Adaptive Change Detection for LongTerm Machinery Monitoring Using Incremental SlidingWindow
 Teng Wang^{1},
 GuoLiang Lu^{1}Email author,
 Jie Liu^{2} and
 Peng Yan^{1}
https://doi.org/10.1007/s1003301701914
© The Author(s) 2017
Received: 10 June 2017
Accepted: 29 September 2017
Published: 25 October 2017
Abstract
Detection of structural changes from an operational process is a major goal in machine condition monitoring. Existing methods for this purpose are mainly based on retrospective analysis, resulting in a large detection delay that limits their usages in real applications. This paper presents a new adaptive realtime change detection algorithm, an extension of the recent research by combining with an incremental slidingwindow strategy, to handle the multichange detection in longterm monitoring of machine operations. In particular, in the framework, Hilbert space embedding of distribution is used to map the original data into the Reproducing Kernel Hilbert Space (RKHS) for change detection; then, a new adaptive threshold strategy can be developed when making change decision, in which a global factor (used to control the coarsetofine level of detection) is introduced to replace the fixed value of threshold. Through experiments on a range of real testing data which was collected from an experimental rotating machinery system, the excellent detection performances of the algorithm for engineering applications were demonstrated. Compared with stateoftheart methods, the proposed algorithm can be more suitable for longterm machinery condition monitoring without any manual recalibration, thus is promising in modern industries.
Keywords
1 Introduction
Detection of structural changes from an operational process is a major goal in machinery monitoring which enables to solve many practical problems ranging from early fault detection, safety protection as well as other process control problems. Existing works are mainly based on a retrospective analysis of a data stream composed of numerical condition monitoring (CM) variables, such as vibration, sound, power consumption. The basic idea of a standard retrospective change detection mainly relies on estimating the logarithm of the likelihood ratio between two distributions [1, 2]. This kind of strategy argues that the detection of a change can be converted into the detection of the parameter difference between the two distributions before and after this change point. As a consequence, the retrospective change detection aims to estimate this parameter difference of distributions based upon likelihood ratio statistics. Change decision can be made by performing a null hypothesis testing with a threshold. Many effective tools for this goal such as the cumulative sum metric (CUSUM) [3–6], geometric moving average (GMA) [7, 8] and the generalized likelihood ratio test (GLRT) [9–12] have been widely used. For example, Willersrud et al. [12] developed the GLRT to make efficient downhole drilling washout detection with the multivariate tdistribution; Reñones et al. [6] used the CUSUM analysis for multitooth machine tool fault detection. Although these methods have been experimentally demonstrated the effectiveness in various fields, due to the requirement of data after change point, a large detection delay is an essential limitation of these methods for real applications [13]. On the other hand, realtime change detection aims to detect changes as soon as possible when a change occurs, this requirement is crucial in many reallife scenarios such as security monitoring [14, 15], health care [16, 17], automated factory [18, 19] as well as machine operation monitoring studied in this paper. In operation of realtime change detection, at each time when a datum is input, it evaluates what extent the input datum is likely to be a changepoint by a certain type of measuring score [20] which does not need any input data after change time. The realtime approaches have succeeded in solving many practical applications (e.g., wind turbine condition monitoring [21], driver vigilance monitoring [22]), and thus are promising [23].
The goal of this paper is to further advance this research line of realtime detection methods. More specifically, our main contributions in this paper are summarized in two folds. The first contribution is to apply a martingalebased framework proposed in our recent article [24] to longterm machine monitoring by combining an incremental slidingwindow strategy. The basic idea of the original martingale is to directly learn a statistical regularity from already observed data, and then detect possible change(s) by investigating how much each data is deviated from the regularity using martingale by testing exchangeability. That framework, however, only works for atmostonepoint change detection, thus unsuitable for the cases containing multiple changes in longterm monitoring applications. In this paper, we introduce an incremental slidingwindow strategy for solving this problem.
Recall that, the threshold value for change decision making is a key factor of detection accuracy. Potential weakness of the majority of exiting algorithms, e.g., Refs. [5–11], is that they need either humanmade instruction/intervention or an offline crossvalidation to confirm the value of threshold before operation, and thus make them largely limited in real applications. Another contribution of this paper is to develop a new adaptive threshold when performing change decision making. In particular, we introduce an alternative factor: a fixedglobal parameter used to control the coarsetofine level of detection, instead of the fixed value of threshold, for change detection (see Section 3.2 for details). By using this factor, at each step of change decision, the threshold value can be adaptively computed from the already observed data.
Besides the methodological extensions of the proposed method, we also conducted validations on an experimental setup to investigate effectiveness/priority of the method for change detection with large datasets. For more details, please see Section 4.
The rest of the paper is structured as follows. Section 2 presents the outline of martingale framework for machine monitoring. Section 3 formulates problems addressed in this paper and provides our proposed methods, followed by experimental results in Section 4. Section 5 concludes this paper and shows the future work.
2 Martingale Based Change Detection for Machinery Monitoring
 (1)
The changes are detected by testing the null hypothesis that all n (strangeness) values (which corresponds to \(x_{1} ,x_{2} , \ldots ,x_{n} ,\) respectively) are exchangeable in the index, through the corresponding exchangeability martingale \(M_{1} ,M_{2} , \ldots ,M_{n}\), where M _{ n } is a measurable function of \(s_{1} ,s_{2} , \ldots ,s_{n}\), satisfying
$$M_{n} = E(M_{n + 1} M_{1} ,M_{2} , \ldots ,M_{n} ).$$(1)  (2)
The following Doob’s inequality [25] can be used for rejecting this null hypothesis for a large value of \(M_{n}\):
$$P(\exists nM_{n} \ge \lambda ) \le \frac{1}{\lambda }.$$(2)  (3)
This (exchangeability) martingale is constructed from a p value, the probability of obtaining a test statistic at least as extreme as the one that was actually observed, and the pvalue is obtained by a strangeness value appropriately determined in each specific application.
On the basis of the above three points, the outline of performing martingale for change detection is described as follows (see Ref. [25] for more details):
That is, if the martingale value M _{ t } is greater than a predefined threshold \(\lambda\), H _{ A } in Eq. (5) is satisfied, i.e., a change occurs on the time t. Otherwise, the martingale test satisfying \(H_{0}\) continues to operate as long as 0 < M _{ t } < λ.
3 Problem Formulation and Proposed Scheme
 (1)
How to deal with multichange detection in longterm monitoring?
 (2)
Is it possible to adaptively compute the threshold value when making change decision?
In the following, we will discuss these two problems in details and provide our proposed schemes.
3.1 Change Detection Using Incremental SlidingWindow
Problem 1. As shown in Eq. (3) and Eq. (5), \(M_{t}\) can be sequentially processed with a fixedlength L slidingwindow over the given data stream, and all possible change candidates \(t \in \{ 1,2, \ldots ,n\}\) are tested. This process however may be unsuitable for longterm monitoring applications. A key feature of real machine operations is temporal variations, i.e., one operation can last for a long time or only a few seconds. Hence, it is difficult to use a fixedlength L slidingwindow to capture transitions (i.e., changes from an operational state to another) in longterm monitoring. More specifically, a small length of L causes overchangedetection and a large length of L causes a large delay. To overcome this problem, we combine the martingale with an incremental slidingwindow strategy [27] to design a realtime change detection algorithm for Eq. (5).
3.2 Adaptive Threshold for Change Detection
Lemma 1. As long as the rademacher average [29], which measures the “size” of a class of realvalued functions with respect to a probability distribution, is well behaved, finite sample yield error converges to zero, thus they empirically approximate \(\mu (P_{x} )\)(see Ref. [28] for more details).
Since we used RBF as the kernel function as given in Eq. (8), an isolated data point can be certified if \(s_{t} \ge \alpha \cdot \sigma\), where \(\alpha\) is a fixedglobal factor controlling the confidence level of detection and \(\sigma\) is the standard deviation computed from existed data (that is, an adaptive threshold).
4 Experimental Verification
 (1)
Will the proposed incremental slidingwindow be more suitable than the fixedlength slidingwindow for longterm machine monitoring?
 (2)
Can the adaptive detection algorithm be effective for change detection and how does it perform with large datasets?
4.1 Experimental Setup
4.2 Experiment I: Performance of Incremental SlidingWindow

The lengthfixed slidingwindow martingale requires more parameters, i.e., \(\lambda\) and L, for performing change detection, which requires a more complicated prior estimation of them before usage;

By the incremental slidingwindow martingale, only one parameter: \(\lambda\) is required, which inspires an extension of change detection by adaptive threshold.
Both of them inspire the adaptive threshold given in Section 3.2, which will be evaluated in the following.
4.3 Experiment II: Performance of Adaptive Threshold
In this section, we will evaluate the proposed adaptive threshold for machine monitoring. Here, it is noted that since in the Section 4.2, we have demonstrated the priority of using incremental slidingwindow for longterm machine monitoring, in this section, we only test the performance of adaptive threshold with incremental slidingwindow.
Precision is the probability that a detection is actually correct, i.e., a true change. Recall is the probability that the detection recognizes a true change.
Apparently, \(F_{1}\) is a harmonic mean between precision and recall, and a high value of \(F_{1}\) ensures reasonably a high balance between precision and recall.
5 Conclusions
In this paper, we have extended our recent work [25] to longterm machine monitoring where two schemes are proposed: 1) using the incremental slidingwindow to solve the problem of multichange detection; and 2) developing an adaptive threshold when making change decision. Experimental results on an experimental setup demonstrated great successes of the proposed method in multichange detection in longterm monitoring. With this, it can be concluded that the improved algorithm is feasible for a new generation of longterm machine monitoring systems. In view of this, further work will be done to continue verifying the capability of the improved algorithm for detecting a wider range of changes when operating a machine to make it ready for commercial exploitation.
In addition, considering that the detection delay is one of essential aspects to be considered when design a detection method, another future work is to extract informative features to represent the raw collected data for modeling in order to further decrease the delay of our method when detecting changes
Notes
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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