Improved Junction Body Flow Modeling Through Data-Driven Symbolic Regression

2019 ◽  
Vol 63 (4) ◽  
pp. 283-293 ◽  
Author(s):  
Jack Weatheritt ◽  
Richard David Sandberg
Keyword(s):  
Reynolds Number ◽  
Symbolic Regression ◽  
Basis Functions ◽  
Training Data ◽  
Data Driven ◽  
High Fidelity ◽  
Turbulent Stress ◽  
Stress Strain ◽  
New Model ◽  
Varying Coefficients

A novel data-driven turbulence modeling framework is presented and applied to the problem of junction body flow. In particular, a symbolic regression approach is used to find nonlinear analytical expressions of the turbulent stress‐strain coupling that are ready for implementation in computational fluid dynamics (CFD) solvers using Reynolds-averaged Navier‐Stokes (RANS) closures. Results from baseline linear RANS closure calculations of a finite square-mounted cylinder with a Reynolds number of <inline-graphic xlink:href="josr09180053inf1.tif"/>, based on diameter and freestream velocity, are shown to considerably overpredict the separated flow region downstream of the square cylinder, mainly because of the failure of the model to accurately represent the complex vortex structure generated by the junction flow. In the present study, a symbolic regression tool built on a gene expression programming technique is used to find a nonlinear constitutive stress‐strain relationship. In short, the algorithm finds the most appropriate linear combination of basis functions and spatially varying coefficients that approximate the turbulent stress tensor from high-fidelity data. Here, the high-fidelity data, or the so-called training data, were obtained from a hybrid RANS/Large Eddy Simulation (LES) calculation also developed with symbolic regression that showed excellent agreement with direct numerical simulation data. The present study, therefore, also demonstrates that training data required for RANS closure development can be obtained using computationally more affordable approaches, such as hybrid RANS/LES. A procedure is presented to evaluate which of the individual basis functions that are available for model development are most likely to produce a successful nonlinear closure. A new model is built using those basis functions only. This new model is then tested, i.e., an actual CFD calculation is performed, on the well-known periodic hills case and produces significantly better results than the linear baseline model, despite this test case being fundamentally different from the training case. Finally, the new model is shown to also improve predictive accuracy for a surface-mounted cube placed in a channel at a cube height Reynolds number of <inline-graphic xlink:href="josr09180053inf2.tif"/> over traditional linear RANS closures.

scholarly journals Parameter Estimation with Data-Driven Nonparametric Likelihood Functions

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 559 ◽  
Author(s):  
Shixiao W. Jiang ◽  
John Harlim
Keyword(s):  
Parameter Estimation ◽  
Likelihood Function ◽  
Spectral Expansion ◽  
Basis Functions ◽  
Training Data ◽  
Data Driven ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Likelihood Functions ◽  
Nonparametric Likelihood

In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood function using a spectral expansion formulation known as the kernel embedding of the conditional distribution. To respect the geometry of the data, we employ this spectral expansion using a set of data-driven basis functions obtained from the diffusion maps algorithm. The theoretical error estimate suggests that the error bound of the approximate data-driven likelihood function is independent of the variance of the basis functions, which allows us to determine the amount of training data for accurate likelihood function estimations. Supporting numerical results to demonstrate the robustness of the data-driven likelihood functions for parameter estimation are given on instructive examples involving stochastic and deterministic differential equations. When the dimension of the data manifold is strictly less than the dimension of the ambient space, we found that the proposed approach (which does not require the knowledge of the data manifold) is superior compared to likelihood functions constructed using standard parametric basis functions defined on the ambient coordinates. In an example where the data manifold is not smooth and unknown, the proposed method is more robust compared to an existing polynomial chaos surrogate model which assumes a parametric likelihood, the non-intrusive spectral projection. In fact, the estimation accuracy is comparable to direct MCMC estimates with only eight likelihood function evaluations that can be done offline as opposed to 4000 sequential function evaluations, whenever direct MCMC can be performed. A robust accurate estimation is also found using a likelihood function trained on statistical averages of the chaotic 40-dimensional Lorenz-96 model on a wide parameter domain.

scholarly journals A Data-Driven Surrogate Approach for the Temporal Stability Forecasting of Vegetation Covered Dikes

Water ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Elahe Jamalinia ◽  
Faraz S. Tehrani ◽  
Susan C. Steele-Dunne ◽  
Philip J. Vardon
Keyword(s):  
Numerical Simulation ◽  
Water Flux ◽  
Temporal Stability ◽  
Synthetic Data ◽  
Climatic Conditions ◽  
Training Data ◽  
Data Driven ◽  
Data Set ◽  
Surface Cracking ◽  
Real Time Analysis

Climatic conditions and vegetation cover influence water flux in a dike, and potentially the dike stability. A comprehensive numerical simulation is computationally too expensive to be used for the near real-time analysis of a dike network. Therefore, this study investigates a random forest (RF) regressor to build a data-driven surrogate for a numerical model to forecast the temporal macro-stability of dikes. To that end, daily inputs and outputs of a ten-year coupled numerical simulation of an idealised dike (2009–2019) are used to create a synthetic data set, comprising features that can be observed from a dike surface, with the calculated factor of safety (FoS) as the target variable. The data set before 2018 is split into training and testing sets to build and train the RF. The predicted FoS is strongly correlated with the numerical FoS for data that belong to the test set (before 2018). However, the trained model shows lower performance for data in the evaluation set (after 2018) if further surface cracking occurs. This proof-of-concept shows that a data-driven surrogate can be used to determine dike stability for conditions similar to the training data, which could be used to identify vulnerable locations in a dike network for further examination.

scholarly journals Data-driven deep density estimation

2021 ◽  
Author(s):  
Patrik Puchert ◽  
Pedro Hermosilla ◽  
Tobias Ritschel ◽  
Timo Ropinski
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Population Data ◽  
Training Data ◽  
Data Driven ◽  
Discrete Observations ◽  
Efficient Manner ◽  
Continuous Models ◽  
3D Scans ◽  
Spatial Locations

AbstractDensity estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in 2D sensor readings, or reconstructing scenes from 3D scans. In this paper, we introduce a learned, data-driven deep density estimation (DDE) to infer PDFs in an accurate and efficient manner, while being independent of domain dimensionality or sample size. Furthermore, we do not require access to the original PDF during estimation, neither in parametric form, nor as priors, or in the form of many samples. This is enabled by training an unstructured convolutional neural network on an infinite stream of synthetic PDFs, as unbound amounts of synthetic training data generalize better across a deck of natural PDFs than any natural finite training data will do. Thus, we hope that our publicly available DDE method will be beneficial in many areas of data analysis, where continuous models are to be estimated from discrete observations.

A Copula-Based Sampling Method for Data-Driven Prognostics and Health Management

2013 ◽  
Author(s):  
Zhimin Xi ◽  
Rong Jing ◽  
Pingfeng Wang ◽  
Chao Hu
Keyword(s):  
Sampling Method ◽  
Failure Time ◽  
Health Management ◽  
Remaining Useful Life ◽  
Training Data ◽  
Data Driven ◽  
Prognostics And Health Management ◽  
Statistical Relationship ◽  
Cooling Fans ◽  
On Line

This paper develops a Copula-based sampling method for data-driven prognostics and health management (PHM). The principal idea is to first build statistical relationship between failure time and the time realizations at specified degradation levels on the basis of off-line training data sets, then identify possible failure times for on-line testing units based on the constructed statistical model and available on-line testing data. Specifically, three technical components are proposed to implement the methodology. First of all, a generic health index system is proposed to represent the health degradation of engineering systems. Next, a Copula-based modeling is proposed to build statistical relationship between failure time and the time realizations at specified degradation levels. Finally, a sampling approach is proposed to estimate the failure time and remaining useful life (RUL) of on-line testing units. Two case studies, including a bearing system in electric cooling fans and a 2008 IEEE PHM challenge problem, are employed to demonstrate the effectiveness of the proposed methodology.

Imitation of Demonstrations Using Bayesian Filtering With Nonparametric Data-Driven Models

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Nurali Virani ◽  
Devesh K. Jha ◽  
Zhenyuan Yuan ◽  
Ishana Shekhawat ◽  
Asok Ray
Keyword(s):  
Particle Filtering ◽  
Dynamic Models ◽  
Training Data ◽  
Data Driven ◽  
Conditional Density ◽  
Bayesian Filtering ◽  
State Dependent ◽  
State Evolution ◽  
And Control ◽  
Nonparametric Kernel

This paper addresses the problem of learning dynamic models of hybrid systems from demonstrations and then the problem of imitation of those demonstrations by using Bayesian filtering. A linear programming-based approach is used to develop nonparametric kernel-based conditional density estimation technique to infer accurate and concise dynamic models of system evolution from data. The training data for these models have been acquired from demonstrations by teleoperation. The trained data-driven models for mode-dependent state evolution and state-dependent mode evolution are then used online for imitation of demonstrated tasks via particle filtering. The results of simulation and experimental validation with a hexapod robot are reported to establish generalization of the proposed learning and control algorithms.

High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence

2021 ◽  
Author(s):  
Yaomin Zhao ◽  
Richard D. Sandberg
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Suction Side ◽  
Rotor Blades ◽  
High Fidelity ◽  
Mean Flow ◽  
High Pressure Turbine ◽  
Flow Shear ◽  
Phase Lock ◽  
The Mean

Abstract We present the first wall-resolved high-fidelity simulations of high-pressure turbine (HPT) stages at engine-relevant conditions. A series of cases have been performed to investigate the effects of varying Reynolds numbers and inlet turbulence on the aerothermal behavior of the stage. While all of the cases have similar mean pressure distribution, the cases with higher Reynolds number show larger amplitude wall shear stress and enhanced heat fluxes around the vane and rotor blades. Moreover, higher-amplitude turbulence fluctuations at the inlet enhance heat transfer on the pressure-side and induce early transition on the suction-side of the vane, although the rotor blade boundary layers are not significantly affected. In addition to the time-averaged results, phase-lock averaged statistics are also collected to characterize the evolution of the stator wakes in the rotor passages. It is shown that the stretching and deformation of the stator wakes is dominated by the mean flow shear, and their interactions with the rotor blades can significantly intensify the heat transfer on the suction side. For the first time, the recently proposed entropy analysis has been applied to phase-lock averaged flow fields, which enables a quantitative characterization of the different mechanisms responsible for the unsteady losses of the stages. The results indicate that the losses related to the evolution of the stator wakes is mainly caused by the turbulence production, i.e. the direct interaction between the wake fluctuations and the mean flow shear through the rotor passages.

Data-driven method for training data selection for deep learning

2021 ◽  
Author(s):  
C. Lacombe ◽  
I. Hammoud ◽  
J. Messud ◽  
H. Peng ◽  
T. Lesieur ◽  
...  
Keyword(s):  
Deep Learning ◽  
Training Data ◽  
Data Selection ◽  
Data Driven ◽  
Selection For ◽  
Training Data Selection
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