Multi-sensor slope change detection

Abstract

We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset will have increasing or decreasing means. The subset and the rate-of-changes are unknown. Our procedure uses a mixture statistics, which assumes that each sensor is affected by the change-point with probability p 0 . Analytic expressions are obtained for the average run length (ARL) and the expected detection delay (EDD) of the mixture procedure, which are demonstrated to be quite accurate numerically. We establish the asymptotic optimality of the mixture procedure. Numerical examples demonstrate the good performance of the proposed procedure. We also discuss an adaptive mixture procedure using empirical Bayes. This paper extends our earlier work on detecting an abrupt change-point that causes a mean-shift, by tackling the challenges posed by the non-stationarity of the slope-change problem.

Advancing cement-based materials design through data science approaches

“…The determination of the onset of the pozzolanic reaction in surface resistivity measurements as shown in Figure 9 has a subjective component, lacking any statistical analysis, which makes it challenging to implement in practice to identify new SCM sources. To overcome this, an approach known as slope change-point detection [44,45] was applied on the processed data, shown in Figure 9a. The goal of slope change-point detection is to see if a stochastic process or time-series has changed, usually using measurable parameters such as the mean or variance.…”

Sequential (Quickest) Change Detection: Classical Results and New Directions

“…There are also works investigating non-i.i.d. data under some specific settings, e.g., multi-sensor slope change detection [28], linear regression models [63], [221], generalized autoregressive conditional heteroskedasticity (GARCH) models [22], non-stationary time series [42], general stochastic models [195], [200], and hidden Markov models [62]. We refer to [196] for more recent developments on this topic.…”

“…Although this fact only holds strictly for stopping times for algorithms such as the CUSUM and SR when observations are i.i.d. [156], this method has been widely used and is verified to be highly accurate in practice (see examples in [28], [115], [188], [236]). Thus, for a large m, P ∞ {τ ≤ m} ∼ 1 − e −λ b m , where λ b is the parameter of the exponential distribution.…”

System-Level Predictive Maintenance: Review of Research Literature and Gap Analysis

“…[Fang et al, 2017b] develop methods for improved multivariate RUL regression, including feature selection. [Cao et al, 2018] proposes a change point detection modeling a (linear) gradual degradation to a subset of sensor streams (p0), where observations before and after the change point k are assumed to be i.i.d. normal.…”