Reduced Order Model Predictions Research Articles

Nonlinear Reduced Order Modeling of Heated Structures with Temperature-Dependent Properties

This paper focuses on extending coupled structural–thermal reduced order modeling approaches for the prediction of the nonlinear geometric response of heated structures to efficiently account for temperature-dependent structural and thermal properties. Structurally, a linear dependence of the elasticity tensor and thermal expansion coefficient is assumed consistently with typical material behavior. The resulting structural reduced order model (ROM) equations exhibit polynomials of the temperature generalized coordinates, the coefficients of which are readily identified. A different strategy is proposed for conductance and capacitance properties which typically depend nonlinearly on temperature. It relies on splitting the temperature generalized coordinates into a small set of dominant ones having a nonlinear effect on the ROM conductances and capacitances and a much larger set affecting them linearly. The inclusion of uncertainty in the structural ROM is also addressed extending earlier work limited to temperature independent properties. These strategies are exemplified on a representative hypersonic vehicle panel undergoing a full mission profile and with aero-thermal–structural coupling. The ROM predictions are observed to be very close to the full finite element ones for the mean model. Moreover, an uncertainty analysis demonstrates the strong sensitivity of the response to the structural model in the strongly nonlinear regions of the trajectory.

Automated optimal experimental design strategy for reduced order modeling of aerodynamic flow fields

Aerodynamic flow fields reveal essential physical insights (such as shocks) that substantially affect aerodynamic performance. However, conventional flow field computations require time-consuming simulations. Alternatively, reduced-order models (ROMs) allow fast flow field predictions, enabling real-time decision-making. Efficient sampling is required to train ROMs without incuring prohibitive costs. In this paper, we propose a fully automated optimal experimental design (Auto-OED) strategy on proper orthogonal decomposition (POD) for ROM-based rapid flow field predictions. Auto-OED uses two individual optimal experimental design (OED) strategies, automatically selects the number of POD bases for the first sampling strategy, and intelligently switches to the second strategy on the fly. We showcased the Auto-OED strategy on airfoil flow field predictions in the transonic regime. OED-based ROMs were constructed over 20 trials for robustness tests with a total of 40 training samples in each trial, including 16 random initial samples by Latin hypercube sampling (LHS) and 24 OED samples. The results demonstrated that the ROM predictions completely based on LHS had an error of 1.6×10−3 while the existing OED strategies-based ROMs over 20 trials achieved a mean error (μerr) of 7.5×10−4 with a standard deviation (σerr) of 9.0×10−5. In contrast, the best Auto-OED ROM achieved the lowest μerr of 7.5×10−4 and lowest σerr of 6.2×10−5. These error reductions confirm the viability of the proposed Auto-OED-based ROM in fluid field predictions and potentially other engineering applications of a similar type.

Hybrid AI-Analytical Modeling of Droplet Dynamics on Inclined Heterogeneous Surfaces

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

The influence of fluid–structure interaction on cloud cavitation about a rigid and a flexible hydrofoil. Part 3

Experimental studies of the influence of fluid–structure interaction on cloud cavitation about a stiff stainless steel (SS) and a flexible composite (CF) hydrofoil have been presented in Parts I (Smithet al.,J. Fluid Mech., vol. 896, 2020a, p. A1) and II (Smithet al.,J. Fluid Mech., vol. 897, 2020b, p. A28). This work further analyses the data and complements the measurements with reduced-order model predictions to explain the complex response. A two degrees-of-freedom steady-state model is used to explain why the tip bending and twisting deformations are much higher for the CF hydrofoil, while the hydrodynamic load coefficients are very similar. A one degree-of-freedom dynamic model, which considers the spanwise bending deflection only, is used to capture the dynamic response of both hydrofoils. Peaks in the frequency response spectrum are observed at the re-entrant jet-driven and shock-wave-driven cavity shedding frequencies, system bending frequency and heterodyne frequencies caused by the mixing of the two cavity shedding frequencies. The predictions capture the increase of the mean system bending frequency and wider bandwidth of frequency modulation with decreasing cavitation number. The results show that, in general, the amplitude of the deformation fluctuation is higher, but the amplitude of the load fluctuation is lower for the CF hydrofoil compared with the SS hydrofoil. Significant dynamic load amplification is observed at subharmonic lock-in when the shock-wave-driven cavity shedding frequency matches with the nearest subharmonic of the system bending frequency of the CF hydrofoil. Both measurements and predictions show an absence of dynamic load amplification at primary lock-in because of the low intensity of cavity load fluctuations with high cavitation number.

On Sampling Rate Limits in Bistable Microbeam Sensors

Bifurcation-based sensors, implementing stability boundaries monitoring in bistable microstructures, may manifest higher sensitivity and robustness when compared to their statically operated counterparts. In the operation of these devices, two key questions arise: 1) how to reliably identify the critical events associated with the transition between two stable states; 2) what is the maximal sampling rate allowing to identify these critical events in a periodically actuated device. Motivated by the potential implementation as a bifurcation-based flow sensor, in this work we experimentally explore the transient snap-through (ST) and snap-back (SB) dynamics of a bistable initially curved ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$500 \,\mu \text{m}$ </tex-math></inline-formula> long and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.5\, \mu \text{m}$ </tex-math></inline-formula> wide) electrostatically actuated single-crystal Si microbeam. We employ a threshold-based approach for the ST and SB events detection and identify two mechanisms determining the maximal sampling frequency of the device: a phase lag between the voltage signal and the mechanical response and free decaying vibrations following the buckling event. In accordance with our experimental results and consistently with the reduced-order model predictions for the bistable beam operating at atmospheric pressure, at the actuation signal frequency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 0.6$ </tex-math></inline-formula> KHz, which is still much lower than the beam’s natural frequency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 110 $ </tex-math></inline-formula> KHz, the free oscillations engendered by one critical event (ST or SB) interfere with the consecutive one, preceding its emergence. On the other hand, an inherent phase lag ultimately hinders the abrupt ST and SB transitions at these actuating frequencies. [2021-0091]

Single Electrode Bidirectional Switching of Latchable Prestressed Bistable Micromechanical Beams

Electrostatically actuated, bistable, curved micromechanical beams can exhibit latching, wherein the beams remain in two distinct stable states without an applied voltage. These structures could serve as building blocks in a variety of applications such as micromechanical logic elements, switches, non-volatile memories, and low power consumption sensors. However, the design of such devices is challenging since such structures are prone to symmetry breaking, which consequently inhibits latching. Generally, asymmetric responses may be circumvented by introducing a tailored axial compressive prestress. In this work we explore, both theoretically and experimentally, the influence of prestress on the single electrode, bidirectional dynamic switching of curved, latchable, single crystal Si <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 1000 \;\mu \text{m}$ </tex-math></inline-formula> long and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 3.5\;\mu \text{m}$ </tex-math></inline-formula> wide beams. We use Joule heating to apply the necessary prestress required to eliminate symmetry breaking and ensure latching. In accordance with reduced-order model predictions, our experimental findings show that prestress plays a key role in the dynamic response of the beam. Our results demonstrate bidirectional operation using a single electrode, fostering a compact footprint device for tailoring the axial stress and dynamic conditions.

A simplified model for drag evaluation of a streamlined body with leading-edge damage

A reduced-order model (ROM) is proposed for efficient drag prediction on a streamlined body with surface imperfections that emulate leading-edge roughness or erosion-induced damage. Surface imperfections are idealised as forward-facing step(s) for which the chordwise position, spanwise length, and distribution of steps are varied. It is hypothesised that superposed a bilinear dependencies on the chordwise location and spanwise length of individual steps comprising the damage provide for reasonable ROM predictions of the corresponding change in total drag on the streamlined body. Direct numerical simulations are applied to test the ROM hypotheses and to study interactions between the three-dimensional steps and the separated near-wall turbulent flow fields, justifying the underlying terms and form of the ROM. Insights into the flow physics influencing both form and friction contributions to total drag are revealed, and satisfactory model performance is demonstrated for complex damage idealisations that emulate fracture of laminated wind turbine blades.

Reduced Order Modeling for fire sprinkler sprays

A Reduced Order Model (ROM) providing a highly detailed description of the sprinkler spray has been developed for engineering applications. The new ROM approach combines an elegantly parameterized analytical description of the dispersed spray with a tightly integrated high-fidelity description of the initial spray capable of producing a complete quantitative map of the entire sprinkler spray field from centerline to edge and ceiling to floor. The complex spray field is mapped using a sparsely sampled phase-space accounting for all drops produced by the sprinkler. The spray is mapped through fast two-dimensional trajectory calculations spanning this discretized phase-space to produce quantitative views of the spray in regions of interest or in its entirety. Spray patterns are easily extracted from this spray field according to attributes of interest. The ROM is demonstrated by comparing predicted and measured spray patterns generated below a commercial sprinkler. These spray patterns are quantified through spatial distributions of volume flux showing good agreement between measurements and ROM predictions (average error of 0.44 mm/min or 5% of peak volume flux). The speed and robustness of the ROM provide an unprecedented quantitative view of fire sprinkler spraying performance with sufficient accuracy for potential use in engineering design applications.

Generation of a reduced-order model of an Unmanned Combat Air Vehicle using indicial response functions

Within the NATO STO AVT-251 Task Group, a generic Unmanned Combat Air Vehicle (UCAV) planform was redesigned based on requirements derived from parts of the flight envelope of the defined mission. Because of the lambda-shape planform and associated flow phenomena including shocks and vortices, the aerodynamic design process relies heavily on high-fidelity predictions from computational fluid dynamics (CFD). These simulations enable accurate flight dynamics predictions, allowing for the identification of any potential performance issues early in the design process. Potentially, a complete flight dynamics model can be derived from CFD calculations provided that the underlying reduced order model (ROM) captures the underlying physics contained within the CFD results. This work investigates the creation of a nonlinear ROM using indicial response functions. The response functions are obtained using a grid motion approach that separates the effects of angle of attack and pitch rate. This approach is demonstrated using three different CFD codes from various organizations: ENSOLV at Royal Netherlands Aerospace Centre, USM3D at NASA Langley Research Center, and Kestrel at the United States Air Force Academy. ROM predictions were generated for a manoeuver resembling a low-speed pull-up. The predictions are found to be sensitive to the quality of the steady-state solutions from which step-response calculations were started, as well as the convergence of the step responses themselves. Nevertheless, the indicial response method is shown to provide aerodynamic predictions with acceptable accuracy including transient effects, and as such is a promising method for computationally efficient flight dynamics predictions.

Uncertainty Quantification and Sensitivity Analysis for Computational FFR Estimation in Stable Coronary Artery Disease

The main objectives of this study are to validate a reduced-order model for the estimation of the fractional flow reserve (FFR) index based on blood flow simulations that incorporate clinical imaging and patient-specific characteristics, and to assess the uncertainty of FFR predictions with respect to input data on a per patient basis. We consider 13 patients with symptoms of stable coronary artery disease for which 24 invasive FFR measurements are available. We perform an extensive sensitivity analysis on the parameters related to the construction of a reduced-order (hybrid 1D-0D) model for FFR predictions. Next we define an optimal setting by comparing reduced-order model predictions with solutions based on the 3D incompressible Navier-Stokes equations. Finally, we characterize prediction uncertainty with respect to input data and identify the most influential inputs by means of sensitivity analysis. Agreement between FFR computed by the reduced-order model and by the full 3D model was satisfactory, with a bias ([Formula: see text]) of [Formula: see text] at the 24 measured locations. Moreover, the uncertainty related to the factor by which peripheral resistance is reduced from baseline to hyperemic conditions proved to be the most influential parameter for FFR predictions, whereas uncertainty in stenosis geometry had greater effect in cases with low FFR. Model errors related to solving a simplified reduced-order model rather than a full 3D problem were small compared with uncertainty related to input data. Improved measurement of coronary blood flow has the potential to reduce uncertainty in computational FFR predictions significantly.

Reduced-order modeling for energy performance contracting

Buildings subject to Energy Performance Contracts (EPCs) are usually quite complex public buildings, sometimes relatively old and usually barely documented from the technical standpoint. Gathering comprehensive and reliable technical information is a time consuming and expensive process that has to be carried out within the submission deadline. In these conditions, the standard approach to energy performance forecasting which uses detailed simulation is practically unfeasible.This paper proposes a reduced-order modeling approach that is tailored to the EPC tendering phase. The proposed methodology extends a third order building model, introducing explicit, albeit still abstract, representations of the heating/cooling system, of the weather influence and of the end-user gains. The extended parameter set reflects to a large degree the information that is readily available in practical on-site surveying, or that can be easily calculated from that information. As a consequence of the simplified physics, a knowledge driven, practical calibration procedure, which provides an effective way of reducing uncertainty, is proposed. The calibration procedure analyses the uncertainty present in the available knowledge and uses the constraints imposed by the implemented physics on the parameters’ dynamic to assess their value estimation.The modeling approach is exemplified through three case studies: the first one provides the comparison of the reduced-order model predictions with the outcomes of a detailed model of a small hospital, the second one is used to compare the reduced-order model predictions with the detailed measurements of energy consumption of a real building, and the third case study exemplifies the use in operational context with scarce information.

Nonlinear analysis of an acoustically excited laminar premixed flame

The nonlinear effects of the fully coupled two-way interactions between a disturbance field defined by an amplitude variation of the inflow velocity distribution and a laminar premixed flame incorporating gas expansion effects are investigated by numerically solving the conservation equations of a compressible fluid. Results of the higher harmonics of the flame front perturbation for two burnt to unburnt temperature ratios show how the nonlinear transfer of flame response is affected by the hydrodynamic instability and the shear layer effect. The flame response at the fundamental forcing frequency, i.e., the flame-describing function can be well predicted by the reduced-order model (ROM) for both investigated temperature ratios at low Markstein length values, where the balance between the flame stretch effects and the hydrodynamic instability is insignificant. However, at high Markstein lengths the balance between the flame stretch and the hydrodynamic instability influences the flame response characteristics at all excitation amplitudes. The nonlinear study of the flame front perturbation indicates that differences in the higher harmonic content of the overall nonlinear flame response between the detailed computation and the ROM predictions are located at the flame front just before the flame pockets separate. Thus, the shear layer and the hydrodynamic instability effect determine the nonlinear character of the flame response through the nonlinearity introduced at the flame base, the location of flame pocket separation, and the annihilation process at the flame tip especially at high Markstein length values. In addition, the flame base movement response is compared to a recent developed reduced-order flame base model to understand the findings with respect to the assumption of flame attachment at the burner lips.

Unsteady aerodynamic prediction for dynamic stall of wind turbine airfoils with the reduced order modeling

A surrogate based reduced order method is developed for the prediction of the unsteady dynamic loading of wind turbine airfoils under dynamic stall situation. S809 airfoil undergoing sinusoidal pitch oscillation at different reduced frequencies, mean angles of attack and pitch oscillation amplitudes at Re = 106 are simulated by the CFD method. Then, the Kriging function is selected to establish the unsteady and nonlinear aerodynamic model with training cases generated by the CFD method. The results reveal an encouraging agreement between the CFD simulations and the reduced order model predictions. Furthermore, Ohio State University measurement data and Leishman–Beddoes model predictions for test cases are also included. Because CFD has good accuracy simulation for flow field around the airfoil under dynamic stall condition, the reduced order model can more effectively predict the airfoil nonlinear hysteretic behavior than L–B model. In addition, the reduced order method has relatively less computational cost compared with the CFD method. Therefore, it would be useful in engineering conditioning for aero-elastic analysis and design optimization of wind turbines.

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

The Roles of Statics and Dynamics in Determining Transitions Between Atomic Friction Regimes

We introduce a model AFM tip/substrate system that includes full atomistic detail as well as system compliance to study the transitions between three regimes of atomic friction: smooth sliding, stick-single slip, and stick-multiple slip. We characterize these atomic friction regimes in terms of static and dynamic effects, and investigate how the slip modes affect the mean friction. Molecular statics calculations show that reduced-order model predictions of possible transitions between slip regimes are generally adequate for a fully atomistic system, even for complex reaction coordinates. However, molecular dynamics simulations demonstrate that, while static features of the system govern possible slip regimes, dynamic effects ultimately determine actual transitions between slip regimes.

A robust adaptive model reduction method for damage simulations

In our opinion, many of complex numerical models in materials science can be reduced without losing their physical sense. Due to solution bifurcation and strain localization of continuum damage problems, damage predictions are very sensitive to any model modification. Most of the robust numerical algorithms intend to forecast one approximate solution of the continuous model despite there are multiple solutions. Some model perturbations can possibly be added to the finite element model to guide the simulation toward one of the solutions. Doing a model reduction of a finite element damage model is a kind of model perturbation. If no quality control is performed the prediction of the reduced-order model (ROM) can really differ from the prediction of the full finite element model. This can happen using the snapshot Proper Orthogonal Decomposition (POD) model reduction method. Therefore, if the expected purpose of the reduced approximation is to estimate the solution that the finite element simulation should give, an adaptive reduced-order modeling is required when reducing finite element damage models.We propose an adaptive reduced-order modeling method that enables to estimate the effect of loading modifications. The Rousselier continuum damage model is considered. The differences between the finite element prediction and the one provided by the adapted reduced-order model (ROM) remain stable although various loading perturbations are introduced. The adaptive algorithm is based on the APHR (A Priori Hyper Reduction) method. This is an incremental scheme using a ROM to forecast an initial guess solution to the finite element equations. If, at the end of a time increment, this initial prediction is not accurate enough, a finite element correction is added to the ROM prediction. The proposed algorithm can be viewed as a two step Newton–Raphson algorithm. During the first step the prediction belongs to the functional space related to the ROM and during the second step the correction belongs to the classical FE functional space. Moreover the corrections of the ROM predictions enable to expand the basis related to the ROM. Therefore the ROM basis can be improved at each increment of the simulation. The efficiency of the adaptive algorithm is checked comparing the amount of global linear solutions involved in the proposed scheme versus the amount of global linear solutions involved in the classical incremental Newton–Raphson scheme. The quality of the proposed approximation is compared to the one provided by the classical snapshot Proper Orthogonal Decomposition (POD) method.