Moving Window Principal Component Analysis Research Articles

Unsupervised analysis of NIRS spectra to assess complex plant traits: leaf senescence as a use case

BackgroundAs a rapid and non-destructive method, Near Infrared Spectroscopy is classically proposed to assess plant traits in many scientific fields, to observe enlarged genotype panels and to document the temporal kinetic of some biological processes. Most often, supervised models are used. The signal is calibrated thanks to reference measurements, and dedicated models are generated to predict biological traits. An alternative unsupervised approach considers the whole spectra information in order to point out various matrix changes. Although more generic, and faster to implement, as it does not require a reference data set, this latter approach is rarely used to document biological processes, and does requires more information of the process.MethodsIn our work, an unsupervised model was used to document the flag leaf senescence of durum wheat (Triticum turgidum durum). Leaf spectra changes were observed using Moving Window Principal Component Analysis (MWPCA). The dates related to earlier and later spectra changes were compared to two key points on the senescence time course: senescence onset (T0) and the end of the leaf span (T1) derived from a supervised strategy.ResultsFor almost all leaves and whatever the signal pre-treatments and window size considered, the MWPCA found significant spectral changes. The latter was highly correlated with T1 (0.59 ≤ r ≤ 0.86) whereas the correlations between the first significant spectrum changes and T0 were lower (0.09 ≤ r ≤ 0.56). These different relationships are discussed below since they define the potential as well as the limitations of MWPCA to model biological processes.ConclusionOverall, our study demonstrates that the information contained in the spectra can be used when applying an unsupervised method, here the MWPCA, to characterize a complex biological phenomenon such leaf senescence. It also means that using whole spectra may be relevant in agriculture and plant biology.

Fault monitoring using novel adaptive kernel principal component analysis integrating grey relational analysis

The kernel principal component analysis (KPCA) is widely used as a fault monitoring tool for complex nonlinear chemical processes in recent years. The cumulative contribution rate that extracts the kernel principal is usually obtained relied on a fixed model, which cannot be employed for time-varying chemical processes. Hence, a novel adaptive kernel principal component analysis (AKPCA) integrating grey relational analysis (GRA) (AKPCA-GRA) is proposed to dynamically monitor the fault occurrence. A moving window integrating the threshold method is used to adaptively extract the kernel principal for chemical processes. Then the corresponding T2 and Q statistics calculated by the selected kernel principal based on the AKPCA decides whether the fault has occurred. Moreover, the GRA method is used to analyze and calculate the correlation coefficient of abnormal features obtained based on the APKCA method, which provides the operational guidance for the nonlinear chemical process to find out the variable causing the fault. Finally, the proposed method is verified using the Tennessee Eastman (TE) process. The case results demonstrate that the proposed method outperforms the KPCA, the KPCA based on the threshold and the moving window principal component analysis, the support vector machine (SVM) and the Logistic Regression (LR) in terms of the missed alarm rate (MAR) and the false alarm rate (FAR), which can effectively analyze the variables causing the fault.

A Data-Driven Design for Gas Turbines Exit Temperature Spread Condition Monitoring System

One of the most complex and costly systems in the industry is the Gas turbine (GT). Because of the complexity of these assets, various indicators have been used to monitor the health condition of different parts of the gas turbine. Turbine exit temperature (TET) spread is one of the significant indicators that help monitor and detect faults such as overall engine deterioration and burner fault. The goal of this article is to use data-driven approaches to monitor TET data to detect faults early, as fault detection can have a significant impact on gas turbine reliability and availability. In this study, the TET data of v94.2 GT is measured by six temperature transmitters to show a detailed profile. According to the statistical tests, TET data are high dimensional and time-dependent in the real world industry. Hence, three distinctive methods in the field of the gas turbine are proposed in this study for early fault detection. Conventional principal component analysis (PCA), moving window PCA (MWPCA), and incremental PCA (IPCA) were implemented on TET data. According to the results, the conventional PCA model is a non-adaptive method, and the false alarm rate is high due to the incompatibility of this approach and the process. The MWPCA based on V-step-ahead and IPCA approaches overcame the non-stationary problem and reduced the false alarm rate. In fact, these approaches can distinguish between the normal time-varying and slow ramp fault processes. The results showed that IPCA could detect fault situations faster than MWPCA based on V-step-ahead in this study.

A framework to automate fault detection and diagnosis based on moving window principal component analysis and Bayesian network

Through Condition-Based Maintenance strategy, planners can monitor the health of the machinery and recommend actions based on the information obtained. Nevertheless, this approach depends on the successful establishment of Fault Detection and Diagnosis (FDD) processes. Although FDD is a research area in full growth with the development of several methods and heuristics, the availability of data from systems under a fault condition is still scarce in many applications, mainly related to complex systems. In many circumstances, only data from the system in healthy conditions is available and the applied FDD method should be able to detect variations in system conditions and diagnose faults without the need for previous labeled fault data. In this context, this article proposes a hybrid framework to automate FDD based on Moving Window Principal Component Analysis (MWPCA) and Bayesian Network (BN). First, the knowledge base on technical systems is organized to support the next steps of the framework. Then, the detection and diagnosis processes are performed sequentially through MWPCA and BN. The framework was implemented in the analysis of a simplified model of a hydrogenerator, considering real and simulated data. The results showed that the proposed method was able to detect and diagnose several simulated failures.

Operational Modal Analysis for Vibration Control Following Moving Window Locality Preserving Projections for Linear Slow-Time-Varying Structures

Modal parameters can reflect the dynamic characteristics of the structure and can be used to control vibration. To identify the operational modal parameters of linear slow-time-varying structures only from non-stationary vibration response signals, a method based on moving window locality preserving projections (MWLPP) algorithm is proposed. Based on the theory of “time freeze”, the method selects a fixed length window and takes the displacement response signal in each window as a stationary random sequence. The locality preserving projections algorithm is used to identify the transient modal frequency and modal shape of the structure at this window. The low-dimensional embedding of the displacement response data set calculated by locality preserving projections (LPP) corresponds to the modal coordinate response matrix, and the transformation matrix corresponds to the modal shape matrix. The simulation results of the mass slow-time-varying three degree of freedom (DOF) and the density slow-time-varying cantilever beam show that the new method can effectively identify the modal shape and modal natural frequency of the linear slow-time-varying only from the non-stationary vibration response signal, and the performance is better than the moving window principal component analysis (MWPCA).

Taking climate change into account: Non‐stationarity in climate drivers of ecological response

Abstract Changes in the global climate system are creating increasingly non‐analogue climate conditions with expectations of non‐stationarity among climate drivers. Decoupling among climate drivers complicates the assessment of ecological response to the changing climate as characteristics that could be once treated as a suite of conditions now need to be treated as potentially independent with possible synergistic effects. Ecologists commonly use ordination techniques (often principal component analysis; PCA) on large climate and environmental datasets to reduce a range of variables to a few axes that are uncorrelated with each other and often explain large proportion of the variation in the original data. However, non‐stationarity, with correlations among variables changing over time, can affect this approach. Here, we use a 37‐year climate dataset from the Niwot Ridge Long Term Ecological Research site (Colorado, USA) to present the use of both moving window principal component analysis and moving window correlation analysis to determine non‐stationarity in climate data. Relationships among climate variables and between input variables and PCA axes changed over time; this obscured interpretation of relationships between PCA axes and an ecological response (plant biomass), suggesting that one‐time PCA for environmental variables may lead to inappropriate inferences. Synthesis. Care must be taken in analysing climate–ecological relationships when predictor variables exhibit non‐stationarity. We present a conceptual decision‐making tree to help ecologists consider when to use PCA and extract axis scores or use alternative approaches for incorporating non‐stationarity into subsequent analysis, including testing variables individually to aid in interpretation, break point analyses and averaging PC scores.

Real-Time Monitoring of Yogurt Fermentation Process by Aquaphotomics Near-Infrared Spectroscopy.

Automated quality control could have a substantial economic impact on the dairy industry. At present, monitoring of yogurt production is performed by sampling for microbiological and physicochemical measurements. In this study, Near-Infrared Spectroscopy (NIRS) is proposed for non-invasive automated control of yogurt production and better understanding of lactic acid bacteria (LAB) fermentation. UHT (ultra-high temperature) sterilized milk was inoculated with Bulgarian yogurt and placed into a quartz cuvette (1 mm pathlength) and test-tubes. Yogurt absorbance spectra (830–2500 nm) were acquired every 15 min, and pH, in the respective test-tubes, was measured every 30 min, during 8 h of fermentation. Spectral data showed substantial baseline and slope changes with acidification. These variations corresponded to respective features of the microbiological growth curve showing water structural changes, protein denaturation, and coagulation of milk. Moving Window Principal Component Analysis (MWPCA) was applied in the spectral range of 954–1880 nm to detect absorbance bands where most variations in the loading curves were caused by LAB fermentation. Characteristic wavelength regions related to the observed physical and multiple chemical changes were identified. The results proved that NIRS is a valuable tool for real-time monitoring and better understanding of the yogurt fermentation process.

An improved approach for fault detection by simultaneous overcoming of high-dimensionality, autocorrelation, and time-variability.

The control charts with the Principal Component Analysis (PCA) approach and its extension are among the data-driven methods for process monitoring and the detection of faults. Industrial processing data involves complexities such as high dimensionality, auto-correlation, and non-stationary which may occur simultaneously. An efficient fault detection technique is an approach that is robust against data training, sensitive to all the feasible faults of the process, and agile to the detection of the faults. To date, approaches such as the recursive PCA (RPCA) model and the moving-window PCA (MWPCA) model have been proposed when data is high-dimensional and non-stationary or dynamic PCA (DPCA) model and its extension have been suggested for autocorrelation data. But, using the techniques listed without considering all aspects of the process data increases fault detection indicators such as false alarm rate (FAR), delay time detection (DTD), and confuses the operator or causes adverse consequences. A new PCA monitoring method is proposed in this study, which can simultaneously reduce the impact of high-dimensionality, non-stationary, and autocorrelation properties. This technique utilizes DPCA property to decrease the effect of autocorrelation and adaptive behavior of MWPCA to control non-stationary characteristics. The proposed approach has been tested on the Tennessee Eastman Process (TEP). The findings suggest that the proposed approach is capable of detecting various forms of faults and comparing attempts to improve the detection of fault indicators with other approaches. The empirical application of the proposed approach has been implemented on a turbine exit temperature (TET). The results demonstrate that the proposed approach has detected a real fault successfully.

Synchrophasor based islanding detection for microgrids using moving window principal component analysis and extended mathematical morphology

Extensive deployment of non-dispatchable renewable energy sources in microgrids (MGs) has led to frequent fault events, DG and line trips and is arduous to discriminate islanding events (IEs) from other transient conditions. For enhanced grid security, time synchronised data from phasor measurement units is utilised. However, data handling at the control centre is tedious as system variables monitored often exhibit non-linear characteristics that impose a problem to the operator in discriminating between islanding and non-IEs. To cope with this, a zero non-detection zone, reliable and precise islanding detection method for data-intensive grid-connected MG, is proposed. Voltage phasors, frequency and rate of change of frequency from various locations are processed through moving window principal component analysis (MWPCA) cascaded with extended mathematical morphological filter (EMMF). MWPCA reduces data dimensionality and Q statistics obtained are passed to EMMF, which acts as a non-linear filter. Further, the islanding detecting factor identified all IEs within the prescribed time limit with minimum false alarms. Accuracy, precision and reliability demonstrated by using a case study model using DIgSILENT are encouraging. It can be adopted by operators to run MG securely. Further, testing of the proposed method on a typical utility feeder shows promising results.

Multivariate log file analysis for multi-leaf collimator failure prediction in radiotherapy delivery.

Background and PurposeMotor failure in multi-leaf collimators (MLC) is a common reason for unscheduled accelerator maintenance, disrupting the workflow of a radiotherapy treatment centre. Predicting MLC replacement needs ahead of time would allow for proactive maintenance scheduling, reducing the impact MLC replacement has on treatment workflow. We propose a multivariate approach to analysis of trajectory log data, which can be used to predict upcoming MLC replacement needs.Materials and methodsTrajectory log files from two accelerators, spanning six and seven months respectively, have been collected and analysed. The average error in each of the parameters for each log file was calculated and used for further analysis. A performance index (PI) was generated by applying moving window principal component analysis to the prepared data. Drops in the PI were thought to indicate an upcoming MLC replacement requirement; therefore, PI was tracked with exponentially weighted moving average (EWMA) control charts complete with a lower control limit.ResultsThe best compromise of fault detection and minimising false alarm rate was achieved using a weighting parameter (λ) of 0.05 and a control limit based on three standard deviations and an 80 data point window. The approach identified eight out of thirteen logged MLC replacements, one to three working days in advance whilst, on average, raising a false alarm, on average, 1.1 times a month.ConclusionsThis approach to analysing trajectory log data has been shown to enable prediction of certain upcoming MLC failures, albeit at a cost of false alarms.

Fault detection in a grid-connected photovoltaic system using adaptive thresholding method

In this paper, an adaptive monitoring scheme with Fuzzy Logic Filter (FLF) is developed and applied to monitor a Grid-Connected Photovoltaic System (GCPVS). This method is based on Principal Component Analysis (PCA) and Moving Window Principal Component Analysis (MWPCA). It is designed to generate adaptive thresholds for its monitoring indices. The FLF filters the monitoring indices to reduce the number of False Alarms (FA) and increase the Fault Detection Rate (FDR). The application is carried out on the GCPVS of the Power Electronics and Renewable Energy Research Laboratory (PEARL) of Malaya University. The proposed technique is compared against PCA method in terms of FAR reduction. The detection ability of the adaptive thresholding with FLF monitoring scheme is tested first on simulated faults then it is applied to detect a real abnormal behaviour. The results show that the proposed method is effective in reducing the number of false alarms and in detecting different types of faults with high accuracy.

A combined monitoring scheme with fuzzy logic filter for plant-wide Tennessee Eastman Process fault detection

Principal Component Analysis (PCA) is the most common Multivariate Statistical Process Control (MSPC) method that is widely used for Fault Detection and Diagnosis (FDD). Since early abnormality detection with high accuracy is required for safe and reliable process operation, False Alarms Rate (FAR), Missed Detection Rate (MDR) and the detection time delay are the major factors that must be taken into consideration when developing any process monitoring scheme. Unfortunately, the PCA performance, with fixed limits, is weak in terms of the stated factors. In contrast, conventional Moving Window PCA (MWPCA) is an adaptive technique which updates both the PCA model and the thresholds once a new normal observation is available. Yet, MWPCA methodology still does not reduce the MDR and the detection delay. In this paper, a Modified MWPCA (MMWPCA) with Fuzzy Logic Filter (FLF) is proposed to enhance the monitoring performance of PCA. It is an adaptive approach with a fixed model that combines both aforementioned techniques. The aim of using FLF is to ensure robustness to false alarms without affecting the Fault Detection (FD) performance. The application of the proposed method has been carried out on the Tennessee Eastman Process (TEP). Hold-one and hold-five MMWPCA with FLF are applied and compared to recent FDD work in the literature. The obtained results demonstrate the superiority of the proposed technique in detecting different types of faults with high accuracy and with shorter time delay.

FT-NIR characterization with chemometric analyses to differentiate goldenseal from common adulterants

Goldenseal (Hydrastis canadensis L.) has been a popular herb since the 1970s, with a US market share of over $32 million in 2014. Wild goldenseal has been listed in the Convention on International Trade in Endangered Species for decades. Limits in supply and greed for profit have led to adulteration with similar but more accessible and inexpensive plant materials. Fourier transform near-infrared spectroscopy (FT-NIR) coupled with three different chemometric models, partial least squares (PLS) regression, soft independent modeling of class analogy (SIMCA), and moving window principal component analysis (MW-PCA) provide fast, simple, nondestructive approaches to differentiating pure goldenseal from 4 common pure adulterants (yellow dock, yellow root, coptis, Oregon grape). All three models successfully differentiated authentic goldenseal from adulterants. The models were t-tested for detection of goldenseal intentionally mixed with individual adulterants at 2% to 95% theoretical levels made computationally. The PLS model was unable to detect adulterants mixed with goldenseal at any level. The SIMCA model was the best for detection of yellow root and Oregon grape adulteration in goldenseal, as low as 10%. The MW-PCA model proved best for detection of yellow dock at ≥ 15% and coptis adulteration ≥5% in goldenseal. This study demonstrates that NIR spectroscopy coupled with chemometric analyses is a good tool for industry and investigators to implement for rapid detection of goldenseal adulteration in the marketplace, but also indicates that the specific approach to chemometric analysis must be evaluated and selected on a case-by-case basis in order to achieve useful sensitivity and specificity.

Moving window self-iteration PCE based OMA for slow linear time-varying structures

In order to reduce the time and space complexity of operational modal analysis (OMA) for slow linear time-varying (SLTV) structures based on moving window principal component analysis (MWPCA), this paper proposes a new moving window self-iteration principal component extraction (MWSIPCE) method. Different from getting principal components by singular value decomposition (SVD) or eigenvalue decomposition (EVD) in MWPCA algorithm, MWSIPCE just extracts the first-several-orders principal components by self-iteration. Comparing with MWPCA, MWSIPCE has lower time and space complexity. What’s more, this paper explains the reason of modal exchange in some data windows in detail, and gives an illustration to how to set window length L. The OMA results on non-stationary vibration response simulation signal of time-varying cantilever beam under white noise excitation show that this method can well identify the time-varying transient modal parameters (natural frequencies and modal shapes) for SLTV structures and has less time and space consume, the algorithm is also more precise than MWPCA.

Detection of Nucleation during Cooling Crystallization through Moving Window PCA Applied to in Situ Infrared Data

The method here proposed based on the moving window principal component analysis can be employed in time-varying processes tracked through in situ spectroscopy. In the case under investigation, it aimed to detect the nucleation during crystallization processes. For this purpose, statistical indexes were employed, and the contribution plot helped identifying the spectral variables that were changing due to nucleation. Isonicotinamide was here considered as a model active pharmaceutical ingredient, and its cooling crystallization was monitored by means of in situ infrared spectroscopy. The procedure allowed to overcome issues that may be encountered with static principal component analysis, since it could distinguish the slow-varying changes due to external perturbations (temperature) from abnormal events such as the sudden concentration decrease related to the crystallization. The proposed method was demonstrated to correctly detect nucleation without any a priori knowledge of the peaks involved in the pro...

An extension to RPCA parameter selection and process monitoring

Multivariate Statistical Process Control (MSPC) techniques such as Principal Component Analysis (PCA) and Partial Least Squares (PLS) have found wide application especially in the statistical modeling and monitoring of chemical processes. However, real industrial processes often violate the assumptions underlying MSPC since they exhibit time-varying and non-stationary behavior. Adaptive PCA-based monitoring procedures such as Moving Window PCA (MWPCA) and Recursive PCA (RPCA) have been proposed to tackle this issue. Although the parameter selection for those procedures is critical to their proper implementation, this topic is rarely covered in the literature.This paper examines two methods for MWPCA and RPCA parameter selection using the Tennessee Eastman process as an example. Based on the findings a novel procedure for RPCA parameter selection as well as a extension to RPCA will be proposed and demonstrated.

Capturing the tacit knowledge of the skilled operator to program tool paths and tool orientations for robot belt grinding

This paper describes a novel methodology for generating grinding tool paths, orientations and grinding parameters based on the captured trajectories of a surface finishing tool operated by the skilled operator. First, a variable frame size moving window principal component analysis is performed on the trajectories. Next, features such as the amplitude, speed of the tool centre point, direction of travel, average position, contact force and orientation of the grinder are calculated. Kernel k-means clustering is applied to the trajectory’s feature vectors for segmentation into the tool path primitives. The robotic tool path primitives would be ordered similar to the manual tool path primitives in the grinding strategy. The robotic tool path primitives are then generated based on the boundaries of the manual tool path primitive in a computer-aided manufacturing software. Anchor points are selected from the corners and at intermediate sections along the robotic tool path to inherit the orientations of the manual tool path. Using the inherited skilled operator tool orientations, spherical linear interpolation and spherical spline quaternion interpolation are used to interpolate the orientations for the robotic tool path points along the cross curves, followed by the flow curves, respectively. A finite element model of the belt grinding process is also introduced to quantify the effect of the contact wheel serrations on the material removal rate. This is to account for the difference in contact wheel design between the handheld and robotic grinding tool. The programmed robotic tool paths generated from the trajectories captured from a skilled operator were proven to be able to grind the workpiece to the desired profile within the desired tolerance in a pre-production environment.

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

Integrated data-driven analytics to identify instability signatures in nonstationary financial time series

ABSTRACTWith the objective of identifying instability signatures of the financial system, this article integrates two classes of data-driven techniques. The first class of techniques is utilized to investigate macroeconomic behaviour by aggregating an ensemble of heterogeneous nonstationary time-series data and the second class of techniques examines the local dynamics of the microstructures in each time series. Moving window principal component analysis (PCA) and functional PCA (fPCA) are shown to extract collective signatures of the financial system for understanding macroeconomic behaviour, and the Synchrosqueezing and Markov switching techniques are used to study local dynamics within each individual time series. The integrated data analytics successfully identifies the diverse events from 1986 to 2012. All events, both major and minor, have been identified by fPCA. The major economic events, especially the 2008 Great Recession, along with several minor events, showed a strong leading indicator in the density index derived from Synchrosqueezing. The capability of this integrated analytics suite is demonstrated in this article, and it motivates further studies encompassing data sets from broader sectors. As a complement to existing model-driven approach, this would lead to achieving a robust and reliable method that can help in taking measures to avoid catastrophic collapse in the constantly evolving financial system.

Overview of PCA-Based Statistical Process-Monitoring Methods for Time-Dependent, High-Dimensional Data

High-dimensional and time-dependent data pose significant challenges to statistical process monitoring. Dynamic principal-component analysis, recursive principal-component analysis, and moving-window principal-component analysis have been proposed to cope with high-dimensional and time-dependent features. We present a comprehensive review of this literature for the practitioner encountering this topic for the first time. We detail the implementation of the aforementioned methods and direct the reader toward extensions that may be useful to their specific problem. A real-data example is presented to help the reader draw connections between the methods and the behavior they display. Furthermore, we highlight several challenges that remain for research in this area.