Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
滚动轴承是旋转机械系统的关键部件之一,其振动性能对机械设备的运行质量有重要影响。为确定轴承性能演变趋势,对轮毂轴承的全寿命周期振动时间序列进行了研究。首先,按照是否超过标定值,将轴承振动时间序列分为性能未退化和性能退化序...滚动轴承是旋转机械系统的关键部件之一,其振动性能对机械设备的运行质量有重要影响。为确定轴承性能演变趋势,对轮毂轴承的全寿命周期振动时间序列进行了研究。首先,按照是否超过标定值,将轴承振动时间序列分为性能未退化和性能退化序列,并且将其按照时间顺序等分为10个子序列;然后,采用了最大熵原理模型逐一分析了子序列,寻找了参数最早发生明显变化的序列;最后,按照时间顺序继续细分了该子序列,分析了每个子序列的参数变化趋势,并对比了参数变化序列对应的轴承服役时间。研究结果表明:通过对比映射参数、各阶原点矩、拉格朗日乘子与轴承性能变化之间的规律,可验证映射参数表征轴承性能演变的可行性;第8个子序列映射参数a减小了53.3%,映射参数b增加了43.2%;第8个子序列继续细分时,第9个子序列映射参数a减小了44.5%,映射参数b增加了38.7%;与标定失效时间(189 h 41 min)相比,采用最大熵模型可提前175 min实现对轴承的性能失效预报。采用最大熵模型可以对轴承性能进行失效预报。展开更多
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
文摘滚动轴承是旋转机械系统的关键部件之一,其振动性能对机械设备的运行质量有重要影响。为确定轴承性能演变趋势,对轮毂轴承的全寿命周期振动时间序列进行了研究。首先,按照是否超过标定值,将轴承振动时间序列分为性能未退化和性能退化序列,并且将其按照时间顺序等分为10个子序列;然后,采用了最大熵原理模型逐一分析了子序列,寻找了参数最早发生明显变化的序列;最后,按照时间顺序继续细分了该子序列,分析了每个子序列的参数变化趋势,并对比了参数变化序列对应的轴承服役时间。研究结果表明:通过对比映射参数、各阶原点矩、拉格朗日乘子与轴承性能变化之间的规律,可验证映射参数表征轴承性能演变的可行性;第8个子序列映射参数a减小了53.3%,映射参数b增加了43.2%;第8个子序列继续细分时,第9个子序列映射参数a减小了44.5%,映射参数b增加了38.7%;与标定失效时间(189 h 41 min)相比,采用最大熵模型可提前175 min实现对轴承的性能失效预报。采用最大熵模型可以对轴承性能进行失效预报。
