Machine learning-based design strategy for weak vibration pipes conveying fluid

doi:10.1007/s10483-025-3276-7

摘要/Abstract

Abstract:

Multi-constrained pipes conveying fluid, such as aircraft hydraulic control pipes, are susceptible to resonance fatigue in harsh vibration environments, which may lead to system failure and even catastrophic accidents. In this study, a machine learning (ML)-assisted weak vibration design method under harsh environmental excitations is proposed. The dynamic model of a typical pipe is developed using the absolute nodal coordinate formulation (ANCF) to determine its vibrational characteristics. With the harsh vibration environments as the preserved frequency band (PFB), the safety design is defined by comparing the natural frequency with the PFB. By analyzing the safety design of pipes with different constraint parameters, the dataset of the absolute safety length and the absolute resonance length of the pipe is obtained. This dataset is then utilized to develop genetic programming (GP) algorithm-based ML models capable of producing explicit mathematical expressions of the pipe’s absolute safety length and absolute resonance length with the location, stiffness, and total number of retaining clips as design variables. The proposed ML models effectively bridge the dataset with the prediction results. Thus, the ML model is utilized to stagger the natural frequency, and the PFB is utilized to achieve the weak vibration design. The findings of the present study provide valuable insights into the practical application of weak vibration design.

Key words: pipe conveying fluid, machine learning (ML), pipe design strategy, resonance, genetic programming (GP), inverse design, preserved frequency band (PFB)

中图分类号:

O326

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(7): 1215-1236.

Tianchang DENG, Hu DING, S. KITIPORNCHAI, Jie YANG. Machine learning-based design strategy for weak vibration pipes conveying fluid[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(7): 1215-1236.

图/表 22

Parameter	Notation	Value	Unit
Outer radius	$R$	3	mm
Internal radius	$r$	2.4	mm
Young's modulus	$E$	194	GPa
Density of pipe	$ρ p$	7 930	kg/m³
Velocity of fluid	$V f$	30	m/s
Density of fluid	$ρ f$	872	kg/m³

Number of clips	Data size	ML model	RMSE (training)	$R 2$ (training)
4	9 744	Eq. (21)	0.034 712	0.879 76

Number of clips	Data size	ML model	RMSE (training)	$R 2$ (training)
4	807	Eq. (23)	0.004 482 3	0.961 12

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