T2 Statistic Research Articles

Neighborhood preserving neural network for fault detection

A novel statistical feature extraction method, called the neighborhood preserving neural network (NPNN), is proposed in this paper. NPNN can be viewed as a nonlinear data-driven fault detection technique through preserving the local geometrical structure of normal process data. The “local geometrical structure ” means that each sample can be constructed as a linear combination of its neighbors. NPNN is characterized by adaptively training a nonlinear neural network which takes the local geometrical structure of the data into consideration. Moreover, in order to extract uncorrelated and faithful features, NPNN adopts orthogonal constraints in the objective function. Through backpropagation and eigen decomposition (ED) technique, NPNN is optimized to extract low-dimensional features from original high-dimensional process data. After nonlinear feature extraction, Hotelling T2 statistic and the squared prediction error (SPE) statistic are utilized for the fault detection tasks. The advantages of the proposed NPNN method are demonstrated by both theoretical analysis and case studies on the Tennessee Eastman (TE) benchmark process. Extensive experimental results show the superiority of NPNN in terms of missed detection rate (MDR) and false alarm rate (FAR). The source code of NPNN can be found in https://github.com/htzhaoecust/npnn.

Tailored meta-analysis: an investigation of the correlation between the test positive rate and prevalence

Background and ObjectiveMeta-analysis may produce estimates that are unrepresentative of a test's performance in practice. Tailored meta-analysis (TMA) circumvents this by deriving an applicable region for the practice and selecting the studies compatible with the region. It requires the test positive rate, r and prevalence, p being estimated for the setting but previous studies have assumed their independence. The aim is to investigate the effects a correlation between r and p has on estimating the applicable region and how this affects TMA. MethodsSix methods for estimating 99% confidence intervals (CI) for r and p were investigated: Wilson's ± Bonferroni correction, Clopper-Pearson's ± Bonferroni correction, and Hotelling's T2 statistic ± continuity correction. These were analyzed in terms of the coverage probability using simulation trials over different correlations, sample sizes, and values for r and p. The methods were then applied to two published meta-analyses with associated practice data, and the effects on the applicable region, studies selected, and summary estimates were evaluated. ResultsHotelling's T2 statistic with a continuity correction had the highest median coverage (0.9971). This and the Clopper-Pearson method with a Bonferroni correction both had coverage consistently above 0.99. The coverage of Hotelling's CI's varied the least across different correlations. For both meta-analyses, the number of studies selected was largest when Hotelling's T2 statistic was used to derive the applicable region. In one instance, this increased the sensitivity by over 4% compared with TMA estimates using other methods. ConclusionTMA returns estimates that are tailored to practice providing the applicable region is accurately defined. This is most likely when the CI for r and p are estimated using Hotelling's T2 statistic with a continuity correction. Potentially, the applicable region may be obtained using routine electronic health data.

Bioimpedance analysis as an indicator of muscle mass and strength in a group of elderly subjects.

To assess the association between whole-body and calf impedance vectors and muscle mass and strength in a group of elderly individuals. We carried out a cross-sectional observational study on a sample of 113 elderly people. Anthropometric parameters (weight, height and body circumferences) were determined. Body composition was evaluated using conventional bioimpedance analysis (BIA) and vector bioimpedance analysis (BIVA) (whole-body and calf BIVAs), and muscle strength was determined (manual dynamometry). The results were analyzed using the Student t-test or the Mann-Whitney U, and the correlations using the Pearson or Spearman test. To compare BIVA results among the subgroups established, the Mahalanobis distance (dM) was calculated and the Hotelling T2 statistic was used. Statistical significance was set to p < 0.05. Nearly half the sample was overweight. Based on waist circumference, 66.7% of the males and 94.9% of the females showed risk of metabolic complications; calf circumference indicated no risk of disability or skeletal muscle mass depletion. However, BIA and dynamometry detected risk of sarcopenia in more than half the subjects. Whole-body BIVA results agreed with those of the BIA, given that most impedance vectors in both sexes were to the right of major axis of the tolerance ellipses. This shows cell mass depletion. While the whole-body BIVA distinguished the subjects having loss of muscle mass and strength, the specific BIVA (calf) only did so in individuals with muscle mass loss. Whole-body BIVA detects loss of muscle mass and strength, while calf BIVA only distinguishes subjects having muscle mass loss. The localized BIVA might be an alternative to conventional BIA or whole-body BIVA to assess body composition in the elderly.

Increased separability of K-edge nanoparticles by photon-counting detectors for spectral micro-CT.

X-ray CT/micro-CT methods with photon-counting detectors (PCDs) and high Z materials are a hot research topic. One method using PCDs allows for spectral imaging in 5 energy windows while conventional X-ray detectors only collect energy-integrating data. To demonstrate the enhanced separation of contrast materials by using PCDs, multivariate analysis, and linear discriminant methods. Phantoms containing iodine and aqueous nanomaterials were scanned on a MARS spectral micro-CT. Image volumes were segmented into separate material-specific populations. Contrast comparisons were made by calculating T2 test statistics in the univariate, pseudo-conventional and multivariate, spectral CT data sets. Separability after Fisher discriminant analysis (FDA) was also assessed. The T2 values calculated for material comparisons increased as a result of the spectral expansion. The majority of the tested contrast agents showed increased T2 values by a factor of ∼2 -3. The total significant T2 statistics in the pure and mixed lanthanide image sets increased in the spectral data set. This work consolidates the groundwork for photon-counting-based material decomposition with micro-CT, facilitating future development of novel nanomaterials and their preclinical applications.

Mesoporosity based classification of ZSM-5 nano catalysts using DRIFT spectroscopy and chemometrics.

DRIFT spectra were used for classification of ZSM-5 catalysts according to their mesopore volumes. The spectra were pretreated by Savitzky-Golay smoothing and standard normal variate (SNV) algorithms prior to outlier detection by Hotelling T2 statistic technique. Supervised classification was applied to the spectra using partial least squares-discriminant analysis (PLS-DA) and soft independent modelling of class analogies (SIMCA) algorithms. The samples were classified into three classes related to their mesopore volumes by the proposed method and the results were in accordance with N2 physisorption textural analysis using Brunauer-Emmett-Teller (BET) model. The confusion matrix and classification efficiency parameters including sensitivity, specificity, accuracy and precision were calculated. Classification accuracy of 96% and error rate of 2% was obtained using PLS-DA algorithm while SIMCA algorithm by providing 100% classification accuracy and zero error rate proved better performance in classification of ZSM-5 catalysts.

Rapid and non-invasive multivariate approach for the quality control of raw milk from mountain areas based on proton transfer reaction mass spectrometry data.

A rapid and non-invasive method for the control of milk by proton transfer reaction mass spectrometry was developed. The approach has the potential to verify the geographic origin and altitude of dairy farms, provided that the cows have been extensively grazed with forage that reflects the botanical composition of the mountain environment. Over a 1-month period, a total of 116 samples were analysed by proton transfer reaction mass spectrometry (PTRMS). A multivariate control chart based on the Hotelling T2 statistic was built with PTRMS data and, for comparison, with the chemical parameters obtained by infrared spectroscopy (FTIR, MilkoScan). The headspace analysis of the samples led to characteristic volatile profiles. Farms located in different mountain areas were discriminated by the protonated molecules m/z 45 (acetaldehyde), 59 (acetone), 73 (2-butanone) and 89 (butyric acid, ethyl acetate, pentanol). Milk samples were also discriminated according to the altitude of the farms according to m/z 45, 59, 63 (dimethyl sulfide), 73 (propionic acid, methyl acetate) and 81 (terpenes). A multivariate control chart based on PTRMS data was used for the quality control of milk. Milk samples from farms located at different mountain areas and altitudes were successfully discriminated.

Robust Monitoring of Industrial Processes in the Presence of Outliers in Training Data

Data-driven process monitoring methods often use classical multivariate statistical analysis (MSA) techniques for data analysis and modeling, with the assumption that the training data contains only observations associated with normal operating conditions of a process. In practice, the training data of an industrial process may contain outliers. Classical MSA methods can be affected by outliers so strongly that the resulting monitoring methods do not allow to detect true process faults. In this paper, a robust process monitoring method is proposed to cope with the presence of outliers in the training data. First, the minimum covariance determinant (MCD) estimator is used for outlier detection and to obtain the robust estimation of location and scatter of training data. A robust fault detection index, called the robust T2 statistic, is then defined based on the MCD estimator. Squared variable deviation magnitude (SVDM) is defined as a robust measure of the deviation of a process variable from the normal ra...

Process system fault detection and diagnosis using a hybrid technique

This paper presents a hybrid methodology to detect and diagnose the faults in dynamic processes based on principal component analysis (PCA) with T2 statistics and a Bayesian network (BN). It deals with the uncertainty generated by the multivariate contribution plots and improves the diagnostic capacity by updating the BN with multiple likelihood evidence. It can diagnose the root cause of the process fault precisely as well as identify the fault propagation pathway. This methodology has been applied to the continuous stirred tank heater and the Tennessee Eastman chemical process for twelve fault scenarios. The result shows that it provides better diagnostic performance over conventional principal component analysis with hard evidence-based approaches.

HSIC-based kernel independent component analysis for fault monitoring

For nonlinear and non-Gaussian industrial processes, KICA is a mature and successful method for fault monitoring. However, a fixed-point ICA algorithm uses a negative entropy method, which has relatively high requirements for non-quadratic function and initial point; accuracy is unsatisfactory. The calculation of control limits of Hotelling's T2 statistic is based on a kernel density estimation, which is difficult to calculate and implement and sometimes cannot guarantee accuracy. In this paper, the kernel independent component analysis method based on the Hibert-Schmidt independence criterion (HSIC) is used instead of the fixed-point ICA algorithm for fault monitoring to improve the accuracy of the independent element. We obtain the independent element directly from the objective function, rather than through the combination of KPCA and ICA. At the same time, we use the direct binomial expansion theorem to obtain the control limit, which reduces computational complexity and implementation difficulty and improves accuracy. The control limit is improved to obtain multi-fault diagnosis. Gray-level information and color information of each frame of the video are respectively read through the information entropy and HSV spatial color histogram. Experimental results show the advantage and effectiveness of the proposed approach. Meanwhile, shadow variables are introduced to smooth the statistics. The contributions of this paper are as follows. 1) Using the kernel independent component method based on HSIC for fault monitoring improves speed and accuracy. 2) The binomial expansion theorem is used instead of traditional kernel density estimation to calculate the control limit, which improves the results of fault monitoring. 3) A method of fault detection using information entropy, HSV color histogram and multivariate statistical analysis is presented.

Adaptive multivariate double sampling and variable sampling interval Hotelling's T2 charts

AbstractIn this article, two adaptive multivariate charts, which combine the double sampling (DS) and variable sampling interval (VSI) features, called the adaptive multivariate double sampling variable sampling interval T2 (AMDSVSI T2) and the adaptive multivariate double sampling variable sampling interval combined T2 (AMDSVSIC T2) charts, are proposed. The real purpose of using the proposed charts is to provide flexibility by enabling the sampling interval length of the DS T2 chart to be varied so that the chart's sensitivity can be enhanced. The fundamental difference between the two proposed charts is that when a second sample is taken, the AMDSVSI T2 chart uses the information of the combined sample mean vectors while the AMDSVSIC T2 chart uses the information of the combined T2 statistics, in deciding about the process status. This research is motivated by existing combined DS and VSI charts in the literature, which show convincing performance improvement over the standard DS chart. Consequently, it is believed that adopting this existing approach in the multivariate case will enable superior multivariate DS charts to be proposed. Numerical results show that the proposed charts outperform the existing standard T2 and other adaptive multivariate charts, in detecting shifts in the mean vector, for the zero‐state and steady‐state cases. The performances of both charts when the shift sizes in the mean vector are unknown are also measured. The application of the AMDSVSI T2 chart is illustrated with an example.

A semiparametric nonlinear mixed model approach to phase I profile monitoring

ABSTRACTWhen process data follow a particular curve in quality control, profile monitoring is suitable and appropriate for assessing process stability. Previous research in profile monitoring focusing on nonlinear parametric (P) modeling, involving both fixed and random-effects, was made under the assumption of an accurate nonlinear model specification. Lately, nonparametric (NP) methods have been used in the profile monitoring context in the absence of an obvious linear P model. This study introduces a novel technique in profile monitoring for any nonlinear and auto-correlated data. Referred to as the nonlinear mixed robust profile monitoring (NMRPM) method, it proposes a semiparametric (SP) approach that combines nonlinear P and NP profile fits for scenarios in which a nonlinear P model is adequate over part of the data but inadequate of the rest. These three methods (P, NP, and NMRPM) account for the auto-correlation within profiles and treats the collection of profiles as a random sample with a common population. During Phase I analysis, a version of Hotelling’s T2 statistic is proposed for each approach to identify abnormal profiles based on the estimated random effects and obtain the corresponding control limits. The performance of the NMRPM method is then evaluated using a real data set. Results reveal that the NMRPM method is robust to model misspecification and performs adequately against a correctly specified nonlinear P model. Control charts with the NMRPM method have excellent capability of detecting changes in Phase I data with control limits that are easily computable.

Diagnosis of Fluid Leaks in Pipelines Using Dynamic PCA

In this paper, a data-driven system based on PCA is described to detect and quantify fluid leaks in an experimental pipeline. A dynamic PCA implementation (DPCA) was used to capture the process dynamics because the system variables are time-correlated. To detect leaks online, the Hotelling’s T2 statistic and the squared prediction error (SPE) were used as residuals, which are compared against statistically defined thresholds from a set of training data. To determine the number of delays to be included in the DPCA model as well as the number of principal components to be used, a tuning process was executed to find the residual with the optimal number of delays and components that showed the best correlation between the residuals and the leakage size. This allowed the construction of a regression model to estimate the flow rate of the leaks directly from the residual.

Intermittent Fault Detection with T2 Control Chart

Multivariate statistical analysis using the Hotellings T2 statistic (T2 control chart) is one of the most effective data-driven methods for fault detection. However, existing T2 control charts in the literature mainly focus on permanent faults, and intermittent faults are relatively rarely considered. In fact, due to the small magnitude and short duration characteristics, traditional multivariate statistical methods are not sensitive to intermittent faults, resulting in much missed detection. Thus in this paper, the T2 control chart with consecutive observations is designed for permanent fault detection and intermittent fault detection respectively. In order to analyze the detection ability of proposed methods, definitions of being guaranteed detectable are introduced both for permanent faults and intermittent faults. Then, sufficient conditions for the defined fault detectability are derived for both kinds of faults respectively. Moreover, optimal window length for intermittent fault detection is discussed. Finally a simulation study is carried out to show the effectiveness of the proposed methods.

Robust Principal Component Pursuit for Fault Detection in a Blast Furnace Process

Since blast furnaces are generally controlled by operators, the minor faults regarded as disturbances might be contained in the collected data matrix. This can severely affect sample distributions, which leads to arbitrary fault detection results using traditional data-driven methods. In this paper, a novel fault detection method named robust principal component pursuit (PCP) to handle minor faults is proposed. The minor faults are separated from columns and rows, respectively, in the training matrix via two matrix norms. By applying the proposed robust PCP method, a low rank matrix containing important process information, as well as explicit variable relationships, and a block sparse matrix containing minor faults are derived. Moreover, the convergence of the proposed method is discussed. Hotelling’s T2 statistic is potentially useful for online process monitoring in the low rank matrix. Finally, to evaluate the decomposition capacity of the proposed method for a matrix containing minor faults, a compar...

An improved plant‐wide fault detection scheme based on PCA and adaptive threshold for reliable process monitoring: Application on the new revised model of Tennessee Eastman process

AbstractAn improved process monitoring scheme is presented in this paper, it is based on the integration of multivariate and univariate statistical analysis methods. Instead of conventional fixed control limits, adaptive thresholds are developed for common fault detection indices used with principal component analysis, including the Hotelling T2 statistic and the sum of squared prediction error known as the Q statistic. The thresholds are updated based on a modified exponentially weighted moving average chart with a limited window length. The primary goal of this strategy is to enhance the performance of principal component analysis–based process monitoring method and overcome its shortcomings, by increasing fault detection rate to improve monitoring sensitivity and eliminating false alarms to ensure higher robustness and reliability. Fault detection in the revised model of Tennessee Eastman process benchmark is also investigated. The developed monitoring scheme is tested and compared with conventional fixed threshold technique, and its performance is evaluated across various types of process faults. The obtained results demonstrate the promising capabilities of the developed scheme.

MRI Cartilage Assessment of the Subtalar and Midtarsal Joints During a Transcontinental Ultramarathon - New Insights into Human Locomotion.

MR measurements can be accurately performed during 4486 km of running, opening a window into in vivo assessment of hindfoot articular cartilage under extreme ultra-endurance loading. This observational cross-sectional study included 22 randomized participants of TransEurope FootRace between Italy and the North Cape, which was accompanied by a trailer-mounted 1.5T MRI scanner over 9 weeks. Four follow up MR examinations of subtalar and midtarsal joints were performed. Statistics of cartilage T2* and thickness were obtained. Nearly all observed joints showed an initial significant mean T2* increase of 20.9% and 26.3% for the left and right side, followed by a relative decrease of 28.5% and 16.0% during the second half, respectively. It could be demonstrated that mobile MRI field studies allow in vivo functional tissue observations under extreme loading. Elevated T2* values recovered during the second half of the ultramarathon supported the evidence that this response is a physiological adaptive mechanism of chondrocyte function via upregulation of de novo synthesis of proteoglycans and collagen. These changes occurred in a distinct asymmetric pattern leaving a "biochemical signature" of articular cartilage that allows in vivo insight into joint loading. In conclusion, the normal articular cartilage of the hindfoot is resilient and adaptive, leaving extreme endurance activities up to limitless human ambition.

Combining just‐in‐time modelling and batch‐wise unfolded PLS model for the derivative‐free batch‐to‐batch optimization

In this work, a derivative‐free batch‐to‐batch optimization method is proposed. In order to conquer the difficulties in building a first principal model, a local batch‐wise unfolded PLS (BW‐PLS) model is used to accurately describe the concerned region, and the first principal model based dynamic optimization problem is transformed into a static one. The just‐in‐time (JIT) modelling method is employed to dynamically update the local BW‐PLS model upon request, and the nonlinearity and abrupt changes from one batch run to another can be effectively resolved. Then the proposed local BW‐PLS model with JIT modelling method is integrated into the trust‐region framework. Not only can the issue of plant‐model mismatch be dealt with, but also the computation of the experimental gradients can be avoided. In addition, taking the advantages of PLS regression, the Hotelling's T2 statistic is utilized as a hard constraint to ensure the reliability of the optimal solution. Extension to handle soft inequality constraints is also included in this work. Finally, the efficacy of the proposed batch‐to‐batch optimization method is illustrated via a toy example and a simulated cobalt oxalate synthesis process under different operating conditions, and satisfied optimization performances were obtained.

Multi‐block principal component analysis based on variable weight information and its application to multivariate process monitoring

The traditional principal component analysis (PCA)‐based process monitoring method builds a global statistical model and omits the mining of the local variable behaviours, which may degrade the fault detection performance. Considering this problem, this paper proposes a variable weight information‐based multi‐block PCA (VWI‐MBPCA) method. Firstly, a sequence hierarchical clustering algorithm is proposed to divide the full PCA component space into several sub‐blocks, where the components sharing similar variable weight information are gathered together and then the sub‐block T2 statistic is constructed for monitoring sub‐block components. Further, the variables with small weight information on each component sub‐block are extracted to build an additional sub‐PCA model, where the statistic is developed to compensate the sub‐block T2 statistic. In order to integrate the monitoring results of each sub‐block, Bayesian inference is applied to construct an overall T2 statistic. To identify the faulty variables, a multi‐block PCA contribution plot is designed by choosing some specific blocks to highlight fault information. Finally, simulations on a numerical example and the benchmark Tennessee Eastman (TE) process are used to demonstrate the strengths of the proposed method.

Modified kernel principal component analysis using double-weighted local outlier factor and its application to nonlinear process monitoring

Traditional kernel principal component analysis (KPCA) based nonlinear process monitoring method may not perform well because its Gaussian distribution assumption is often violated in the real industrial processes. To overcome this deficiency, this paper proposes a modified KPCA method based on double-weighted local outlier factor (DWLOF-KPCA). In order to avoid the assumption of specific data distribution, local outlier factor (LOF) is introduced to construct two LOF-based monitoring statistics, which are used to substitute for the traditional T2 and SPE statistics, respectively. To provide better online monitoring performance, a double-weighted LOF method is further designed, which assigns the weights for each component to highlight the key components with significant fault information, and uses the moving window to weight the historical statistics for reducing the drastic fluctuations in the monitoring results. Finally, simulations on a numerical example and the Tennessee Eastman (TE) benchmark process are used to demonstrate the superiority of the proposed DWLOF-KPCA method.

P25.04: Stillbirth and fetal growth restriction from umbilical artery and ductus venosus diastolic waveform assessment: a systematic review and meta‐analysis

To assess the risks of stillbirth in early growth restricted fetuses with absent/reverse end-diastolic velocity in umbilical artery (UA) or ductus venosus (DV). We conducted a literature search to identify relevant studies that provided data on early growth restricted fetuses requiring delivery before 34 weeks, with information on stillbirth rate and the presence of absent/reverse end-diastolic velocity in the UA or DV. Both fixed and random effects models were applied. Between-study heterogeneity was assessed using the X2 (Cochrane Q), t2 and I2 statistics. Publication bias was evaluated and quantified by Egger method. A total of 35 studies were included in this analysis. The overall prevalence of stillbirth was 0.05%. Twenty-five studies reported a higher risk of stillbirth in UA waveform analysis. OR under random effects model was 7.32 (p<0.001) with no heterogeneity between them (t2=0.15). Publication bias through Egger k-coefficient was not significant (p=0.58). Fourteen studies showed an increased risk of stillbirth in DV analysis. OR under random effects model was 11.95 (p=0.001). Q statistic of 23.10 (p=0.03) and 46% I2, suggests the presence of heterogeneity throughout publications. Egger k-coefficient method of -1.18 (p=0.283) depicts absence of publication bias. Supporting information can be found in the online version of this abstract Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.