## 1 Introduction  
The fluid-induced vibration detection technology for the multiphase sink vortex is widely used in developing detection systems for process production, such as in energy conversion in hydroelectric generation, supplying stability for liquid rocket fuel systems, and the condition monitoring of nuclear cooling reactors. Various vortices in the above-mentioned mechanical-equipment flow channels often appear as complex spatial structures. The vortex flow phases are difficult to forecast because of generated physical phenomena such as multiphase coupling, material transfer, and fluid-structure coupling shock. The surface fluid or solid particles sucked by the vortex are a multiphase and multiphysics field coupling dynamics issue during the vortex formation process. Its intense gas-liquid-solid suction coupling effect can form energy-pulse and nonlinear shock vibration, which can be the cause of many adverse effects in the industrial production process [1; 2; 3]. In the above industrial process, the issue of vortex gas entrainment for a liquid rocket fuel system is a primary difficulty for safe manufacturing. Vortex gas cores formed by external disturbances can rapidly reduce a system's reliability, and a large number of bubbles can cause an unstable and costly combustion. The vortex generates a sequence of irregular pulsing pressures in the turbine unit of a tidal hydropower facility. These may result in increased pulsing stresses on the pipe connection mechanism, and the resulting shock vibration severely damages hydraulic equipment [4]. Some interactions, such as the vortex and wave, can create intense disturbance responses and can damage the purity of molten steel in the steel flow refining process, resulting in industrial production accidents and economic losses [5; 6; 7]. Therefore, it is vital to study the fluid-induced vibration detection technology of the multiphase sink vortex and to realize online detection and active control for its dynamic evolution process. The above technical applications show that the vortex generation process is the primary cause of fluid-induced vibration, and a vibration distortion feature occurs in the critical transition stage. Vortex modeling and critical transition state detection are difficult to achieve due to the vortex's three-dimensional, unstable, turbulent, nonlinear, and spatiotemporal multiscale coupling as well as due to a lack of precise knowledge of its suction process [8; 9]. Meanwhile, the flow-control equipment that creates a vortex often includes various mechanical constraints such as pipes, screens, and valves, forming a complicated dynamic system with the flow channel. Due to the fluid, nonlinear excitation acting on the flow channel, the pipeline will have distinct vibration features that can be used to describe its functioning condition. However, in practical engineering applications, detection techniques are often exposed to extreme environmental disturbances such as high temperature (1400 \({}^{\circ}\)C), high pressure (15 MPa), and high-frequency shock disturbances (200 dB). As a result, video inputs from industrial monitoring systems make it impossible to observe vortex flow fields directly. The shock vibration caused by vortex energy may reduce the accuracy and service life of a vibration detection system, resulting in a low detection-success rate, poor real-time performance, and unstable operation. This has become a critical technical bottleneck for fluid-induced vibration detection systems. Countries and institutions around the world, particularly in Western developed countries, have placed a high priority on tackling the issues mentioned above. In the late 1980s, Germany successfully developed vortex-detecting technology based on the electromagnetic induction theory. It has a broad range of applications in the continuous casting process, including steel flow detection [10].