The cavitation can cause erosion on the surface of the runner blades, resulting in cracks and peeling, which in turn affects the efficiency and safety of the Francis runner [18; 19]. Some experts also gained a better understanding of the strong pressure pulsations in the vaneless space between runner blades and guide vanes of the Francis turbines through on-site measurements [20]. Under off-design conditions, draft tube vortex phenomena may occur in the Francis turbine unit, and the draft tube pressure pulsation can aggravate the hydraulic vibration of the turbine unit and even threaten the stability and safety of the Francis turbine unit [21]. The complex flow characteristics inside Francis turbines of a model Francis runner under different operating conditions can show the visible unstable flow and vortex inside the runner flow channel [22]. Long-term operation under off-design conditions will significantly reduce the efficiency of the Francis turbines, which not only affects power output but also increases the operating cost of the turbine units [23]. The unsteady flow under off-designed loads will provoke high vibration and stress on Francis units, which may cause serious damage to the mechanical structure and shorten the service life of Francis turbines. Many scholars have reported flow-induced failure and cracks in hydraulic turbines. Pressure and stress measurements have been performed on prototype Francis runners to gain a deeper understanding of the physical mechanisms of unsteady flow and flow-induced structural vibrations and stresses in the Francis turbine unit under various operation conditions [24]. The vibration measurements of a simplified hydraulic turbine model have been carried out to monitor vibrations and stresses in hydraulic machinery with novel distributed fiber optic sensing techniques [25; 26]. Some scholars have reported the flow-induced damage on the Francis turbines. The unsteady flow-induced stresses of Francis runners have been studied through field measurements and numerical simulations [27], and they found that the maximum flow-induced stress in the runner is strongly correlated with parameters including the pressure pulsation level, unit rotating speed, and the numbers of runner blades and guide vanes. Other researchers analyzed the Francis runner failures and concluded that the damage was caused by stress concentration at the junction between the runner blade and the crown, which was caused by the combination of cavitation damage and high-cycle fatigue when the turbine unit was running under low-part loads. [PERSON] et al. conducted a study on the flow-induced stress of the turbine runners based on site measurements and simulations [27]. [PERSON] et al. [28] reported the runner blade failure in a 200 MW Francis hydraulic turbine and concluded the blade cracking was due to a combination of high cycle fatigue and cavitation damage of the runner operating at low loads. [PERSON] et al. [29] found that the cracking of the Francis runner blade was initiated by the uneven weld surface and accelerated by the hydrogen embrittlement of the welding filler material. [PERSON] et al. [30] observed the crack areas on the Francis turbine runner blades were caused by operating load conditions that deviated from the design condition. [PERSON] et al. [31] revealed that the causes for the crack in runner blades were the flow-induced resonance at off-design conditions and the high dynamic stresses in the Francis runner. The causes of cracks in Francis runners are not always the same, but a common finding is that the cracks are induced by the turbulent flow of Francis runners operating under off-design conditions.