The new nonprobabilistic criterion of failure for dynamical systems based on convex models
The new nonprobabilistic criterion of failure for dynamical systems based on convex models
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DOI：
10.1016/j.mcm.2003.08.006
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发表时间：
2004-07
期刊：
影响因子：
--
通讯作者：
Z. Qiu;P. Müller;A. Frommer
中科院分区：
文献类型：
--
作者：
Z. Qiu;P. Müller;A. Frommer
通过一个反例，说明了Ben-Haim基于凸模型的动力系统鲁棒可靠性理论似乎存在一些问题。指出凸模型的展开性质是凸模型与真实的向量的加法，凸模型的平移性质是凸模型的标量乘。利用凸模型的超矩形或区间向量的偏序关系，给出了有界不确定性动力系统可靠性的一个正确判据。在此基础上，提出了不同于Ben-Haim的展开函数。根据Ben-Haim的思想，基于新的展开函数，我们再次定义了输入、失效和总体可靠性指标。通过本-海姆的例子，我们得到了一些与他不同的结果。所得结论和结果对Ben-Haim稳健可靠性理论的进一步发展具有一定的参考价值。
By a counter example, we show that there seem to be some problems in Ben-Haim's theory of robust reliability of dynamical systems based on convex models. We still point out that the property of the expansion of convex models is just the addition of a convex model and a real vector, and the property of the translation of convex models is just the scalar multiplication convex models. By means of the partial-order relation of the superscribed hyperrectangle or interval vectors of convex models, we present a correct criterion of reliability of the dynamical system with bounded uncertainty. Based on them, we propose the expansion function which is different from the one of Ben-Haim. Following Ben-Haim's thoughts, based on the new expansion function, we again define the input, failure, and overall reliability indices. By Ben-Haim's example, we obtain some results different from his. The conclusion and results may be thought of as to the further development of Ben-Haim's robust reliability.