最大熵准则识别材料疲劳寿命分布

疲劳寿命具有很大的分散性,是工程结构设计中必须考虑的因素。为了降低主观不确定性的引入,得到更合理的疲劳寿命分布类型,提出一种用于识别疲劳寿命概率分布类型的一般计算方法。该方法首先根据疲劳试验样本信息确定疲劳寿命的前四阶统计矩;基于统计矩信息,利用最大熵准则确定疲劳寿命的概率分布类型。在基于最大熵准则识别疲劳寿命分布时,利用Lagrange乘子法求解最大熵分布。采用已有的航空铝合金2024-T351板件疲劳裂纹扩展试验数据验证所提计算方法的合理性和有效性。结果表明:所提方法能够高效地识别材料疲劳寿命分布类型,并且不局限于单峰标准分布类型。

Maximum entropy principle for identifying the fatigue life distribution of material

It is well-known that the fatigue lives of metal material have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. A rational computational method is proposed for identifying the probability distribution of fatigue life in this paper, in order to reduce the introduction of subjective uncertainties and obtain rational probability distribution. Firstly the sample statistics are used to estimate the first four statistical moments of fatigue life. Then, based on all those statistical moment constraints, the maximum entropy principle is employed to identify a rational probability distribution for fatigue life of interest. An accurate algorithm based on optimization theory is also presented to find the Lagrange multipliers in maximum entropy distribution, which can avoid the numerical singularity when solving a system of equations. The rationality and effectiveness of the proposed method are demonstrated by the experimental data of 2024-T351 aluminum alloy specimens available in the literature.