Estimation of Natural Frequencies of Pipe–Fluid–Mass System by Using Causal Discovery Algorithm

This paper employs a novel approach to investigating the dynamic behavior of a pipe conveying fluid and the relationship between the variables that influence it, based on causal inference. The pipe is modeled as a beam with Rayleigh beam theory and Hamilton’s variation principle is demonstrated to obtain the equation of motion. Concentrated mass at various locations is introduced using the Dirac delta function. The fluid in the pipe has no compression properties and no viscosity. The non-dimensional equations of motion of the pipe–fluid–mass system are achieved by using the approach of the fluid–structure interaction problem. The non-dimensional partial differential equations of motion are converted into matrix equations and the values of natural frequencies are obtained by using the Finite Differences Method. The relationship between the variables is investigated by causal discovery using the produced natural vibration frequencies dataset. Moreover, the Bayesian Network's probability distribution is fitted to the discretized data using the structural model created through causal discovery, resulting in trustworthy predictions without the need for sophisticated analysis. The findings highlighted that the proposed causal discovery can be an alternative practical way for real-time applications of pipe conveying fluid systems.