Conventional Principal Component Analysis Method Research Articles

Robust Fault Detection in Monitoring Chemical Processes Using Multi-Scale PCA with KD Approach

Effective fault detection in chemical processes is of utmost importance to ensure operational safety, minimize environmental impact, and optimize production efficiency. To enhance the monitoring of chemical processes under noisy conditions, an innovative statistical approach has been introduced in this study. The proposed approach, called Multiscale Principal Component Analysis (PCA), combines the dimensionality reduction capabilities of PCA with the noise reduction capabilities of wavelet-based filtering. The integrated approach focuses on extracting features from the multiscale representation, balancing the need to retain important process information while minimizing the impact of noise. For fault detection, the Kantorovich distance (KD)-driven monitoring scheme is employed based on features extracted from Multiscale PCA to efficiently detect anomalies in multivariate data. Moreover, a nonparametric decision threshold is employed through kernel density estimation to enhance the flexibility of the proposed approach. The detection performance of the proposed approach is investigated using data collected from distillation columns and continuously stirred tank reactors (CSTRs) under various noisy conditions. Different types of faults, including bias, intermittent, and drift faults, are considered. The results reveal the superior performance of the proposed multiscale PCA-KD based approach compared to conventional PCA and multiscale PCA-based monitoring methods.

Perturbation analysis on PCA plus graph embedding methods and PCA plus exponential graph embedding methods

PCA plus graph embedding (PCA+GE) methods are popular techniques for dimensionality reduction and face recognition. In these methods, the principal component analysis (PCA) is used first, and then some graph embedding methods are applied. In practice, the data is often perturbed or contaminated, and it has been found that PCA is sensitive to noise, which may affect the accuracy of the subsequent classification. Moreover, the PCA+GE methods can be unstable after data perturbation. To the best of our knowledge, however, there are few results on perturbation analysis of this type of methods. In this work, we show the reason from a matrix perturbation analysis point of view. The main aim of this paper is to look for the reasons that cause the instability. To overcome the difficulty of instability, a framework of PCA plus exponential graph embedding methods is proposed to take the place of the conventional PCA plus graph embedding methods. The computational cost of the proposed methods is comparable to that of the original counterparts, and our methods are much more stable in terms of recognition accuracy. Numerical experiments show the effectiveness of our theoretical results, and demonstrate the efficiency of the new methods on some real-world data sets.

An enhanced temporal algorithm- coupled optimized adaptive sparse principal component analysis methodology for fault diagnosis of chemical processes

Principal component analysis (PCA) is a classic fault diagnosis method widely used in chemical process data modeling. However, the limitation of PCA to handle dynamic and time-variant data has been progressively exposed with the ever-increasing development of artificial intelligence technologies and applications of automation systems in the chemical industry. In this paper, an enhanced temporal algorithm-coupled optimized adaptive sparse PCA (ETA-OASPCA) methodology is proposed with the aim to improve the conventional PCA method by introducing temporal state computation and dynamic adaptive sparsity. The ETA is constructed to extract the state transitions of the time-variant process data by introducing the “Transition” and “Hold”, acquire the region of interest by employing a Maximum Fuzzy c-means (MFCM) method, and then use the region time prediction automaton to label the possible abnormal states. The introduction of dynamic adaptive sparsity in PCA, achieved by presenting an iterative interior point optimization method to update the dynamic sparse penalty term, can impose sparsity constraints on dynamic data calculations, thus enhancing the interpretability of the PCA model. The effectiveness of the proposed method was validated through its application in the Eastman Tennessee process, showing that an average fault detection rate, false alarm rate, and latency of 99.4%, 0.37%, and 4.11 mins can be achieved, respectively.

An enhanced principal component analysis method with Savitzky–Golay filter and clustering algorithm for sensor fault detection and diagnosis

Sensors are critical components of heating, ventilation, and air-conditioning systems. Sensor faults can impact control regulations, resulting in an uncomfortable indoor environment and energy wastage. To detect and identify sensor faults quickly, this study proposes an enhanced principal component analysis (PCA) method using the Savitzky–Golay (SG) filter and density-based spatial clustering of applications with noise (DBSCAN) algorithm. First, the DBSCAN algorithm is used to automatically divide the dataset into sub-datasets with different working conditions to reduce the interference information and concentrate the information of each training set. Then, each sub-dataset is smoothed using the SG algorithm to reduce the effects of data fluctuations. The processed dataset is used to build a sub-PCA model that ultimately identifies and locates faults. The proposed strategy is validated using field operating data for 20 air-handling unit (AHU) systems, as obtained from a large commercial building. The fault detection performances of multiple strategies are compared and analysed under different degrees of bias in single AHU and multiple AHU systems. The verification results show that the proposed DBSCAN-SG-PCA model offers significant improvements in fault detection accuracy and fault identification sensitivity over the conventional PCA method. Compared with the SG-PCA model, the proposed model reduces the amount of data required for fault detection by an average of 13.7%, and the Youden index is increased by an average of 0.21. Furthermore, the fault detection accuracy of the proposed model is ±0.7 °C.

Seismic Image Dip Estimation by Multiscale Principal Component Analysis

Dip estimation of geological structures plays an important role in geophysical applications. Principal component analysis (PCA) is a common approach to estimating local dips by decomposing the local gradients of a seismic migration image and obtaining its principal eigenvector. However, PCA is difficult to obtain robust and high-resolution dip estimations for low signal-to-noise ratio (SNR) migration images, while multiscale schemes in digital image processing can achieve a better compromise between noise robustness and dip resolution. Therefore, we propose to adopt a multiscale PCA (MPCA) method coupled with a propagation-weight-based fusion mechanism for seismic dip estimation of low SNR migration image. MPCA consists of three steps: 1) constructing an image pyramid by repeating the low-pass filter from fine to coarse scales; 2) estimating the dip using the PCA method at each scale of the image pyramid; and 3) fusing the multiscale dip estimations using propagation weights from coarse to fine scales. We test the MPCA method on an omnidirectional dip pattern and three seismic migration images and compare with the conventional PCA and multiscale methods. The results demonstrate that MPCA yields robust and high-resolution dip estimations for low SNR seismic migration images.

Derivation of a Dynamic Market Risk Signal Using Kernel PCA and Machine Learning

Kernel principal component analysis (PCA) is an extension of the conventional PCA method that employs a kernel transformation whereby hidden patterns in possibly multidimensional data may be detected and extracted more explicitly. In this article, the author applies the method of kernel PCA to a currency prediction case study and derives an aggregate market signal. It is observed that this signal has desirable information-compression properties and may be used as a predictive risk indicator in the return prediction models. Used alongside common drivers of exchange rates, a kernel PCA signal enhances in-sample and out-of-sample risk-adjusted performance across a range of machine learning strategies. In particular, the author observes that a kernel PCA signal remains robust and predictive during volatile market conditions. The kernel PCA signal may be used as a machine learning feature to inform and support data-driven risk management strategies. TOPICS:Big data/machine learning, derivatives Key Findings • This article develops a risk signal based on the method of kernel PCA. • Kernel PCA conveys desirable information on market dynamics. • Currency machine learning strategies benefit from this kernel PCA feature.

Root causality analysis at early abnormal stage using principal component analysis and multivariate Granger causality

As fault detection technologies have been developed, process fault diagnosis at early abnormal stage has come to be considered a major problem. In this work, a method to analyze the root cause of faults is developed to provide proper information at the early abnormal stage. First, principal component analysis (PCA) is used for the early detection of the process fault. Then, the contributions, from which the normal portion is removed, are decomposed by singular value decomposition (SVD) method to select the hierarchical sensors. Finally, the multivariate Granger causality (MVGC) method is used to construct the sensor causalities using the hierarchical sensors. The developed methodology is verified using the liquefied natural gas fractionation process model, which embeds a sufficient number of highly correlated sensors. The results are compared with the conventional principal component analysis method and amplification of the residual contribution method to verify the advantages of the proposed method.

An Improved Principal Component Analysis in the Fault Detection of Multi-sensor System of Mobile Robot

To cope with the fault detection in dynamic conditions of inertial components in the mobile robots, an improved principal component analysis (PCA) method was proposed. This work took a five gyroscopes redundancy allocation model to realize the measurement of the attitude. It is hard to distinguish the fault message from dynamic message in dynamic system that results in false alarm and missing inspection, so we firstly used the parity vector to preprocess the measurement data from the sensors. A fault was detected when the preprocessed data was dealt with PCA method. The effectiveness of the improved PCA method introduced in this paper was verified by comparing fault detection capabilities of conventional PCA method under the dynamic conditions of the step fault. The results of the simulation and experimental verification of the method was expected to contribute to the fault detection and improve the accuracy and reliability of the multi-sensors system in dynamic conditions.

An enhanced PCA method with Savitzky-Golay method for VRF system sensor fault detection and diagnosis

Sensor faults of air conditioning systems are harmful to optimal control strategies and system performance resulting in poor control of the indoor environment and waste of energy. In order to improve the fault detection and diagnosis (FDD) performance, this paper presents an enhanced sensor fault detection and diagnosis method based on the Satizky-Golay (SG) method and principal component analysis (PCA) method for the VRF system, namely SG-PCA method. Due to the volatility of the original data set of VRF system, the original data are smoothed using SG method at first. Then, the smoothed data are used for PCA model training and fault detection and diagnosis. In order to determine parameters of the SG method, an optimization index is proposed, which is calculated by the signal to noise ratio (SNR), the standard deviation (SD) and the self-detection efficiency. This SG-PCA method for VRF system sensor FDD is validated using field operation data of the VRF system. Various sensor faults at different fault levels are introduced. The results have showed that the SG-PCA method can significantly improve the fault detection and diagnosis performance compared to conventional PCA method.

Adaptive partitioning PCA model for improving fault detection and isolation

In chemical process, a large number of measured and manipulated variables are highly correlated. Principal component analysis (PCA) is widely applied as a dimension reduction technique for capturing strong correlation underlying in the process measurements. However, it is difficult for PCA based fault detection results to be interpreted physically and to provide support for isolation. Some approaches incorporating process knowledge are developed, but the information is always shortage and deficient in practice. Therefore, this work proposes an adaptive partitioning PCA algorithm entirely based on operation data. The process feature space is partitioned into several sub-feature spaces. Constructed sub-block models can not only reflect the local behavior of process change, namely to grasp the intrinsic local information underlying the process changes, but also improve the fault detection and isolation through the combination of local fault detection results and reduction of smearing effect. The method is demonstrated in TE process, and the results show that the new method is much better in fault detection and isolation compared to conventional PCA method.

An introduction to factor analysis for radio frequency interference detection on satellite observations

A novel radio frequency interference (RFI) detection method is introduced for satellite-borne passive microwave radiometer observations. This method is based on factor analysis, in which variability among observed and correlated variables is described in terms of factors. In the present study, this method is applied to the Tropical Rainfall Measuring Mission (TRMM)/TRMM Microwave Imager (TMI) and Aqua/Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) satellite measurements over the land surface to detect the RFI signals, respectively, in 10 and 6 GHz channels. The RFI detection results are compared with other traditional methods, such as spectral difference method and principal component analysis (PCA) method. It has been found that the newly proposed method is able to detect RFI signals in the C- and X-band radiometer channels as effectively as the conventional PCA method.

Monitoring multi-mode plant-wide processes by using mutual information-based multi-block PCA, joint probability, and Bayesian inference

A multi-mode plant-wide process monitoring scheme that integrates mutual information (MI)-based multi-block principal component analysis (PCA), joint probability, and Bayesian inference is developed. Given that the prior process is not always available, an MI-based block division method is proposed to divide blocks automatically by considering both cross-relations and high-order statistical information among variables. The PCA monitoring model is established in each sub-block and each mode, and a joint probability based on T2 statistics is defined to identify running-on mode. Then, the statistics in different sub-blocks are combined by using Bayesian inference to provide an intuitive indication. Finally, an improved contribution plot method is proposed to identify the root cause of faults. The feasibility and efficiency of the proposed method are evaluated by case studies on a numerical process and the Tennessee Eastman benchmark process. Monitoring results and comparisons with conventional PCA methods indicate the superiority of the proposed method.

Just‐in‐time reorganized PCA integrated with SVDD for chemical process monitoring

Although principal component analysis (PCA) is widely used for chemical process monitoring, improvements in the selection of principal components (PCs) are still needed. Given that the determination of complicated and changing fault information is not guaranteed using offline‐selected PCs, this study proposes a just‐in‐time reorganized PCA model that objectively selects the PCs online for process monitoring. The importance of the PCs is evaluated online by kernel density estimation. The PCs indicating more varied information are then selected to reorganize the PCA model. Given that the most useful fault information is concentrated, support vector data description is used to replace traditional statistics, thereby relaxing the Gaussian assumption of the process data. The monitoring performances of the proposed method are evaluated under three cases. Compared with conventional PCA methods, more varied information is captured online, and the monitoring performances are improved. © 2014 American Institute of Chemical Engineers AIChE J, 60: 949–965, 2014

Evaluation-based closed-loop errors using principal component analysis and self-organisation map with an application to a pickling process

Closed-loop control is a basic technology in control engineering. Its role is to avoid the tracking error between set points and real variables. The evaluation of plant performance can be based on multivariate statistical process control connected to closed-loop errors behaviour. Due to its practicality, this approach has found many applications in several industries. This paper suggests a combined use of principal component analysis (PCA) and self-organisation map (SOM) algorithms to evaluate the process on the basis of closed-loop errors dynamic. Generally, it is possible to evaluate a product quality in the basis of the dynamic changes of the closed-loop control errors. In this paper, a new method based on the analysis of the control errors is proposed; it is carried out by a combined use of the PCA-SOM algorithm. Comparatively to the conventional PCA method, this new technique is characterised by the performant indexes that give an accurate evaluation of the process variability and its impact on the product quality. As shown in the different simulation results, the proposed approach gives a global evaluation and improves considerably the performance of computed indexes used for the evaluation of the controlled process.

Principal Component Analysis by $L_{p}$ -Norm Maximization

This paper proposes several principal component analysis (PCA) methods based on Lp-norm optimization techniques. In doing so, the objective function is defined using the Lp-norm with an arbitrary p value, and the gradient of the objective function is computed on the basis of the fact that the number of training samples is finite. In the first part, an easier problem of extracting only one feature is dealt with. In this case, principal components are searched for either by a gradient ascent method or by a Lagrangian multiplier method. When more than one feature is needed, features can be extracted one by one greedily, based on the proposed method. Second, a more difficult problem is tackled that simultaneously extracts more than one feature. The proposed methods are shown to find a local optimal solution. In addition, they are easy to implement without significantly increasing computational complexity. Finally, the proposed methods are applied to several datasets with different values of p and their performances are compared with those of conventional PCA methods.

Chemical processes monitoring based on weighted principal component analysis and its application

Conventional principal component analysis (PCA)-based methods employ the first several principal components (PCs) which indicate the most variances information of normal observations for process monitoring. Nevertheless, fault information has no definite mapping relationship to a certain PC and useful information might be submerged under the retained PCs. A new version of weighted PCA (WPCA) for process monitoring is proposed to deal with the situation of useful information being submerged and reduce missed detection rates of T2 statistic. The main idea of WPCA is building conventional PCA model and then using change rate of T2 statistic along every PC to capture the most useful information in process, and setting different weighting values for PCs to highlight useful information when online monitoring. Case studies on Tennessee Eastman process demonstrate the effectiveness of the proposed scheme and monitoring results are compared with conventional PCA method.

Classification and Source Determination of Medium Petroleum Distillates by Chemometric and Artificial Neural Networks: A Self Organizing Feature Approach

Three different medium petroleum distillate (MPD) products (white spirit, paint brush cleaner, and lamp oil) were purchased from commercial stores in Glasgow, Scotland. Samples of 10, 25, 50, 75, 90, and 95% evaporated product were prepared, resulting in 56 samples in total which were analyzed using gas chromatography-mass spectrometry. Data sets from the chromatographic patterns were examined and preprocessed for unsupervised multivariate analyses using principal component analysis (PCA), hierarchical cluster analysis (HCA), and a self organizing feature map (SOFM) artificial neural network. It was revealed that data sets comprised of higher boiling point hydrocarbon compounds provided a good means for the classification of the samples and successfully linked highly weathered samples back to their unevaporated counterpart in every case. The classification abilities of SOFM were further tested and validated for their predictive abilities where one set of weather data in each case was withdrawn from the sample set and used as a test set of the retrained network. This revealed SOFM to be an outstanding mechanism for sample discrimination and linkage over the more conventional PCA and HCA methods often suggested for such data analysis. SOFM also has the advantage of providing additional information through the evaluation of component planes facilitating the investigation of underlying variables that account for the classification.

Improve robustness of sparse PCA by L1-norm maximization

Various sparse principal component analysis (PCA) methods have recently been proposed to enhance the interpretability of the classical PCA technique by extracting principal components (PCs) of the given data with sparse non-zero loadings. However, the performance of these methods is prone to be adversely affected by the presence of outliers and noises. To alleviate this problem, a new sparse PCA method is proposed in this paper. Instead of maximizing the L2-norm variance of the input data as the conventional sparse PCA methods, the new method attempts to capture the maximal L1-norm variance of the data, which is intrinsically less sensitive to noises and outliers. A simple algorithm for the method is specifically designed, which is easy to be implemented and converges to a local optimum of the problem. The efficiency and the robustness of the proposed method are theoretically analyzed and empirically verified by a series of experiments implemented on multiple synthetic and face reconstruction problems, as compared with the classical PCA method and other typical sparse PCA methods.

Adaptive process monitoring using efficient recursive PCA and moving window PCA algorithms

In process monitoring, principal component analysis (PCA) is a very popular method and has found wide applications. Conventionally, a fixed PCA model is used for monitoring. This paper presents the use of both recursive PCA (RPCA) and moving window PCA (MWPCA) to online update the PCA model and its corresponding control limits for monitoring statistics. An efficient algorithm is derived based on rank-one matrix update of the covariance matrix, which is tailored for RPCA and MWPCA computations. By the proposed method, the performance of process monitoring can be improved in two aspects. First, more consistent PCA model and control limits for monitoring statistics are resulted because of the increasing number of normal observations for modeling. Second, for parameter-varying processes, when natural drifting behavior or changing of operation region is acceptable, more reasonable PCA model and control limits for monitoring statistics are obtained in an adaptive manner. Simulation results have shown the effectiveness of the proposed approaches compared to the conventional PCA and RPCA methods.

Alzheimer's disease detection in functional images using 2D Gabor wavelet analysis

Presented is a Gabor wavelet (GW) based analysis of functional brain images by integrating the 2D GW representation of the images for image classification applied to early diagnosis of Alzheimer's disease. The 2D GW representation of the brain images is processed by means of a principal component analysis (PCA) for feature extraction and support vector machines (SVMs) for image classification. The proposed method yields up to 96% classification accuracy with 100% sensitivity, thus becoming an accurate method for image classification. Comparison between the conventional PCA plus SVM method and the proposed method is also provided. In addition, the proposed method with Gabor wavelets increases the outcomes of other methods based on voxel as features (VAF), PCA, and so on.