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Increasing accuracy in the interval analysis by the improved format of interval extension based on the first order Taylor series

机译：基于一阶泰勒级数的改进的区间扩展格式提高了区间分析的准确性

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摘要

When the dependence of the function on uncertain variables is non-monotonic in interval, the interval of function obtained by the classic interval extension based on the first order Taylor series will exhibit significant errors. In order to reduce theses errors, the improved format of the interval extension with the first order Taylor series is developed here considering the monotonicity of function. Two typical mathematic examples are given to illustrate this methodology. The vibration of a beam with lumped masses is studied to demonstrate the usefulness of this method in the practical application, and the necessary input data of which are only the function value at the central point of interval, sensitivity and deviation of function. The results of above examples show that the interval of function from the method developed by this paper is more accurate than the ones obtained by the classic method.
机译：当函数对不确定变量的依赖性在区间上为非单调时，基于一阶泰勒级数的经典区间扩展所获得的函数区间将表现出明显的误差。为了减少这些误差，在此考虑函数的单调性，开发了具有一阶泰勒级数的区间扩展的改进格式。给出了两个典型的数学示例来说明这种方法。研究了具有集中质量的梁的振动，以证明该方法在实际应用中的有效性，其必要的输入数据仅是间隔，灵敏度和函数偏差中心点的函数值。以上示例的结果表明，本文方法开发的函数区间比经典方法获得的函数区间更准确。

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