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Distributionally robust fault detection design and assessment for dynamical systems
Automatica ( IF 6.4 ) Pub Date : 2021-01-04 , DOI: 10.1016/j.automatica.2020.109434
Chao Shang , Steven X. Ding , Hao Ye

We present a novel distributionally robust optimization approach for integrated design and assessment of fault detection system. Its salient feature is the guaranteed robustness against the inexactness of probability distribution of unknown disturbances. The integrated design problem is formulated as a distributionally robust chance constrained program (DRCCP). It maximizes fault detectability subject to the constraint on the worst-case false alarm rate among a continuum of probability distributions. The moment-based and Wasserstein ambiguity sets are used as two different ways of uncertainty description, which differ manifestly from generic settings where disturbances follow either Gaussian or norm-bounded assumptions. We show that the use of two different ambiguity sets in fault detection leads to specific statistical properties. To solve DRCCPs efficiently, we develop exact reformulations and tailored solution algorithms, and in some cases the optimal solution turns out to be classical fault detection design. In addition, a distributionally robust assessment strategy is developed, which evaluates the worst-case and best-case detectability under known faults by solving tractable convex programs. The efficacy of the proposed approach is illustrated on the fault detection of a laboratory three-tank system.



中文翻译:

动态系统的分布式鲁棒故障检测设计和评估

我们提出了一种新颖的分布式鲁棒优化方法,用于故障检测系统的集成设计和评估。它的显着特征是针对未知干扰的概率分布的不精确性保证了鲁棒性。集成设计问题被表述为分布鲁棒的机会受限程序(DRCCP)。它受连续概率分布中最坏情况下的虚警率的约束,可最大程度地提高故障检测能力。基于矩的模糊集和Wasserstein模糊度集被用作不确定性描述的两种不同方式,这明显不同于扰动遵循高斯或范数约束假设的一般设置。我们表明在故障检测中使用两个不同的歧义集会导致特定的统计属性。为了有效地解决DRCCP,我们开发了精确的公式和量身定制的解决方案算法,在某些情况下,最佳解决方案是经典的故障检测设计。另外,开发了一种分布鲁棒的评估策略,该算法通过解决易处理的凸规划来评估已知故障下的最坏情况和最佳情况可检测性。在实验室三缸系统的故障检测中说明了该方法的有效性。

更新日期:2021-01-04
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