Sequential Detection of Abrupt Changes in ARMA Models

In this study, the performance of moving cut data-approximate entropy (MC-ApEn) to detect abrupt dynamic changes was investigated. Numerical tests in a time series model indicate that the MC-ApEn method is suitable for the detection of abrupt dynamic changes for three types of meteorological data: daily maximum temperature, daily minimum temperature, and daily precipitation. Additionally, the MC-ApEn method was used to detect abrupt climate changes in daily precipitation data from Northwest China and the Pacific Decadal Oscillation (PDO) index. The results show an abrupt dynamic change in precipitation in 1980 and in the PDO index in 1976. The times indicated for the abrupt changes are identical to those from previous results. Application of the analysis to observational data further confirmed the performance of the MC-ApEn method. Moreover, MC-ApEn outperformed the moving t test (MTT) and the moving detrended fluctuation analysis (MDFA) methods for the detection of abrupt dynamic changes in a simulated 1000-point daily precipitation dataset.

Successful speech recognition is highly dependent on appropriate speech segmentation. The poor efficiency of the sequential detection of abrupt changes in the signals with relatively short stationary intervals, as is the case with speech signals, can be improved by the off-line maximum likelihood segmentation algorithm. In this paper the new segmentation algorithm is presented. For the a priori known number of segments, the algorithm determines such signal partitions for which the sum of segment distortion is minimal. The generalized maximum likelihood distortion measure has been introduced, and has proven to be particularly efficient on short signal segments. In the case of an unknown number of segments, its estimate is obtained comparing the reduction of the distortion. The asymptotic properties of the distortion sequence have been analyzed, which led to the definition of the presented segmentation algorithm. The introduced measure can be applied both to the AR and ARMA models. The segmentation algorithm is verified on test signals as well as on the natural speech signal, for which the pitch synchronous framing scheme is applied. The experimental results also include a comparison of the AR and ARMA model-based segmentations. The first results show that ARMA model-based segmentation gives somewhat better results than the AR model algorithm.

This study is devoted to detection of abrupt changes in electrocardiogram (ECG). A linear time-variant model with Gaussian white noise is used to describe the real ECG signal, based on the estimated system parameters and tuned covariances of noise, the off-line and on-line generalised likelihood ratio (GLR) tests for ECG signal are developed for change detection. For comparison, the test algorithm uses Levinson, recursive least squares (RLS) methods to obtain the filter models parameters of ECG. Furthermore, windowed on-line GLR test algorithm is developed, which works more effectively in real-time situation. The simulation results with real data show the effectiveness of the application.

Long-term trend and abrupt changes of major climate variables in the Taihu Basin were investigated based on the mean, maximum and minimum air temperature, diurnal temperature range (DTR), precipitation, relative humidity and sunshine duration at six meteorological stations from 1954 to 2006. Results showed that the long-term trend for annual precipitation was not statistically significant during the past 53 years, but a wetter tendency was detected and the increasing centre for annual precipitation was located in the southeast of the study area. Mean air temperature has increased by 1.43°C, similar trends were also identified for maximum and minimum air temperature, which have increased by 1.06 and 1.54°C, respectively, while DTR exhibited a slight decreasing trend with a rate of about −0.09°C/(10 year). The annual mean relative humidity and sunshine duration exhibited a decreasing trend, with Kendall slope values of −0.99%/10 year and −7.797 h/10 year, respectively. Examination of long-range dependence showed that all climate variables exhibited strong persistence at annual scale except minimum air temperature. Detection of abrupt changes using nonparametric Mann–Kendall and Pettitt methods showed different results. Abrupt changes occurred in the 1980s and 2000s for annual precipitation using the nonparametric Mann–Kendall method, while no abrupt changes were detected using the Pettitt method. Abrupt changes of temperature and relative humidity took place in the early 1990s using the nonparametric Mann–Kendall method, which occurred in the late and mid 1980s using the Pettitt method, while abrupt changes of sunshine duration and DTR detected by two methods occurred in the similar period. The result will be helpful for local flood control and drought relief in urban planning and construction under future global climate change.

This paper addresses the problem of accurate estimation and rapid adaptation of abrupt frequency changes from noisy sinusoidal signals. A two‐filter adaptive algorithm is proposed to achieve the seemingly contradictory objectives. This algorithm is derived from an iterative batch procedure that has been proved to yield consistent and asymptotically Gaussian estimates for constant‐frequency estimation. These properties provide a basis for the detection of abrupt changes in the time‐varying frequency. Combining the high accuracy of narrow‐band/long‐memory filtering with the high adaptability of wide‐band/short‐memory filtering, the two‐filter approach is particularly suitable for tracking time‐varying frequencies that can be approximately modeled as piecewise‐constant functions of time. Simulation results are reported that justify the viability of the method.

The historical flood-level time series of the River Nile (AD 622–1470) is chosen to identify abrupt climate changes by applying global and local analysis techniques: the Mann–Kendall test and a non-hierarchical cluster analysis method to improve the Mann–Kendall test; a multiscale moving t-test with correction to the degree of freedom and an antisymmetric wavelet transform. The global estimates show three distinct epochs, AD 622–1078, 1079–1325 and 1326–1470, coinciding with larger scale climate changes: a relatively cool age, the Little Climatic Optimum of the Middle Ages, and an interim period before the Little Ice Age. The local estimates reveal the following results. The reference time of abrupt changes can be clearly identified, the associated time-scale coincides with the persistent anomaly period, and the maximum absolute t-value is statistically significant. There are about eight almost synchronous abrupt changes in the minimum and maximum River Nile flood levels, many of them are associated with 35–45 year persistence time-scales. An association of these short time-scales with those of interdecadal variability reported for the mid- and high-latitude sea-surface temperature of the North Atlantic is suggested, although information on phase coherence is not available. ©1997 by the Royal Meteorological Society. Int. J Climatol., 17: 1301–1315 (1997) (No. of Figures: 9 No. of Tables: 1 No. of

This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

The detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed. A cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test. For input design, the objectives are taken to be to decrease the detection time and, at the same time, to ensure a tolerable false alarm rate. Both off-line auxiliary inputs and on-line generation of the input signal by a linear output feedback are considered. The problem is first introduced for the two-hypotheses case and then the design techniques are extended to the general multiple-hypotheses case.

The problem of change detection in the poles of signals having unknown time varying zeroes is addressed. Instead of the test statistics based upon the standard likelihood ratio approach, which is of no help in this case because of the unknown zeroes, there is used a test statistics based on an identification method (instrumental variables), which is known to decouple the AR and MA coefficients of the model. The procedure has been used for change detection in modal characteristics of a single degree of freedom oscillator and of a vibrating structure, a multi-story reinforced concrete building, subject to a strong seismic motion.

The analysis of remote sensing data enables us to detect changes and monitor land surface temperature (LST). However, analysis of times series data poses some challenges, including weather conditions, seasonality and noise, that limit the effectiveness of change detection algorithms. While existing algorithms perform relatively well for detecting abrupt transitions, reliable detection of gradual changes is more difficult. In this paper, we formulate the problem of spatiotemporal LST detection as a statistical sequential change detection problem. LST images are modeled as stochastic processes, with temperature changes reflected as changes in the parameters (i.e., mean) of the process. A generalized likelihood ratio test is used to detect these changes and estimate the exact time/space where they occur. To minimize processing time and memory requirements, we represent LST images by their reduced dimensionality using direct cosine transformation followed by principal component analysis. Statistical sequential analysis is used to provide a unified mathematical framework for the detection of both abrupt and gradual changes in LST observations of Bridgeton Missouri landfill over 17 years.

The detection of abrupt changes in the generative parameters of time series data, known as Change-Point Detection (CPD), is a fundamental challenge in signal processing, data mining, and machine learning. While supervised deep learning methods have achieved remarkable success in this domain, they rely heavily on large-scale, accurately annotated datasets. In many real-world applications, such as industrial anomaly detection and physiological signal monitoring, obtaining frame-level labels is prohibitively expensive and requires expert domain knowledge. Conversely, unsupervised methods often suffer from high false-positive rates due to their inability to distinguish between noise and varying semantic states. To bridge this gap, this paper proposes a novel Semi-Supervised Change-Point Detection framework based on Consistency Training. We introduce a dual-branch architecture that enforces predictive consistency between original temporal sequences and their stochastically augmented views. By leveraging a rigorous set of temporal augmentations—including magnitude scaling, permutation, and time-warping—we enable the model to learn robust feature representations from unlabeled data while refining decision boundaries using a limited set of labeled examples. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach significantly outperforms state-of-the-art unsupervised methods and achieves competitive performance against fully supervised baselines using only 10% of the labeled data.

The paper shows a new approach to the dynamic detection of the M1 & M2 electromyographic stretch reflex evoked activity (SR EMG), based on the detection of abrupt changes within the SR EMG signal on a trial-by-trial basis in the time-domain, using the generalized likelihood ratio test (AGLR). This algorithm was experimented on 16 healthy subjects (8 males and 8 females). The method makes possible the detection of the M1 & M2 responses in single, individual trials, on a trial-by-trial basis. The novelty which the method brings consists in using only the time-domain to provide the real time detection of the M1 & M2 in specific experimental closed loop paradigms, comparing to the complexity and time-consumption while using frequency/scale domains.

Detection of Abrupt Changes: Theory and Application

This article proposes a new adaptive commissioning methodology for arc flash mitigation in steel manufacturer users considering the Tap-to-Tap varying current consumption. This process is achieved through adaptative protection settings computed to reduce the total clearing time of relays adding the restriction of the incident energy. The proposed methodology carries out the detection of abrupt changes in current consumption to detect Tap-to-Tap change in operation stages of electric arc furnaces. The application of this methodology is performed on a steel manufacturer user and shows the reduction of the incident energy values according to Tap-to-Tap operation cycle.

This study addresses the crucial detection of offsets in GNSS time series for accurate velocity estimations, vital in geosciences and engineering. Existing methods are challenged by correlated noise and can suffer from over-segmentation or high false positive rates. A novel methodology is proposed that combines a modified bilateral filter and an adapted implementation of the Pruned Exact Linear Time (PELT) algorithm, optimizing the detection of abrupt changes in the presence of complex noise. The technique was evaluated using a set of 3450 synthetic time series and 45 real time series from Global Navigation Satellite System (GNSS) stations located in Northern Europe. In the synthetic time series, the success threshold of 80 % was exceeded for the horizontal component with offsets of 1.2 mm, and the 90 % threshold for offsets of 1.4 mm. For the vertical component, 80 % success was achieved with offsets of 4 mm and 90 % with offsets of 5 mm. Regarding the real time-series, success percentages of 87.1 % were obtained for the East component, 74.4 % for the North component, and 74.2 % for the vertical component (Up). This hybrid technique enhances the identification of real offsets in GNSS time series, simplifying monitoring and paving the way for fully automated workflows.