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Predicting wind pressures around circular cylinders using machine learning techniques

Gang Hu, K. C. S. Kwok

arXiv:1901.06752v1cs.LGphysics.flu-dynstat.ML

TL;DR

Predicting wind pressures around circular cylinders matters for engineering safety, and accumulated measurements offer data for machine-learning models. The study compares three regression methods and finds GBRT predicts mean and fluctuating pressures accurately within the studied Reynolds-number and turbulence-intensity ranges.

  • Problem

    Predicting cylinder wind pressures is challenging but important for engineering safety, and accumulated pressure datasets offer a basis for machine-learning models.

    Source: §1 · pp. 1–2

  • Method

    The study trains models to predict mean and fluctuating pressures around smooth cylinders and compares decision trees, random forests, and GBRT.

    Source: §1 · p. 3, §4.1 · p. 15

  • Results

    GBRT performs best for both pressure types and predicts accurately for Re from 10^4 to 10^6 and Ti from 0% to 15%.

    Source: §6 · p. 19

  • Takeaways & Limitations

    Within the studied Re and Ti range, GBRT offers an efficient and economical alternative to wind-tunnel tests and computational fluid-dynamics simulations.

    Source: §6 · p. 19

    Insufficient data excludes surface roughness, and unavailable data prevent coverage of Re from 10^6 to 10^8.

    Source: §5 · p. 18

Abstract

from arXiv · show

Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to train models to predict wind pressures around circular cylinders. Wind pressures around smooth circular cylinders are a function of mainly the Reynolds number (Re), turbulence intensity (Ti) of the incident wind, and circumferential angle of the cylinder. Considering these three parameters as the inputs, this study trained two ML models to predict mean and fluctuating pressures respectively. Three machine learning algorithms including decision tree regressor, random forest, and gradient boosting regression trees (GBRT) were tested. The GBRT models exhibited the best performance for predicting both mean and fluctuating pressures, and they are capable of making accurate predictions for Re ranging from 10^4 to 10^6 and Ti ranging from 0% to 15%. It is believed that the GBRT models provide very efficient and economical alternative to traditional wind tunnel tests and computational fluid dynamic simulations for determining wind pressures around smooth circular cylinders within the studied Re and Ti range.

1. Introduction

Circular-cylinder flow is difficult to predict, yet its aerodynamic characteristics matter to the safety of engineering structures. This study uses accumulated wind-pressure data to develop machine-learning models for pressure prediction.

1. Introduction

  • Circular-cylinder flow separation varies with incident flow, turbulence, geometry, and surface roughness, complicating aerodynamic characterization important to engineering safety.Applications include heat exchangers, bridge cables, silos, chimneys, and cooling towers.Source: §1 · p. 1
  • Wind-tunnel tests and computational fluid dynamics remain time-consuming and expensive ways to determine pressure for a particular cylinder dimension and flow field.Source: §1 · p. 2
  • Accumulated circular-cylinder wind-pressure datasets provide a basis for training machine-learning models to predict pressures.Source: §1 · p. 2
  • The study develops regression models for mean and fluctuating pressures of smooth cylinders across Reynolds-number and turbulence-intensity combinations with sufficient training data.It also introduces prior-study data and compares model performance.Source: §1 · p. 3

2. Literature review and data collection

Cylinder surface pressures depend mainly on Reynolds number, incident turbulence intensity, and circumferential angle. The review covers how these factors shape flow and pressure, then describes the collected experimental data and its scope.

2. Literature review and data collection

  • Surface pressure around a smooth cylinder depends mainly on Reynolds number, turbulence intensity, and circumferential angle.Source: §2 · p. 3

2.1. Effects of Reynolds number

  • Reynolds number strongly affects cylinder flow patterns and force coefficients, with studies spanning low-to-high Reynolds-number regimes and laboratory and field measurements.The review cites pressure and force measurements in wind tunnels and on structures including towers, stacks, chimneys, and cooling towers.Source: §2.1 · pp. 3–4

2.2. Effects of turbulence intensity of incident wind

  • Turbulence intensity influences cylinder pressures, with reported effects depending on Reynolds-number regime and cylinder location.Studies report effects on windward pressure fluctuations, leeward fluctuations, separation position, and pressure or force coefficients.Source: §2.2 · pp. 4–5

2.3. Effects of circumferential angle of circular cylinder

  • Pressure varies around the circumference: mean pressure falls from the stagnation point to a minimum, rises near separation, then stays nearly constant in the wake.Fluctuating pressure also varies with circumferential angle.Source: §2.3 · p. 5

2.4. Data collection of surface pressures around circular cylinders

  • Published experimental studies supply the pressure data used to train models, with their test details summarized in Table 1.Source: §2.4 · p. 6, Table 1 · p. 6
  • The study uses half-cylinder pressure data over 0°–180° and holds randomly selected data aside for validation; collected data broadly cover Re 10^4–10^6 and Ti 0%–15%.The coverage applies to both mean and fluctuating pressure coefficients.Source: §2.4 · pp. 7–8, Figure 6 · p. 7

3. Machine learning algorithms and prediction model training

The study trains DTR, RF, and GBRT models and evaluates them with 10-fold cross-validation and a three-stage training-testing-validation process. It compares the algorithms and tunes their hyperparameters to predict mean and fluctuating pressure coefficients.

3. Machine learning algorithms and prediction model training

  • The study trains decision tree regressor (DTR), random forest (RF), and gradient boosting regression trees (GBRT) to predict mean and fluctuating pressures around smooth circular cylinders.The models are implemented using scikit-learn.Source: §3 · p. 8

3.1.1. k-fold cross-validation

  • 10-fold cross-validation trains and validates on different subsets across ten rounds, then averages the models’ accuracy estimates.The study adopts 10 folds as a compromise between the number of performance estimates, training-set size, and overlap between training sets.Source: §3.1.1 · p. 8

3.1.2. 3-stage evaluation process

  • The three-stage evaluation uses 90% of the data for training and 10% for testing, tunes algorithms and hyperparameters with cross-validation, then tests the selected model.The final model is built using all training data and assessed on the testing subset.Source: §3.1.2 · pp. 8–9

3.2.1. Decision tree regression

  • For mean-pressure DTR, the 10-fold MSE is minimized at maximum depth 20, maximum leaf nodes 1250, and minimum leaf samples 2.For fluctuating-pressure DTR, the respective selected values are 20, 1500, and 2.Source: §3.2.1 · pp. 9–10, Figure 8 · p. 10

3.2.2. Ensemble methods

  • Ensembles average predictions from multiple weak learners; unlike parallel bagging, sequential boosting fits learners in sequence.The study describes a single learner as sensitive to training data and not robust.Source: §3.2.2 · p. 11

(a) Bagging regression trees: Random Forest (RF)

  • RF reduces correlation among bagged trees through randomized feature selection, while GBRT fits each new tree to current residuals and combines trees using a learning rate.RF considers a predefined subset of features at each split; the study evaluates GBRT’s learning rate, tree depth, tree count, and subsampling fraction using 10-fold cross-validation.Source: (a) Bagging regression trees: Random… · p. 11, (b) Boosting: Gradient Boosting… · pp. 13–14
  • GBRT minimizes squared-error loss by fitting trees sequentially to residuals; its learning rate scales each tree, while tree depth controls fitted interactions.For mean pressure coefficients, the selected values were learning rate 0.01, depth 8, 5000 trees, and subsampling fraction 0.3; for fluctuating pressure coefficients, they were 0.01, 16, 3000, and 0.3.Source: (b) Boosting: Gradient Boosting… · pp. 13–14

4. Results and analyses

GBRT is the best-performing tested model for both mean and fluctuating pressure coefficients. Final GBRT models accurately predict pressures across the held-out Reynolds-number and turbulence-intensity combinations, with minor discrepancies in some cases.

4.1. Performance evaluations of ML models

  • GBRT had the best test performance for both mean and fluctuating pressure coefficients, outperforming RF and DTR in the reported comparisons.For mean pressure, the comparison uses R-squared scores and MSE; the fluctuating-pressure comparison also identifies GBRT as best.Source: §4.1 · p. 15, Figure 15 · p. 15, Figure 17 · p. 16

4.2. Final ML models for predicting mean and fluctuating pressure coefficients

  • The final GBRT models were trained on the full dataset after 12 Reynolds-number and turbulence-intensity sets were randomly set aside for validation.The held-out sets were excluded from the training and testing data at the outset.Source: §4.2 · pp. 16–17
  • Accurate mean- and fluctuating-pressure predictions were obtained across six held-out Reynolds-number and turbulence-intensity sets for each model, with minor discrepancies in some cases.The tested scope spans Re 10^4–10^6 and Ti 0%–15%.Source: §4.2 · p. 17, Figure 18 · p. 17, Figure 19 · p. 18

5. Discussions

The models predict pressures across the studied Reynolds-number and turbulence-intensity ranges, though some cases show minor discrepancies. Missing data constrain coverage of roughness effects and higher Reynolds numbers.

5. Discussions

  • The models predict wind pressures for Re from 10^4 to 10^6 and Ti from 0% to 15%, with minor discrepancies in some cases.The authors anticipate that adding data could diminish these discrepancies.Source: §5 · p. 18
  • Surface roughness is excluded from the models because data addressing its effects are insufficient.Source: §5 · p. 18
  • The models do not cover Re from 10^6 to 10^8 because relevant data are unavailable, but could be upgraded when such data become available.Source: §5 · p. 18

6. Concluding remarks

The study uses prior experimental pressure data to train and compare machine-learning models for smooth circular cylinders. GBRT performs best for both pressure types within the studied conditions, supporting ML’s potential in wind engineering and motivating work on high-Re flows and roughness effects.

6. Concluding remarks

  • The study trained decision tree regressor, random forest, and GBRT models using mean and fluctuating pressure data collected from prior experimental studies.Source: §6 · pp. 18–19
  • GBRT models performed best for predicting both mean and fluctuating pressure coefficients and accurately predicted them for smooth cylinders across Re from 10^4 to 10^6 and Ti from 0% to 15%.Source: §6 · p. 19
  • The study demonstrates ML’s potential in wind engineering and identifies high-Re flows and surface-roughness effects as issues for further work.Source: §6 · p. 19
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