Abstract
Machine learning algorithms provide the fluid dynamics field with powerful tools to efficiently and accurately classifying vortex shedding wake modes. This research presents an effective strategy that applies machine learning methods to classify vortex shedding modes produced by an oscillating cylinder. A 2-dimensional computational fluid dynamic (CFD) simulation using OpenFOAMv2006 was developed to simulate a bladeless wind turbines vortex shedding behaviour. The simulations were conducted at two wakes modes (2S, 2P) and a transition mode (2PO). The local flow measurements were recorded using four sensors: vorticity, flow speed, stream-wise and transverse stream-wise velocity components. The time-series data was transformed into the frequency domain to generate a reduced feature vector. A variety of supervised machine learning models were quantitatively compared based on classification accuracy. The best performing models were then evaluated based on the effects of data corruption on the models' performance. The velocity sensors orientated transverse to the pre-dominant flow ($u_y$) achieved a minimum increase in testing accuracy of 15\% compared to the next best sensor. The random forest and $k$-nearest neighbour models, using $u_y$, achieved 99.3\% and 99.8\% classification accuracy, respectively. The feature noise analysis conducted showed a maximum reduction of accuracy of 11.7\% and 21.2\% at the highest noise level for the respective models. The random forest algorithm and the transverse stream-wise component of the velocity feature vector provided the best balance of testing accuracy and robustness to data corruption. The results highlight the proposed methods' ability to accurately identify vortex structures in the wake of an oscillating cylinder using feature extraction. The method was proposed as a valuable tool for controlling a bladeless wind turbine, but its' applications can be extended more generally for any case of vortex shedding mode classification.
Methods
The 2-dimensional domain and boundary conditions used for the numerical study are shown below.
From the simulations, the data from four types of sensors was recorded: namely, flow speed, $|u|$, the $x$-component of velocity, $u_x$, the $y$-component of velocity, $u_y$, and the vorticity, $\omega$.
An example of the $x$ velocity component data signal taken along the sampling line is shown below with the corresponding CFD vorticity color map.
Machine learning algorithms are founded on using optimization techniques to build a representative model to fit a set of data and, in this case, make label classifications. Supervised machine learning algorithms supplies the machine learning algorithms with labelled data from a supervisor/expert. The learning parameters (hyper-parameters) of each machine learning model were tuned to determine the best model concerning the bias/variance trade-off. Cross-validation was conducted for the hyperparameter tuning stage and repeated on the training set to give insight into the model's generalizability and the predictive performance on the application to new datasets. The cross-validation method implemented in this study was 5-fold cross-validation. Six supervised machine learning models were investigated for classification: logistic regression, support vector machines, decision tree, random forest, multilayer perceptron (MLP), and $k$-nearest neighbours ($k$-NN).
Results
The frequency-domain feature space for each of the local measurement sensors is shown below.
Machine Learning Model Performance
Several machine learning models were evaluated using the classification accuracy during the cross-validation and testing phases. The cross-validation scores give insight into the models' behaviour with new datasets and reveal the bias/variance behaviours of each. The mean and standard deviation of the cross-validation scores were plotted for each machine learning model trained using the four local measurements, as shown below.
- 𝑦 -component of the velocity ( $u_y$) achieved the most improved testing accuracy (>15%).
- Random forest and 𝑘 -nearest neighbour models reported the highest testing accuracy of 99.3% and 99.8%, respectively
Feature Noise Analysis
Machine learning algorithms are built to model the input data used to develop the classifier. The resolution of experimental fluid sensor data will never match that of numerical studies, and increased noise will impact the classification performance for real-world applications. The feature noise analysis evaluates the impact of increasing feature corruption on the selected machine learning models' accuracy.
The selected models' robustness to data corruption for flow classification is shown below.
- Random forest was the most robust to data corruption accuracy reduction (11.7%) for the 20% CvD case.
- $𝑘$−NN algorithm reported the most significant reduction in accuracy (21.2%) for the CvD case at 20% noise
Conclusion
The combination of CFD simulation data and machine learning algorithms resulted in an effective method of identifying the vortex structures in the wake of a bladeless wind turbine requiring less computational resource and input data. The proposed strategy provides a useful tool that can be implemented in experimental setups to aid in a bladeless wind turbine's control and performance. The methods were illustrated with the example of a bladeless wind turbine, but we believe that the methods apply more generally to any case of classification of vortex shedding. The results of this study could be expanded for more complex vortex shedding modes or conducted at a higher Reynolds number where the flow transitions into even more complex flow regimes. Future work could extend the noise analysis to higher levels of corruption or explore other sensor noise representations.