Autocorrelated Processes Research Articles

On-line recognition of mixture control chart patterns using hybrid CNN and LSTM for auto-correlated processes

Statistical process control (SPC), designed to detect and identify process disturbances, is an effective quality control method for ensuring process stability. Owing to the growing automation of the industry, the manufacturing process can be autocorrelated. Engineer process control (EPC) is typically used to address autocorrelation. However, process disturbances can be offset by feedback compensation, making control chart patterns (CCPs) difficult to identify. Most studies on control chart pattern recognition (CCPR) techniques are based on a single abnormal control chart pattern (CCP). However, a mixture of CCPs can occur during real-world manufacturing processes. With the development of intelligent manufacturing systems, early detection of abnormal concurrent CCPs has become an important issue. In this study, a hybrid model combining a convolutional neural network (CNN) and long short-term memory (LSTM) in an online detection system was used to recognize the concurrent CCPR problem in SPC-EPC processes. The results showed that the average accuracy of the deep learning CNN-LSTM method was 99.83%, which was significantly better than that of the machine learning method. In addition, the running time of the CNN-LSTM model was shortened. In a comparison of online monitoring between the deep learning method and the machine learning method, the CNN-LSTM model for an online monitoring system identified abnormal concurrent patterns faster. Therefore, the proposed CNN-LSTM online monitoring scheme can be applied confidently and successfully to identify mixture CCPs in an SPC-EPC process.

Spectrum estimation for voiced speech using average weighted linear prediction

In many different areas, such as neurophysics, geophysics, and communication, it is vital to effectively handle signals when there is unwanted disturbance. Linear prediction (LP) methods provide precise modeling capabilities for various parametric models and are used in a wide range of fields such as predicting future data, compressing speech, analyzing spectra, filling in missing signals, and decreasing noise. LP is especially beneficial in speech processing systems. Speech analysis and synthesis greatly relies on spectral envelopes, which are closely connected to models of speech production and perception. However, the performance of the LP method may decline when limited information is involved in pitch synchronous analysis. In order to overcome this constraint, we developed the implementation of the Average Weighted Linear Prediction (AWLP) technique, which does not require the use of a window. The AWLP utilizes a signal of weighted prediction error acquired from the autocorrelation process of LP. By performing this action, it provides a more precise estimation of the power spectrum and coefficients used for vocal tract parametric models. Importantly, the effectiveness of the AWLP can be seen in both pitch synchronous and asynchronous analyses, which means it is appropriate for situations where segments are chosen randomly. We confirm the effectiveness of the AWLP technique by employing it on both synthetic voice and real speech. Additionally, we assess its effectiveness by comparing it to the direct autocorrelation technique and a modified autocorrelation (MA) approach. To sum up, the AWLP method presents a hopeful solution for reliable spectral analysis that addresses the divide between pitch synchronous and asynchronous situations.

Procedure for monitoring autocorrelated processes using LSTM Autoencoder

Procedure for monitoring autocorrelated processes using LSTM Autoencoder

Structural Damage Identification Based on Preprocessing Samples Mixed Training of Multi-Channel and Multi-Source Dynamic Response Data

Previous studies have shown that sampling processing and identification methods for neural networks damage identification in multi-channel and multi-source structural dynamic response data exhibit diversity, and the robustness and generalization issues of the model have not been effectively solved. This paper proposes a sample preprocessing technique and mixed training method suitable for multi-channel and multi-source dynamic response data to optimize the current structural damage identification methods based on neural networks. Through multi-dimensional discrete autocorrelation processing and Fourier transform, the preprocessed datasets from multiple sensors with multi-channel can access multi-channel CNN. Furthermore, the measured datasets from the actual structures are mixed with numerical simulation datasets before being used for neural network model training to address the model calibration and the imbalanced sample size under each classification label. The results of extensive model experiments and finite element verification of specimens show that the method performs outstandingly in detecting and identifying damage to simply supported beam structures using multi-channel CNN. The neural network model trained with preprocessed samples exhibits excellent robustness. The model using the mixed training method still performs well in identifying the accuracy of damage location and degree in simply supported beam structures after changing beam section and initial excitation. The method has certain generalization ability in detecting unknown damage in simply supported beam structures.

Monitoring the mean of autocorrelated data with long memory from cable production using one‐sided runs rules schemes with ARFIMA (1,d,1) model

AbstractClassical control charts were developed with the assumption that the quality characteristics being monitored are independent. However, observations from several time‐dependent processes, such as industrial or manufacturing, are bound to be autocorrelated such that their autocorrelations decay gradually (long memory) rather than exponentially (short memory). Runs rules monitoring schemes have been proposed in Statistical Process Control literature to monitor processes in the presence of autocorrelation by incorporating the autoregressive integrated moving average (ARIMA) class of models which can only handle autocorrelation with a short memory. This paper therefore incorporates the autoregressive fractionally integrated moving average (ARFIMA (1,d,1)) model into four one‐sided runs rules schemes to monitor the mean of an autocorrelated process with long memory. The performance of these four one‐sided schemes was assessed using average run length (ARL) and expected ARL (EARL) metrics. Based on the ARL and EARL of the improved runs rules (IRR) schemes, the IRR5‐of‐5 and IRR2‐of‐7 were found to issue an out‐of‐control signal faster than the corresponding standard runs rules (RR) schemes, RR5‐of‐5 and RR2‐of‐7, respectively. Also, the four one‐sided schemes IRR5‐of‐5, IRR2‐of‐7, RR5‐of‐5, and RR2‐of‐7 in their steady state condition perform better than their corresponding zero state condition. We further observed that as the fractional parameter d increases, the detection ability of the monitoring schemes reduces. The application of the four one‐sided schemes was demonstrated on the diameter of cable production.

DTMSgram: a novel optimal demodulation frequency band selection method for wheelset bearings fault diagnosis under wheel-rail excitation

Due to the influence of the wheel-rail excitation and complex transmission path, the fault signature of wheelset bearings is often obscured by complex background noise, which brings great challenges to the adaptive determination of the informative frequency band (IFB) in envelope analysis. In this paper, the vibration response characteristics of the axle box under wheel–rail excitation are revealed through full-scale bench tests. The experimental results show that tread damage will provoke periodic transient impacts and it has an obvious sparsity in the frequency domain. Inspired by this feature, a DTMSgram method is proposed to enhance the fault feature components of vibration signals through time-domain and frequency-domain noise reduction technology, and improve the accuracy of demodulation frequency band selection. Firstly, the amplitude spectrum of different weight coefficients is used to preprocess the vibration signal and adjust the full band component of the vibration signal. Then, the autocorrelation process is performed on each layer’s narrowband filtered signal envelope in kurtogram to further reduce noise interference from a time-domain perspective. Moreover, a two-dimensional color map is constructed showing the normalized squared envelope spectrum of the IFBs determined simultaneously from the modified signal. Finally, the effectiveness of the proposed method is verified by simulated signal and experimental data of three sets of full-size wheelset bearing systems. The analysis results indicate this proposed method can effectively overcome the influence of complex wheel–rail excitation interference and can diagnose multi-source faults simultaneously.

Derivation of correlation dimension from spatial autocorrelation functions.

Spatial complexity is always associated with spatial autocorrelation. Spatial autocorrelation coefficients including Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation process is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, a scaling exponent such as fractal dimension can be used to compensate for the shortcoming of characteristic length parameters such as Moran's index. This paper is devoted to finding an intrinsic relationship between Moran's index and fractal dimension by means of spatial correlation modeling. Using relative step function as spatial contiguity function, we can convert spatial autocorrelation coefficients into spatial autocorrelation functions. By decomposition of spatial autocorrelation functions, we can derive the relation between spatial correlation dimension and spatial autocorrelation functions. As results, a series of useful mathematical models are constructed, including the functional relation between Moran's index and fractal parameters. Correlation dimension proved to be a scaling exponent in the spatial correlation equation based on Moran's index. As for empirical analysis, the scaling exponent of spatial autocorrelation of Chinese cities is Dc = 1.3623±0.0358, which is equal to the spatial correlation dimension of the same urban system, D2. The goodness of fit is about R2 = 0.9965. This fractal parameter value suggests weak spatial autocorrelation of Chinese cities. A conclusion can be drawn that we can utilize spatial correlation dimension to make deep spatial autocorrelation analysis, and employ spatial autocorrelation functions to make complex spatial autocorrelation analysis. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes. The work may inspire new ideas for spatial modeling and exploration of complex systems such as cities.

Applied Bayesian structural health monitoring: Inclinometer data anomaly detection and forecasting

AbstractInclinometer probes are devices that can be used to measure deformations within earthwork slopes. This paper demonstrates a novel application of Bayesian techniques to real‐world inclinometer data, providing both anomaly detection and forecasting. Specifically, this paper details an analysis of data collected from across the entire UK rail network.Inclinometers are a standard tool of geotechnical site monitoring. Data from these instruments is often used in risk analysis and decision‐making. However, discerning anomalous data points and forecasting future behaviour from inclinometer data requires significant ‘engineering judgement’ (subjective appraisal). This is because the observational data is derived from complex physical phenomena and contains complex spatio‐temporal correlations. Additionally, the practical demands of data collected from remote sites over several years tends to introduce systematic errors. These issues make the interpretation of inclinometer data challenging.Practitioners have effectively two goals when processing monitoring data. The first is to identify any anomalous or dangerous movements, and the second is to predict potential future adverse scenarios by forecasting. In this paper we apply Uncertainty Quantification (UQ) techniques by implementing a Bayesian approach to anomaly detection and forecasting for inclinometer data. Subsequently, both costs and risks may be minimised by quantifying and evaluating the appropriate uncertainties. This framework may then act as an enabler for enhanced decision making and risk analysis.We show that inclinometer data can be described by a latent autocorrelated Markov process derived from measurements. This can be used as the transition model of a non‐linear Bayesian filter. This allows for the prediction of system states. This learnt latent model also allows for the detection of anomalies: observations that are far from their expected value may be considered to have ‘high surprisal’, that is they have a high information content relative to the model encoding represented by the learnt latent model.We successfully apply the forecasting and anomaly detection techniques to a large real‐world data set in a computationally efficient manner. Although this paper studies inclinometers in particular, the techniques are broadly applicable to all areas of engineering UQ and Structural Health Monitoring (SHM).

Robust design of ARMA and ACC charts for imperfect and autocorrelated processes under uncertainty

Occurring disruptions and faults violate the perfectness of a production process in determining Economic Production Quantity (EPQ). Integrating EPQ, Statistical Process Control (SPC), and maintenance terms has brought satisfactory outcomes for such an imperfect process. Under the violated independence assumption, the Autoregressive Moving Average (ARMA) chart has been applied in the integrated models. Under autocorrelation, the extended Acceptance control chart (ACC) has indicated significant reductions in costs. Nevertheless, it has not been applied to any integrated modeling yet. Until now, constant input factors have been considered for modeling imperfect and autocorrelated processes. Uncertainty in estimating those factors can deteriorate the effectiveness of models. We present the first robust design for imperfect and autocorrelated processes under uncertainty. We apply a particle swarm optimization algorithm to provide solutions. The investigations of simple and integrated modeling indicate that applying the ACCs causes better statistical and economic results. Also, a real-life application is presented.

Multivariate control charts for monitoring a bivariate correlated count process with application to meningococcal disease.

In recent years, with the increasing number and complexity of infectious diseases, the idea of using control charts to monitor public health and disease has been proposed. In this paper, we study multivariate control charts for monitoring a bivariate integer-valued autocorrelation process with bivariate Poisson distribution and select the optimal control scheme by comparing the performance of control charts. Furthermore, the meningococcal patient event in two states in Australia serves as an example to illustrate the application of these methods. The results show that the D exponentially weighted moving average control scheme can detect the changes in the mean value faster, which is a significant advantage.

Single and dual reference-free CUSCORE charts for detecting unknown patterned mean shifts

Most of the control charts in the literature focus on detecting constant mean shifts. In practice, dynamic and time-varying process mean shifts are prevalent in the monitoring of feedback-control and autocorrelated processes. The cumulative score (CUSCORE) charts have been proposed in the literature to detect dynamic and time-varying process shifts. One of such control charts is a reference-free CUSCORE (called RFCS-I) chart that may detect unknown patterned mean shifts effectively. In this paper, single and dual CUSCORE charts are developed to enable an efficient detection of unknown patterned mean shifts. The developed single CUSCORE chart, called the RFCS-II chart, is based on the control charting structure of the Crosier CUSUM (called CU-II) chart. Additionally, two RFCS-I charts are integrated with reflecting boundaries, while an integration of two RFCS-II charts is also made, to develop the dual RFCS-I (DRFCS-I) and dual RFCS-II (DRFCS-II) charts, respectively. In addition, the RFCS-I and RFCS-II charts are integrated to propose the mixed dual reference-free CUSCORE chart, called the MDRFCS chart. In essence, four CUSCORE charts, i.e. the RFCS-II, DRFCS-I, DRFCS-II and MDRFCS charts are suggested in this paper. The Monte Carlo simulation and a real application illustrate the superiority of these developed CUSCORE charts over their existing counterparts when detecting patterned mean shifts in terms of zero-state and steady-state relative mean indexes.

Economic design of residuals MEWMA control chart with variable sampling intervals and sample size

In order to improve the monitoring efficiency of the multivariable autocorrelation process and reduce the cost of process control, an economic design method of residual Multivariate Exponentially Weighted Moving Average (MEWMA) control charts with variable sample size and sampling intervals (VSSIs) was proposed. First, residual MEWMA control charts with VSSI were designed for monitoring multivariable autocorrelation processes. Second, the economic model of the VSSI residual MEWMA control chart was established, and a data example was given. The optimal design parameters of the control chart were obtained by using a genetic algorithm to minimize the expected cost per unit time. Third, using orthogonal experimental design and regression analysis, a sensitivity analysis of the economic model was carried out to get the relationship between the model parameters and the design parameters of the control chart. Finally, through the optimality analysis, it was verified that the proposed economic model was superior to the models established by the variable sampling intervals strategy and the variable sample size strategy and had less expected cost per unit time.

A Novel Scheme of Control Chart Patterns Recognition in Autocorrelated Processes

Control chart pattern recognition (CCPR) can quickly recognize anomalies in charts, making it an important tool for narrowing the search scope of abnormal causes. Most studies assume that the observations are normal, independent and identically distributed (NIID), while the assumption of independence cannot always be satisfied under continuous manufacturing processes. Recent research has considered the existence of autocorrelation, but the recognition rate is overestimated. In this paper, a novel scheme is proposed to recognize control chart patterns (CCPs) in which the inherent noise is autocorrelated. By assuming that the inherent noise follows a first-order autoregressive (AR (1)) process, the one-dimensional convolutional neural network (1DCNN) is applied for extracting features in the proposed scheme, while the grey-wolf-optimizer-based support vector machine (GWOSVM) is employed as a classifier. The simulation results reveal that the proposed scheme can effectively identify seven types of CCPs. The overall accuracy is 89.02% for all the autoregressive coefficients, and the highest accuracy is 99.43% when the autoregressive coefficient is on the interval (−0.3, 0]. Comparative experiments indicate that the proposed scheme has great potential to identify CCPs in autocorrelated processes.

Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart

Numerical evaluation of the average run length (ARL) when detecting changes in the mean of an autocorrelated process running on an exponentially weighted moving average (EWMA) control chart has received considerable attention. However, accurate computation of the ARL of changes in the mean of a long-memory model with an exogenous (X) variable, which often occurs in practice, is challenging. Herein, we provide an accurate determination of the ARL for long-memory models such as the fractionally integrated MAX processes (FIMAX) with exponential white noise running on an EWMA control chart by using an analytical formula based on an integral equation. From a computational perspective, the analytical formula approach is accomplished by solving the solution for the integral equation obtained via the Fredholm integral equation of the second kind. Moreover, the existence and uniqueness of the solution for the analytical formula were confirmed via Banach’s fixed-point theorem. Its efficacy was compared with that of the ARL derived by using the well-known numerical integral equation (NIE) technique under the same circumstances in terms of the ARL percentage accuracy and computational processing time. The percentage accuracy was 100%, which indicates excellent agreement between the two methods, and the analytical formula also required much less computational processing time. An example to illustrate the effectiveness of the proposed approach with a process involving real data running on an EWMA control chart is also provided herein. The explicit formula method offers an accurate determination of the ARL and a new approach for validating its computation, especially for long-memory scenarios running on EWMA control charts.

Generalization of Cointegration Arbitrage Based on GARCH Model, Improved by Marginal Probability Distribution

As the Russia Ukraine War broke out in February, 2022, a series of international sanctions led to a panic among international hot moneys and slumps in global stock markets. For such a volatile market, hedging strategy is in a position to avoid risks. In finance, the correlation among financial derivative is always a topical issue and investors are concerned about the statistical methods to model the volatility. Recent years, the rapid development in data science makes it possible to record and manipulate massive data of financial derivative series, of which activates statistical arbitrage, a hedging strategy by pairs trading. The most widespread method in practice is cointegration arbitrage and many experiments show that it can always generate positive profits. This paper introduces the backgrounds of statistical arbitrage and relative definitions in cointegration arbitrage like time series, stationary, autocorrelation process, integration and cointegration. Based on the features of financial derivative series, this paper also illustrates error correction model, ARCH model and GARCH model. Finally, this paper shows the current strategy of cointegration arbitrage and raises some improvement by marginal probability distribution.

Local projections, autocorrelation, and efficiency

It is well known that Local Projections (LP) residuals are autocorrelated. Conventional wisdom says that LP have to be estimated by OLS and that GLS is not possible because the autocorrelation process is unknown and/or because the GLS estimator would be inconsistent. I show that the autocorrelation process of LP can be written as a Vector Moving Average (VMA) process of the Wold errors and impulse responses and that autocorrelation can be corrected for using a consistent GLS estimator. Monte Carlo simulations show that estimating LP with GLS can lead to more efficient estimates.

Digital infrared chromatic aberration correction algorithm for a membrane diffractive lens based oncoherent imaging.

Aiming at the wide-spectrum chromatic aberration problem of membrane diffractive lenses, the concept of the digital chromatic aberration correction infrared imaging system was proposed. The principle of digital chromatic aberration correction was given, and the chromatic aberration correction of this system was completed on a computer, which is based on a wavelength-tunable laser local oscillator coherent detection detector. Compared with the chromatic aberration correction method for traditional lenses, this membrane diffractive optical system exhibited characteristics of small size, low weight, and low complexity. The digital chromatic aberration correction application conditions of this membrane diffractive optical system were analyzed. In addition, the main parameters and imaging simulation results were given. The center wavelength of this membrane diffractive optical system is 1.55µm, and its spectral range is 1.50-1.60µm. The application of autocorrelation processing to infrared complex images after digital chromatic aberration correction followed by incoherent accumulation of the received corrected complex images based on multiple stepping wavelengths could significantly improve the imaging signal-to-noise ratio.

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.