-order Modeling of Human Body for Brain Hypothermia Treatment

Brain hypothermia treatment （BHT） is an active therapy for severe brain injury. It makes the temperature of the brain track a given temperature input curve so as to reduce the risk of tissue damage. BHT requires a brain-temperature control system because of environmental disturbances and changes in the human body. The thermal models of the human body devised so far are usually of a very high order and are not suitable for controlling brain temperature. This paper presents a method of finding a reducedorder thermal model of the human body for use in BHT. It combines minimal realization and balanced realization. Unlike other methods, this method yields a reduced-order model that is based on system theory and that takes the frequency characteristics of human thermal sensation into account. It features high precision in the frequency band for BHT and is suitable for the control of brain temperature.

Dynamics of a Stochastic Epidemic Model with Age-group

A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.

Distributed non-cooperative robust MPC based on reduced-order models

In this paper, a non-cooperative distributed MPC algorithm based on reduced order model is proposed to stabilize large-scale systems. The large-scale system consists of a group of interconnected subsystems. Each subsystem can be partitioned into two parts： measurable part, whose states can be directly measured by sensors, and the unmeasurable part. In the online computation phase, only the measurable dynamics of the corresponding subsystem and neighbour-to-neighbour communication are necessary for the local controller design. Satisfaction of the state constraints and the practical stability are guaranteed while the complexity of the optimization problem is reduced. Numerical examples are given to show the effectiveness of this algorithm.