Reduced Order Modeling & Controller Design for Mass Transfer in a Grain Storage System

This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations(PDE). It is quite difficult to obtain the humidity profiles from the PDE model. Hence, a discretization method is applied to obtain an equivalent ordinary differential equation model. However, after applying the discretization technique, the cost of solving the system increases as the size increases to a few thousands. It may be noted that after discretization,the degree of freedom of the system remain the same while the order increases. The large dynamic model is reduced using a proper orthogonal decomposition based technique and an equivalent model but of much reduced size is obtained. A controller based on optimal control theory is designed to obtain an input such that the output humidity reaches a desired profile and also its stability is analyzed.Numerical results are presented to show the validity of the reduced model and possible further extensions are identified.

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.

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.

Assessment of a two-surface plasticity model for hexagonal materials

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.

A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD

Aerothermoelasticity is one of the key technologies for hypersonic vehicles. Accurate and efficient computation of the aerothermodynamics is one of the primary challenges for hypersonic aerothermoelastic analysis. Aimed at solving the shortcomings of engineering calculation, compu- tation fluid dynamics （CFD） and experimental investigation, a reduced order modeling （ROM） framework for aerothermodynamics based on CFD predictions using an enhanced algorithm of fast maximin Latin hypercube design is developed. Both proper orthogonal decomposition （POD） and surrogate are considered and compared to construct ROMs. Two surrogate approaches named Kriging and optimized radial basis function （ORBF） are utilized to construct ROMs. Furthermore, an enhanced algorithm of fast maximin Latin hypercube design is proposed, which proves to be helpful to improve the precisions of ROMs. Test results for the three-dimensional aerothermody- namic over a hypersonic surface indicate that： the ROMs precision based on Kriging is better than that by ORBF, ROMs based on Kriging are marginally more accurate than ROMs based on POD- Kriging. In a word, the ROM framework for hypersonic aerothermodynamics has good precision and efficiency.

A Numerical Study on Hydraulic Fracturing Problems via the Proper Generalized Decomposition Method

The hydraulic fracturing is a nonlinear,fluid-solid coupling and transient problem,in most cases it is always time-consuming to simulate this process numerically.In recent years,although many numerical methods were proposed to settle this problem,most of them still require a large amount of computer resources.Thus it is a high demand to develop more efficient numerical approaches to achieve the real-time monitoring of the fracture geometry during the hydraulic fracturing treatment.In this study,a reduced order modeling technique namely Proper Generalized Decomposition(PGD),is applied to accelerate the simulations of the transient,non-linear coupled system of hydraulic fracturing problem,to match this extremely tight response time constraint.The separability of the solution in space and time dimensions is studied for a simplified model problem.The solid and fluid equations are coupled explicitly by inverting the solid discrete problem,and a simple iterative procedure to handle the non-linear characteristic of the hydraulic fracturing problem is proposed in this work.Numeral validation illustrates that the results of PGD match well with these of standard finite element method in terms o f fracture opening and fluid pressure in the hydro-fracture.Moreover,after the off-line calculations,the numerical results can be obtained in real time.

Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

A projection-based reduced order model(ROM)based on the Fourier collocation method is proposed for compressible flows.The incorporation of localized artificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM for shock-dominated flows.Furthermore,for Euler systems,ROMs built on the conservative and the skew-symmetric forms of the governing equation are compared.To ensure efficiency,the discrete empirical interpolation method(DEIM)is employed.An alternative reduction approach,exploring the sparsity of viscosity is also investigated for the viscous terms.A number of one-and two-dimensional benchmark cases are considered to test the performance of the proposed models.Results show that stable computations for shock-dominated cases can be achieved with ROMs built on both the conservative and the skew-symmetric forms without additional stabilization components other than the viscosity model and filtering.Under the same parameters,the skew-symmetric form shows better robustness and accuracy than its conservative counterpart,while the conservative form is superior in terms of efficiency.

Review of Proper Orthogonal Decomposition Method Applied to Computational Aeroelasticity

Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.

Reduced order model for unsteady aerodynamic performance of compressor cascade based on recursive RBF

Based on Recursive Radial Basis Function(RRBF)neural network,the Reduced Order Model(ROM)of compressor cascade was established to meet the urgent demand of highly efficient prediction of unsteady aerodynamics performance of turbomachinery.One novel ROM called ASA-RRBF model based on Adaptive Simulated Annealing(ASA)algorithm was developed to enhance the generalization ability of the unsteady ROM.The ROM was verified by predicting the unsteady aerodynamics performance of a highly-loaded compressor cascade.The results show that the RRBF model has higher accuracy in identification of the dimensionless total pressure and dimensionless static pressure of compressor cascade under nonlinear and unsteady conditions,and the model behaves higher stability and computational efficiency.However,for the strong nonlinear characteristics of aerodynamic parameters,the RRBF model presents lower accuracy.Additionally,the RRBF model predicts with a large error in the identification of aerodynamic parameters under linear and unsteady conditions.For ASA-RRBF,by introducing a small-amplitude and highfrequency sinusoidal signal as validation sample,the width of the basis function of the RRBF model is optimized to improve the generalization ability of the ROM under linear unsteady conditions.Besides,this model improves the predicting accuracy of dimensionless static pressure which has strong nonlinear characteristics.The ASA-RRBF model has higher prediction accuracy than RRBF model without significantly increasing the total time consumption.This novel model can predict the linear hysteresis of dimensionless static pressure happened in the harmonic condition,but it cannot accurately predict the beat frequency of dimensionless total pressure.

Static aeroelastic analysis including geometric nonlinearities based on reduced order model

This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model（ROM）.The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities;meanwhile,the non-planar effects of aerodynamics and follower force effect have been considered.ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method（FEM） especially in aeroelastic solutions.The approach for structure modeling presented here is on the basis of combined modal/finite element（MFE） method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis.Moreover,the non-planar aerodynamic force is computed by the non-planar vortex lattice method（VLM）.Structure and aerodynamics can be coupled with the surface spline method.The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

Active Control Law Design for Flutter/LCO Suppression Based on Reduced Order Model Method

Active stability augmentation system is an attractive and promising technology to suppress flutter and limit cycle oscillation (LCO). In order to design a good active control law, the control plant model with low order and high accuracy must be provided, which is one of the most important key points. The traditional model is based on low fidelity aerodynamics model such as panel method, which is unsuitable for transonic flight regime. The physics-based high fidelity tools, reduced order model (ROM) and CFD/CSD coupled aeroservoelastic solver are used to design the active control law. The Volterra/ROM is applied to constructing the low order state space model for the nonlinear unsteady aerodynamics and static output feedback method is used to active control law design. The detail of the new method is demonstrated by the Goland+ wing/store system. The simulation results show that the effectiveness of the designed active augmentation system, which can suppress the flutter and LCO successfully.

A reduced order model for coupled mode cascade flutter analysis

A Reduced Order Model(ROM)based analysis method for turbomachinery cascade coupled mode flutter is presented in this paper.The unsteady aerodynamic model is established by a system identification technique combined with a set of Aerodynamic Influence Coefficients(AIC).Subsequently,the aerodynamic model is encoded into the state space and then coupled with the structural dynamic equations,resulting in a ROM of the cascade aeroelasticity.The cascade flutter can be determined by solving the eigenvalues of the ROM.Bending-torsional coupled mode flutter analysis for the Standard Configuration Eleven(SC11)cascade is used to validate the proposed method.

Development and Application of a Reduced Order Model for the Control of Self-Sustained Instabilities in Cavity Flows

Flow around a cavity is characterized by a self-sustained mechanism in which the shear layer impinges on the downstream edge of the cavity resulting in a feedback mechanism.Direct Numerical Simulations of the flow at low Reynolds number has been carried out to get pressure and velocity fluctuations,for the case of un-actuated and multi frequency actuation.A Reduced Order Model for the isentropic compressible equations based on the method of Proper Orthogonal Decomposition has been constructed.The model has been extended to include the effect of control.The Reduced Order dynamical system shows a divergence in time integration.A method of calibration based on the minimization of a linear functional of error,to the sensitivity of the modes,is proposed.The calibrated low order model is used to design a feedback control of cavity flows based on an observer design.For the experimental implementation of the controller,a state estimate based on the observed pressure measurements is obtained through a linear stochastic estimation.Finally the obtained control is introduced into the Direct Numerical Simulation to obtain a decrease in spectra of the cavity acoustic mode.

NeuroPNM:Model reduction of pore network models using neural networks

Reacting particle systems play an important role in many industrial applications,for example biomass drying or the manufacturing of pharmaceuticals.The numerical modeling and simulation of such systems is therefore of great importance for an efficient,reliable,and environmentally sustainable operation of the processes.The complex thermodynamical,chemical,and flow processes that take place in the particles are a particular challenge in a simulation.Furthermore,typically a large number of particles is involved,rendering an explicit treatment of individual ones impossible in a reactor-level simulation.One approach for overcoming this challenge is to compute effective,physical parameters from single-particle,high-resolution simulations.This can be combined with model reduction methods if the dynamical behaviour of particles must be captured.Pore network models with their unrivaled resolution have thereby been used successfully as high-resolution models,for instance to obtain the macroscopic diffusion coeffcient of drying.Both parameter identification and model reduction have recently gained new impetus by the dramatic progress made in machine learning in the last decade.We report results on the use of neural networks for parameter identification and model reduction based on three-dimensional pore network models(PNM).We believe that our results provide a powerful complement to existing methodologies for reactor-level simulations with many thermally-thick particles.

Simulating dispatchable grid services provided by flexible building loads:State of the art and needed building energy modeling improvements

End-use electrical loads in residential and commercial buildings are evolving into flexible and cost-effective resources to improve electric grid reliability,reduce costs,and support increased hosting of distributed renewable generation.This article reviews the simulation of utility services delivered by buildings for the purpose of electric grid operational modeling.We consider services delivered to(1)the high-voitage bulk power system through the coordinated action of many,distributed building loads working together,and(2)targeted support provided to the operation of low-voltage electric distribution grids.Although an exhaustive exploration is not possible,we emphasize the ancillary services and voltage management buildings can provide and summarize the gaps in our ability to simulate them with traditional building energy modeling(BEM)tools,suggesting pathways for future research and development.

Stall flutter prediction based on multi-layer GRU neural network

The modeling of dynamic stall aerodynamics is essential to stall flutter, due to the flow separation in a large-amplitude pitching oscillation process. A newly neural network based Reduced Order Model(ROM) framework for predicting the aerodynamic forces of an airfoil undergoing large-amplitude pitching oscillation at various velocities is presented in this work. First, the dynamic stall aerodynamics is calculated by solving RANS equations and the transitional SST-γ model. Afterwards, the stall flutter bifurcation behavior is calculated by the above CFD solver coupled with structural dynamic equation. The critical flutter speed and limit-cycle oscillation amplitudes are consistent with those obtained by experiments. A newly multi-layer Gated Recurrent Unit(GRU) neural network based ROM is constructed to accelerate the calculation of aerodynamic forces. The training and validation process are carried out upon the unsteady aerodynamic data obtained by the proposed CFD method. The well-trained ROM is then coupled with the structure equation at a specific velocity, the Limit-Cycle Oscillation(LCO) of stall flutter under this flow condition is predicted precisely and more quickly. In order to predict both the critical flutter velocity and LCO amplitudes after bifurcation at different velocities, a new ROM with GRU neural network considering the variation of flow velocities is developed. The stall flutter results predicted by ROM agree well with the CFD ones at different velocities. Finally, a brief sensitivity analysis of two structural parameters of ROM is carried out. It infers the potential of the presented modeling method to depict the nonlinearity of dynamic stall and stall flutter phenomenon.

Reliability and Sensitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique

The improved line sampling （LS） technique, an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of flutter with random structural parameter in transonic flow. The improved LS technique is a novel methodology for reliability and sensitivity analysis of high dimensionality and low probability problem with implicit limit state function, and it does not require any approximating surrogate of the implicit limit state equation. The improved LS is used to estimate the flutter reliability and the sensitivity of a two-dimensional wing, in which some structural properties, such as frequency, parameters of gravity center and mass ratio, are considered as random variables. Computational fluid dynamics （CFD） based unsteady aerodynamic reduced order model （ROM） method is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the safety margin of flutter is founded by using the critical velocity of flutter. The results show that the improved LS technique can effectively decrease the computational cost in the random uncertainty analysis of flutter. The reliability sensitivity, defined by the partial derivative of the failure probability with respect to the distribution parameter of random variable, can help to identify the important parameters and guide the structural optimization design.

l_(1)-based calibration of POD-Galerkin models of two-dimensional unsteady flows

This paper discusses a physics-informed methodology aimed at reconstructing efficiently the fluid state of a system.Herein,the generation of an accurate reduced order model of twodimensional unsteady flows from data leverages on sparsity-promoting statistical learning techniques.The cornerstone of the approach is l_(1) regularised regression,resulting in sparselyconnected models where only the important quadratic interactions between modes are retained.The original dynamical behaviour is reproduced at low computational costs,as few quadratic interactions need to be evaluated.The approach has two key features.First,interactions are selected systematically as a solution of a convex optimisation problem and no a priori assumptions on the physics of the flow are required.Second,the presence of a regularisation term improves the predictive performance of the original model,generally affected by noise and poor data quality.Test cases are for two-dimensional lid-driven cavity flows,at three values of the Reynolds number for which the motion is chaotic and energy interactions are scattered across the spectrum.It is found that:(A)the sparsification generates models maintaining the original accuracy level but with a lower number of active coefficients;this becomes more pronounced for increasing Reynolds numbers suggesting that extension of these techniques to real-life flow configurations is possible;(B)sparse models maintain a good temporal stability for predictions.The methodology is ready for more complex applications without modifications of the underlying theory,and the integration into a cyberphysical model is feasible.

Application of nonlinear fatigue damage models in power electronic module wirebond structure under various amplitude loadings

This paper presents mean fatigue lifetime predic- tion of a wire-bond structure model in power electronic module using a failure physics approach that integrates high fidelity modelling and reduced order modelling. Loading current with variable amplitudes is applied to a finite element model of simplified wirebond structures. The resulting accumulated fatigue damage due to random loads is predicted by using reduced order modelling based on failure physics, a cycle counting algorithm, and various nonlinear fatigue damage models widely used in the literature. The reduced order mod- elling approach based on failure physics uses prediction data for the electro-thermo-mechanical behaviour of the wire-bond design of a power module obtained through non-linear transient finite element simulations, in particular for the fatigue life-time of the aluminium wire attached to the silicon chip of the wire in the module. The reduced order models that capture the black box function of the accumulated plastic strain are used in pre- dicting the mean fatigue life time of the wire bond structure under random loads. One of the widely used cycle counting algorithms, rainflow counting algorithm, is used to count cycles of the temperature profile at the specific point of the wire bond structure in a power electronic module. The cycle data from the rainflow algorithm mean life time of the wire bond structure are predicted with various cumulative fatigue models. Non-linear cumulative fatigue models such as damage curve approach （DCA）, double linear damage rule （DLDR）, and double dam- age curve approach （DDCA）, and linear cumulative fatigue damage model such as Palmgren-Miner rule are used to predict the mean fatigue life of the wire bond structure, and the results are compared.