Autocorrelated Processes Research Articles

Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation (LFM) signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio (SNR), a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper. This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency, and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator. On this basis, the corresponding relationship between the reference frequency of the frequency-aligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method, and the frequency information of the LFM signal is determined. Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of −25 dB.

Distribution-free multivariate time-series monitoring with analytically determined control limits

We consider the problem of detecting a shift in the mean of a multivariate time-series process with general marginal distributions and general cross- and auto-correlation structures. We propose a distribution-free monitoring procedure that does not need model fitting or trial-and-error calibration for control limits, which makes the procedure convenient to be implemented when a facility consists of many processes to be monitored. The main idea is to convert each observation vector into a one-dimensional T 2 quantity that captures cross-correlation. The T 2 quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the T 2 quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three competing procedures on simulated data with various cross- and auto-correlation and real data from a wafer etching process. The proposed procedure delivers actual in-control average run lengths close to the target and shows comparable or better performance in detecting a shift in mean than the competitors.

Moho reflections within seismic noise autocorrelations

The noise recorded at a seismic station has information about some properties of the medium such as their discontinuities. The depth of these changes in velocity can be retrieved using auto-correlation and stacking methods applied to the seismic noise. We developed a new method to constrain Moho reflections hidden within the autocorrelation of seismic noise. This is done by filtering the data in different frequency bands (each one defined by a central frequency), applying the auto-correlation and stacking process per central frequency and finally stacking the frequencies of interest. Synthetic tests showed that phases associated with a discontinuity at depth arrive at the same lag time across different frequencies, while side lobes and constructive interactions of the random noise have time shifts in the lag time. We tested the method using data from the MASE array installed in Central Mexico and the results show a good agreement with previous works. We found that exploring the frequency content with different bandwidth filters and stacking only those with useful information helps to improve the SNR and to find the phase associated with the Moho discontinuity at depth.

Change-Point detection for autocorrelated multivariate Poisson processes

ABSTRACT Statistical process control for count data has attracted increasing attention in recent years. The need for efficient control charts suitable for autocorrelated multivariate count processes is well recognized. However, there is a scarcity of research aiming to take into account the autocorrelation among the multivariate count data. We are motivated to study the Phase I analysis of autocorrelated multivariate Poisson processes to detect and estimate change points in reference datasets. A change-point method is proposed based on the multivariate Poisson INAR(1) model by integrating generalized likelihood ratio tests with the binary segmentation procedure. A diagnostic procedure for pinpointing the location of the change point is also discussed. Our simulation results show that the proposed method has a better performance than the benchmark method, across a range of possible shifts, in the detection effectiveness and diagnostic accuracy. Furthermore, a real example from the manufacturing industry is used to illustrate the implementation steps of the proposed method.

How to find the variables causing outliers in a multivariate autocorrelated process control: a study in simulation and an extruder machine

How to find the variables causing outliers in a multivariate autocorrelated process control: a study in simulation and an extruder machine

A GLMM approach for combining multiple relative abundance surfaces

Abstract Spatio‐temporal maps of organismal density or relative abundance are fundamental to many applications in conservation and ecology. There are often a number of data sources to inform species maps, including citizen science monitoring programs, remote sensing, geolocation data from satellite‐tagged animals and formal scientific surveys. In these cases, it may be desirable to come up with a single map integrating all data sources. We introduce a novel two‐step method for combining inference about relative abundance maps using multiple data sources. Log‐scale relative abundance surfaces are first estimated from individual data sets, and resultant surfaces are then treated as ‘data’ within a generalized linear mixed model framework with a spatially autocorrelated mean process. We also introduce generalizations allowing data misalignment and predictive processes to decrease computational burden. Using simulation, we show that our approach frequently outperfoms other approaches, including basing inference on a single surface, or taking a simple arithmetic mean (although the arithmetic mean performs well when there are few surfaces). We then demonstrate our method using citizen science and satellite‐tracking data of Steller sea lions in Alaska. In this case, relative abundance surfaces consisted of an effort‐adjusted map developed from platform‐of‐opportunity sightings and a utilization distribution developed from geolocation records. The resulting combined surface represented a compromise between single‐data source predictions. Our approach should be useful for ecologists seeking to reconcile alternative species distribution maps, particularly when individual surfaces are prone to bias, when there is no obvious common currency (e.g. point process), or when computational demands preclude a fully integrated analysis.

Multichannel Clutter Modeling, Analysis, and Suppression for Missile-Borne Radar Systems

When a missile-borne radar system works in downward-looking surveillance mode, the broadened ground clutter signal in virtue of platform high-speed motion will be received by the radar receiver, which will cause difficulty in moving target detection and attacking. Unlike airborne and spaceborne platforms, a missile-borne platform exhibits some unique motion characteristics, such as diving, spinning, and coning, causing the clutter space–time distribution property significantly different from those of airborne and spaceborne radar platforms. In addition, the forward target striking requirements make the missile-borne clutter space–time spectrum further exhibit the severe range-dependent property. To deal with these issues, accurate motion modeling of a missile-borne radar platform is first carried out in this article, where the complex platform motions including forward-looking diving, spinning, and coning are considered. Then, the autocorrelation processing combined with iterative adaptive approach is applied to estimate the clutter angle-Doppler center frequencies, so as to effectively realize the clutter nonstationary compensation along spatial and temporal directions. Finally, a time-domain sliding window-based subspace projection method is proposed to achieve the robust clutter suppression. Both simulation and real-measured radar data processing results are presented to validate the effectiveness and feasibility of the proposed algorithm.

A neural network-based control chart for monitoring and interpreting autocorrelated multivariate processes using layer-wise relevance propagation

Recent advances in sensing and information technology are enabling multivariate sensory data from industrial equipment to be collected at a high sampling frequency. The resulting data streams often exhibit strong autocorrelation. In this study, we propose a neural network-based residual control chart to monitor the autocorrelated multivariate processes for real-time detection of abnormal equipment performance. Furthermore, we propose an interpretation method, based on layer-wise relevance propagation (LRP), to identify the responsible variable when an out-of-control condition is detected by the control chart. We compare the proposed techniques with several existing methods. Numerical studies and a real-data application demonstrate that the proposed method has good monitoring performance and can provide effective interpretation results. The proposed methods can be applied broadly for system condition monitoring and change detection in a variety of industrial systems applications.

Joint non-parametric estimation of mean and auto-covariances for Gaussian processes

Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc.1

Microtremor array method using spatial autocorrelation analysis of Rayleigh-wave data

Microtremor array measurements, and passive surface wave methods in general, have been increasingly used to non-invasively estimate shear-wave velocity structures for various purposes. The methods estimate dispersion curves and invert them for retrieving S-wave velocity profiles. This paper summarizes principles, limitations, data collection, and processing methods. It intends to enable students and practitioners to understand the principles needed to plan a microtremor array investigation, record and process the data, and evaluate the quality of investigation result. The paper focuses on the spatial autocorrelation processing method among microtremor array processing methods because of its relatively simple calculation and stable applicability.Highlights1. A summary of fundamental principles of calculating phase velocity from ambient noise2. General recommendations for MAM data collection and processing using SPAC methods3. A discussion of limitations and uncertainties in the methods

Desensitized control charts with operational importance for autocorrelated processes

ABSTRACT Organizations that achieved higher capabilities to meet expectations by successfully implementing quality improvement plans can make adjustments to process monitoring without any losses for customers. This approach may reduce costs due to desensitization in monitoring. In this regard, the acceptance control chart (ACC) under the assumptions of independence and normality has already been introduced. However, in practice, particular correlation patterns can be extracted among samples that violate the assumption of independence. Autocorrelation reduces the performance of traditional control charts. In the present study, three types of ACC are extended for monitoring the mean of the most widely used autocorrelated processes. The performance of the proposed charts is evaluated using statistical measures. It is found that the residual-based exponentially weighted moving average ACC (R-EWMA-ACC) has the best performance. Also, two numerical examples illustrate its application. Moreover, optimizing the economic-statistical model indicates that the R-EWMA-ACC spends less than the ARMA control chart.

The tales that the distribution tails of non-Gaussian autocorrelated processes tell: efficient methods for the estimation of the k-length block-maxima distribution

ABSTRACT The focal point of this work is the estimation of the distribution of maxima without the use of classic extreme value theory and asymptotic properties, which may not be ideal for hydrological processes. The problem is revisited from the perspective of non-asymptotic conditions, and regards the so-called exact distribution of block-maxima of finite-sized k-length blocks. First, we review existing non-asymptotic approaches/models, and introduce an alternative and fast model. Next, through simulations and comparisons (using asymptotic and non-asymptotic models), involving intermittent processes (e.g. rainfall), we highlight the capability of non-asymptotic approaches to model the distribution of maxima with reduced uncertainty and variability. Finally, we discuss an alternative use of such models that concerns the theoretical estimation of the multi-scale probability of obtaining a zero value. This is a useful finding when the scope is the multi-scale modelling of intermittent hydrological processes (e.g. intensity–duration–frequency models). The work also provides step-by-step recipes and an R package.

Deep learning-based automatic optical inspection system empowered by online multivariate autocorrelated process control

Deep learning-based automatic optical inspection system empowered by online multivariate autocorrelated process control

An SVM-GA based monitoring system for pattern recognition of autocorrelated processes

An SVM-GA based monitoring system for pattern recognition of autocorrelated processes

Literature Review on Control Charts for Autocorrelated Processes

This research aims to present a literature review (LR) on control charts for autocorrelated processes, intending to contribute to the scientific knowledge of the process management area. The article was constructed having a research question defined ex-ante, elaborated based on the literature, where a research protocol adapted from Tranfield, Denyer, and Smart (2003) was systematized according to the methodological rigor demanded in the literature review, which resulted in the composition of the research corpus. The research corpus was evaluated in detail using the bibliometric packages HistCite, VOSviewer, package R and Iramuteq. It was evaluated the validity of the 3 bibliometric laws were verified: Lotka's Law, Bradford's Law, and Zipf's Law based on the authors’ citation and co-citation techniques. This study is considered as relevant and original since it is the first literature review on control charts for autocorrelated processes. The results confirmed the 3 classical bibliometric laws for the researched corpus. As a practical implication, this review provides support for quality management scholars to unlock potential research gaps. The main limitation of the work refers to the composition of the textual corpus, given that databases of national journals were not consulted due to the difficulty in terms of compatibility of the software used in this research.

Data Normalization and Anomaly Detection in a Steel Plate-Girder Bridge Using LSTM

Modal properties are recognized as indicators reflecting structural condition in structural health monitoring (SHM). However, changing environmental and operational variables (EOVs) cause variability in the identified modal parameters and subsequently obscure damage effects. To address the issue caused by EOV-related variability, this study investigated the variability of modal frequencies in long-term SHM of a steel plate-girder bridge. A Bayesian fast Fourier transform (FFT) method was used for operational modal analysis in a probabilistic viewpoint. Bayesian linear regression (BLR) and Gaussian process regression (GPR) models were utilized to capture the variability in the identified most probable values (MPVs) of modal frequencies as temperature-driven models, and the limitation of these models for data normalization with latent EOVs is discussed. To overcome the interference of latent EOVs indirectly, a long short-term memory (LSTM) network was established to trace the variability as an autocorrelated process, with a traditional seasonal autoregressive integrated moving average (SARIMA) model as a benchmark. Finally, an anomaly detection method based on residuals of one-step-ahead predictions by LSTM was proposed associating with the Mann-Whitney U-test.

Statistical design of an adaptive synthetic X¯$\bar{X}$ control chart for autocorrelated processes

AbstractThis paper aims to design a variable parameters synthetic control chart for first‐order AR(1) autocorrelated data following a Gaussian process. To improve the statistical performance in detecting small changes and maintaining a low false alarm rate, the variable parameters control chart was combined with the Conforming Run Length (CRL) sub‐chart to determine when to implement tight or relaxed control and intervene to identify an assignable cause. The statistical design of the proposed chart was performed under a discrete‐time Markov chain approach and a non‐linear programming mathematical model to obtain, using a genetic algorithm (GA), the values of the design parameters that minimise the average time to signal the out‐of‐control state (). A sensitivity analysis was performed to examine the behaviour of the in the face on changes in the parameters. Also, a performance evaluation was conducted to compare the proposed chart with other adaptive synthetic charts, the synthetic control chart and the chart developed by Costa and Machado. Our results indicate that this proposal is faster to detect small changes in the process mean considering the autocorrelation of the data.

On-line Recognition of Abnormal Patterns in Bivariate Autocorrelated Process Using Random Forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time. Meanwhile, the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics. This goes against the statistical I.I.D assumption in using the multivariate control charts, which may lead to the performance of multivariate control charts collapse soon. Meanwhile, the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation, and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities. This study proposed a pattern recognition model using Random Forest (RF) as pattern model to detect and identify the abnormalities in bivariate autocorrelated process. The simulation experiment results demonstrate that the model is superior on recognition accuracy (RA) (97.96%) to back propagation neural networks (BPNN) (95.69%), probability neural networks (PNN) (94.31%), and support vector machine (SVM) (97.16%). When experimenting with simulated dynamic process data flow, the model also achieved better average running length (ARL) and standard deviation of ARL (SRL) than those of the four comparative approaches in most cases of mean shift magnitude. Therefore, we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process. Although bivariate autocorrelated process is focused in this study, the proposed model can be extended to multivariate autocorrelated process control.

Dual CUSUM Charts for Monitoring Autocorrelated AR (1) Processes Mean With s-Skipping Sampling Scheme

In statistical process monitoring, it is often assumed that the sequential observations generated by processes are independent and identically distributed (iid). However, in real practice, these observations tend to exhibit an autocorrelation pattern. Thus, an autocorrelated process yields misleading results in terms of a high false alarm rate and slow detection of process changes if employing iid-based designed monitoring schemes. Therefore, in this article, we propose the dual cumulative sum (DCUSUM) and dual Crosier’s CUSUM (DCCUSUM) mean charts for monitoring the autocorrelated processes using a first-order autoregressive model. Monte Carlo simulations are extensively used to compute the performance measures: the average run length, standard deviation run length, extra quadratic loss, and relative average run length of the two-sided DCUSUM and DCCUSUM charts under both the zero-state and steady state cases. It is observed that as the level of autocorrelation increases, the performance of the studied charts deteriorates. Thus, a s-skipping sampling scheme is incorporated to reduce the negative effect of autocorrelation. To demonstrate the effect of autocorrelation and highlight implications further, a simulated dataset with a shift in the process mean is considered.

Long-Distance Detection for Periodic Vibration Signal in Φ-OTDR System Using Global Phase Demodulation Method

In order to overcome the limitation of weak intensity of Rayleigh backward scattering signal for long-distance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Phi } $ </tex-math></inline-formula> -OTDR system, a global phase demodulation method is proposed to extend the sensing distance without additional optical amplification. The localization limitation of conventional difference cumulative average algorithm is firstly analyzed. The global phase demodulation is carried out for all the signals on the whole sensing fiber. The autocorrelation processing is then realized to obtain the autocorrelation curves, on which the difference values between two instants can be used to locate the position of vibration signal. Experimental results show that according to the characteristics of autocorrelation curves, the vibration signal and noise signal can be distinguished. The sinusoidal signal with a frequency of 5 Hz and the third harmonic signal with the frequency of 5 Hz, 10 Hz, 15 Hz can be successfully located on the sensing fiber with the length of 90 km, without additional optical amplification. This method can achieve the long-distance detection for periodic vibration signal in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Phi } $ </tex-math></inline-formula> -OTDR system.