Reduced-order Model Research Articles

Reduced order modeling for optimal aerodynamic design and operation of the industrial air-jet ejector

Reduced order modeling for optimal aerodynamic design and operation of the industrial air-jet ejector

Parameter Regression for Porous Electrodes Employed in Lithium-Ion Batteries and Application to Ni0.89Co0.05Mn0.05Al0.01O2

We develop a parameter regression scheme that can be used with battery models of interest to the battery-analysis community. We show that the recent reduced order model (ROM1, 2022 J. Electrochem. 169 070520, DOI: 10.1149/1945–7111/ac7c93), which is based on a perturbation solution, can be used in place of the full system of nonlinear partial differential equations with minimal loss of accuracy for the conditions of this work, which are relevant for electric vehicle applications. The use of the computationally efficient ROM1, cast in the Python programming language, along with a routine native to Python for the nonlinear regression of model parameters through the minimization of the squared differences between experimental results and model calculations, provides a fast method for the overall endeavor. We apply the procedure to examine Ni0.89Co0.05Mn0.05Al0.01O2, a high-capacity material that is of increasing interest with respect to electric vehicles and other products that rely on batteries of high energy density. Difficulties encountered in this work include the large number of parameters governing the battery model, parameter sensitivity in the regression analyses, and the potential for multiple solutions. We close this publication with a discussion of these challenges and open questions with respect to parameter identification.

Accelerating the BoR-FIT-MoM Method With the Use of the Model Order Reduction Techniques

Accelerating the BoR-FIT-MoM Method With the Use of the Model Order Reduction Techniques

Second-order Arnoldi accelerated boundary element method for two-dimensional broadband acoustic shape sensitivity analysis

This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm.

Total harmonic distortion estimation in piezoelectric micro-electro-mechanical-system loudspeakers via a FEM-assisted reduced-order-model

Piezoelectric micro-electro-mechanical-system (MEMS) loudspeakers are attracting growing research interest in the last years due to the increasing interest towards miniaturization required by new wireless audio devices. Finite Element Models (FEM) and Lumped Element Models (LEM) able to accurately simulate their linear response have been recently proposed in the literature. However, a nonlinear model suitable to predict the Total Harmonic Distortion (THD) of these devices is to date still missing. In this work, we present a FEM-assisted lumped-parameters equivalent circuit for THD estimation which accounts for geometric nonlinearities and piezoelectric hysteresis. The loudspeaker nonlinear electro-mechanical domain is simulated through a Reduced Order Model (ROM) which considers as basis function the pre-stressed undamped actuated mode of the device computed via FEM, to account for loudspeaker diaphragms of arbitrarily complex geometry. Parameters of the acoustical circuit are computed through analytical formulas. The good matching between numerical predictions and experimental results, carried out on a piezoelectric MEMS loudspeaker prototype for in-ear condition, demonstrates the accuracy of the proposed tool.

Reduced order model enhanced source iteration with synthetic acceleration for parametric radiative transfer equation

Applications such as uncertainty quantification, shape optimization, and optical tomography, require solving the radiative transfer equation (RTE) many times for various parameters. Efficient solvers for RTE are highly desired.Source Iteration with Synthetic Acceleration (SISA) is a popular and successful iterative solver for RTE. Synthetic Acceleration (SA) acts as a preconditioning step to accelerate the convergence of Source Iteration (SI). After each source iteration, classical SA strategies introduce a correction to the macroscopic particle density by solving a low order approximation to a kinetic correction equation. For example, Diffusion Synthetic Acceleration (DSA) uses the diffusion limit. However, these strategies may become less effective when the underlying low order approximations are not accurate enough. Furthermore, they do not exploit low rank structures concerning the parameters of parametric problems.To address these issues, we propose enhancing SISA with data-driven ROMs for the parametric problem and the corresponding kinetic correction equation. First, the ROM for the parametric problem can be utilized to obtain an improved initial guess. Second, the ROM for the kinetic correction equation can be utilized to design a low rank approximation to it. Unlike the diffusion limit, this ROM-based approximation builds on the kinetic description of the correction equation and leverages low rank structures concerning the parameters. We further introduce a novel SA strategy called ROMSAD. ROMSAD initially adopts our ROM-based approximation to exploit its greater efficiency in the early stage of SISA, and then automatically switches to DSA to leverage its robustness in the later stage. Additionally, we propose an approach to construct the ROM for the kinetic correction equation without directly solving it.Through a series of numerical tests, we compare the proposed methods with SI-DSA and DSA preconditioned Krylov solver. Particularly, for a multiscale parametric pin-cell problem, ROMSAD achieves approximately 10 times the acceleration compared to SI-DSA and 4 times acceleration compared to DSA preconditioned GMRES.

Physics-informed neural networks for phase locked loop transient stability assessment

A significant increase in renewable energy production is necessary to achieve the UN’s net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in synchronism with the grid can cause fast transient behavior during grid faults leading to instability. However, assessing all the probable scenarios is impractical, so determining the stability boundary or region of attraction (ROA) is necessary. However, using EMT simulations or Reduced-order models (ROMs) to accurately determine the ROA is computationally expensive. Alternatively, Machine Learning (ML) models have been proposed as an efficient method to predict stability. However, traditional ML algorithms require large amounts of labeled data for training, which is computationally expensive. This paper proposes a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear transient dynamics of a inverter with a PLL-based controller under fault with less labeled training data. The proposed PINN algorithm can be incorporated into conventional simulations, accelerating EMT simulations or ROMs by over 100 times. The PINN algorithm’s performance is compared against a ROM and an EMT simulation in PSCAD for the CIGRE benchmark model C4.49, demonstrating its ability to accurately approximate trajectories and ROAs of a inverter with a PLL-based controller under varying grid impedance.

A Comparative Study on the Efficiencies of Aerodynamic Reduced Order Models of Rigid and Aeroelastic Sweptback Wings

A Comparative Study on the Efficiencies of Aerodynamic Reduced Order Models of Rigid and Aeroelastic Sweptback Wings

Reduced-order helicopter model identification from closed-loop data

This paper presents the development of an algorithm for open-loop transfer functions identification and reduced-order modelling of a dynamical system, from closed-loop data with highly correlated inputs. Suitable for aeronautical applications (particularly for intrinsically unstable vehicles such as helicopters), it allows the identification of aircraft transfer functions from the knowledge of the time histories of arbitrary external inputs and the corresponding actuated controls and responses. After a numerical verification of the proposed approach considering a simple analytical aircraft dynamical system, it is successfully applied to a realistic engineering problem consisting of identifying the transfer functions of the AW-09 helicopter that relate pilot inputs to vehicle attitude and kinematics. It is shown that helicopter responses to arbitrary pilot inputs predicted by the reduced-order model representation of the helicopter dynamics based on the rational approximation of the identified transfer functions are in good agreement with those determined through the high-fidelity nonlinear flight dynamics solver used to evaluate the closed-loop database.

Nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers based on complex nonlinear modes

In this study, the nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers (ESDFDs) are investigated based on complex nonlinear modes (CNMs). The finite element method (FEM) combined with a full-3D friction model is introduced to construct the governing equation for the system. Additionally, the Craig–Bampton technique is applied to downscale the finite element model of the system. Based on the reduced order model (ROM), the nonlinear modal damping ratio of the target mode is employed to measure the dry friction damping performance of active ESDFD. The effects of the active ESDFD position, normal force, and tangential contact stiffness on the nonlinear modal damping ratio and modal frequency are analysed. Moreover, the softening characteristics of the active ESDFD are revealed, and the critical speed intervals of the active ESDFD/dual-rotor system are determined. Furthermore, by using the harmonic balance–alternating frequency/time domain (HB–AFT) method, the steady-state response of the system under unbalanced excitation is calculated. The accuracy and effectiveness of nonlinear modal analysis are validated based on the relationships between nonlinear modes and steady-state unbalanced responses. Conversely, the vibration mitigation effects of active ESDFD are determined by the unbalanced response amplitude. Additionally, the controllable region and optimal normal force for effective vibration control in the target mode are defined. Depending on the controllable region, a control strategy for turning on/off the optimal normal force is developed. The findings demonstrate that the developed control strategy enables the active ESDFD to significantly reduce the response amplitude of the dual-rotor system across various excitation levels, showing substantial potential for engineering applications.

Evaluation of Prediction Model for Compressor Performance Using Artificial Neural Network Models and Reduced-Order Models

Evaluation of Prediction Model for Compressor Performance Using Artificial Neural Network Models and Reduced-Order Models

Applying Machine Learning Techniques: Uncertainty Quantification in Nonlinear Dynamics Characters Predictions via Gated Recurrent Unit-Based Reduced-Order Models

The development of reduced-order models has been a pivotal advancement in the computational analysis of fluid dynamics, substantially simplifying the complexity and boosting the efficiency of simulations. The accuracy and practicality of these models largely depend on the reduction techniques applied and the inherent characteristics of the fluid dynamics systems they represent. In this paper, we introduce an innovative machine-learning framework for assessing model uncertainty in computationally intensive reduced-order models. By combining subspace construction methods with advanced Bayesian inference techniques, our approach effectively captures the posterior distribution of model parameters, thereby providing an accurate representation of uncertainty in aerodynamic performance predictions. We employ the NACA0012 airfoil as a case study to validate our method’s ability to enhance the efficiency of reduced-order models and precisely measure the uncertainty inherent in predictions made by recurrent neural networks. It is important to note that our approach is influenced by specific constraints and variables that significantly impact the mean and variability of the predicted final lift coefficient distribution. Our findings indicate that setting the goodness of fit (R2) threshold above 0.985 markedly improves the correlation between Computational Fluid Dynamics (CFD) outcomes and model predictions, increasing from 72.2% to 97.9% as the interval amplification factor adjusts from 1.5 to 3. However, this adjustment causes a considerable expansion of the confidence interval, from 0.0737 to 0.1282, an increase of over 70%. Despite these challenges, our machine learning-based methodology provides essential insights into the further development of reduced-order modeling and uncertainty quantification in fluid dynamics. This highlights the need for ongoing research into the model parameters, especially in applications concerning aircraft control systems, to meet design specifications and ensure system reliability.

Model reduction on manifolds: A differential geometric framework

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which emphasizes the geometric nature of the objects involved. The crucial ingredient is the construction of an embedding for the low-dimensional submanifold and a compatible reduction map, for which we discuss several options. Our general framework allows capturing and generalizing several existing MOR techniques, such as structure preservation for Lagrangian- or Hamiltonian dynamics, and using nonlinear projections that are, for instance, relevant in transport-dominated problems. The joint abstraction can be used to derive shared theoretical properties for different methods, such as an exact reproduction result. To connect our framework to existing work in the field, we demonstrate that various techniques for data-driven construction of nonlinear projections can be included in our framework.

Reduced order modeling of hybrid soft-rigid robots using global, local, and state-dependent strain parameterization

Reduced order modeling of hybrid soft-rigid robots using global, local, and state-dependent strain parameterization

Benchmarking the Performance of the Actuator-Disk Method for Low-Pressure Axial Flow Fan Simulation

Abstract The actuator-disk method is a cost-effective simulation tool that implicitly represents the rotor of a turbomachine using a blade-element approach combined with two-dimensional (2D) airfoil coefficient input data. Actuator-disk models further rely upon empirical coefficient corrections to modify the 2D input data to better mimic physical blade aerodynamic characteristics. However, the fabrication of high-fidelity, general-purpose corrections remains a formidable challenge, so the limits of actuator-disk model accuracy have never been rigorously tested and remain uncertain. This is especially the case for low-pressure axial flow fan models, given the relative lack of empirical corrections conceived specifically for fan rotor simulation. In this study, benchmark performance limits of the actuator-disk method for axial flow fan analysis are explored. The limits of the modeling approach are interrogated by simulating actuator-disk fan models embedded with accurate physical blade data derived from explicit three-dimensional (3D) fan model computations. It is subsequently shown that even with a near-precise coefficient description, the method remains unreliable. However, using an unconventional actuator-disk model formulation that is based directly on 3D blade force inputs, it is demonstrated that the accuracy of conventional models can be noticeably enhanced if the input coefficient data is artificially manipulated. This nonphysical tuning of the input coefficient data is required to compensate for the simplified flow fields produced by the reduced-order modeling approach. The needed coefficient adjustments, referred to as modeling corrections, are subsequently defined and explained alongside the presentation of new realistic performance targets for future actuator-disk fan model variants.

Characterizing and improving the performance of molten-salt-steam heat exchangers in concentrating solar power plants

Shell-and-tube heat exchangers (HXs) for steam generation from molten salts in concentrating solar power (CSP) plants experience thermal fatigue due to significant temperature gradients and inherent transient operation. Molten salt-steam HX design lifespans exceed actual lifespans, and, as a consequence, designers overpredict plant profitability and operators neglect appropriate prescriptions to optimize these lifetimes. This study refines HX lifespan estimates with data benchmarked against thermal-fluid mechanical modeling of stress and accumulated fatigue. Reduced-order thermal models of the molten salt-steam, shell-and-tube evaporator and superheater predict transient temperature profiles along the two HXs salt-steam flow paths. The modeled evaporator and superheater temperature profiles enable assessment of cyclic stresses within the HX tubesheets, where molten-salt HX failures are most common. Evaporator and superheater performance data from a current 110 MWelec commercial CSP plant provide a basis for validating the reduced-order HX models. HX life predictions derived from stochastic failure distributions serve as inputs for simulating and optimizing existing plant operations. The impact of the updated lifespans on overall plant revenue depends on operating scenarios. This study suggests that typical ramping rates for a CSP plant with a high-temperature Rankine cycle result in an evaporator and superheater life of approximately 10 and 25 years, respectively, compared to the design target of 30 years. Reduced HX lifespans decrease operational plant revenue on average by 4.6-5.1%. Furthermore, there may be as many as four HX replacements over the 30-year lifetime of the plant; and, purchase agreement loss due to failure to meet contractual production requirements can have ramifications that include the risk of bankruptcy.

Reduced-Order Modeling of Indirect Fluidized-Bed Particle Receivers with Axial Dispersion

Oxide particles present a heat transfer and thermal energy storage (TES) media for next-generation concentrating solar power (CSP) plants where the high-temperature particle TES can provide dispatchable solar power [1]. Transferring heat to flowing particles can be a challenge and bubbling fluidization is a promising method for increased heat transfer between the oxide particles and confining walls. Using experimentally calibrated correlations for particle-wall heat transfer coefficients [2], this study explores in a quasi-1D model of a narrow-channel counterflow fluidized bed how the high heat transfer coefficients from bubbling fluidization enable cavity-based indirect particle receivers. Particle-wall heat transfer coefficients exceeding 800 W m-2 K-1 support angled solar fluxes > 200 kW m-2 from high normal fluxes > 1200 kW m-2 with wall temperatures < 900 oC. Parametric studies identify how gas flows, solar fluxes, and receiver heights impact receiver solar efficiency for a CSP plant. These modeling studies provide a basis for the development of an indirect narrow-channel fluidized particle receiver that has the potential to operate at normal solar fluxes over 1000 kW m-2 and solar efficiencies above 85%.

Multifidelity Methodology for Reduced-Order Models with High-Dimensional Inputs

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction—employing proper orthogonal decomposition and model-based active subspace—with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component–active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design.

Application and comparison of several adaptive sampling algorithms in reduced order modeling

Model Order Reduction (MOR) techniques have extensive applications across scientific and engineering disciplines, such as neutron field reconstruction of nuclear reactor cores, thermoelastic field reconstruction, fluid, and solid mechanics. In the process of building a Reduced Order Model (ROM), the selection of the basis functions in the offline stage is crucial and directly depends on the parameter space sampling strategy. This problem has always been a challenge in MOR. Research into adaptive sampling algorithms has become a hot topic in recent years. To better understand the application of these algorithms to MOR, this paper focuses on three prevalent adaptive sampling algorithms: pseudo-gradient sampling, adaptive sparse grid sampling, adaptive training set extension. These have been successfully applied in various applications, including nuclear reactor cores, molten salt reactor system, power system for convection problems. We systematically assess and compare their performance, finding that adaptive sampling algorithms excel in sampling divergent and oscillating areas and are generally better than the standard sampling strategy. Specifically, the pseudo-gradient sampling algorithm is effective for small-scale scenarios, while the other two algorithms are designed for large-scale sampling. Their practicality is confirmed through successful applications in nuclear reactor cores.

Krylov subspace model order reduction of linear dynamical systems with quadratic output

This paper presents Krylov subspace model order reduction of linear dynamical systems with quadratic output. To reach this goal, the quadratic transfer function with two variables is taken into consideration. The Krylov subspaces are established at the finite and the infinite frequency points where both the one-sided and the two-sided projection cases are discussed. The moment matching is accordingly studied and the quadratic transfer function of the reduced system resulting from the two-sided projection case can match more moments. Finally, numerical results illustrate the performance of the proposed Krylov model order reduction methodology.