Dynamic Principal Component Research Articles

Gdpc: An R Package for Generalized Dynamic Principal Components

gdpc is an R package for the computation of the generalized dynamic principal components proposed in Peña and Yohai (2016). In this paper, we briefly introduce the problem of dynamical principal components, propose a solution based on a reconstruction criteria and present an automatic procedure to compute the optimal reconstruction. This solution can be applied to the non-stationary case, where the components need not be a linear combination of the observations, as is the case in the proposal of Brillinger (1981). This article discusses some new features that are included in the package and that were not considered in Peña and Yohai (2016). The most important one is an automatic procedure for the identification of both the number of lags to be used in the generalized dynamic principal components as well as the number of components required for a given reconstruction accuracy. These tools make it easy to use the proposed procedure in large data sets. The procedure can also be used when the number of series is larger than the number of observations. We describe an iterative algorithm and present an example of the use of the package with real data.

Gearbox Incipient Fault Detection Based on Deep Recursive Dynamic Principal Component Analysis

As a part of the energy transmission chain, gearboxes are considered as important components in rotating machines, and the gearbox failure results in costly economic losses. Therefore, it is necessary to detect the appearance of incipient gearbox faults by implementing an appropriate detected model. The incipient failure characteristics of the gearbox are weak and hidden in a set of time-varying series signals the vibration signals, which is difficult to effectively extract under the background of strong noise. The PCA method is not effective in detecting weak fault features in time-varying signals, so this paper proposes a method based on Deep Recursive Dynamic Principal Component Analysis (Deep RDPCA) to detect incipient faults in gearboxes. The proposed approach is modeled via both the deep decomposed theorems and time-varying dynamic model based on traditional PCA to extract characteristic of time-varying and weak fault information under the background of strong noise. The proposed method could get a better real-time reflection for changed system by introducing “Moving Window” technologies, so that the incipient fault of gearbox could be detected accurately, too. Finally, the effect of Deep RDPCA-based fault diagnosis is compared with the results of PCA, DPCA, RDPCA, Deep PCA, and Deep DPCA methods. It is concluded that the proposed method can effectively capture the time-varying relationship of process variables and accurately extract the weak fault characteristics in the vibration signal, which effectively improves the fault detection performance.

Abnormal node detection method for time-sharing heating energy consumption in multi-storey buildings based on drosophila algorithm

In order to solve the problem of high energy consumption of time-sharing heating in multi-storey buildings caused by abnormal node, it is necessary to study the detection method of abnormal node of heating energy consumption. Based on fruit flies algorithm of multi-storey building time-sharing heating energy consumption of the abnormal node detection method, using synchronous sequential PLD multi-storey building heating system of heating time-sharing data, put optimisation algorithm is introduced into EEMD algorithm, noise by flies optimisation calculation the corresponding threshold, remove the noise, the IMF component complete data denoising processing. Based on the recursive dynamic principal component analysis method, the detection model of abnormal heating energy consumption nodes is constructed to realise the detection of abnormal heating energy consumption nodes in multi-storey buildings. Experimental results show that the proposed method has good denoising effect, low false alarm rate and high detection rate.

Adaptive-learning model predictive control for complex physiological systems: Automated insulin delivery in diabetes

An adaptive-learning model predictive control (AL-MPC) framework is proposed for incorporating disturbance prediction, model uncertainty quantification, pattern learning, and recursive subspace identification for use in controlling complex dynamic systems with periodically recurring large random disturbances. The AL-MPC integrates online learning from historical data to predict the future evolution of the model output over a specified horizon and proactively mitigate significant disturbances. This goal is accomplished using dynamic regularized latent variable regression (DrLVR) approach to quantify disturbances from the past data and forecast their future progression time series. An enveloped path for the future behavior of the model output is extracted to further enhance the robustness of the closed-loop system. The controller set-point, penalty weights of the objective function, and constraints criteria can be modified in advance for the expected periods of the disturbance effects. The proposed AL-MPC is used to regulate glucose concentration in people with Type 1 diabetes by an automated insulin delivery system. Simulation results demonstrate the effectiveness of the proposed technique by improving the performance indices of the closed-loop system. The MPC algorithm integrated with DrLVR disturbance predictor has compared to MPC reinforced with dynamic principal component analysis linked with K-nearest neighbors and hyper-spherical clustering (k-means) technique. The simulation results illustrate that the AL-MPC can regulate the glucose concentrations of people with Type 1 diabetes to stay in the desired range (70–180) mg/dL 84.4% of the time without causing any hypoglycemia and hyperglycemia events.

Dynamic principal component analysis with missing values

Dynamic principal component analysis (DPCA), also known as frequency domain principal component analysis, has been developed by Brillinger [Time Series: Data Analysis and Theory, Vol. 36, SIAM, 1981] to decompose multivariate time-series data into a few principal component series. A primary advantage of DPCA is its capability of extracting essential components from the data by reflecting the serial dependence of them. It is also used to estimate the common component in a dynamic factor model, which is frequently used in econometrics. However, its beneficial property cannot be utilized when missing values are present, which should not be simply ignored when estimating the spectral density matrix in the DPCA procedure. Based on a novel combination of conventional DPCA and self-consistency concept, we propose a DPCA method when missing values are present. We demonstrate the advantage of the proposed method over some existing imputation methods through the Monte Carlo experiments and real data analysis.

Remaining useful life prediction of lubricating oil with dynamic principal component analysis and proportional hazards model

Lubricating oil contains a lot of tribological information of the machine and plays an important role in machine health. Oil degrades with serving time and causes severe wear afterwards, which is a complex dynamic process, and difficult to be accurately described by a single property. Therefore, the main purpose of deterioration prediction is to estimate the remaining useful life that the oil can still fulfill its functions by analyzing oil condition monitoring data. With a large amount of oil condition monitoring data collected, a vector autoregressive model is applied to the original oil data to describe the dynamic deterioration process. Then dynamic principal component analysis, an effective dimensionality reduction method, is employed to obtain the principal components capturing the most information of the oil data. The proportional hazards model is then built to calculate the failure risk of the lubricating oil based on the condition monitoring information, where its baseline function represents the aging process assuming to follow the Weibull distribution and its positive link function represents the influence of covariates (the principal components) on the failure risk. Finally, the remaining useful life prediction of lubricating oil can be obtained by explicit formulas of the characteristics such as the conditional reliability function and the mean residual life function. This work provides an approach to assess the health of lubricating oil, and a guidance for oil maintenance strategy.

Dynamic principal component regression for forecasting functional time series in a group structure

ABSTRACTWhen generating social policies and pricing annuity at national and subnational levels, it is essential both to forecast mortality accurately and ensure that forecasts at the subnational level add up to the forecasts at the national level. This has motivated recent developments in forecasting functional time series in a group structure, where static principal component analysis is used. In the presence of moderate to strong temporal dependence, static principal component analysis designed for independent and identically distributed functional data may be inadequate. Thus, through using the dynamic functional principal component analysis, we consider a functional time series forecasting method with static and dynamic principal component regression to forecast each series in a group structure. Through using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database [(2019). National Institute of Population and Social Security Research. Available at http://www.ipss.go.jp/p-toukei/JMD/index-en.asp (data downloaded on 14 August 2018)], we investigate the point and interval forecast accuracies of our proposed extension, and subsequently make recommendations.

Pattern recognition in tornado-like vortices at different swirl ratios

A new paper examines the dynamic structure of tornado-like vortices at different swirl ratios using a novel dynamic principal component analysis technique.

Non-transformed Principal Component Technique on Weekly Construction Stock Market Price

The fast-growing urbanization has contributed to the construction sector becoming one of the major sectors traded in the world stock market. In general, non-stationarity is highly related to most of the stock market price pattern. Even though stationarity transformation is a common approach, yet this may prompt to originality loss of the data. Hence, the non-transformation technique using a generalized dynamic principal component (GDPC) were considered for this study. Comparison of GDPC was performed with two transformed principal component techniques. This is pertinent as to observe a larger perspective of both techniques. Thus, the latest weekly two-years observations of nine constructions stock market price from seven different countries were applied. The data was tested for stationarity before performing the analysis. As a result, the mean squared error in the non-transformed technique shows eight lowest values. Similarly, eight construction stock market prices had the highest percentage of explained variance. In conclusion, a non-transformed technique can also present a better resultoutcome without the stationarity transformation.

Reflectance spectra recovery from a single RGB image by adaptive compressive sensing

A new adaptive compressive sensing-based method is proposed for recovering spectral reflectance from a single RGB image by using dynamic principal components that are calculated from the dynamic eigenvector subspace. The dynamic eigenvector subspace is formed by its similarity to the RGB trichromatic values of the original and not just the neighbors to the target. Unlike recovering spectral reflectance using fixed principal components, the novelty of the proposed method is the use of the dynamic principal component by applying an adaptive compressive sensing method under the dynamic eigenvector subspace. The effectiveness of the proposed and the existing methods are compared by reviewing the spectral recovery accuracy under different illuminants and cameras. As the spectral recovery results show, the proposed method is an effective spectral reflectance recovery method.

Consistency of generalized dynamic principal components in dynamic factor models

This note shows that when the data follows a dynamic factor model, the reconstruction provided by the generalized dynamic principal components introduced in Peña and Yohai (2016) converges in mean square to the common part of the factor model as both the number of time series and the number of observations diverge to infinity at any rate. A simulation study shows that the method indeed provides accurate estimations of the common part, having a mean square error smaller than competitors.

Concurrent Fault Detection and Anomaly Location in Closed-Loop Dynamic Systems With Measured Disturbances

Most data-driven process monitoring approaches consider the fault detection as a binary classification issue: normal or abnormal. All deviations from the nominal operating condition can trigger the same alarms. They fail to distinguish different fluctuation patterns and locate the positions of anomalies, such as the normal deviations in operating conditions, sensors faults, actuator faults, and process faults. A new process monitoring strategy based on orthogonal decomposition (OD) is proposed for the concurrent detection and location of different deviation patterns. OD is performed to discriminate the dynamics of data driven by measured disturbances and unmeasured disturbances in the same control system. This way, the original variable space is decomposed into the deterministic subspace and stochastic subspace. A dynamic principal component analysis-based subspace identification technique is used to construct the monitoring indices in the deterministic and stochastic subspaces, respectively. Two case studies show the validity of the OD-based process monitoring approach. Note to Practitioners —Fault diagnosis based on process data models always focused on analyzing variables’ contributions to the anomaly in the past practice. But it is frequently difficult to decide the root causes just using the variables’ contributions because different faults may induce a similar variation of the same variable. This paper provides a new scheme to locate the faulty components, including the sensor faults, actuator faults, process faults, and disturbance variations. It is more pertinent to learn about the fault locations than variables’ contributions. Moreover, by locating faults first and then figuring out variables’ contributions to a specific location, more detailed and precise diagnosis conclusions can be drawn when being compared with the results of using the variables’ contributions in a global system. This new method is purely data driven and it has no demand for complex process knowledge.

DYNAMIC PRINCIPAL COMPONENT REGRESSION: APPLICATION TO AGE-SPECIFIC MORTALITY FORECASTING

AbstractIn areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be treated as a discrete or continuous variable, a dimension reduction technique, such as principal component analysis (PCA), is often implemented. However, in the presence of moderate-to-strong temporal dependence, static PCA commonly used for analyzing independent and identically distributed data may not be adequate. As an alternative, we consider a dynamic principal component approach to model temporal dependence in a time series of curves. Inspired by Brillinger’s (1974, Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston) theory of dynamic principal components, we introduce a dynamic PCA, which is based on eigen decomposition of estimated long-run covariance. Through a series of empirical applications, we demonstrate the potential improvement of 1-year-ahead point and interval forecast accuracies that the dynamic principal component regression entails when compared with the static counterpart.

Forecasting Multiple Time Series With One-Sided Dynamic Principal Components

We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models. Supplementary materials for this article are available online.

Cryptocurrency Risks and Asset Allocation: What do Quantile Regressions, Spectral Analysis, and M-GARCH-based Dynamic Principal Components Say?

Cryptocurrency Risks and Asset Allocation: What do Quantile Regressions, Spectral Analysis, and M-GARCH-based Dynamic Principal Components Say?

Degradation Data-Driven Time-To-Failure Prognostics Approach for Rolling Element Bearings in Electrical Machines

Time-to-failure (TTF) prognostic plays a crucial role in predicting remaining lifetime of electrical machines for improving machinery health management. This paper presents a novel three-step degradation data-driven TTF prognostics approach for rolling element bearings (REBs) in electrical machines. In the degradation feature extraction step, multiple degradation features, including statistical features, intrinsic energy features, and fault frequency features, are extracted to detect the degradation phenomenon of REBs using complete ensemble empirical mode decomposition with adaptive noise and Hilbert–Huang transform methods. In degradation feature reduction step, the degradation features, which are monotonic, robust, and correlative to the fault evolution of the REBs, are selected and fused into a principal component Mahalanobis distance health index using dynamic principal component analysis and Mahalanobis distance methods. In TTF prediction step, the degradation process and local TTF of the REBs are observed by an exponential regression-based local degradation model, and the global TTF is predicted by an empirical Bayesian algorithm with a continuous update. A practical case study involving run-to-failure experiments of REBs on PRONOSTIA platform is provided to validate the effectiveness of the proposed approach and to show a more accurate prediction of TTF than the existing major approaches.

Time-Varying General Dynamic Factor Models and the Measurement of Financial Connectedness

We propose a new time-varying Generalized Dynamic Factor Model for high-dimensional, locally stationary time series. Estimation is based on dynamic principal component analysis jointly with singular VAR estimation, and extends to the locally stationary case the one-sided estimation method proposed by Forni et al. (2017) for stationary data. We prove consistency of our estimators of time-varying impulse response functions as both the sample size T and the dimension n of the time series grow to infinity. This approach is used in an empirical application in order to construct a time-varying measure of financial connectedness for a large panel of adjusted intra-day log ranges of stocks. We show that large increases in long-run connectedness are associated with the main financial turmoils. Moreover, we provide evidence of a significant heterogeneity in the dynamic responses to common shocks in time and over different scales, as well as across industrial sectors.

Classification of Profit-Based Operating Regions for the Tennessee Eastman Process using Deep Learning Methods

Abstract The focus of this work is on the classification of an input-design space into different regions of input conditions that result in different corresponding ranges of productivity costs in the Tennessee Eastman Process (TEP). Although similar classification tasks had been previously carried out using linear multivariate statistical data analysis methods, these are of limited efficacy when dealing with highly non-linear dynamics. In this work, we present two Deep Learning Tools for classification: using either supervised learning or un-supervised learning. For classification with supervised learning a Recurrent Neural Network (RNN) known as Long Short-Term Memory (LSTM) is trained on normalized training data. Since deep learning networks generally involve a large number of nodes and parameters an algorithm named Sequential Layer-wise Relevance Propagation (SLRPFP) is proposed for selecting the relevant inputs and for pruning the LSTM network such that the test accuracy at each step is maintained or even improved. For classification with unsupervised learning, main features from the input dataset are first extracted using an Autoencoder. Then a Multi-dimensional Support Vector Machines (MSVM) model is applied to the features identified by the autoencoder. The performance of the proposed supervised and unsupervised deep learning approaches are compared to an approach that combines linear Dynamic Principal Component Analysis (DPCA) and a MSVM based classification and conclusions are drawn on the relative advantages of the deep learning methods.

Performance Analysis of Dynamic PCA for Closed-Loop Process Monitoring and Its Improvement by Output Oversampling Scheme

The performance of dynamic principal component analysis (DPCA)-based fault detection and diagnosis in a closed-loop system is studied and its improvement by the output oversampling scheme is proposed in this paper. By the subspace decomposition technique, DPCA with the closed-loop data for fault detection does not perform better than DPCA with the open-loop data. Moreover, using fault reconstruction based on DPCA to determine the root cause would also become invalid in the closed loop. To eliminate the adverse effect of feedback control on the performance of the DPCA model, a new algorithm that directly constructs DPCA based on the closed-loop data is investigated using the output oversampled data without excitations in the reference signals. The associated enhanced characteristics of the sampled data in the output oversampling scheme are analyzed. A simulated continuous stirred tank heater illustrates that the proposed algorithm can significantly improve the DPCA performance of process monitoring and fault reconstruction in closed-loop systems.

Parallel quality-related dynamic principal component regression method for chemical process monitoring

Traditional quality-related process monitoring mainly focuses on the magnitude change of the quality variables caused by additive faults. However, the abnormal fluctuations in the quality variables caused by multiplicative faults are often overlooked. In this paper, a novel parallel dynamic principal component regression (P-DPCR) algorithm is proposed to monitor the changes in the magnitude and fluctuation of the quality variables simultaneously. Firstly, in order to eliminate the interference of quality-unrelated variables, the quality-related process variables are selected on the basis of correlation analysis. Secondly, the dynamic extension and moving window are carried out for process variables and quality variables, in which the dynamic variables space (called X-space/Y-space) and the variance space (called VX-space/VY-space) are constructed. Afterwards, double quality-related statistics based on the regression model of these four spaces are given, and the comprehensive monitoring decision can be obtained. Finally, two numerical cases and the Tennessee Eastman process are used to show the effectiveness of the proposed method.