Recursive Principal Component Analysis Research Articles

Design of Electronic Voltage Transformer Error Pattern Recognition and Classification Algorithm Based on Data Mining

With the development of smart grids, electronic voltage transformer (EVT) has gradually entered the stage of large-scale applications. Accurately identifying errors in electronic voltage transformers is crucial for the stability of power systems. Strengthening the measurement accuracy of EVT is of great significance for the operation of power systems and measurement and protection devices. However, due to the limitations of traditional verification methods, there are still challenges. To better improve the accuracy of transformer identification, a data-driven method for enhancing transformer error evaluation and prediction was developed. Based on the low accuracy of traditional EVT error verification and the difficulty of monitoring, data mining technology is proposed for EVT error analysis and evaluation. Recursive principal component analysis is used to separate errors from EVT measurement data, and feature statistics are used to monitor its operating status. Then, regression analysis under support vector machines is added to predict errors for active error correction and better evaluation of its status. The evaluation of the transformer monitoring dataset shows that the classification accuracy of error detection of the proposed method exceeds 93%, and the deviation between the predicted error value and the actual error value is less than 0.05%. Compared with methods such as artificial neural networks and ARMA, the average error rate has been reduced by more than 18%. The accuracy and average accuracy of the algorithm proposed in the study exceeded 80%, with values of 96.23% and 85.12%, respectively. The average error of the ratio difference feature of the EVT is only 0.023, and the average error of the angle difference is less than 0.01, which is much smaller than the algorithm used for comparison. The application response time is less than 0.1 s and the evaluation threshold can better identify data anomalies, with high application accuracy. This method can effectively provide real-time evaluation tools for the operational status of electronic voltage transformers and more accurately and proactively identify transformer errors from conventional data. This study provides an important data-driven solution for improving power grid reliability.

Adaptive Cointegration Analysis and Modified RPCA With Continual Learning Ability for Monitoring Multimode Nonstationary Processes.

This study investigates nonstationary process monitoring under frequently varying modes, where new modes are allowed to emerge constantly. However, in current multimode process monitoring methods, generally, data are required from all possible modes and mode identification is realized by prior knowledge for multimode nonstationary processes. In contrast, recursive methods update a monitoring model based on the successive data. However, they forget the learned knowledge gracefully and fail to track drastic variations. Aimed at nonstationary data in each mode, this article proposes an adaptive cointegration analysis (CA) to distinguish real faults from normal variations, which updates a model once a normal sample is encountered and adapts to the gradual change in the cointegration relationship. Then, a modified recursive principal component analysis (RPCA) with continual learning ability is developed to deal with the remaining dynamic information, wherein elastic weight consolidation is adopted to consolidate the previously learned knowledge when a new mode appears. The preserved information is beneficial for establishing a more accurate model than traditional RPCA and avoiding drastic performance degradation for future similar modes. In addition, novel statistics are proposed with prior knowledge and thresholds are calculated by recursive kernel density estimation to enhance the performance. An in-depth comparison with recursive CA and recursive slow feature analysis is conducted to emphasize the superiority, in terms of the algorithm accuracy, memory properties, and computational complexity. Compared with state-of-the-art recursive algorithms, the effectiveness of the proposed method is shown by studying on a numerical case and a practical industrial system.

Detection of Cyber Attacks on a Water Treatment Process

This paper investigates the detection of cyber attacks in a kind of critical infrastructure, the water treatment processes. For this purpose, the real data from the secure water treatment testbed (SWaT) in the iTrust Centre for Research in Cyber Security at the Singapore University of Technology and Design have been used in the investigation. More than 30 different attacks happen on the communication network between the programmable logic controller (PLC) and the sensors/actuators. After understanding the basic working mechanism of the SWaT process, an attack detection system is developed systematically, which consists of a limit value check and safety rule unit, a model-based monitoring unit and a data-driven monitoring unit. To cope with the nonstationary behavior of some water chemical properties such as pH and oxidation reduction potential, the recursive principal component analysis (RPCA) is applied in the data-driven part. It is shown how to divide the SWaT process suitably to integrate the model-based and data-driven monitoring for the SWaT process. The comparison shows that the proposed attack detection system outperforms other existing attack detection systems for the SWaT process.

An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

Estimation of respiratory rate and effort from a chest-worn accelerometer using constrained and recursive principal component analysis

Objective. Measurement of respiratory rate and effort is useful in various applications, such as the diagnosis of sleep apnea and early detection of patient deterioration in medical conditions, such as infections. A chest-worn accelerometer may be an easy and non-intrusive method, provided it is accurate and robust. We investigate the use of a novel method that can perform under realistic sleeping conditions such as variable sensor positions and body posture. Approach. Twenty subjects (aged 46–65 years) wore an accelerometer on the chest and a respiratory impedance plethysmography band as a reference. The subjects underwent an experimental protocol lasting approximately 90 min, under various postures and with different sensor positions. We used a novel, constrained, and recursive form of principal component analysis (PCA) to estimate the respiratory effort signal robustly. To obtain an estimate for the respiratory rate, first, multiple estimates were aggregated into a single frequency. Subsequently, a quality index was determined, such that unreliable estimates could be identified, and a trade-off could be made between coverage (percentage of time that the quality index is above a threshold) and limits of agreement. Main results. Results were determined over all recorded data, including changes in sensor position and posture. For respiratory effort, it was found that recursive and constrained computation of PCA reduced the estimation error significantly. For respiratory rate, a relation between coverage and limits of agreement was determined. If a minimum coverage of 80% was required, the limits of agreement could be kept below 1.45 breaths per minute. If the limits of agreement were constrained to 0.2 breaths per minute, a mean coverage of 5% was still attainable. Significance. We have shown that chest-worn accelerometery can be a robust and accurate method for measurement of respiratory features under realistic conditions.

Dynamic multimode process monitoring using recursive GMM and KPCA in a hot rolling mill process

The increasing competitive market has put forward higher demand for iron and steel production process, which is characterized by high-dimensional, nonlinear and multi-scale coupling. The newly rising internet of things (IoT) and advanced communication technologies have promoted the widespread application of data-driven process monitoring methods. To deal with the multimode and non-stationary properties of hot rolling production, a dynamic multimode process monitoring method is proposed based on the recursive Gaussian mixture model (RGMM) and recursive kernel principal component analysis (RKPCA). The proposed approach is applied to the monitoring of the hot-rolled strip thickness oversizing, and comparative experiments are conducted with KPCA, GMM-KPCA on actual production data. Results show that the proposed method shows better performance than conventional methods in terms of fault detection rate and false alarm rate when detecting time-varying multimode faults. The proposed method has also been integrated into an actual system and has been running smoothly in large steel mills in China.

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.

Online Evaluation for the Accuracy of Electronic Voltage Transformer Based on Recursive Principal Components Analysis

The electronic voltage transformer (EVT) has received much attention with the recent global trend to establish smart grids and digital substations. One of the main issues of the EVT is the deterioration of its performance with long-term operation which affects the control and protection systems it is employed for and hence the overall reliability of the power grids. This calls for the essential need for a reliable technique to regularly assess the accuracy of operating EVT in real-time. Unfortunately, traditional calibration methods cannot detect the incipient EVT performance change in real-time. As such, this paper presents a new online method to evaluate the accuracy of the EVT. In this regard, the Q-statistic is calculated based on the recursive principal components analysis (RPCA) using the output data of EVT to map up the changes of metering error on the electric–physics relationship. By employing the output data of the EVT along with the power grid characteristics, the performance of the EVT is evaluated without the need for a standard transformer, as per the current industry practice. Results show that the proposed method can assess the EVT with a 0.2 accuracy class.

Recursive principal component analysis for model order reduction with application in nonlinear Bayesian filtering

Proper orthogonal decomposition (POD) is a useful technique for feature extraction, model order reduction and data compression and has been widely used in different science and engineering disciplines. Numerous papers have been published on the application of offline POD, i.e., batch POD (BPOD) in civil and mechanical engineering encompassing Karhunen–Loève decomposition (KLD), principal component analysis (PCA), and singular value decomposition (SVD). Nevertheless, online POD which is more suited for online feature extraction and monitoring has been scarcely addressed when dealing with civil and mechanical systems, particularly in structural dynamics. In this paper, a number of recursive POD (RPOD) methods in form of recursive PCA (RPCA) are overviewed with their application to structural dynamics. RPCA with numerical eigenvalue decomposition (EVD), incremental principal component analysis (IPCA), matrix perturbation method, and Kalman filter RPCA (KFRPCA) are presented; their performance is probed in terms of initialization, structural parameter modification, noisy observation, and alteration of loading statistics. The novel KFRPCA algorithm developed in this paper is reformulated to resolve the unobservability issue of higher modes which was present in its previous version in the published literature. Online stochastic output-only system identification is presented by synergizing RPCA with nonlinear Bayesian filter. Augmented extended Kalman filter (AEKF) is employed to perform unknown-input dual estimation.

Zero-point fault detection of load cells in truck scale based on recursive principal component analysis and comprehensive evaluation method

A zero-point fault of load cells in truck scale is a typical small fault and it is difficult to be detected online. This paper proposes a new method for detecting zero-point fault online by combining a recursive principal component analysis (RPCA) with a comprehensive evaluation method (CEM). In this new method, firstly, the principal component model is updated online and the estimation of load cells is obtained by the principal recursive algorithm based on rank-1 modification, and then the four statistics, i.e., the Hotelling’s T2 statistic, the squared prediction error (SPE) statistic, the Hawkins TH2 statistic, and the principal component related variable residual (PVR) statistic, are used to construct a comprehensive evaluation method (CEM) for fault detection. This proposed method is applied to detecting the zero-point fault of load cells in truck scale, and the experimental results show that the accuracy of the zero-point fault detection is far higher than that of the traditional method (i.e., it is detected by only using any one of the four statistics, such as SPE, T2, TH2, PVR), which proves the effectiveness of this proposed method.

An online and real-time adaptive operational modal parameter identification method based on fog computing in Internet of Things

A large number of smart devices make the Internet of Things world smarter. However, currently cloud computing cannot satisfy real-time requirements and fog computing is a promising technique for real-time processing. Operational modal analysis obtains modal parameters that reflect the dynamic properties of the structure from the vibration response signals. In Internet of Things, the operational modal analysis method can be embedded in the smart devices to achieve structural health monitoring and fault detection. In this article, a four-layer framework for combining fog computing and operational modal analysis in Internet of Things is designed. This four-layer framework introduces fog computing to solve tasks that cloud computing cannot handle in real time. Moreover, to reduce the time and space complexity of the operational modal analysis algorithm and support the real-time performance of fog computing, a limited memory eigenvector recursive principal component analysis–based operational modal analysis approach is proposed. In addition, by examining the cumulative percent variance of principal component analysis, this article explains the reasons behind the identified modal order exchange. Finally, the time-varying operational modal identification results from non-stationary random response signals of a cantilever beam whose density changes slowly indicate that the limited memory eigenvector recursive principal component analysis–based operational modal analysis method requires less memory and runtime and has higher stability and identification effect.

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.

A New Online Operational Modal Analysis Method for Vibration Control for Linear Time-Varying Structure

From the viewpoint of vibration control, if the amplitude of the main frequencies of the vibration response can be reduced, the vibration energy of the structure is greatly reduced. Modal parameters, including modal shapes, natural frequencies, and damping ratios, can reflect the dynamics of the structure and can be used to control the vibration. This paper integrates the idea of “forgetting factor weighting” into eigenvector recursive principal component analysis, and then proposes an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor (ERPCAWF). The proposed method can identify the transient natural frequencies and transient modal shapes online and realtime using only nonstationary vibration response signals. The identified modal parameters are also suitable for online, real-time health monitoring and fault diagnosis. Finally, the modal identification results from a three-degree-of-freedom weakly damped linear time-varying structure shows that the ERPCAWF-based OMA method can effectively identify transient modal parameters online using only nonstationary response signals. The results also show that the ERPCAWF-based approach is faster, requires less memory space, and achieves higher identification accuracy and greater stability than autocorrelation matrix recursive PCA with a forgetting factor-based OMA.

Multivariate statistical approaches for an early detection of foaming in a refinery SCOT unit

Abstract The formation of foam in amine units is an issue that plant operators and field personnel are confronted with on a regular basis. The inability to take proper actions in due time may result in plant downtime and increased emissions. Steep rises in differential pressure indicate foam formation, and are monitored manually in practice. Antifoaming agent is added in order to reduce foaming, but this is usually carried out under time pressure. Hence, plant operating authorities have expressed a strong interest in a data-driven solution capable of providing an early warning against foaming. The classical univariate alarm associated with differential pressure can be ineffective for foaming detection due to high misdetection rates and its lateness of detection. Modern univariate approaches based on pattern recognition techniques may not be suitable either for an early detection, as no universally distinctive features of differential pressure are observed prior to foaming in the present study. In this contribution, the multivariate statistical process monitoring approach based on principal component analysis (PCA) is applied to the early detection of foaming in a continuously operated Shell Claus Off-gas Treating (SCOT) unit of a major refinery in Germany. The results are extended to facilitate fully automated and adaptive modeling based on exponentially weighted recursive principal component analysis (EWRPCA).

Online incipient fault diagnosis based on Kullback‐Leibler divergence and recursive principle component analysis

In “Online Incipient Fault Diagnosis Based on Kullback-Leibler Divergence and Recursive Principal Component Analysis” by Chai, Tao, Mao, Zhang, and Zhu,1 the Acknowledgements section with the following text was omitted. This work was supported by the National Natural Science Foundation of China (Grants No. 61374135 and 61633005). The authors regret the omission.

Study on fault diagnosis algorithm in WSN nodes based on RPCA model and SVDD for multi-class classification

For characteristics of the wireless sensor network (WSN) nodes data streaming in the application environment, the limitations of conventional principal component analysis (PCA) method which depend on the static model in practical application are discussed, an online fault diagnosis algorithm in WSN nodes based on recursive PCA (RPCA) model and support vector data description (SVDD) for multi-class classification is proposed in this paper. The main contents of the method include:The algorithm first applies recursive eigenvalue decomposition techniques based on first-order perturbation (FOP) analysis to update the PCA model adaptively and realize the online fault detection, and then uses SVDD based multi-class classification algorithm to diagnose the fault types. Experimental results show that the algorithm can satisfy the real time needs of data stream processing, but also can track the data changes well. The experimental results based on data sets in real field and experimental data off our typical node failures demonstrate the effectiveness of the proposed algorithm. The algorithm proposed in this paper would improve the safety factor of monitoring sites and it can allows us to know the working state of the node in time and repair or replace it at first time.

Issue Highlights

The Canadian Journal of Chemical EngineeringVolume 96, Issue 2 p. 423-423 Issue HighlightsFree Access Issue Highlights First published: 02 January 2018 https://doi.org/10.1002/cjce.22973AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat 426 Online Incipient Fault Diagnosis Based on Kullback–Leibler Divergence and Recursive Principle Component Analysis Yi Chai, Songbing Tao, Wanbiao Mao, Ke Zhang and Zhiqin Zhu For principal component analysis (PCA), the Hotelling's T2, that is the most common used statistical distance, can fail in detecting small shifts such as a sensor incipient fault with low fault-to-noise ratio (FNR). In this study, a realistic online diagnosis method for incipient faults with low FNR is presented utilizing the Kullback-Leibler divergence (KLD) and recursive PCA. From simulations, it is shown that the proposed approach can detect, isolate, and estimate the sensor incipient fault of the multivariate AR system successfully. 444 Modified Partial Least Square for Diagnosing Key-Performance-Indicator-Related Faults Siyuan He, Youqing Wang and Changqing Liu Faults related to a key performance indicator (KPI) should be paid much attention in the field of multivariate statistical process monitoring. To detect KPI faults, the process data should be divided into KPI-related and KPI-unrelated parts; however, all existing methods did not decompose the residual space according to KPI. In this study, balancing the influence of principal component space and residual space on KPI, the authors find the suitable projection matrix for partial least square (PLS), which can achieve perfect partition of process data in terms of KPI. The novel modification is named as KPI-PLS. 463 Fault Diagnosis Based on the Integration of Exponential Discriminant Analysis and Local Linear Embedding Ruixuan Wang, Jing Wang, Jinglin Zhou and Haiyan Wu The paper proposes two fault diagnosis methods based on the fusion of the exponential discriminant analysis and manifold learning methods, LLEDA and NPEDA. LLEDA, a parallel strategy, focuses on the global supervised discriminant with the tradeoff of local nonlinearity preserving. NPEDA, a cascaded strategy, implements the discriminant analysis with each data firstly constructed by the linear weighted combination of its neighbours. These methods both combine the global discriminant analysis with local structure preserving, so they are particularly suitable for the feature extraction of data with strong nonlinearity and high dimensions. References 1 Y. Chai, S. Tao, W. Mao, K. Zhang, Z. Zhu, Can. J. Chem. Eng. 2018, 96, 426. 2 S. He, Y. Wang, C. Liu, Can. J. Chem. Eng. 2018, 96, 444. 3 R. Wang, J. Wang, J. Zhou, H. Wu, Can. J. Chem. Eng. 2018, 96, 463 Volume96, Issue2February 2018Pages 423-423 ReferencesRelatedInformation

Recursive Principal Component Analysis-Based Data Outlier Detection and Sensor Data Aggregation in IoT Systems

Internet of Things (IoT) is emerging as the underlying technology of our connected society, which enables many advanced applications. In IoT-enabled applications, information of application surroundings is gathered by networked sensors, especially wireless sensors due to their advantage of infrastructure-free deployment. However, the pervasive deployment of wireless sensor nodes generate massive amount of sensor data, and data outliers are frequently incurred due to the dynamic nature of wireless channels. As operation of IoT systems relies on sensor data, data redundancy and data outliers could significantly reduce the effectiveness of IoT applications or even mislead systems into unsafe conditions. In this paper, a cluster-based data analysis framework is proposed using recursive principal component analysis (R-PCA), which can aggregate the redundant data and detect the outliers in the meantime. More specifically, at a cluster head, spatially correlated sensor data collected from cluster members are aggregated by extracting the principal components (PCs), and potential data outliers are determined by the abnormal squared prediction error score, which is defined as the square of residual value after extraction of PCs. With R-PCA, the parameters of PCA model can be recursively updated to adapt to the changes in IoT systems. Cluster-based data analysis framework also releases the computational and processing burdens on sensor nodes. Practical databases-based simulations have confirmed that the proposed framework efficiently aggregates the correlated sensor data with high recovery accuracy. The data outlier detection accuracy is also improved by the proposed method compared to other existing algorithms.

Online incipient fault diagnosis based on Kullback‐Leibler divergence and recursive principle component analysis

AbstractFault detection and isolation (FDI) methods based on the principal component analysis (PCA) model have achieved a large number of theoretical studies and applications, especially for complex and highly dimensional processes. However, the Hotelling's T2, that is the most common used statistical distance, can fail in detecting small shifts such as a sensor incipient fault with low fault‐to‐noise ratio (FNR). Although an incipient fault develops slowly, it cannot be ignored and is necessary to be detected early enough to avoid more serious consequences. In this study, a realistic online diagnosis method for incipient faults with low FNR is presented. Based on probability distribution measure, the Kullback‐Leibler divergence (KLD) is utilized to compare the probability density of each of the latent scores to a reference one. Under the hypothesis of Gaussian distribution, dynamic changes of KLDs are computed via the mean and variance of score vectors, which can be updated online utilizing the recursive principal component analysis (RPCA). From simulations, it is shown that the proposed approach can detect, isolate, and estimate the sensor incipient fault of the multivariate AR system successfully.

Real time damage detection using recursive principal components and time varying auto-regressive modeling

Abstract In this paper, a novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using Recursive Principal Component Analysis (RPCA) in conjunction with Time Varying Auto-Regressive Modeling (TVAR) is proposed. In this method, the acceleration data is used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by TVAR modeling of the first transformed response, to detect the change in the dynamic behavior of the vibrating system from its pristine state to contiguous linear/non-linear-states that indicate damage. Most of the works available in the literature deal with algorithms that require windowing of the gathered data owing to their data-driven nature which renders them ineffective for online implementation. Algorithms focussed on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection is missing, which motivates the development of the present framework that is amenable for online implementation which could be utilized along with suite experimental and numerical investigations. The RPCA algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants, using the rank-one perturbation method. TVAR modeling on the principal component explaining maximum variance is utilized and the damage is identified by tracking the TVAR coefficients. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data without requiring any baseline data. Numerical simulations performed on a 5-dof nonlinear system under white noise excitation and El Centro (also known as 1940 Imperial Valley earthquake) excitation, for different damage scenarios, demonstrate the robustness of the proposed algorithm. The method is further validated on results obtained from case studies involving experiments performed on a cantilever beam subjected to earthquake excitation; a two-storey benchscale model with a TMD and, data from recorded responses of UCLA factor building demonstrate the efficacy of the proposed methodology as an ideal candidate for real time, reference free structural health monitoring.