Fatigue life prediction of the wire rope based on grey theory under small sample condition

•Grey model reduces the computational difficulty of reliability life data prediction.•The sample size of fatigue test is reduced based on the improved GM (1,1) model.•The model based on reliability stress-life curve has higher prediction accuracy.•Combining grey theory with the Miner rule can increase application scope of model.•The fatigue failure of wire rope is a problem of multiaxial fatigue. The fatigue life prediction of wire rope has the characteristics of large sample size required and many uncertain factors. In this paper, the 40 6 × 31SW FC type wire rope is taken as the research object. Under the condition of fatigue life data of small sample size, the fatigue life prediction of wire rope under different load conditions is realized based on gray theory. As a first step, for the problems existing in the current fatigue life prediction of wire rope, this paper constructs an improved GM (1,1) model and predicts the reliability life data of wire rope under small sample size condition. Subsequently, based on this, combined with the equivalent alternating stress of the critical locations of wire rope during the fatigue test, the reliability stress-life curve of the critical locations of wire rope is determined; Finally, the fatigue life prediction model of wire rope is obtained by combining with the cumulative damage theory of fatigue. The fatigue life of wire rope under different loads is predicted and compared with the experimental value. The results show that the proposed method has high accuracy in predicting the small sample fatigue life of wire rope under single and combined loading conditions, which proves the effectiveness of this method.