基于多窗口滑动平均T2控制图的间歇性故障检测及可检测性
Detection and Detectability of Intermittent Faults Based on Moving Average T2 Control Charts with Multiple Window Lengths
摘要：
到目前为止，间歇性故障（IF）的检测和可检测性的问题还没有得到充分的研究，在多元统计框架。干扰的特点是幅值小、持续时间短，传统的单次观测的多元统计方法不再有效。因此，在本文中，移动平均T^2控制图（MA-TCCs）与多个窗口长度，同时使用一个银行的MA-TCCs具有不同的窗口长度，提出了解决IF检测问题。提出了减少虚警/漏报和推断IF出现和消失时刻的方法。为了分析干扰函数的检测能力，引入了保证可检测性的概念，它是对原有的永久故障可检测性概念的扩展和推广。在此基础上，给出了干扰可探测的充要条件，这些干扰可能出现和消失多次，且出现的次数和持续时间不同。在此基础上，进一步讨论了两个重要窗长的优化性质。通过这种方式，建立了一个分析IF可探测性的理论框架，并就如何使理论结果适用于实际应用进行了扩展讨论。最后，数值算例和连续搅拌釜反应器（CSTR）过程的仿真研究表明了所开发方法的有效性。
英文摘要：
So far, problems of intermittent fault (IF) detection and detectability have not been fully investigated in the multivariate statistics framework. The characteristics of IFs are small magnitudes and short durations, and consequently traditional multivariate statistical methods using only a single observation are no longer effective. Thus in this paper, moving average T^2 control charts (MA-TCCs) with multiple window lengths, which simultaneously employ a bank of MA-TCCs with different window lengths, are proposed to address the IF detection problem. Methods to reduce false/missing alarms and infer the IFs' appearing and disappearing time instances are presented. In order to analyze the detection capability for IFs, definitions of guaranteed detectability are introduced, which is an extension and generalization of the original fault detectability concept focused on permanent faults (PFs). Then, necessary and sufficient conditions are derived for the detectability of IFs, which may appear and disappear several times with different magnitudes and durations. Based on these conditions, some optimal properties of two important window lengths are further discussed. In this way, a theoretical framework for the analysis of IFs' detectability is established as well as extended discussions on how the theoretical results can be adapted to real-world applications. Finally, simulation studies on a numerical example and the continuous stirred tank reactor (CSTR) process are carried out to show the effectiveness of the developed methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
