The objective of this study is to identify system parameters from the recorded response of base isolated buildings,such as USC hospital building,during the 1994 Northridge earthquake.Full state measurements are not av...The objective of this study is to identify system parameters from the recorded response of base isolated buildings,such as USC hospital building,during the 1994 Northridge earthquake.Full state measurements are not available for identification.Additionally,the response is nonlinear due to the yielding of the lead-rubber bearings.Two new approaches are presented in this paper to solve the aforementioned problems.First,a reduced order observer is used to estimate the unmeasured states.Second,a least squares technique with time segments is developed to identify the piece-wise linear system properties.The observer is used to estimate the initial conditions needed for the time segmented identification.A series of equivalent linear system parameters are identified in different time segments.It is shown that the change in system parameters,such as frequencies and damping ratios,due to nonlinear behavior of the lead-rubber bearings,are reliably estimated using the presented technique.It is shown that the response was reduced due to yielding of the lead-rubber bearings and period lengthening.展开更多
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 g...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.展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
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. Aim...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.展开更多
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 performa...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.展开更多
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 con...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.展开更多
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 ...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.展开更多
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 orde...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.展开更多
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 wi...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.展开更多
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...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.展开更多
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 ...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.展开更多
Based on linear matrix inequalities (LMI), the design method of reduced order controllers of mixed sensitivity problem is studied for flight control systems. It is shown that there exists a controller with order not ...Based on linear matrix inequalities (LMI), the design method of reduced order controllers of mixed sensitivity problem is studied for flight control systems. It is shown that there exists a controller with order not greater than the difference between the generalized plant order and the number of independent control variables, if the mixed sensitivity problem is solvable for strict regular flight control plants. The proof is constructive, and an approach to design such a controller can be obtained in terms of a pair of feasible solution to the well known 3 LMI. Finally, an example of mixed sensitivity problem for a flight control system is given to demonstrate practice of the approach.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
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 void...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.展开更多
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 pr...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.展开更多
A novel statistical second-order reduced multiscale(SSRM)approach is established for nonlinear composite materials with random distribution of grains.For these composites considered in this work,the complex microstruc...A novel statistical second-order reduced multiscale(SSRM)approach is established for nonlinear composite materials with random distribution of grains.For these composites considered in this work,the complex microstructure of grains,including their shape,orientation,size,spatial distribution,volume fraction and so on,results in changing of the macroscopic mechanical properties.The first-and second-order unit cell functions based on two-scale asymptotic expressions are constructed at first.Then,the expected homogenized parameters are defined,and the nonlinear homogenization equation on global structure is established,successively.Further,an effective reduced model format for analyzing second-order nonlinear unit cell problem with less computation cost is introduced in detail.Finally,some numerical examples for the materials with varying distribution models are evaluated and compared with the data by theoretical models and experimental results.These examples illustrate that the proposed SSRM approaches are effective for predicting the macroscopic properties of the random composite materials and supply a potential application in actual engineering computation.展开更多
This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance...This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance.On one hand,the reduced order extended state observer(ROESO) and reduced order cascade extended state observer(ROCESO) are proposed for the case that the system state can be measured directly.On the other hand,the extended state observer(ESO) and the cascade extended state observer(CESO) are presented for another case when the system state cannot be measured directly.It is shown that combination of ROCESO and CESO can achieve a highly effective observation result.In addition,the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper.Finally,numerical simulations are given to illustrate the effectiveness of the proposed methods.展开更多
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)...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.展开更多
Quad-curl equations with Navier type boundary conditions are studied in this paper.Stable order reduced formulations equivalent to the model problems are presented,and finite element discretizations are designed.Optim...Quad-curl equations with Navier type boundary conditions are studied in this paper.Stable order reduced formulations equivalent to the model problems are presented,and finite element discretizations are designed.Optimal convergence rates are proved.展开更多
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...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.展开更多
文摘The objective of this study is to identify system parameters from the recorded response of base isolated buildings,such as USC hospital building,during the 1994 Northridge earthquake.Full state measurements are not available for identification.Additionally,the response is nonlinear due to the yielding of the lead-rubber bearings.Two new approaches are presented in this paper to solve the aforementioned problems.First,a reduced order observer is used to estimate the unmeasured states.Second,a least squares technique with time segments is developed to identify the piece-wise linear system properties.The observer is used to estimate the initial conditions needed for the time segmented identification.A series of equivalent linear system parameters are identified in different time segments.It is shown that the change in system parameters,such as frequencies and damping ratios,due to nonlinear behavior of the lead-rubber bearings,are reliably estimated using the presented technique.It is shown that the response was reduced due to yielding of the lead-rubber bearings and period lengthening.
文摘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.
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
基金supported by the National Natural Science Foundation of China (Nos. 11372036, 50875024)Excellent Young Scholars Research Fund of Beijing Institute of Technology of China (No. 2010Y0102)
文摘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.
基金co-National Science and Technology Major Project(No.2017-II-0009-0023)Innovation Guidance Support Project for Taicang Top Research Institutes(No.TC2019DYDS09)。
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.11372036)
文摘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.
文摘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.
基金National Natural Science Foundation of China (10902082)New Faculty Research Foundation of XJTUthe Fundamental Research Funds for the Central Universities (xjj20100126)
文摘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.
基金supported by the National Science and Technology Major Project, China (No. 2017-II-0009-0023)the Aeronautical Science Foundation of China(No. 2020Z039053004)the Fundamental Research Funds for the Central Universities, China (No. 3102019OQD701)
文摘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.
文摘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.
基金supported by a Marie Curie Early Stage Research Training Fellowship of the European Community’s Sixth Framework Programme under contract number MEST CT 2005020301.
文摘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.
基金Aeronautical Science Foundation of China! ( 97E5 10 18) Shanghai Provincial Young Science Foundation of China !( 199910 18)
文摘Based on linear matrix inequalities (LMI), the design method of reduced order controllers of mixed sensitivity problem is studied for flight control systems. It is shown that there exists a controller with order not greater than the difference between the generalized plant order and the number of independent control variables, if the mixed sensitivity problem is solvable for strict regular flight control plants. The proof is constructive, and an approach to design such a controller can be obtained in terms of a pair of feasible solution to the well known 3 LMI. Finally, an example of mixed sensitivity problem for a flight control system is given to demonstrate practice of the approach.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
基金support of this work by the National Science Foundation (CMMI Award no.1932975)。
文摘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.
基金the National Science Foundation of China(Grant Nos.51804033 and 51936001)China Postdoctoral Science and Foundation(Grant No.2018M641254)+3 种基金Beijing Postdoctoral Research Foundation(2018-ZZ-045)the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality(Grant No.IDHT20170507)Program of Great Wall Scholar(Grant No.CIT&TCD20180313)Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(Grant No.KZ201810017023).
文摘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.
基金This study was funded by the National Natural Science Foundation of China(Grant 11701123)Fundamental Research Funds for the Central Universities(Grant HIT.NSRIF.2020017).
文摘A novel statistical second-order reduced multiscale(SSRM)approach is established for nonlinear composite materials with random distribution of grains.For these composites considered in this work,the complex microstructure of grains,including their shape,orientation,size,spatial distribution,volume fraction and so on,results in changing of the macroscopic mechanical properties.The first-and second-order unit cell functions based on two-scale asymptotic expressions are constructed at first.Then,the expected homogenized parameters are defined,and the nonlinear homogenization equation on global structure is established,successively.Further,an effective reduced model format for analyzing second-order nonlinear unit cell problem with less computation cost is introduced in detail.Finally,some numerical examples for the materials with varying distribution models are evaluated and compared with the data by theoretical models and experimental results.These examples illustrate that the proposed SSRM approaches are effective for predicting the macroscopic properties of the random composite materials and supply a potential application in actual engineering computation.
基金supported by the National Natural Science Foundation of China(61573332,61601431)Fundamental Research Funds for the Central Universities(WK2100100028)
文摘This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance.On one hand,the reduced order extended state observer(ROESO) and reduced order cascade extended state observer(ROCESO) are proposed for the case that the system state can be measured directly.On the other hand,the extended state observer(ESO) and the cascade extended state observer(CESO) are presented for another case when the system state cannot be measured directly.It is shown that combination of ROCESO and CESO can achieve a highly effective observation result.In addition,the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper.Finally,numerical simulations are given to illustrate the effectiveness of the proposed methods.
文摘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.
基金The work of the first author was supported in part by Yunnan Provincial Science and Technology Department Research Award:Interdisciplinary Research in Computational Mathematics and Mechanics with Applications in Energy Engineering(Grant No.2009CI128)Yunnan Provincial Science and Technology Project(Grant No.2014RA071)The work of the second author was supported partially by the National Natural Science Foundation of China with Grant Nos 11471026 and 11871465 and National Centre for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences.
文摘Quad-curl equations with Navier type boundary conditions are studied in this paper.Stable order reduced formulations equivalent to the model problems are presented,and finite element discretizations are designed.Optimal convergence rates are proved.
基金Funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)-Project-ID 422037413-TRR 287.
文摘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.