## 1 Introduction  
Pump station engineering guarantees the optimal allocation and scheduling of water resources. As an important underwater rotating component of a pump unit, the impeller is the most vulnerable structure among all structural components during actual operation. Cracks and even ruptures of the blades are not rare in numerous pump and hydropower stations around the world and severely threaten the safe and stable operation of pump units. Thus, the study of the structural characteristics of pump units is urgently required.  
With the development of fluid-structure interaction (FSI) computational techniques, plenty of studies have emerged with regard to the finite element analysis of structural characteristics of hydraulic machinery. [PERSON] et al. [1] studied the stress and deformation characteristics of a multiple-stage centrifugal pump with the effect of structural parameters and temperature through one-way coupled FSI. The results showed that the deformation and the stress distributions vary significantly with the operating point, and cases in hot fluid conditions are more critical. [PERSON] [2] analyzed the hydrodynamic damping in hydraulic turbines, which is found to be dependent on the nodal diameter of the mode shape, and the damping effect is proportional to the free-stream flow velocity. [PERSON] et al. [3] conducted a structural static analysis on a Francis turbine runner; under different water heads and openings of the guide vanes, the rules of the equivalent stress and deformation of the runner were obtained and analyzed. [PERSON] et al. [4] calculated the impeller dynamic stress of a single-blade centrifugal sewage pump in different working conditions and obtained the dynamic stress distribution of the impeller rotor system by using bidirectional FSI. On the basis of FSI, [PERSON] et al. [5] numerically investigated the deformation of impellers in a low-rigidity pump, with the results being consistent with those obtained via experiments in circulating water channels. [PERSON] et al. [6] conducted a study into the flow-induced noise of a centrifugal pump in consideration of FSI. Additionally, multiple scholars have studied FSI problems by introducing the immersed boundary method (IBM), which could avoid the numerical instability induced by grid deformation due to FSI [7; 8; 9; 10; 11]. Among the current studies on FSI [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11], few are related to the structural dynamic stress of axial-flow pump impellers, and the structural response to the transient fluid-structure interaction (FSI) of axial-flow pump impellers has not been studied in depth. Meanwhile, the overall structure of an impeller has been selected as the research object for finite element analysis in the majority of studies [13; 14; 15; 16; 17], which could not show the performance of a real pump impeller accurately. Furthermore, a great amount of numerical simulations lack comparison and validation, which leads to uncertain reliability. Therefore, this paper aims to study the dynamic stress improvement in depth to enhance the reliability of impellers based on real blade models and to validate the simulation accuracy by comparing the models with the results of a prototype test.  
In this paper, a bidirectional FSI study of an impeller blade in the whole flow system of a shaft-extension axial-flow pump is carried out to obtain the distribution of dynamic stress characteristics of impeller blades with different heads. Moreover, a thickening method for the stress state improvement of blade roots and an experimental method to measure the dynamic stress of real underwater rotating machinery are presented, which could give a valuable reference in respect to theoretical design and engineering applications.