An interval inverse method based on high dimensional model representation and affine arithmetic
An interval inverse method based on high dimensional model representation and affine arithmetic
复制标题
一种基于高维模型表示和仿射算法的区间反演方法
DOI：
10.1016/j.apm.2018.07.009
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发表时间：
2018-11
影响因子：
5
通讯作者：
Zhang Zheng
中科院分区：
文献类型：
--
作者：
Liu Jie;Cai Heng;Jiang Chao;Han Xu;Zhang Zheng
本文提出一种通过高维模型表示和仿射算法的区间反演方法，可以有效解决具有区间不确定性的反演问题。首先，当只能从有限数量的实验测量中获得响应的界限时，可以采用区间模型来描述测量响应和识别参数的不确定性。其次，为了合理估计测量响应与计算响应之间的接近程度，针对区间反问题构建了误差区间和相应的优化模型。第三，利用高维模型表示来近似原始系统模型，并采用仿射算法来有效计算响应边界。最后，利用遗传算法求解区间反问题的优化模型，确定系统参数的上下界。通过三个算例验证了该方法的正确性和有效性。
This paper proposes an interval inverse method through a high dimensional model representation and affine arithmetic, which can effectively solve inverse problems with interval uncertainty. Firstly, when only the bounds of responses can be obtained from a limited number of experimental measurements, an interval model can be employed to describe the uncertainty of the measured responses and identified parameters. Secondly, in order to reasonably estimate the degree of the closeness between the measured and calculated responses, an error interval and corresponding optimization model are constructed for the interval inverse problem. Thirdly, a high dimensional model representation is utilized to approximate the original system model, and an affine arithmetic is adopted to efficiently calculate the response bounds. Finally, the optimization model for interval inverse problem is solved using genetic algorithm to identify the upper and lower bounds of the system parameters. Three examples are studied to demonstrate the correctness and effectiveness of the proposed method.
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