模糊等价关系下滚动轴承振动性能变异分析

在小样本且概率分布未知条件下，提出模糊等价关系和自助最大熵模型，并通过变异概率分析滚动轴承振动性能变异过程。对滚动轴承振动加速度原始数据分组得到样本，选定本征样本，计算各样本间的模糊等价系数；运用自助最大熵模型建立各样本的概率密度函数，通过交集法得到各样本相对于本征样本的变异概率，建立模糊等价系数和变异概率的关系曲线以实现对变异过程的监控；通过仿真和实验案例验证了所提模型的可行性和正确性。实验结果表明:随着磨损直径的逐渐增大，变异概率曲线呈“躺椅状”非线性上升趋势，对应滚动轴承磨损的3个阶段，即初级磨合阶段、正常性能退化阶段和性能恶化阶段。 

Analysis of vibration performance variation of rolling bearing under fuzzy equivalence relation

In the case of small samples with unknown probability distribution, the fuzzy equivalence relation and bootstrap maximum entropy models were proposed, and the variation process of vibration performance of rolling bearing was analyzed by variation probability. The original data of rolling bearing vibration acceleration was grouped into the samples, and then the intrinsic sample was selected to calculate the fuzzy equivalent coefficients between the samples. The bootstrap maximum entropy model was used to establish the probability density function of each sample, and the variation probability of each sample relative to the intrinsic sample was calculated by the intersection method. The relation curve between the fuzzy equivalent coefficients and variation probabilities was established to realize the monitoring of the variation process. The feasibility and correctness of the proposed model were verified by simulation and experimental cases. Experimental investigation showed that the variation probability curve presented nonlinear upward trend like “deck chair” with the increase of wear diameter, which corresponded to the three stages of rolling bearing wear, namely the initial running stage, the normal performance degradation stage and the performance deterioration stage.