Combination Of Proper Orthogonal Decomposition Research Articles

An efficient reduced order model for nonlinear transient porous media flow with time-varying injection rates

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.

Air distribution and coal blending optimization to reduce slagging on coal-fired boiler water wall based on POD reduced order modeling for CFD

Slagging is a common phenomenon interfering with the safe and efficient operation of coal-fired boilers. Due to the lack of monitoring methods for species and temperature distribution near the water wall, which is critical for slagging formation, it is a tricky problem to detect and reduce the slagging in real time. A method for slagging distribution prediction and anti-slagging optimization of a 330 MW tangentially coal-fired boiler is developed in this paper. Proper orthogonal decomposition (POD) reduced order modeling and support vector machine (SVM) are used to predict the distribution of temperature and O2 near the water wall by taking 15 variables as input parameters (load, coal types, primary air rate, secondary air rate, excess air coefficient, and secondary air velocities). Next, fuzzy comprehensive evaluation (FCE) is employed to quantify the slagging occurrence and distribution on the water wall. Furthermore, the real time slagging prediction is realized with the combination of POD, SVM, and FCE. Finally, the conventional genetic algorithm (CGA) and simulated annealing genetic algorithm (SAGA) are adopted to optimize the air distribution schemes and coal blending schemes to reduce the slagging ratio, and their performances are compared. The results indicate that the predictions of temperature and O2 with POD show a good agreement with CFD simulations. In the optimization process, whether air distribution is optimized alone or both coal blending and air distribution are optimized simultaneously, the performance of SAGA is better than that of CGA. After optimizing the air distribution with SAGA, the slagging ratio of a typical operating condition with a load of 330 MW is reduced from 14.21% to 7.16%. The slagging ratio is further reduced to 5.36% after optimizing air distribution and coal blending schemes simultaneously. The proposed slagging prediction and optimization for anti-slagging opens a new perspective to alleviate slagging of water walls effectively.

A rapid method to predict biaxial fatigue life of automotive wheels using proper orthogonal decomposition and radial basis function algorithm

This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests are being developed to evaluate wheel performance. However, these simulations are computationally expensive due to the need to simulate multiple discrete loading cases within a given biaxial spectrum. To address this issue, we propose a novel approach that utilizes proper orthogonal decomposition and radial basis function algorithm to improve computational efficiency. By leveraging high-fidelity simulation results from a small number of loading cases, a reduced order model is constructed to accurately predict the tire-rim interface force fields required for wheel strength calculations. The reduced order model significantly reduces the computational time by 65.4% for simulating all loading cases, while maintaining a maximum predicted error of less than 2% compared to the high-fidelity model. Subsequently, the predicted interface forces are mapped onto the rim surface for strength calculation, and the wheel fatigue life is determined using the Brown-Miller multiaxial damage criterion. Comparative analysis with experimental results demonstrates the desirable accuracy of our method in simulating the stress-strain history, crack initiation position, and minimum fatigue life of the wheel. Overall, the proposed method offers a powerful tool for the rapid fatigue analysis of spectrum-loaded wheels, providing an efficient and accurate means of predicting biaxial fatigue life.

Multi-Objective Optimization of Variable Density Multi-Layer Insulation for Liquid Hydrogen Containers Based on Reduced-Order Surrogate Model

For liquid hydrogen transportation, thermal insulation materials that are lightweight, compact and exhibit high-performance have been pursued for several decades, and variable density multi-layer insulation (VD-MLI) has been regarded as a promising choice. The thermal insulation performance of the insulation materials is important, but is not at the top of the list; many constraints, such as the space and weight of the insulation structures, are imposed on the design of a VD-MLI. Consequently, this makes the optimization of VD-MLIs more complicated. The present authors conducted a multi-objective optimization of a VD-MLI stacked with specific insulation units. The number of repetitions of the basic insulation unit was regarded as the dimensionless design parameter of the VD-MLI. Based on the experimentally validated layer-by-layer (LBL) model for MLI design, the multi-objective optimization of VD-MLI for liquid hydrogen storage was conducted by the combination of proper orthogonal decomposition with a general regression neural network (POD-GRNN) surrogate model optimization framework. The results showed that the optimal solutions for VD-MLI configurations could be achieved under different constraints. The present optimization framework provides a new reference for the optimization of VD-MLI for cryogenic liquid storage.

Porous cylinder arrays for optimal wake and drag characteristics

The root systems of mangroves, a tree species found in intertidal tropical and subtropical coastal zones, provide a natural barrier that dissipates wave energy effectively and reduces sediment erosion. Here, we use a combination of experiments and numerical simulations to examine the wake and drag characteristics of porous arrays of cylinders, which serve as simplified models of mangrove root networks. Optimal arrangements of the arrays are obtained by coupling Navier–Stokes simulations with a multi-objective optimization algorithm, which seeks configurations that minimize wake enstrophy and maximize drag on the porous structure. These optimal configurations are investigated using particle image velocimetry, and the internal and external flows around the porous arrays are analysed using a combination of proper orthogonal decomposition and Lagrangian particle tracking. Large variations in drag and enstrophy are observed by varying the relative positions of the cylinders, which indicates that the geometrical arrangement of porous arrays plays a prominent role in determining wake and drag characteristics. A sensitivity analysis suggests that enstrophy is more sensitive than drag to specific cylinder placement, and depends on distinctive flow patterns that develop in the interior due to interactions among neighbouring cylinders. Arrays with higher drag involve a combination of larger projected frontal area and minimal flux through the interior, leading to increased wake enstrophy, which is unfavourable for particle deposition and erosion. Based on the analysis of characteristics associated with the optimal arrays, several manually designed arrays are tested, and they display the expected behaviour with regard to drag and enstrophy.

Analysis of an unsteady quasi-capillary channel flow with time-resolved PIV and RBF-based super-resolution

We investigate the interface dynamics in an unsteady quasi-capillary channel flow. The configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Both advancing and receding contact lines were analyzed to test the validity of classic models for dynamic wetting and to study the flow field near the interface. The operating conditions are characterized by a large acceleration, thus dominated by inertia. The shape of the moving meniscus was retrieved using Laser-Induced Fluorescence-based image processing, while the flow field near was analyzed via Time-Resolved Particle Image Velocimetry (TR-PIV). The TR-PIV measurements were enhanced in the post-processing, using a combination of Proper Orthogonal Decomposition and Radial Basis Functions to achieve super-resolution of the velocity field. Large counter-rotating vortices were observed, and their evolution was monitored in terms of the maximum intensity of the Q-field. The results show that classic contact angle models based on interface velocity cannot describe the evolution of the contact angle at a macroscopic scale. Moreover, the impact of the interface dynamics on the flow field is considerable and extends to several capillary lengths below the interface.

Model Order Reduction for Real-Time FPGA-Based Finite Element Transient Simulation of Three-Phase Transformer

The finite element method (FEM) is commonly used in modeling the electromagnetic field of transformers with high accuracy; however, the computation time of the FEM is prohibitively high for real-time simulation due to high model order. Reducing the model order is helpful to improve the computational efficiency of the FEM. The proper orthogonal decomposition (POD) is an efficient method to reduce the linear model order but encounters difficulties with nonlinear models. In this paper, a model order reduction (MOR) method based on the combination of POD and the transmission-line modeling (TLM) is proposed to reduce the nonlinear finite element model order and computation time. The TLM method is used to separate the nonlinear components from the model, and then the POD is used to reduce the linear domain order of the model. The nonlinear components obtained by TLM can be solved in parallel on the field programmable gate array (FPGA) to improve computational efficiency further. This paper has studied the transient states of a three-phase transformer with the current excitation and field-circuit coupling. The real-time hardware emulation results are validated by results from offline simulation using Comsol®.

A surrogate model for real-time dynamic simulation of dielectric elastomer actuators via long short-term memory networks

A surrogate model for dynamical behavior of dielectric elastomer actuators was proposed, the reduced-order framework was based on long short-term memory (LSTM) networks, and the combination of proper orthogonal decomposition with the Galerkin projection. To capture the latent dynamics of actuators, both the displacement and velocity fields were employed in this framework with the enforced electric potential signals, and two stacked architectures of LSTM networks were proposed to predict the dynamical evolution. The performance of the proposed surrogate model was demonstrated through two bimorph actuator concepts. The results show that the proposed model is a promising, reliable, and computationally efficient approach for the real-time simulation.

Time Resolved PIV of the Flow Field Underneath an Accelerating Meniscus

We present an experimental analysis of the flow field near an accelerating contact line using time-resolved Particle Image Velocimetry (TR-PIV). Both advancing and receding contact lines are investigated. The analyzed configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Large counter-rotating vortices were observed and analyzed in terms of the maximum intensity of the Q-field. To compute smooth spatial derivatives and improve the measurement resolution in the post-processing stage, we propose a combination of Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF). The RBFs are used to regress the spatial and temporal structures of the leading POD modes, so that “high-resolution” modes are obtained. These can then be combined to reconstruct high-resolution fields that are smooth and robust against measurement noise and amenable to analytic differentiation. The results show significant differences in the flow topology between the advancing and the receding cases despite velocity and acceleration of contact lines are comparable in absolute values. This suggests that the flow dynamics are tightly linked to the shape of the interface, which significantly differs in the two cases.

Combination of polynomial chaos and Kriging for reduced-order model of reacting flow applications

The combination of Proper Orthogonal Decomposition (POD) with Kriging has been shown to be a reliable choice for the development of Reduced-Order Models (ROMs) for the prediction of combustion data at unexplored operating conditions. In this study, POD is combined with Polynomial Chaos Expansion (PCE), with a combination of PCE and Kriging (PC-Kriging) and with Artificial Neural Networks (ANN) for the development of a ROM that can predict 2D combustion data for unexplored operating conditions. The choice of Non-negative Matrix Factorization (NMF) instead of POD as compression method is also investigated. This method is chosen because it can intrinsically guarantee the non-violation of physical constraints such as positivity of chemical species mass fractions, although POD's data reconstruction errors are lower. The performances of the POD and NMF in combination with the proposed supervised methods are compared, with prediction normalized root mean squared errors (NRMSE) being less than 10% for spatial fields of temperature, CH4 and O2 for all approaches.

Efficient uncertainty quantification of CFD problems by combination of proper orthogonal decomposition and compressed sensing

In the current paper, an efficient surrogate model based on combination of Proper Orthogonal Decomposition (POD) and compressed sensing is developed for affordable representation of high dimensional stochastic fields. In the developed method, instead of the full (or classical) Polynomial Chaos Expansion (PCE), the ℓ1-minimization approach is utilized to reduce the computational work-load of the low-fidelity calculations. To assess the model capability in the real engineering problems, two challenging high-dimensional CFD test cases namely; i) turbulent transonic flow around RAE2822 airfoil with 18 geometrical uncertainties and ii) turbulent transonic flow around NASA Rotor 37 with 3 operational and 21 geometrical uncertainties are considered. Results of Uncertainty Quantification (UQ) analysis in both test cases showed that the proposed multi-fidelity approach is able to reproduce the statistics of quantities of interest with much lower computational cost than the classical regression-based PCE method. It is shown that the combination of the POD with the compressed sensing in RAE2822 and Rotor 37 test cases gives respectively computational gains between 1.26–7.72 and 1.79–9.05 times greater than the combination of the POD with the full PCE.

Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

This paper presents a novel framework for stochastic analysis of linear elastic fracture problems. Monte Carlo simulation (MCs) is adopted to address the multi-dimensional uncertainties, whose computation cost is reduced by combination of Proper Orthogonal Decomposition (POD) and the Radial Basis Function (RBF). In order to avoid re-meshing and retain the geometric exactness, isogeometric boundary element method (IGABEM) is employed for simulation, in which the Non-Uniform Rational B-splines (NURBS) are employed for representing the crack surfaces and discretizing dual boundary integral equations. The stress intensity factors (SIFs) are extracted by M integral method. The numerical examples simulate several cracked structures with various uncertain parameters such as load effects, materials, geometric dimensions, and the results are verified by comparison with the analytical solutions.

Surrogate Models for Optimization of Dynamical Systems

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven mechanism to construct low dimensional surrogate models. These surrogate models reduce the computational time for solution of the complex optimization problems by using training instances derived from the evaluations of the true objective functions. The surrogate models are constructed using combination of proper orthogonal decomposition and radial basis functions and provides system responses by simple matrix multiplication. Using relative maximum absolute error as the measure of accuracy of approximation, it is shown surrogate models with latin hypercube sampling and spline radial basis functions dominate variable order methods in computational time of optimization, while preserving the accuracy. These surrogate models also show robustness in presence of model non-linearities. Therefore, these computational efficient predictive surrogate models are applicable in various fields, specifically to solve inverse problems and optimal control problems, some examples of which are demonstrated in this paper.

The POD–DEIM reduced-order method for stochastic Allen–Cahn equations with multiplicative noise

In this paper, we propose a reduced-order method (ROM) based on the Monte Carlo finite difference method (FDM) or Monte Carlo finite element method (FEM) for the stochastic Allen–Cahn (SAC) equation with multiplicative noise. The reduction method is a combination of proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). In the theoretical part, the error bounds of full-order method (FOM) and POD–DEIM are provided, as well as the computational complexity of FOM and POD–DEIM. In the numerical experiments section, several two-dimensional SAC examples with multiplicative noise are considered. Using the Monte Carlo FDM and Monte Carlo FEM as the reference methods, the POD–DEIM has obvious advantage in the computational efficiency. And with the encryption in the space or time direction, this advantage is more prominent.

A generalized DEIM technique for model order reduction of porous media simulations in reservoir optimizations

High computational requirements limit the applications of subsurface flow simulation for practical problems, especially in the case of well-control optimization that requires lots of simulations. This has motivated the development of reduced-order models, particularly the methods based on Proper Orthogonal Decomposition (POD), to reduce the computational costs of the reservoir simulations. These methods construct several bases in order to transform the parameters of the simulation from a higher-dimensional space onto a lower-dimensional space. In this paper, a new method, GDEIM, based on the combination of POD, Galerkin projection and Discrete Empirical Interpolation Method (DEIM) with the generalized eigenvalue problem, is introduced and examined for a well-control optimization problem which leads to more accurate results in the reconstruction of the Full Order Model (FOM) compared with POD-DEIM despite much lower simulation costs.

Propeller influence on the aeroelastic stability of High Altitude Long Endurance aircraft

AbstractThis work investigates the propeller’s influence on the stability of High Altitude Long Endurance aircraft, incorporating all resultant loads at the propeller hub, propeller slipstream, and gyroscopic loads. Such effects are usually neglected in the aeroelastic simulation of HALE aircraft. For that goal, a previously developed framework, which couples a geometrically nonlinear structural solver with an Unsteady Vortex Lattice method (uVLM) for lifting surfaces and a Viscous Vortex Particle (VVP) method for propeller slipstream, was employed to generate time-data series. Also, a method, based on a combination of Proper Orthogonal Decomposition and system identification, to extract dynamic information (frequencies, damping, and modes) of the aircraft from a time-series signal is proposed and successfully tested for a purely structural case, for which reference data is available. The method is then applied to investigate the stability of aeroelastic cases. The results demonstrate that the presence of propellers can influence the aeroelastic stability of a Very Flexible Aircraft.

Experimental Analysis of Cooling Fan Noise by Wavelet-Based Beamforming and Proper Orthogonal Decomposition

We use the proper orthogonal decomposition (POD) method to decompose acoustic imaging from wavelet-based beamforming results into their corresponding modes, and demonstrate the method to analyze the noise characteristics of small-dimensional components, where research literature is still scarce. In particular, we consider the noise from a central processing unit (CPU) cooling fan, though the developed method could find realistic applications in a wider scheme of electronic industry. In addition to developing the new analysis method, we also endeavor to prepare a realistic experimental setup with a CPU cooling fan in an anechoic room. The results show that the combination of POD and wavelet-based beamforming methods is suitable for CPU cooling fan acoustic imaging, which can enhance the analysis ability of acoustic imaging test. The results offered in this work are helpful in cooling fan design and evaluation, which would open doors to a wide range of industrial applications.

Sensing the turbulent large-scale motions with their wall signature

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

Stochastic field representation using bi-fidelity combination of proper orthogonal decomposition and Kriging

In the current paper efficient uncertainty quantification (UQ) of high dimensional stochastic fields is performed via a bi-fidelity surrogate model. The method is based on combination of proper orthogonal decomposition (POD) and Kriging method. In the developed method, the trend function of the Kriging model is estimated via a low cost POD, whilst the stochastic Gaussian contribution is tuned using a limited number of high-fidelity computations. The proposed method is applied to three test cases, including a highly nonlinear test function, thermally driven flow in a cavity with stochastic wall temperatures and turbulent heat transfer in a ribbed channel with stochastic heat flux boundary condition. Implementing both POD and POD–Kriging methods leads to significant reduction of computational cost in comparison to the classical full polynomial chaos expansion (PCE) with least cost saving of more than 60%. Furthermore, in all cases combined POD–Kriging method performs either superior or at least similar to the POD method. More specifically, in surrogate models with lower number of low- and high-fidelity samples greater gains in accuracy are obtained. Consequently, for a specific level of accuracy, POD–Kriging method requires lower computational cost.

Dynamic Data-Driven Multi-Step-Ahead Prediction with Simulation Data and Sensor Measurements

In this paper, the authors propose a dynamical data-driven prediction framework to estimate a system’s behavior multiple steps ahead. The main contribution of this work is in the construction of a new recursive multi-input/multi-output (REC-MIMO) strategy, which can attain real-time estimation through a combination of expensive simulation data (offline) and sensor measurements (online). This framework is composed of an offline phase and an online phase. In the offline phase, a multi-input/multi-output strategy is employed for constructing a predictive model for the system’s dynamical responses from simulation data. The offline phase is accomplished through a combination of proper orthogonal decomposition and Gaussian process. By using the measurement data collected from sensors, a recursive strategy is used to iteratively enhance multi-step-ahead predictions by using a new reduced-order particle filter method during the online phase. An illustrative example involving aeroelastic responses of a joined-wing SensorCraft is used to demonstrate the effectiveness of the proposed framework. It has been shown that state predictions obtained through the REC-MIMO strategy have accuracy comparable to those obtained from high-fidelity simulations with significant reduction in computational expense. It is envisioned that the proposed methodology can be used to support system decision making in an efficient manner.