Dynamic Principal Component Research Articles

Statistical modeling of the power grid from a wind farm standpoint

In this study, we derive a statistical model of a power grid from the wind farm's standpoint based on dynamic principal component analysis. The main advantages of our model compared to the previously developed models are twofold. Firstly, our proposed model benefits from logged data of an offshore wind farm over several years which results in the development of a useful model for practical purposes. Secondly, the derived model is computationally inexpensive. Considering an arbitrary wind turbine generator, we show that the behavior of the power grid at the connection point can be represented by 4 out of 9 registered variables, i.e. 3-phase voltages, 3-phase currents, frequency, and generated active and reactive powers. We further prove that the dynamic nature of the system can be optimally captured by a time lag shift of two samples. To extend the derived model of a wind turbine generator to a wind farm, we propose an algorithm that optimally combines the principal components and scores. The principal components are estimated by the optimization of a cost function based on the modeling error while the scores are selected corresponding to the worst case scenario among the wind turbine generators. Our results show that the optimized principal components result in the modeling error less than 5% and the selected scores cover the variance of the data with probability higher than 95% among all generators in the wind farm.

Do sovereign rating announcements affect emerging market exchange rate correlations? A multivariate DCC-GARCH approach

ABSTRACTThis article investigates the effects of sovereign credit rating announcements on time-varying exchange rate return correlations for a sample of 11 emerging market countries over the period 2002–2015. The data set covers daily exchange rates and long-term foreign currency sovereign ratings, outlooks and watch list. The pairwise time-varying correlations are derived by corrected Dynamic Conditional Correlation (cDCC) modelling which is a member of multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models family. Furthermore, to capture the global factor effect, a dynamic-weighted index is created by using dynamic principal component (DPC) analysis. Findings suggest that some of the emerging market exchange rate co-movements are affected by rating announcements. Upgrades of Moody’s and downgrades of Fitch lead to spillovers. Main source of these spillovers are sovereign credit rating changes of European countries, especially Czech Republic and Turkey. Countries with high amount of external debt, large current account deficit and speculative grade are more prone to be influenced by announcements on a foreign country’s long-term sovereign rating.

Data-driven root cause diagnosis of faults in process industries

Data driven fault detection and diagnosis methods become more and more attractive in modern industries especially process industries. They can not only guarantee safe operation but also greatly improve product quality. For example, dynamic principal component analysis models and reconstruction based contribution are widely applicable in many occasions. However, there is one issue which does not receive enough attention, namely locating the root cause of a fault when it occurs. In this paper, a framework of root cause location is proposed to address this issue, including both stationary faults and nonstationary faults. A case study on Tennessee Eastman process is used to demonstrate the usage and effectiveness of these approaches. Results show the proposed framework is valid.

Online monitoring method for multiple operating batch processes based on local collection standardization and multi‐model dynamic PCA

AbstractTo handle multiple operations and non‐Gaussian problems which widely exist in complex industry processes, a new online monitoring method for multi‐operation batch processes is proposed by combing local collection standardization and multi‐model dynamic principal component analysis (LCS‐MMDPCA). Since a series of operations are often manually manipulated by operators, in general, the statistics of each batch data do not follow Gaussian distribution, which results in a failure for the construction of a multivariate statistical model. To target multiple operations and non‐Gaussian problems, we first split the complex batch processes into a sequence of stages. Subsequently, the data in each stage are clustered according to the operations. Then, we exploit the Local Collection Standardization (LCS) method to make the data belonging to the same cluster obey Gaussian distribution. At last, we adopt MMDPCA to model the complex industry processes with multiple operations and non‐Gaussian features. Experimental results on fault detection in ladle furnace steelmaking process showed the advantages of the proposed method in comparison to multiway kernel principal component analysis (MKPCA) and multiway dynamic principal component analysis (MDPCA).

Generalized Dynamic Principal Components

ABSTRACTBrillinger defined dynamic principal components (DPC) for time series based on a reconstruction criterion. He gave a very elegant theoretical solution and proposed an estimator which is consistent under stationarity. Here, we propose a new enterally empirical approach to DPC. The main differences with the existing methods—mainly Brillinger procedure—are (1) the DPC we propose need not be a linear combination of the observations and (2) it can be based on a variety of loss functions including robust ones. Unlike Brillinger, we do not establish any consistency results; however, contrary to Brillinger’s, which has a very strong stationarity flavor, our concept aims at a better adaptation to possible nonstationary features of the series. We also present a robust version of our procedure that allows to estimate the DPC when the series have outlier contamination. We give iterative algorithms to compute the proposed procedures that can be used with a large number of variables. Our nonrobust and robust procedures are illustrated with real datasets. Supplementary materials for this article are available online.

Canonical correlation analysis based fault diagnosis method for structural monitoring sensor networks

The health conditions of in-service civil infrastructures can be evaluated by employing structural health monitoring technology. A reliable health evaluation result depends heavily on the quality of the data collected from the structural monitoring sensor network. Hence, the problem of sensor fault diagnosis has gained considerable attention in recent years. In this paper, an innovative sensor fault diagnosis method that focuses on fault detection and isolation stages has been proposed. The dynamic or auto-regressive characteristic is firstly utilized to build a multivariable statistical model that measures the correlations of the currently collected structural responses and the future possible ones in combination with the canonical correlation analysis. Two different fault detection statistics are then defined based on the above multivariable statistical model for deciding whether a fault or failure occurred in the sensor network. After that, two corresponding fault isolation indices are deduced through the contribution analysis methodology to identify the faulty sensor. Case studies, using a benchmark structure developed for bridge health monitoring, are considered in the research and demonstrate the superiority of the new proposed sensor fault diagnosis method over the traditional principal component analysis-based and the dynamic principal component analysis-based methods.

Online process monitoring for complex systems with dynamic weighted principal component analysis

Conventional multivariate statistical methods for process monitoring may not be suitable for dynamic processes since they usually rely on assumptions such as time invariance or uncorrelation. We are therefore motivated to propose a new monitoring method by compensating the principal component analysis with a weight approach. The proposed monitor consists of two tiers. The first tier uses the principal component analysis method to extract cross-correlation structure among process data, expressed by independent components. The second tier estimates auto-correlation structure among the extracted components as auto-regressive models. It is therefore named a dynamic weighted principal component analysis with hybrid correlation structure. The essential of the proposed method is to incorporate a weight approach into principal component analysis to construct two new subspaces, namely the important component subspace and the residual subspace, and two new statistics are defined to monitor them respectively. Through computing the weight values upon a new observation, the proposed method increases the weights along directions of components that have large estimation errors while reduces the influences of other directions. The rationale behind comes from the observations that the fault information is associated with online estimation errors of auto-regressive models. The proposed monitoring method is exemplified by the Tennessee Eastman process. The monitoring results show that the proposed method outperforms conventional principal component analysis, dynamic principal component analysis and dynamic latent variable.

Fault detection and diagnosis of an industrial copper electrowinning process

Electrowinning is a key process in the production of high purity copper from copper sulphide minerals. Fault detection and diagnosis based on the industrial operating data would be desirable to avoid abnormal operation and ensure high product quality. In this paper, a fault detection and diagnosis algorithm using dynamic principal component analysis (DPCA) is applied to the industrial selenium/tellurium removal and copper electrowinning process. From the principal components obtained using DPCA, Hotelling and SPE are calculated to determine whether a fault has occurred. Tests on normal and faulty data sets confirm that the DPCA‐based fault detection method is effective for the industrial system. Contribution plots of variables to are obtained to determine the variables that contribute to the fault and to help locate the root causes of the fault. The DPCA‐based fault detection and diagnosis provide a convenient approach for enhancing the process operation and product quality for the industrial copper electrowinning system.

A systematic comparison of PCA‐based Statistical Process Monitoring methods for high‐dimensional, time‐dependent Processes

High‐dimensional and time‐dependent data pose significant challenges to Statistical Process Monitoring. Most of the high‐dimensional methodologies to cope with these challenges rely on some form of Principal Component Analysis (PCA) model, usually classified as nonadaptive and adaptive. Nonadaptive methods include the static PCA approach and Dynamic Principal Component Analysis (DPCA) for data with autocorrelation. Methods, such as DPCA with Decorrelated Residuals, extend DPCA to further reduce the effects of autocorrelation and cross‐correlation on the monitoring statistics. Recursive Principal Component Analysis and Moving Window Principal Component Analysis, developed for nonstationary data, are adaptive. These fundamental methods will be systematically compared on high‐dimensional, time‐dependent processes (including the Tennessee Eastman benchmark process) to provide practitioners with guidelines for appropriate monitoring strategies and a sense of how they can be expected to perform. The selection of parameter values for the different methods is also discussed. Finally, the relevant challenges of modeling time‐dependent data are discussed, and areas of possible further research are highlighted. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1478–1493, 2016

Fault Diagnosis Method on Polyvinyl Chloride Polymerization Process Based on Dynamic Kernel Principal Component and Fisher Discriminant Analysis Method

In view of the fact that the production process of Polyvinyl chloride (PVC) polymerization has more fault types and its type is complex, a fault diagnosis algorithm based on the hybrid Dynamic Kernel Principal Component Analysis-Fisher Discriminant Analysis (DKPCA-FDA) method is proposed in this paper. Kernel principal component analysis and Dynamic Kernel Principal Component Analysis are used for fault diagnosis of Polyvinyl chloride (PVC) polymerization process, while Fisher Discriminant Analysis (FDA) method was adopted to make failure data for further separation. The simulation results show that the Dynamic Kernel Principal Component Analyses to fault diagnosis of Polyvinyl chloride (PVC) polymerization process have better diagnostic accuracy, the Fisher Discriminant Analysis (FDA) can further realize the fault isolation, and the actual fault in the process of Polyvinyl chloride (PVC) polymerization production can be monitored by Dynamic Kernel Principal Component Analysis.

Monitoring of Distillation Column Based on Indiscernibility Dynamic Kernel PCA

Aiming at complicated faults detection of distillation column industrial process, it has faced a grave challenge. In this paper, a new indiscernibility dynamic kernel principal component analysis (I-DKPCA) method is presented and applied to distillation column. Compared with traditional statistical techniques, I-DKPCA not only can capture nonlinear property and dynamic characteristic of processes but also can extract relevant variables from all the variables. Applying this new method to distillation column process (a hardware-in-the-loop simulation system), the results prove the proposed method has great advantages, that is, lower missing rate and higher detection rate for the faults, compared with KPCA and DPCA.

Assessing Water Poverty in China Using Holistic and Dynamic Principal Component Analysis

The Water Poverty Index (WPI) expands the analysis of China’s water crises from hydrology to a broader focus on integrated water resources management including economic and social factors. This index was revised by principal component analysis (PCA) to avoid arbitrariness of weights and collinearity between variables. However, the traditional PCA is primarily oriented for static data, and it fails to reveal the evolutionary trend of data over time. Moreover, the conventional normalization methods are not adequate when the dimension of time is added to the data. In this study, the transformation of centralized logarithm of initial variable and holistic and dynamic principal component analysis are firstly proposed, then the improved methods are applied to assess water poverty in China using panel data from 2004 to 2012. The estimated WPI shows the growing scale and the clustering trend of regional water poverty. The analysis of influential factors reveals that aquatic environmental pollution is a vital driver of water poverty. Water resource endowment is the second important factor concerning regional water poverty. Inability to adapt to water scarcity, which leads to weak physical water access and low efficiency of water use, is still a critical driver of regional water poverty. Finally, the regional disparities and alleviation strategies of water poverty are discussed.

Comprehensive measurement of energy market integration in East Asia: An application of dynamic principal component analysis

The energy market integration (EMI) in East Asia has been carried out for over a decade. Despite the efforts exerted by countries in the region, little has been known about the EMI progress. This paper innovatively applies the dynamic principal component analysis to measure the EMI and its evolution in East Asia between 1995 and 2011. The EMI is measured by using information from all the five dimensions that have been identified in the literature: (1) energy trade liberalisation; (2) investment liberalisation; (3) development of energy infrastructure and its associated institutional arrangements; (4) domestic market openness; and (5) energy pricing reform. Results show that although significant progress has been made for EMI in East Asia, there are significant cross-country disparities in different aspects. Moreover, we show that further efforts towards EMI in general should focus on liberalising national markets first, then phasing out fossil fuel subsidies and finally, liberalising investment regime since national market liberalisation is the least developed dimensions. Certain countries that lag behind in EMI need to learn from either their past experiences or from other nations and focus their efforts on their relatively weak dimensions.

Insight into binding modes of p53 and inhibitors to MDM2 based on molecular dynamic simulations and principal component analysis

ABSTRACTInhibition of the p53–MDM2 interaction is a new therapeutic strategy to activate the wild-type function of p53 in tumors. Molecular dynamics (MD) simulations and calculations of binding free energies were performed to investigate the binding mechanisms of p53 and two inhibitors PMI and VZV to MDM2. The results show that van der Waals interaction is the main force to control the bindings of ligands to the hydrophobic cleft of MDM2, which basically agrees with the previous calculated and experimental studies. The results from the RMSF calculation, cross-correlation analysis and principal component (PC) analysis prove that the ligand bindings produce a significant effect on the conformation of the binding cleft of MDM2. In addition, the calculations of residue-based free energy decomposition suggest that the CH–CH, CH–π, and π–π interactions dominate the bindings of p53 and inhibitors to MDM2. This study can provide significant help for the design of potent inhibitors targeting the p53–MDM2 interaction.

Dynamic process fault detection and diagnosis based on dynamic principal component analysis, dynamic independent component analysis and Bayesian inference

Dynamic principal component analysis (DPCA) and dynamic independent component analysis (DICA), as the frequently-used dimensional reduction methods, have been widely applied to monitor dynamic process. Considering the respective advantages of DPCA and DICA in different data distribution characteristics, this paper proposes a novel process monitoring algorithm named DPCA, DICA and Bayesian Inference (DPCA–DICA–BI). The main idea of DPCA–DICA–BI is to put the process variables with same distribution characteristic (Gaussian or non-Gaussian) into a block on the basis of the variable normality by Jarque–Bera test and then to respectively apply DPCA and DICA in Gaussian and non-Gaussian blocks. Finally, to combine the monitoring performance of both blocks, Bayesian inference is employed to make an integrated decision. The DPCA–DICA–BI as well as PCA, ICA, DPCA, and DICA has been used to a numerical example and Tennessee Eastman process. The simulation results show the superiority of DPCA–DICA–BI.

Sustainability vs credibility of fiscal consolidation

Purpose – The purpose of this paper is to explain why some countries in the eurozone between 2010 and 2012 experienced a dramatic vicious circle between hard austerity plans and rising default risk premia. Were such plans too small, and hence non-credible, or too large, and hence non-sustainable? These questions have prompted theoretical and empirical investigations in the line of the so-called “self-fulfilling beliefs”, where beliefs of unsustainability of fiscal adjustments, and hence default on debt, feed higher risk premia which indeed make fiscal adjustments less sustainable. Design/methodology/approach – Detecting the sustainability factor in the evolution of spreads is uneasy because it is largely non-observable and may be proxied by different variables. In this paper, the authors present the results of a dynamic principal components factor analysis (PCFA) applied to a panel data set of the 11 major EZ countries from 2000 to 2013, consisting of each country’s spread of long-term interest rate over Germany as dependent variable, and an array of leading fiscal and macroeconomic indicators of solvency fiscal effort and its sustainability. Findings – The authors have been able to identify the role of these indicators that combine themselves as significant latent variables in boosting spreads. Moreover, the large joint deterioration of these variables is identifiably located between 2009 and 2012 and particularly for the group of countries under most severe default risk (with Italy and France as borderline cases). The authors also find evidence that the announcement of the European Central Bank Outright Monetary Transactions program has improved the sustainability assessment of sovereign debts. Originality/value – Dynamic PCFA is a rather unusual technique with respect to standard econometric tests of models, which is particularly well-suited to reduce the number of variables in a data set by extracting meaningful linear combinations from the observed variables that may concur to explain a given phenomenon (the dependent variable). These combinations, called “common factors”, can be interpreted as latent, non-observable variables.

Dynamic Principal Components: A New Class of Multivariate GARCH Models

The OGARCH specification is the leading model for a class of multivariate GARCH (MGARCH) models that are based on linear combinations of univariate GARCH specifications. Most MGARCH models in this class adopt a spectral decomposition of the covariance matrix, allowing for heteroskedasticity on at least some of the principal components, while the loading matrix, which maps the conditional principal components to the asset returns, is constant over time. This paper extends the OGARCH model class to allow for time-varying loadings. Our approach closely parallels the DCC modelling approach, introduced as an extension of the CCC model, to allow for dynamic correlations. After introducing an auxiliary process that captures the relevant features of the unobservable loading dynamics, we compute the time-varying loading matrix from the auxiliary process, subject to the necessary orthonormality constraints. The resulting model (the Dynamic Principal Components, or DPC, model) preserves the OGARCH models ease of interpretation and feasibility. In particular, we show that the eigenvectors of the sample covariance matrix can consistently estimate the time-varying loadings intercept term. This property extends to the dynamic framework the well-known analogous property of the OGARCH model. Empirical examples demonstrate the benefits to the loading matrix of introducing time-varying properties.

Using Dynamic Principal Components to Estimate an Alternative Measure of Exchange Market Pressure

Measures of Exchange Market Pressure (EMP) combine exchange-rate depreciations, reserve losses, and interest-rate hikes into a single index, for the purpose of explaining or predicting currency crisis. The standard measure assigns variance-smoothing weights that are fixed throughout the sample periods. Here, we extend the static PCA analysis of Hegerty (2013) to model EMP using the Dynamic Principal Components (DPCA) approach of Forni et al. While the DPCA and the: “standard” measure match in certain cases, they diverge widely in others, suggesting that this alternative must be refined before it can be used in wider practice.

Dynamic factor models with infinite-dimensional factor spaces: One-sided representations

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forniet al. (2000). That paper, however, rests on Brillinger’s dynamic principal components. The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have been dominant in this literature. On the other hand, those estimators require the assumption that the space spanned by the factors has finite dimension. In the present paper, we argue that such an assumption is extremely restrictive and potentially quite harmful. Elaborating upon recent results by Anderson and Deistler (2008a, b) on singular stationary processes with rational spectrum, we obtain one-sided representations for the GDFM without assuming finite dimension of the factor space. Construction of the corresponding estimators is also briefly outlined. In a companion paper, we establish consistency and rates for such estimators, and provide Monte Carlo results further motivating our approach.

A New Method of Dynamic Latent-Variable Modeling for Process Monitoring

Dynamic principal component analysis (DPCA) is widely used in the monitoring of dynamic multivariate processes. In traditional DPCA where a time window is used, the dynamic relations among process variables are implicit and difficult to interpret in terms of variables. To extract explicit latent variables that are dynamically correlated, a dynamic latent-variable model is proposed in this paper. The new structure can improve the modeling and the interpretation of dynamic processes and enhance the performance of monitoring. Fault detection strategies are developed, and contribution analysis is available for the proposed model. The case study on the Tennessee Eastman Process is used to illustrate the effectiveness of the proposed methods.