Dynamic Principal Component Analysis Research Articles

Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors

This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between predictors and the target variable of interest by scaling and combining the predictors and their lagged values, resulting in an effective dynamic forecasting. Unlike the traditional diffusion-index approach, which does not learn the relationships between the predictors and the target variable before conducting PCA, we first rescale each predictor according to their significance in forecasting the targeted variable in a dynamic fashion, and a PCA is then applied to a rescaled and additive panel, which establishes a connection between the predictability of the PCA factors and the target variable. We also propose to use penalized methods such as the LASSO to select the significant factors that have superior predictive power over the others. Theoretically, we show that our estimators are consistent and outperform the traditional methods in prediction under some mild conditions. We conduct extensive simulations to verify that the proposed method produces satisfactory forecasting results and outperforms most of the existing methods using the traditional PCA. An example of predicting U.S. macroeconomic variables using a large number of predictors showcases that our method fares better than most of the existing ones in applications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Industrial process fault detection based on dynamic kernel principal component analysis combined with weighted structural difference

AbstractThe practical application of traditional data‐driven techniques for process monitoring encounters significant challenges due to the inherent nonlinear and dynamic nature of most industrial processes. Aiming at the problem of nonlinear dynamic process monitoring, a novel fault detection method based on dynamic kernel principal component analysis combined with weighted structural difference (DKPCA‐WSD) is proposed in this paper. Initially, the proposed method leverages a sophisticated nonlinear transformation to project the augmented matrix of the original input data into a high‐dimensional feature space, thereby facilitating the establishment of a DKPCA model. Subsequently, the WSD statistic is computed, utilizing a widely known sliding window technique, to quantify the mean and standard deviation differences across data structures. Ultimately, the WSD statistic is utilized for fault detection, completing the process monitoring task. By integrating the capability of DKPCA to capture nonlinear dynamic characteristics with the effectiveness of the WSD statistic in mitigating the impact of non‐Gaussian data distributions, DKPCA‐WSD significantly enhances the monitoring performance of traditional DKPCA in nonlinear dynamic processes. The proposed method is evaluated through a numerical case exhibiting nonlinear dynamic behaviors and a simulation model of a continuous stirred tank reactor. A comparative analysis with conventional methods, including principal component analysis (PCA), dynamic principal component analysis, KPCA, PCA similarity factor (SPCA), DKPCA, and moving window KPCA (MWKPCA), demonstrates that DKPCA‐WSD outperforms traditional fault detection techniques in nonlinear dynamic processes, offering a substantial improvement in monitoring performance.

PROCESS MONITORING IN HYBRID ELECTRIC VEHICLES BASED ON DYNAMIC NONLINEAR METHOD

Highway third-level faults can significantly deteriorate the reliability and performance of hybrid electric vehicle (HEV) powertrains. This study presents a novel process monitoring method aimed at addressing this issue. We propose a multivariate statistical method based on dynamic nonlinear improvement, namely dynamic neural component analysis (DNCA). This method does not require the establishment of precise analytical models; instead, it only necessitates acquiring data from HEV powertrains. Through numerical simulation and real HEV experiments, we demonstrate the effectiveness of this approach in monitoring highway third-level faults. The testing outcomes demonstrate that DNCA outperforms traditional dynamic methods like dynamic principal component analysis (DPCA), conventional nonlinear methods such as kernel PCA (KPCA) and NCA, as well as traditional dynamic nonlinear methods like DKPCA.

Dynamic sparse PCA: a dimensional reduction method for sensor data in virtual metrology

Virtual metrology (VM) is the ideal technique for predicting the quality of every wafer and reducing overall inspection costs in semiconductor manufacturing. The data from numerous monitoring sensors in semiconductor production poses challenges in terms of data dimensionality. Thus, dimensionality reduction techniques are required before building the prediction model in VM. Additionally, to reduce the sensor cost, it is crucial to determine the sensors that contribute significantly to the output of the prediction model. Therefore, in this paper, we propose a dimensionality reduction technique called dynamic sparse principal component analysis to establish global sparsity in the first few principal components. The proposed method seeks extracted features that involve a limited number of sensors in the VM to reduce sensor cost and increase the interpretability of the features while reasonably capturing data variability. The experimental results demonstrate that the proposed method is not sensitive to the scale of the problem and can solve the large-scale high-dimensional problems that are commonly encountered in semiconductor manufacturing.

Raman and photoluminescence signal separation in Raman hyperspectral imagery including noise reduction

AbstractRaman hyperspectral imaging (RHSI) is a valuable tool for gaining crucial information about the chemical composition of materials. However, obtaining clear Raman signals is not always a trivial task. Raw Raman signals can be susceptible to photoluminescence interference and noise. Hence, the preprocessing of RHSI is a required step for an effective and reliable chemical analysis. The main challenge is splitting the measured RHSI into separate Raman photoluminescence signals. Since no golden‐standard exists, it is non‐trivial to validate the correctness of the separated signals. While current state‐of‐the‐art preprocessing methods are effective, they require expert knowledge and involve unintuitive hyperparameters. Current approaches also lack generalizability, requiring extensive hyperparameter tuning on a case‐by‐case basis, while even then results are not always as expected. To this end, this work proposes a novel iterative RHSI preprocessing pipeline for splitting raw Raman signals and noise removal based on linear spline and radial basis function regression (IlsaRBF). The proposed method involves hyperparameters based on the physical properties of Raman spectroscopy, making them intuitive to use. This leads to more robust and stable hyperparameters, reducing the necessity for extensive hyperparameter tuning. A thorough evaluation shows that the proposed method outperforms the current state‐of‐the‐art. Additionally, a cosmic ray identification and removal algorithm (CRIR) and dynamic PCA for noise reduction are introduced. A standalone tool containing our proposed methods is provided, making RHSI preprocessing available to a broader audience, aiding further research and advancements in the field of Raman spectroscopy.

Insights from in silico exploration of major curcumin analogs targeting human dipeptidyl peptidase IV

The goal of this work is to use a variety of in-silico techniques to identify anti-diabetic agents against DPP-IV enzyme from five main curcumin analogues. To produce the successful molecules, five main curcumin analogues were docked into the active site of DPP-IV enzyme. In comparison to the control molecule (Saxagliptin, −6.9 kcal/mol), all the compounds have the highest binding affinity (-7.6 to −7.7 kcal/mol) for the DPP-IV enzyme. These compounds underwent further testing for studies on drug-likeness, pharmacokinetics, and acute toxicity to see the efficacy and safety of compounds. To assess the stability of the docking complex and the binding posture identified during the docking experiment, our study got THC as the lead compound, which was then exposed to 200 ns of molecular dynamic simulation and PCA analysis. Additionally, DFT calculations were conducted to determine the thermodynamic, molecular orbital, and electrostatic potential characteristics of lead compound. Overall, the lead chemical has shown strong drug-like properties, is non-toxic, and has a sizable affinity for the DPP-IV enzyme. Communicated by Ramaswamy H. Sarma

Graphical Principal Component Analysis of Multivariate Functional Time Series

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a unified framework for functional graphical models and dynamic principal component analysis, and further extend it to optimally reconstruct signals from contaminated functional data using graphical-level information. We investigate asymptotic properties of the resulting estimators and illustrate the effectiveness of our proposed approach through extensive simulations. We apply our method to hourly air pollution data that were collected from a monitoring network in China.

Fault detection and diagnosis for chemical processes using dynamic global–local preserving projections

AbstractMost traditional multivariate statistical monitoring methods require an assumption that the observation values at a certain moment and a past moment are statistically independent. However, in actual chemical and biological processes, the sample at a certain moment is often affected by the previous moment. Therefore, given the problem of more false alarms and poor detection ability based on the traditional principal component analysis, this article proposes a dynamic global–local preserving projections (DGLPP) algorithm. Unlike dynamic local preserving projections (DLPP) and dynamic principal component analysis (DPCA), DGLPP controls the global and local information retained in the dimensionality reduction data by introducing weight coefficients, which makes the algorithm applicable to more types of industrial processes. Moreover, new parameter determination methods are also proposed for improved detection and diagnosis. Through the improved contribution graph method, we can see the influence degree of each variable on the fault, to monitor and isolate the fault. Finally, by verifying the operation of the multivariable process and two practical cases, the results show that compared with DPCA, DLPP, and global local retained projection (GLPP) methods, the performance under this method has been significantly improved.

Improved postprocessing of dynamic glucose-enhanced CEST MRI for imaging brain metastases at 3 T

BackgroundDynamic glucose-enhanced (DGE) chemical exchange saturation transfer (CEST) has the potential to characterize glucose metabolism in brain metastases. Since the effect size of DGE CEST is small at 3 T (< 1%), measurements of signal-to-noise ratios are challenging. To improve DGE detection, we developed an acquisition pipeline and extended image analysis for DGE CEST on a hybrid 3-T positron emission tomography/magnetic resonance imaging system.MethodsThis cross-sectional study was conducted after local ethical approval. Static Z-spectra (from -100 to 100 ppm) were acquired to compare the use of 1.2 versus 2 ppm to calculate static glucose-enhanced (glucoCEST) maps in 10 healthy volunteers before and after glucose infusion. Dynamic CEST images were acquired during glucose infusion. Image analysis was optimized using motion correction, dynamic B0 correction, and principal component analysis (PCA) to improve the detection of DGE CEST in the sagittal sinus, cerebrospinal fluid, and grey and white matter. The developed DGE CEST pipeline was applied to four patients diagnosed with brain metastases.ResultsGlucoCEST was strongest in healthy tissues at 2 ppm. Correcting for motion, B0, and use of PCA locally improved DGE maps. A larger contrast between healthy tissues and enhancing regions in brain metastases was found when dynamic B0 correction and PCA denoising were applied.ConclusionWe demonstrated the feasibility of DGE CEST with our developed acquisition and analysis pipeline at 3 T in patients with brain metastases. This work enables a direct comparison of DGE CEST to 18F-fluoro-deoxy-D-glucose positron emission tomography of glucose metabolism in patients with brain metastases.Relevance statementContrast between brain metastasis and healthy brain tissue in DGE CEST MR images is improved by including principle component analysis and dynamic magnetic field correction during postprocessing. This approach enables the detection of increased DGE CEST signal in brain metastasis, if present.Key points• Despite the low signal-to-noise ratio, dynamic glucose-enhanced CEST MRI is feasible at 3 T.• Principal component analyses and dynamic magnetic field correction improve DGE CEST MRI.• DGE CEST MRI does not consequently show changes in brain metastases compared to healthy brain tissue.• Increased DGE CEST MRI in brain metastases, if present, shows overlap with contrast enhancement on T1-weighted images.Graphical

Fault detection, diagnosis and calibration of heating, ventilation and air conditioning sensors by combining principal component analysis and improved bayesian inference

Sensors are crucial components in heating, ventilation and air conditioning (HVAC) systems. When sensors fault, the HVAC system deviates from normal operation, resulting in an increase in energy consumption and a decline in equipment lifespan. Therefore, it is vital to detect, diagnose and calibrate the sensor faults. Bayesian Inference (BI) in data-driven methods is highly effective for sensor calibration. However, its application faces two major shortcomings. First, the conventional BI method cannot effectively calibrate sensor drift faults. Second, the BI method relies on sensor fault detection and diagnosis (FDD). To address these shortcomings, this study proposed an improved BI (imBI) method that enhanced the capability of BI to calibrate drift faults by updating the calibration constant x. Moreover, sensor fault detection, diagnosis and calibration (FDDC) were conducted by combining Principal Component Analysis (PCA) with the imBI method (PCA-imBI). The proposed methods were validated through two case studies involving a chiller system and an air handling unit (AHU) system, having different degrees of bias faults and drift faults in temperature sensors, differential pressure sensors and flow sensors. The results demonstrated that the PCA-imBI method effectively achieved FDDC for both bias and drift faults. Considering the case studies, the average calibration rates for bias and drift faults reached 99.74 % and 95.29 %, respectively. For drift fault calibration, the imBI method outperformed the dynamic calibration method and PCA reconstruction method by 16.04 % and 4.31 %, respectively.

Industrial Process Control Using DPCA and Hierarchical Pareto Optimization

The control of large-scale industrial systems has several criteria, such as ensuring high productivity, low production costs and the lowest possible environmental impact. These criteria must be established for all subsystems of the large-scale system. This study is devoted to the development of a hierarchical control system that meets several of these criteria and allows for the separate optimization of each subsystem. Multicriteria optimization is based on the processing of data characterizing production processes, which makes it possible to organize a multidimensional statistical control process. Using neural networks to model the technological processes of subsystems and the method of dynamic principal component analysis (DPCA) to reduce the dimensionality of control problems allows us to find more efficient solutions. Using the example of a two-level hierarchy, we showed a variant of the connection between two subsystems by parameters.

A novel fault detection scheme for a nonlinear dynamic process based on generalized non‐negative matrix projection‐maximum mean discrepancy: Application on the DAMADICS benchmark process

AbstractIn order to address the issue of minor fault detection in nonlinear dynamic processes, this paper proposes a fault detection method based on generalized non‐negative matrix projection‐maximum mean discrepancy (GNMP‐MMD). Firstly, the GNMP is employed to acquire the residual scores of the samples. Subsequently, a sliding window approach is integrated with MMD for real‐time monitoring of sample status within the residual subspace. In this study, GNMP is utilized to mitigate the impact of non‐Gaussianity in data distribution, while MMD serves to alleviate autocorrelation among samples. A numerical case and experimental data collected from the DAMADICS process are utilized to simulate and validate the proposed method. Compared to traditional principal component analysis (PCA), dynamic principal component analysis (DPCA), dynamic kernel principal component analysis (DKPCA), non‐negative matrix factorization (NMF), GNMP, and MMD, the experiment results clearly illustrate the feasibility of the proposed method.

FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series

We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by common factors, models the remaining idiosyncratic dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via l 1 -regularized Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarizes both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.

An enhanced DPCA fault diagnosis method based on hierarchical cluster analysis

AbstractA large amount of data generated in industrial processes exhibit multi‐modal, nonlinear, time‐domain correlation, and other characteristics. This poses great difficulty for the traditional principal component analysis (PCA) method since it requires that the input data need to conform to the Gaussian distribution. However, the data may have autocorrelation, that is, the data at the current moment will be affected by the past data. To this end, this paper proposes an enhanced dynamic principal component analysis (DPCA) method based on hierarchical clustering analysis. On the basis of the DPCA algorithm, the idea of data classification and enhanced training is used to strengthen the training of the dimensionality reduction matrix. Then, calibration, on‐line monitoring, and fault diagnosis of process data can be conducted. Finally, this paper demonstrates that the performance of the proposed method is greatly improved compared with PCA and DPCA through the Tennessee Eastman process system.

Gas detection strategy to suppress flow rate interference baesd on semiconductor sensor dynamic temperature modulation measurement

Semiconductor gas sensors are widely used in industry, commerce and other fields. Flow rate has great influence on its response, but there was no breakthrough research progress at present. Usually, the interference is overcome by suppressing the expression of flow rate information at the output of the sensor. In this paper, a new research idea is put forward, which uses the ability of expanding output information of dynamic temperature modulation method to express the influence of flow rate on sensor. A typical case of butanone detection by SnO2 sensor was taken as the main experiment. By analyzing the microcosmic characteristic difference between flow rate and concentration in dynamic response, the change rule of dynamic response with flow rate change can be grasped, thus eliminating its interference to qualitative analysis. On the basis of dynamic temperature modulation, PCA and LDA are used to reduce the dimension of data, and the distribution law of two-dimensional score figure is obtained about the change of concentration and flow rate. In addition, the method is validated by using ethyl ether and toluene, and the same experimental phenomena are obtained. The results show that it is not only feasible but also has certain universality to use dynamic temperature modulation method to suppress the influence of flow rate on quantitative analysis.

A novel white component analysis for dynamic process monitoring

Dynamic principal component analysis has long been a popular multivariate statistical process monitoring method. However, the resulting residuals are typically subject to serial correlations, thereby compromising the detection capability in face of dynamic data. In this paper, a novel white component analysis (WCA) model is proposed to enforce latent variables to have noise-like properties, thereby well catering to the independent assumption that is critical in monitoring statistic design. A new whiteness index for finite-length time series is put forward, which acts as the objective of each component. To solve the optimization problem, a tailored algorithm based on alternating direction method of multipliers is developed. Using “white” components, a new W-statistic is coined to effectively detect violation of dynamic relations by inspecting the presence of unmodeled dynamics. By incorporating classical variance-based statistics, we arrive at a new dynamic process monitoring scheme that offers deep insights into abnormal situations. Comprehensive case studies corroborate the validity of the WCA-based process monitoring approach, and in particular, the sensitivity of W-statistic to dynamics anomalies.

A Holistic Evaluation of Multivariate Statistical Process Monitoring in a Biological and Membrane Treatment System.

Unsupervised process monitoring for fault detection and data cleaning is underdeveloped for municipal wastewater treatment plants (WWTPs) due to the complexity and volume of data produced by sensors, equipment, and control systems. The goal of this work is to extensively test and tune an unsupervised process monitoring method that can promptly identify faults in a full-scale decentralized WWTP prior to significant system changes. Adaptive dynamic principal component analysis (AD-PCA) is a dimension reduction method modified to address autocorrelation and nonstationarity in multivariate processes and is evaluated in this work for its ability to continuously detect drift, shift, and spike faults. For spike faults, univariate drift faults, and multivariate shift faults, implementing AD-PCA on data that are subset by treatment processes and operating states with significant differences in covariates and whose model parameters use week-long training windows, moderate cumulative variance, and a high threshold for detection was found to detect faults prior to existing operational thresholds. To improve the consistency with which the AD-PCA method detects out-of-control conditions in real time, additional work is needed to remove outliers prior to model fitting and to detect multivariate drift faults in which the covariates change slowly.

Health Indicator Similarity Analysis-Based Adaptive Degradation Trend Detection for Bearing Time-to-Failure Prediction

Time-to-failure (TTF) prediction of bearings is vital to the prognostic and health management of rotating machines. Owing to the shifty degradation trends (DTs) of bearings, it is still difficult to obtain accurate TTF prognostic results. To solve this problem, this paper proposes an online, continuously updated TTF prognostic method based on health indicator (HI) similarity analysis and DT detection. First, multiple degradation features are extracted and fused to construct principal component HI by using dynamic principal component analysis. Next, exponential degradation models are fitted using the HI values for future state prediction. By regarding several HI values as a tested segment, the DT is detected by analyzing the similarity of the tested segment and the fitted curve. Finally, TTF is predicted by extrapolating the DT to hit the estimated failure threshold. Two case studies based on public bearing datasets demonstrate the superiority of the proposed approach over state-of-the-art methods.

Data-driven supply chain monitoring using canonical variate analysis

The monitoring of supply chain operations and the ability to detect abnormal operation in a timely manner is important to the functioning and economics of a supply chain system. This paper presents a data-driven supply chain monitoring method based on canonical variate analysis (CVA). A sparse CVA algorithm is used to address singular covariance matrices. In addition, a fault impact prediction method that utilizes the time-dependent relationships inherent in the CVA model is proposed. The proposed monitoring scheme is validated on two case studies — the classical beer distribution game, and a more complicated supply chain that has material flow in forward and reverse directions. The performance of CVA in fault detection is examined and compared against dynamic principal component analysis (DPCA) under cross-correlated and autocorrelated demand. Results show that CVA is effective in detecting abnormal supply chain operations, and achieves comparable performance to DPCA in a lower-dimensional latent space.

Exploring the interaction between 3-D structure of TLR 9 and prostaglandin analogues

Toll-like receptor 9 (TLR9) is a class of pattern recognition receptors (PRRs) approved to have an essential role with the development of autoimmune illnesses such as psoriasis and arthritis. TRL9 is predominantly expressed on dendritic cells (DCs) and macrophages, and it mediates antigen presentation to T cells. In this regard, interfering with this interaction by inhibiting TLR9 could be an effective immunotherapy strategy for certain diseases. Based on previous research (Degraaf et al.2014, Farrugia et al., 2017) indicating that prostaglandins play a significant role in regulating or reducing the expression of TLRs, their function against intracellular TLRs such as TLR9 may involve direct inhibition of these receptors. The 3D structure of the human-TLR9 is modelled and described molecularly and then prepared to be docked by prostaglandin analogues, followed by molecular dynamic (MD) simulation, MM/PBSA analysis, and PCA analysis. The study uncovered significant direct interactions between TLR9 and prostaglandin analogues, specifically with the FDA-approved Bimatoprost (BI), which demonstrates the highest binding affinity (calculated as an estimated affinity) and an interesting MM/PBSA score and should be the primary focus of future research into the treatment of autoimmune diseases. In addition, the modelled structure of human-TLR9 and its binding site described in this study could serve as a useful starting point for the development of additional inhibitors.