微分建模法及其在疲劳可靠性研究中的应用

Differential Modeling Method and Applications in Fatigue Reliability Research

很多工程问题可用微分方程描述,由此导出了微分建模方法.该方法的实质是直接用微分方程来描述客观物理现象,同时通过微分近似公式来直接辩识微分方程的系数.该方法用于三参数威布尔分布的参数估计和疲劳性能S N曲线拟合、低周疲劳特性曲线拟合、疲劳裂纹扩展a-N曲线拟合等问题,取得了较好的效果,为疲劳可靠性研究提供了新工具,对工程中建模和数据分析问题也有相当参考价值.

As a large number of problems in engineering can be described by differential equations, differential modeling methods are introduced. The kernel of the matter is that using differential equations describe physical phenomena directly, at the same time, coefficients of differential equation are identified by a approximate difference formula. Proposed method has been applied to estimate parameters of three-parameters Weibull distribution and to research fatigue properties that includes fitting of the fatigue properties S-N curve, low cycle fatigue properties curve and fatigue crack propagation a-N curve. The results indicate that it has high accuracy and low cost. It offers a new tool to modeling and data analyses in engineering.