Developing Formula based on M5 Tree Algorithm to Evaluate Maximum Relative Amplitude of Transverse Waves

Vortex vibrations in structures has been considered in some of engineering problems such as vibration at exchanger tubes and bridge and hydraulic structures designing. Accordingly, evaluation the maximum relative amplitude of transverse waves developed by obstacle, attracts a lot of attention. Reynolds number, Froude number, wave mode, ratio of longitudinal and transverse distances of obstacles to cylinder diameter and arrangement of cylinders used as input variables to M5 model. Ratio of wave amplitude to flow depth considered as an output variable. After training tree model, two different structures proposed for inline and staggered arrangement. There are four and five equations for inline and staggered arrangements proposed by tree model, respectively. In this study, Reynolds number that ignored in existing formula, used as a division variable at inline arrangement and performed important role in proposed equations. Root mean square error in tree model was 0.23 which in compare with other models, has been reduced 46 to 50 percent. In addition, accuracy of tree model estimated 81 percent which about 18 to 38 percent more than other equations. Discrepancy ratio of tree model oscillates between 0.52 and 0.66 which shows the performance of this model in wave maximum relative amplitude estimation.