## 1 Introduction  
High-lift pumping stations and water-diversion irrigation areas have been built in many water-deficient areas due to the continuous development of electric water-lifting equipment and water-diversion irrigation technology in China. These projects have created enormous economic, ecological and social benefits. Thus, ensuring their safe and stable operation is the main task of modernising and developing water conservation in China [1]. Natural and human forces create varying degrees of pipeline vibration during long-term operation at pumping stations [2]. Long-term irregular pipe vibration will lead to the loosening of the pipelines and their auxiliary system, causing catastrophic damage in severe cases [3]. Therefore, it is of great research interest to analyse the vibration characteristics of the pumping station pipeline to avoid its adverse vibrations.  
Chaos is a unique mechanical phenomenon in the vibration of strongly nonlinear structures. Most researchers believe that the vibrations of pipelines are weakly nonlinear,so they mainly focus on studying chaotic phenomena caused by the flow of water and other excitation sources such as flow. There is a scarcity of research on the chaotic processes in the pipeline itself when researching nonlinear problems. It is found that the chaotic phenomena of pipelines do not depend solely on the strength of structural nonlinearity; for some weak nonlinear or even linear structures, chaos occurs [4]. [PERSON] studied the dynamics of a cantilever pipeline with nonlinear constraints and constant internal flow, which discovered the chaotic motion of the system [5]. [PERSON] obtained the chaotic characteristics of the transport pipeline by increasing the nonlinear force and found that the occurrence of chaos is mainly affected by the flow velocity in the pipeline [6]. [PERSON] investigated the nonlinear vibrations of slightly curved pipes that transport fluid with constant velocity [7]. The periodic and chaotic movements have been observed in the transverse vibrations of slightly curved pipes transporting fluid. [PERSON] analysed the chaotic phenomenon in the pipeline vibration caused by the flow pulsation excitation under thermal load and then obtained the relationship between the frequency response and flow velocity [8].  
Research on the chaotic characteristics of pipeline systems mainly focuses on oil-gas pipelines and the mathematical models of pipelines with specific nonlinear constraints. In contrast, the chaotic characteristics of pumping station pipeline systems are rarely studied. Most of the previous research achievements have only analysed the chaotic characteristics of the vibration system but have not further explored the vibrational excitation that caused the chaos. In this paper, the measured vibration responses of the pumping station pipeline in an irrigation area are taken as the research objective. The chaotic characteristics of the vibratory responses of the pumping station pipeline under different working conditions are analysed by using the saturation correlation dimension and the largest Lyapunov exponent. In addition, the IVMD method is used to decompose the vibration responses of the measurement points under typical working conditions. The chaotic characteristics of the IMFs are analysed to obtain the vibratory excitation that causes the chaotic characteristics of the pumping station pipeline.