Multi-objective Optimization of Draft Tube in Francis Turbine Using DOE, RBF and NSGA-II
- Chol Nam Mun, Myong Il Kim
Structures vibrate with their natural frequencies when disturbed from their equilibrium position. These frequencies reduce when an additional mass accumulates on their structures, like ice accumulation on wind turbines installed in cold climate sites. The added mass has two features: the location and quantity of mass. Natural frequencies of the structure reduce differently depending on these two features of the added mass. In this work, a technique based on an artificial neural network (ANN) model is proposed to identify added mass by training the neural network with a dataset of natural frequencies of the structure calculated using different quantities of the added mass at different locations on the structure. The proposed method is demonstrated on a non-rotating beam model fixed at one end. The length of the beam is divided into three zones in which different added masses are considered, and its natural frequencies are calculated using a finite element model of the beam. ANN is trained with this dataset of natural frequencies of the beam as an input and corresponding added masses used in the calculations as an output. ANN approximates the non-linear relationship between these inputs and outputs. An experimental setup of the cantilever beam is fabricated, and experimental modal analysis is carried out considering a few added masses on the beam. The frequencies estimated in the experiments are given as an input to the trained ANN model, and the identified masses are compared against the actual masses used in the experiments. These masses are identified with an error that varies with the location and the quantity of added mass. The reason for these errors can be attributed to the unaccounted stiffness variation in the beam model due to the added mass while generating the dataset for training the neural network. Therefore, the added masses are roughly estimated. At the end of the paper, an application of the current technique for detecting ice mass on a wind turbine blade is studied. A neural network model is designed and trained with a dataset of natural frequencies calculated using the finite element model of the blade considering different ice masses. The trained network model is tested to identify ice masses in four test cases that considers random mass distributions along the blade. The neural network model is able to roughly estimate ice masses, and the error reduces with increasing ice mass on the blade.