The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the...The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.展开更多
In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively(0 p, q ...In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively(0 p, q 1,p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ^(N-1)~γ, where the exponent γ = 2 for N < |p-q|^(-1) and γ = 1 for N > |p-q|^(-1). Our study sheds useful insights into the biased random-walk process.展开更多
提前诊断出机械系统中的异常信息对于防止生产事故的产生非常重要。在各种诊断方法中,符号化时间序列分析(STSA,Symbolic time series analysis)是一种常用的异常诊断方法,然而它的诊断效果和符号化时间序列的形成紧密相关。在对之前方...提前诊断出机械系统中的异常信息对于防止生产事故的产生非常重要。在各种诊断方法中,符号化时间序列分析(STSA,Symbolic time series analysis)是一种常用的异常诊断方法,然而它的诊断效果和符号化时间序列的形成紧密相关。在对之前方法总结分析的基础上,提出了一种高效实用的符号化方法——基于概率密度空间划分的符号化方法。在该方法中,首先对时间序列进行概率密度统计分析,进而确定若干个概率相等的区间,然后对属于特定区间的值赋予一个特定的符号。为了检验该方法的效果,将基于概率密度空间划分的符号化时间序列分析方法用于轴承疲劳实验的异常诊断当中。通过对比实验表明:概率密度符号化方法相比于传统的空间划分方法对异常更加敏感,能够更早诊断出轴承的异常。展开更多
基金National Science and Technology Major Project of China(No.2016ZX04003001)。
文摘The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.
基金Supported by the National Natural Science Foundation of China under Grant No.11205110Shanghai Key Laboratory of Intelligent Information Processing(IIPL-2011-009)Innovative Training Program for College Students under Grant No.2015xj070
文摘In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively(0 p, q 1,p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ^(N-1)~γ, where the exponent γ = 2 for N < |p-q|^(-1) and γ = 1 for N > |p-q|^(-1). Our study sheds useful insights into the biased random-walk process.
文摘提前诊断出机械系统中的异常信息对于防止生产事故的产生非常重要。在各种诊断方法中,符号化时间序列分析(STSA,Symbolic time series analysis)是一种常用的异常诊断方法,然而它的诊断效果和符号化时间序列的形成紧密相关。在对之前方法总结分析的基础上,提出了一种高效实用的符号化方法——基于概率密度空间划分的符号化方法。在该方法中,首先对时间序列进行概率密度统计分析,进而确定若干个概率相等的区间,然后对属于特定区间的值赋予一个特定的符号。为了检验该方法的效果,将基于概率密度空间划分的符号化时间序列分析方法用于轴承疲劳实验的异常诊断当中。通过对比实验表明:概率密度符号化方法相比于传统的空间划分方法对异常更加敏感,能够更早诊断出轴承的异常。
