基于最优加权移动平均T^2控制图的间歇性故障检测
Detection of Intermittent Faults Based on an Optimally Weighted Moving Average T^2 Control Chart with Stationary Observations
摘要：
自20世纪90年代以来，移动平均（MA）型方案，也称为平滑方法，已经在多元统计过程监控（MSPM）框架内得到了很好的建立。然而，它的理论基础仍然局限于平滑独立的数据，其等或指数加权方案的最优性仍然没有得到证明。本文旨在削弱现有MA方法中的独立性假设，并将其推广到更广泛的领域，即处理自相关弱平稳过程。当数据具有自相关性时，用于故障检测的等权和指数加权方法的非最优性被发现，揭示了它们没有有效利用样本的相关性信息的本质，从而产生了最优加权移动平均（OWMA）理论。OWMA方法与Hotelling的$T^2$统计量相结合，形成OWMA $T^2$控制图（OWMA-TCC），以检测更具挑战性的故障类型，即，间歇性故障（IF）。与在时间窗口内对样本施加相等权重的MA方案不同，OWMA-TCC使用相关性（自相关和互相关）信息来找到用于IF检测（IFD）的最佳权重向量（OWV）。为了实现最佳的IFD性能，定义了IF可探测性的概念，并给出了相应的可探测性条件，作为OWV的选择标准。然后，OWV的形式给出的非线性方程的解，其存在性证明的Brouwer不动点理论的援助。此外，对称结构的OWV被揭示，和MA计划的最优性的任何IF方向时，数据表现出没有自相关性被证明。
英文摘要：
The moving average (MA)-type scheme, also known as the smoothing method, has been well established within the multivariate statistical process monitoring (MSPM) framework since the 1990s. However, its theoretical basis is still limited to smoothing independent data, and the optimality of its equally or exponentially weighted scheme remains unproven. This paper aims to weaken the independence assumption in the existing MA method, and then extend it to a broader area of dealing with autocorrelated weakly stationary processes. With the discovery of the non-optimality of the equally and exponentially weighted schemes used for fault detection when data have autocorrelation, the essence that they do not effectively utilize the correlation information of samples is revealed, giving birth to an optimally weighted moving average (OWMA) theory. The OWMA method is combined with the Hotelling's $T^2$ statistic to form an OWMA $T^2$ control chart (OWMA-TCC), in order to detect a more challenging type of fault, i.e., intermittent fault (IF). Different from the MA scheme that puts an equal weight on samples within a time window, OWMA-TCC uses correlation (autocorrelation and cross-correlation) information to find an optimal weight vector (OWV) for the purpose of IF detection (IFD). In order to achieve a best IFD performance, the concept of IF detectability is defined and corresponding detectability conditions are provided, which further serve as selection criteria of the OWV. Then, the OWV is given in the form of a solution to nonlinear equations, whose existence is proven with the aid of the Brouwer fixed-point theory. Moreover, symmetrical structure of the OWV is revealed, and the optimality of the MA scheme for any IF directions when data exhibit no autocorrelation is proven.
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。
