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.

PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL

In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

Reduced combustion time model for methane in gas turbine flow fields

Computational fluid dynamics （CFD） modeling of the complex processes that occur within the burner of a gas turbine engine has become a critical step in the design process. However, due to computer limitations, it is very difficult to completely couple the fluid mechanics solver with the full combustion chemistry. Therefore, simplified chemistry models are required, and the topic of this research was to provide reduced chemistry models for CH4/O2 gas turbine flow fields to be integrated into CFD codes for the simulation of flow fields of natural gas-fueled burners. The reduction procedure for the CH4/O2 model utilized a response modeling technique wherein the full mechanism was solved over a range of temperatures, pressures, and mixture ratios to establish the response of a particular variable, namely the chemical reaction time. The conditions covered were between 1000 and 2500 K for temperature, 0.1 and 2 for equivalence ratio in air, and 0.1 and 50 atm for pressure. The kinetic time models in the form of ignition time correlations are given in Arrhenius-type formulas as functions of equivalence ratio, temperature, and pressure; or fuel-to-air ratio, temperature, and pressure. A single ignition time model was obtained for the entire range of conditions, and separate models for the low-temperature and high-temperature regions as well as for fuel-lean and rich cases were also derived. Predictions using the reduced model were verified using results from the full mechanism and empirical correlations from experiments. The models are intended for （but not limited to） use in CFD codes for flow field simulations of gas turbine combustors in which initial conditions and degree of mixedness of the fuel and air are key factors in achieving stable and robust combustion processes and acceptable emission levels. The chemical time model was utilized successfully in CFD simulations of a generic gas turbine combustor with four different cases with various levels of fuel-air premixing.

Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model

The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties.The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures,in particular to the bilayer structures based on temperature-driven shape-memory polymers(SMPs) and fabricated using the fused deposition modeling(FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency,as the three-dimensional(3D) problem is converted to a two-dimensional(2D) problem.The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.

Reduced EGFR signaling enhances cartilage destruction in a mouse osteoarthritis model

Osteoarthritis （OA） is a degenerative joint disease and a major cause of pain and disability in older adults. We have previously identified epidermal growth factor receptor （EGFR） signaling as an important regulator of cartilage matrix degradation during epiphyseal cartilage development. To study its function in OA progression, we performed surgical destabilization of the medial meniscus （DMM） to induce OA in two mouse models with reduced EGFR activity, one with genetic modification （, was/＋ mice） and the other one with pharmacological inhibition （gefitinib treatment）. Histological analyses and scoring at 3 months post-surgery revealed increased cartilage destruction and accelerated OA progression in both mouse models. TUNEL staining demonstrated that EGFR signaling protects chondrocytes from OA-induced apoptosis, which was further confirmed in primary chondrocyte culture. Immunohistochemistry showed increased aggrecan degradation in these mouse models, which coincides with elevated amounts of ADAMTS5 and matrix metalloproteinase 13 （MMP13）, the principle proteinases responsible for aggrecan degradation, in the articular cartilage after DMM surgery. Furthermore, hypoxia-inducible factor 2α （HIF2α）, a critical catabolic transcription factor stimulating MMP13 expression during OA, was also upregulated in mice with reduced EGFR signaling. Taken together, our findings demonstrate a primarily protective role of EGFR during OA progression by regulating chondrocyte survival and cartilage degradation.

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.

Reduced Life Expectancy Model Analyses of Exposure Time Effects of Endocrine Disruptors to Teleost Fishes Based on Effect Concentration of Hepatic Biomarkers

In this current paper, the exposure time effects on four endocrine disruptors and teleost fishes were evaluated using the reduced life expectancy (RLE) model based on the effect concentration (EC50) of available literature published. The result on the regression analysis over different exposure times has demonstrated that the EC50 of hepatic biomarkers falls with increasing exposure times in a predictable manner. The slopes of the regression equations reflect the strength of the toxic effects on the various teleost fish. The EC50 reduction over time can be interpreted based on the bioconcentration process, which can be used to understand transfer routes of the compounds from water to fish body. RLE model also provides useful information in assessing the toxic effects on fish life expectancy as a result of the occurrence of compounds.

Convective drying of wood chips:Accelerating coupled DEM-CFD simulations with parametrized reduced single particle models

The simulation of industry-scale reactive bulks is challenging due to the complex interaction between fluid and particles.The particles in the bulk and their interaction with the fluid flow can be described by combined Discrete Element Method-Computational Fluid Dynamics(DEM-CFD)models.However,the computational cost of the Finite Volume(FV)methods deployed in these models can become prohibi-tively expensive,especially for high inner-particle resolution.Single particle Reduced Models(RMs)can be used to achieve both fast and accurate descriptions of the processes in each particle.As an example of bulk systems comprising heat and mass transfer,we compared FV and RM simulations for the drying of wood chips in a bulk reactor.A manifold-based nonlinear interpolation was applied to resolve changing boundary conditions for the RM.Our simulations showed that RMs provide accurate values for the thermodynamic state variables of the particles.Furthermore,the time required for the bulk simulation was reduced by 67%with the RMs.It is evident that simulations with high inner-particle resolution can be accelerated by RMs if manifold-based nonlinear interpolation is used to address changing boundary conditions.

Kinetic models of natural gas combustion in an internal combustion engine

In this study, combustion of methane was simulated using four kinetic models of methane in CHEMKIN 4.1.1 for 0-D closed internal combustion （IC） engine reactor. Two detailed （GRIMECH3.0 ＆ UBC MECH2.0） and two reduced （One step ＆ Four steps） models were examined for various IC engine designs. The detailed models （GRIMECH3.0, ＆ UBC MECH2.0） and 4-step models successfully predicted the combustion while global model was unable to predict any combustion reaction. This study illustrated that the detailed model showed good concordances in the prediction of chamber pressure, temperature and major combustion species profiles. The detailed models also exhibited the capabilities to predict the pollutants formation in an IC engine while the reduced schemes showed failure in the prediction of pollutants emissions. Although, there are discrepancies among the profiles of four considered model, the detailed models （GRIMECH3.0 ＆ UBC MECH2.0） produced the acceptable agreement in the species prediction and formation of pollutants.

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.

Bionic Optimisation of the Earthquake Resistance of High Buildings by Tuned Mass Dampers

The optimisation of earthquake resistance of high buildings by multi-tuned mass dampers was investigated using bionic algorithms. In bionic or evolutionary optimisation studies the properties of parents are crossed and mutated to produce a new generation with slightly different properties. The kids which best satisfy the object of the study, become the parents of the next generation. After a series of generations essential improvements of the object may be observed. Tuned mass dampers are widely used to reduce the impact of dynamic excitations on structures. A single mass system and multi-mass oscillators help to explain the mechanics of the dampers. To apply the bionic optimisation strategy to high buildings with passive tuned mass dampers subject to seismic loading a special beam element has been developed. In addition to the 6 degrees of freedom of a conventional beam element, it has 2 degrees of freedom for the displacements of the dampers. It allows for fast studies of many variants. As central result, efficient designs for damping systems along the height of an edifice are found. The impact on the structure may be reduced essentially by the use of such dampers designed to interact in an optimal way.

A Discontinuous Galerkin Method for Blood Flow and Solute Transport in One-Dimensional Vessel Networks

This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel networks.The reduced coupled model describes the variations of vessel cross-sectional area,radially averaged blood momentum and solute concentration in large vessel networks.For the discretization of the reduced transport equation,we combine an interior penalty discontinuous Galerkin method in space with a novel locally implicit time stepping scheme.The stability and the convergence are proved.Numerical results show the impact of the choice for the steady-state axial velocity profile on the numerical solutions in a fifty-five vessel network with physiological boundary data.

The Space-Time CE/SE Method for Solving Reduced Two-Fluid Flow Model

The space-time conservation element and solution element(CE/SE)method is proposed for solving a conservative interface-capturing reducedmodel of compressible two-fluid flows.The flow equations are the bulk equations,combined with mass and energy equations for one of the two fluids.The latter equation contains a source term for accounting the energy exchange.The one and two-dimensional flow models are numerically investigated in this manuscript.The CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious oscillations.In contrast to the existing upwind finite volume schemes,the Riemann solver and reconstruction procedure are not the building block of the suggested method.The method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation.In order to reveal the efficiency and performance of the approach,several numerical test cases are presented.For validation,the results of the current method are compared with other finite volume schemes.

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.

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.

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.