Data Assimilation and Optimal Calibration in Nonlinear Models of Flame Dynamics

Abstract We propose an on-the-fly statistical learning method to take a qualitative reduced-order model of the dynamics of a premixed flame and make it quantitatively accurate. This physics-informed data-driven method is based on the statistically optimal combination of (i) a reduced-order model of the dynamics of a premixed flame with a level-set method, (ii) high-quality data, which can be provided by experiments and/or high-fidelity simulations, and (iii) assimilation of the data into the reduced-order model to improve the prediction of the dynamics of the premixed flame. The reduced-order model learns the state and the parameters of the premixed flame on the fly with the ensemble Kalman filter, which is a Bayesian filter used, for example, in weather forecasting. The proposed method and algorithm are applied to two test cases with relevance to reacting flows and instabilities. First, the capabilities of the framework are demonstrated in a twin experiment, where the assimilated data are produced from the same model as that used in prediction. Second, the assimilated data are extracted from a high-fidelity reacting-flow direct numerical simulation (DNS), which provides the reference solution. The results are analyzed by using Bayesian statistics, which robustly provide the level of confidence in the calculations from the reduced-order model. The versatile method we propose enables the optimal calibration of computationally inexpensive reduced-order models in real-time when experimental data become available, for example, from gas-turbine sensors.

Download Full-text

Data Assimilation and Optimal Calibration in Nonlinear Models of Flame Dynamics

Volume 4B: Combustion, Fuels, and Emissions ◽

10.1115/gt2019-92052 ◽

2019 ◽

Author(s):

Hans Yu ◽

Thomas Jaravel ◽

Matthias Ihme ◽

Matthew P. Juniper ◽

Luca Magri

Keyword(s):

Weather Forecasting ◽

Nonlinear Models ◽

Reduced Order Model ◽

Premixed Flame ◽

Quality Data ◽

Reacting Flow ◽

High Fidelity ◽

Order Model ◽

Reduced Order ◽

Optimal Calibration

Abstract We propose an on-the-fly statistical learning method to take a qualitative reduced-order model of the dynamics of a premixed flame and make it quantitatively accurate. This physics-informed data-driven method is based on the statistically optimal combination of (i) a reduced-order model of the dynamics of a pre-mixed flame with a level-set method, (ii) high-quality data, which can be provided by experiments and/or high-fidelity simulations, and (iii) assimilation of the data into the reduced-order model to improve the prediction of the dynamics of the premixed flame. The reduced-order model learns the state and the parameters of the premixed flame on the fly with the ensemble Kalman filter, which is a Bayesian filter used, for example, in weather forecasting. The proposed method and algorithm are applied to two test cases with relevance to reacting flows and instabilities. First, the capabilities of the framework are demonstrated in a twin experiment, where the assimilated data is produced from the same model as that used in prediction. Second, the assimilated data is extracted from a high-fidelity reacting-flow direct numerical simulation (DNS), which provides the reference solution. The results are analyzed by using Bayesian statistics, which robustly provide the level of confidence in the calculations from the reduced-order model. The versatile method we propose enables the optimal calibration of computationally inexpensive reduced-order models in real time when experimental data becomes available, for example, from gas-turbine sensors.

Download Full-text

A high fidelity cost efficient tensorial method based on combined POD-HOSVD reduced order model of flow field

European Journal of Computational Mechanics ◽

10.1080/17797179.2018.1550963 ◽

2018 ◽

Vol 27 (4) ◽

pp. 342-366

Author(s):

Mohammad Kazem Moayyedi ◽

Milad Najaf beygi

Keyword(s):

Flow Field ◽

Reduced Order Model ◽

High Fidelity ◽

Order Model ◽

Reduced Order ◽

Cost Efficient

Download Full-text

Sparse nonlinear models of chaotic electroconvection

Royal Society Open Science ◽

10.1098/rsos.202367 ◽

2021 ◽

Vol 8 (8) ◽

pp. 202367

Author(s):

Yifei Guan ◽

Steven L. Brunton ◽

Igor Novosselov

Keyword(s):

Charge Density ◽

Coherent Structures ◽

Large Scale ◽

Fluid Transport ◽

Nonlinear Models ◽

Original System ◽

Reduced Order Model ◽

Dimensional System ◽

Order Model ◽

Reduced Order

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

Download Full-text

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Mathematical and Computational Applications ◽

10.3390/mca24020041 ◽

2019 ◽

Vol 24 (2) ◽

pp. 41

Author(s):

Fabien Casenave ◽

Nissrine Akkari

Keyword(s):

High Pressure ◽

Reference Model ◽

Turbine Blades ◽

Reduced Order Model ◽

High Fidelity ◽

Order Model ◽

High Pressure Turbine ◽

Time Step ◽

Reduced Order ◽

Error Indicator

The industrial application motivating this work is the fatigue computation of aircraft engines’ high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes the classical unenriched proper orthogonal decomposition method fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the error indicator becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving five million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

Download Full-text

Active Aeroelastic Control using Multiple Control Surfaces Based on a High-Fidelity Reduced Order Model

TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES ◽

10.2322/tjsass.56.261 ◽

2013 ◽

Vol 56 (5) ◽

pp. 261-268

Author(s):

Gang CHEN ◽

Xian WANG ◽

Yueming LI

Keyword(s):

Reduced Order Model ◽

High Fidelity ◽

Order Model ◽

Multiple Control ◽

Reduced Order ◽

Control Surfaces

Download Full-text

UTILIZING A REDUCED-ORDER MODEL AND PHYSICAL PROGRAMMING FOR PRELIMINARY REACTOR DESIGN OPTIMIZATION

EPJ Web of Conferences ◽

10.1051/epjconf/202124706049 ◽

2021 ◽

Vol 247 ◽

pp. 06049

Author(s):

Ryan Stewart ◽

Todd S. Palmer

Keyword(s):

Genetic Algorithm ◽

Pareto Front ◽

Design Space ◽

Reactor Core ◽

Reduced Order Model ◽

High Fidelity ◽

Order Model ◽

Reduced Order ◽

Physical Programming ◽

Objective Space

Reactor core design is inherently a multi-objective problem which spans a large design space, and potentially larger objective space. This process relies on high-fidelity models to probe the design space, and sophisticated computer codes to calculate the important physics occurring in the reactor. In the past, the design space has been reduced by individuals with extensive knowledge of reactor core design; however, this approach is not always available. In this paper, we utilize a set of high-fidelity models to generate a reduced-order model, and couple this with a genetic algorithm to quickly and effectively optimize a preliminary design for a prototypical sodium fast reactor. We also examine augmenting the genetic algorithm with physical programming to generate the fitness function(s) that evaluates the degree to which a core has been optimized. Physical programming is used in two variations of multi-objective optimization and is compared with a traditional weighting scheme to examine the solutions present on the Pareto front. Optimization on the reduced-order model produces a set of solutions on the Pareto front for a designer to examine. The uncertainty for the objective functions examined in the reduced-order model is less than 7% for the given designs, and improves as additional data points are employed. Utilizing a reduced-order model can significantly reduce the computation time and storage to perform preliminary optimization. Physical programming was shown to reduce the objective space when compared with a traditional weighting scheme. It also provides an intuitive and computationally efficient way to produce a Pareto front that meets the designer’s objectives.

Download Full-text

Nonuniform transformation field analysis based reduced-order model of high-fidelity generalized method of cells

Composite Structures ◽

10.1016/j.compstruct.2021.114365 ◽

2021 ◽

pp. 114365

Author(s):

Karthik Rajan Venkatesan ◽

Aditi Chattopadhyay

Keyword(s):

Reduced Order Model ◽

Field Analysis ◽

High Fidelity ◽

Order Model ◽

Reduced Order ◽

Generalized Method Of Cells ◽

Transformation Field Analysis

Download Full-text

Study on Reduced Order Model in Large-Span Roof Vibration under Wind Actions

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.580-583.3066 ◽

2014 ◽

Vol 580-583 ◽

pp. 3066-3070

Author(s):

Fang Jin Sun ◽

Da Ming Zhang

Keyword(s):

Finite Element ◽

Strain Energy ◽

Strain Energy Function ◽

Element Model ◽

Reduced Order Model ◽

High Fidelity ◽

Order Model ◽

Reduced Order ◽

Large Span ◽

Wind Actions

Reduced order model was for the first time employed for the large-span structure by system identification approach. The structure’s modal amplitudes are utilized to construct strain energy function of the system. A high fidelity finite element model is adopted to calculate modes and strain energy information to determine the unknown coefficients in the strain energy function. Wind-induced responses of a large-span structure were computed by the proposed method. The results were compared well with those obtained from the high fidelity finite element model and experiments. It proves that reduced order model is an effective way to compute large-span structure responses under wind actions when taking aero-elastic effects into account.

Download Full-text