Application of Combined Positive and Reverse Grey-bootstrap Filtering Method in Reliability Evaluation of Rolling Bearing Performance
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摘要: 基于正反向结合灰自助滤波法提取出有效的轴承性能退化信息,从而精准地计算轴承运行过程中的性能可靠度。分别运用正向灰自助滤波法和反向灰自助滤波法对采集到的滚动轴承振动加速度数据进行降噪,并将其进行融合得到新的数据序列;基于概率密度函数交集法,将滤波前后数据序列的概率密度函数交集面积作为定量评定滤波效果的新指标;选定性能阈值,计算各个数据序列的变异个数、变异概率和性能可靠度,定量分析轴承运行过程中的性能变异程度。两个案例均表明正反向结合灰自助滤波法的效果最好,将其用于评估滚动轴承的性能退化过程是可行的。
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关键词:
- 滚动轴承 /
- 性能可靠性 /
- 正反向结合灰自助滤波法 /
- 概率密度函数交集法 /
- 交集面积
Abstract: Based on the combination of positive and reverse grey-bootstrap filtering methods, the effective bearing performance degradation information can be extracted to accurately calculate the performance reliability of bearings in the operation process. The positive and reverse grey-bootstrap filtering methods were used to denoise the collected vibration acceleration data of rolling bearings respectively, which were fused to obtain the new data series. Based on the probability density function-intersection method, the intersection area of probability density functions was taken as a new index to quantitatively evaluate the filtering effect for the data series before and after filtering. The performance threshold was selected to calculate the variation number, variation probability and performance reliability of data series. The variation degree of bearing performance in the operation process was analyzed quantitatively. Both cases show that the combined positive and reverse grey-bootstrap filtering method has the best filtering effect, and It is feasible to use it to evaluate the performance degradation process of rolling bearings. -
表 1 滤波前后各个样本的拉格朗日乘子
Table 1. Lagrange multipliers of samples before and after filtering
样本 拉格朗日乘子 a1 a2 a3 a4 a5 a6 滤波前 1.81 0.32 -0.56 -0.04 -0.04 -0.01 正向滤波 2.04 0.12 -0.71 -0.01 -0.01 -0.01 正反向结合 2.04 0.11 -0.69 0.00 -0.01 -0.01 表 2 滤波前后各个概率密度函数的重合面积(案例1)
Table 2. Overlapped areas of probability density functions before and after filtering(case 1)
样本 交点 重合面积 横坐标1 横坐标2 正向滤波 -0.0471 0.0606 0.9190 正反向结合 -0.047 3 0.061 0 0.929 6 滚动均值滤波 -0.041 5 0.060 2 0.833 7 表 3 各个振动序列的变异个数、变异概率可靠度(案例1)
Table 3. Variation number, variation probability and reliability of different vibration sequences(case 1)
数据序列号 变异个数 变异概率 可靠度/% 1 0 0 100 2 8 0.005 99.50 3 40 0.025 97.53 4 565 0.353 70.25 表 4 各种滤波方法的拉格朗日乘子
Table 4. Lagrange multipliers of various filtering methods
样本 拉格朗日乘子 a1 a2 a3 a4 a5 a6 滤波前 -3.57 3.86 -6.41 -5.94 0.78 0.76 正向滤波 -5.25 5.99 -1.26 -4.43 0.14 0.51 正反向结合 -5.30 5.97 -1.13 -4.37 0.12 0.50 表 5 滤波前后各个概率密度函数的重合面积(案例2)
Table 5. Overlapped areas of probability density functions before and after filtering (Case 2)
方法 交点 重合面积 横坐标1 横坐标2 横坐标3 横坐标4 正向滤波 1.582 5 2.995 1 9.841 8 13.489 6 0.900 2 正反向结合 1.633 3 3.020 9 9.881 6 13.533 0 0.915 7 滚动均值滤波 2.242 2 3.747 6 10.267 4 13.755 7 0.863 8 表 6 各个振动序列的变异个数、变异概率可靠度(案例2)
Table 6. Variation number, variation probability and reliability of different vibration sequences (Case 2)
数据序列号 变异个数 变异概率 可靠度/% 1 0 0 100 2 0 0 100 3 0 0 100 4 0 0 100 5 0 0 100 6 0 0 100 7 0 0 100 8 0 0 100 9 80 0.13 87.91 10 621 1.00 36.79 -
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