Multivariate Statistical Process Monitoring and Control: Recent Developments and Applications to Chemical Industry

Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks and future considerations are made.

Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.

Construction of Inorganic Elemental Fingerprint and Multivariate Statistical Analysis of Marine Traditional Chinese Medicine Meretricis concha from Rushan Bay

Meretricis concha is a kind of marine traditional Chinese medicine(TCM), and has been commonly used for the treatment of asthma and scald burns. In order to investigate the relationship between the inorganic elemental fingerprint and the geographical origin identification of Meretricis concha, the elemental contents of M. concha from five sampling points in Rushan Bay have been determined by means of inductively coupled plasma optical emission spectrometry(ICP-OES). Based on the contents of 14 inorganic elements(Al, As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Mo, Ni, Pb, Se, and Zn), the inorganic elemental fingerprint which well reflects the elemental characteristics was constructed. All the data from the five sampling points were discriminated with accuracy through hierarchical cluster analysis(HCA) and principle component analysis(PCA), indicating that a four-factor model which could explain approximately 80% of the detection data was established, and the elements Al, As, Cd, Cu, Ni and Pb could be viewed as the characteristic elements. This investigation suggests that the inorganic elemental fingerprint combined with multivariate statistical analysis is a promising method for verifying the geographical origin of M. concha, and this strategy should be valuable for the authenticity discrimination of some marine TCM.

Application of multivariate statistical techniques in assessment of surface water quality in Second Songhua River basin,China

Multivariate statistical techniques,such as cluster analysis(CA),discriminant analysis(DA),principal component analysis(PCA) and factor analysis(FA),were applied to evaluate and interpret the surface water quality data sets of the Second Songhua River(SSHR) basin in China,obtained during two years(2012-2013) of monitoring of 10 physicochemical parameters at 15 different sites.The results showed that most of physicochemical parameters varied significantly among the sampling sites.Three significant groups,highly polluted(HP),moderately polluted(MP) and less polluted(LP),of sampling sites were obtained through Hierarchical agglomerative CA on the basis of similarity of water quality characteristics.DA identified p H,F,DO,NH3-N,COD and VPhs were the most important parameters contributing to spatial variations of surface water quality.However,DA did not give a considerable data reduction(40% reduction).PCA/FA resulted in three,three and four latent factors explaining 70%,62% and 71% of the total variance in water quality data sets of HP,MP and LP regions,respectively.FA revealed that the SSHR water chemistry was strongly affected by anthropogenic activities(point sources:industrial effluents and wastewater treatment plants;non-point sources:domestic sewage,livestock operations and agricultural activities) and natural processes(seasonal effect,and natural inputs).PCA/FA in the whole basin showed the best results for data reduction because it used only two parameters(about 80% reduction) as the most important parameters to explain 72% of the data variation.Thus,this work illustrated the utility of multivariate statistical techniques for analysis and interpretation of datasets and,in water quality assessment,identification of pollution sources/factors and understanding spatial variations in water quality for effective stream water quality management.

STUDY ON THE MULTIVARIATE STATISTICAL ESTIMATION OF TROPICAL CYCLONE INTENSITY USING FY-3 MWRI BRIGHTNESS TEMPERATURE DATA

A technique for estimating tropical cyclone(TC) intensity over the Western North Pacific utilizing FY-3Microwave Imager(MWRI) data is developed. As a first step, we investigated the relationship between the FY-3 MWRI brightness temperature(TB) parameters, which are computed in concentric circles or annuli of different radius in different MWRI frequencies, and the TC maximum wind speed(Vmax) from the TC best track data. We found that the parameters of lower frequency channels' minimum TB, mean TB and ratio of pixels over the threshold TB with a radius of 1.0 or 1.5 degrees from the center give higher correlation. Then by applying principal components analysis(PCA)and multiple regression method, we established an estimation model and evaluated it using independent verification data, with the RMSE being 13 kt. The estimated Vmax is always stronger in the early stages of development, but slightly weaker toward the mature stage, and a reversal of positive and negative bias takes place with a boundary of around 70 kt. For the TC that has a larger error, we found that they are often with less organized and asymmetric cloud pattern, so the classification of TC cloud pattern will help improve the acuracy of the estimated TC intensity, and with the increase of statistical samples the accuracy of the estimated TC intensity will also be improved.

Spatial variation assessment of groundwater quality using multivariate statistical analysis(Case Study:Fasa Plain,Iran)

Groundwater is considered as one of the most important sources for water supply in Iran.The Fasa Plain in Fars Province,Southern Iran is one of the major areas of wheat production using groundwater for irrigation.A large population also uses local groundwater for drinking purposes.Therefore,in this study,this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis(CA),Discriminant Analysis(DA),and Principal Component Analysis(PCA).Water quality data was monitored at 22 different wells,for five years(2009-2014)with 10 water quality parameters.By using cluster analysis,the sampling wells were grouped into two clusters with distinct water qualities at different locations.The Lasso Discriminant Analysis(LDA)technique was used to assess the spatial variability of water quality.Based on the results,all of the variables except sodium absorption ratio(SAR)are effective in the LDA model with all variables affording 92.80%correct assignation to discriminate between the clusters from the primary 10 variables.Principal component(PC)analysis and factor analysis reduced the complex data matrix into two main components,accounting for more than 95.93%of the total variance.The first PC contained the parameters of TH,Ca2+,and Mg2+.Therefore,the first dominant factor was hardness.In the second PC,Cl-,SAR,and Na+were the dominant parameters,which may indicate salinity.The originally acquired factors illustrate natural(existence of geological formations)and anthropogenic(improper disposal of domestic and agricultural wastes)factors which affect the groundwater quality.

New Method for Multivariate Statistical Process Monitoring

A new method using discriminant analysis and control charts is proposed for monitoring multivariate process operations more reliably.Fisher discriminant analysis （FDA） is used to derive a feature discriminant direction （FDD） between each normal and fault operations,and each FDD thus decided constructs the feature space of each fault operation.Individuals control charts （XmR charts） are used to monitor multivariate processes using the process data projected onto feature spaces.Upper control limit （UCL） and lower control limit （LCL） on each feature space from normal process operation are calculated for XmR charts,and are used to distinguish fault from normal.A variation trend on an XmR chart reveals the type of relevant fault operation.Applications to Tennessee Eastman simulation processes show that this proposed method can result in better monitoring performance than principal component analysis （PCA）-based methods and can better identify step type faults on XmR charts.

Joint multivariate statistical model and its applications to the synthetic earthquake prediction

Considering the problems that should be solved in the synthetic earthquake prediction at present, a new model is proposed in the paper. It is called joint multivariate statistical model combined by principal component analysis with discriminatory analysis. Principal component analysis and discriminatory analysis are very important theories in multivariate statistical analysis that has developed quickly in the late thirty years. By means of maximization information method, we choose several earthquake prediction factors whose cumulative proportions of total sam-ple variances are beyond 90% from numerous earthquake prediction factors. The paper applies regression analysis and Mahalanobis discrimination to extrapolating synthetic prediction. Furthermore, we use this model to charac-terize and predict earthquakes in North China (30~42N, 108~125E) and better prediction results are obtained.

Quality assessment of Jinhongtang Granule using UFLC-MS/MS and multivariate statistical analysis

Jinhongtang is a traditional Chinese medicine formula composed of Rheum palmatum L.stem,Sargentodoxa cuneata stem,and Taraxacum mongolicum and is used for the treatment of sepsis.However,quality assessment method for Jinhongtang is not available.In present study,we developed a UFLC-MS/MS method to determine 16 analytes in 20 batches of home-made and commercial Jinhongtang.Multivariate statistical analysis revealed the significant differences in the quality of home-made and commercial Jinhongtang and the difference in the quality of home-made samples was more significant.The integrated strategy based on UFLC-MS/MS and multivariate statistical analysis provided a new basis for the overall quality assessment of Jinhongtang.

Study on the Relationship between Soil and Environment Based on Multivariate Statistical Analysis

[Objective] The study aimed to study the relationship between soil and environment on the basis of multivariate statistical analysis. [ Method] Through field investigation, sampling and laboratory analysis, we discussed the relationship between soil properties and environmental factors in Mizhi County, North Shaanxi by using Canoco multivariate statistical analysis. [ Result]According to the effects of various environmental factors on soil properties, the influencing order of environmental factors was land use way 〉 vegetation type 〉 vegetation restoration years 〉 vegeta- tion coverage 〉 slope aspect 〉 gradient 〉 elevation. In a word, soil properties were significantly affected by land use way and vegetation type which were the most important environmental factors of soil properties in spatial variation, while vegetation restoration years were closely related to the ac- cumulation of soil nutrients. [ Condusion]The research could provide theoretical references for the construction of ecological environment in Loess Plateau of China.

Multivariate Statistical Analysis of Large Datasets: Single Particle Electron Microscopy

Biology is a challenging and complicated mess. Understanding this challenging complexity is the realm of the biological sciences: Trying to make sense of the massive, messy data in terms of discovering patterns and revealing its underlying general rules. Among the most powerful mathematical tools for organizing and helping to structure complex, heterogeneous and noisy data are the tools provided by multivariate statistical analysis (MSA) approaches. These eigenvector/eigenvalue data-compression approaches were first introduced to electron microscopy (EM) in 1980 to help sort out different views of macromolecules in a micrograph. After 35 years of continuous use and developments, new MSA applications are still being proposed regularly. The speed of computing has increased dramatically in the decades since their first use in electron microscopy. However, we have also seen a possibly even more rapid increase in the size and complexity of the EM data sets to be studied. MSA computations had thus become a very serious bottleneck limiting its general use. The parallelization of our programs—speeding up the process by orders of magnitude—has opened whole new avenues of research. The speed of the automatic classification in the compressed eigenvector space had also become a bottleneck which needed to be removed. In this paper we explain the basic principles of multivariate statistical eigenvector-eigenvalue data compression;we provide practical tips and application examples for those working in structural biology, and we provide the more experienced researcher in this and other fields with the formulas associated with these powerful MSA approaches.

Water Quality Assessment of a Tropical Mexican Lake Using Multivariate Statistical Techniques

Water quality of Mexican tropical lake Chapala was assessed through multivariate statistical techniques, cluster analysis (CA) and principal component analysis (PCA) at ten different monitoring sites for ten physicochemical variables and six metals. This study evaluated and interpreted complex water quality data sets and apportioned of pollution sources to get better information about water quality. From descriptive statistics results, the highest concentrations of metals occurred during the dry season, and this trend was explained by the fact that an unusual rainy event occurred during the month of February 2009 and brought metals into the lake by runoffs from nearby mountains. According to international criteria for water consumption by aquatic organisms [USEPA], only Zn concentration values were below these criteria whereas the values of Ni, Pb, Cd and Fe were above the corresponding values set in these criteria (Ni: 52 μg·L-1, Pb: 2.5 μg·L-1, Cd: 0.25 μg·L-1, and Fe: 1000 μg·L-1). The correlations were observed by PCA, which were used to classify the samples by CA, based on the PCA scores. Seven significant cluster groups of sampling locations—(sites 4 and 5), (sites 3 and 9), (site 7), (site 10), (sites 2 and 6), (site 8) and (site 1)— were detected on the basis of similarity of their water quality. The results revealed that the stress exerted on the lake caused by waste sources follows the order: domestic > agricultural > industrial.

Using Multivariate Statistical and Geostatistical Methods to Identify Spatial Variability of Trace Elements in Agricultural Soils in Dongguan City,Guangdong,China

Dongguan （东莞） City, located in the Pearl River Delta, South China, is famous for its rapid industrialization in the past 30 years. A total of 90 topsoil samples have been collected from agricultural fields, including vegetable and orchard soils in the city, and eight heavy metals （As, Cu, Cd, Cr, Hg, Ni, Pb, and Zn） and other items （pH values and organic matter） have been analyzed, to evaluate the influence of anthropic activities on the environmental quality of agricultural soils and to identify the spatial distribution of trace elements and possible sources of trace elements. The elements Hg, Pb, and Cd have accumulated remarkably here, incomparison with the soil background content of elements in Guangdong （广东） Province. Pollution is more serious in the western plain and the central region, which are heavily distributed with industries and rivers. Multivariate and geostatistical methods have been applied to differentiate the influences of natural processes and human activities on the pollution of heavy metals in topsoils in the study area. The results of cluster analysis （CA） and factor analysis （FA） show that Ni, Cr, Cu, Zn, and As are grouped in factor F1, Pb in F2, and Cd and Hg in F3, respectively. The spatial pattern of the three factors may be well demonstrated by geostatistical analysis. It is shown that the first factor could be considered as a natural source controlled by parent rocks. The second factor could be referred to as ＂industrial and traffic pollution sources＂. The source of the third factor is mainly controlled by long-term anthropic activities, as a consequence of agricultural activities, fossil fuel consumption, and atmospheric deposition.

Multivariate Statistical Analysis of Dominating Groundwater Mineralization and Hydrochemical Evolution in Gao,Northern Mali

Population growth and expanding urbanization have caused persistent shortages and contamination of groundwater resources in Mali,Africa.The increase in groundwater salinity makes it more difficult for residents to obtain drinking water,it is necessary to clarify the causes and control factors of groundwater mineralization in Gao region,northern Mali.Based on the analysis of the hydrochemical composition of groundwater in 24 boreholes,Piper and Sch?eller diagrams,principal component analysis(PCA)and hierarchical cluster analysis(HCA)are used to carry out multivariate statistical analysis on the main ions.The results show that the groundwater samples are weakly alkaline,with pH values ranging from 5.83 to 8.40,and the average values of boreholes are 7.50,respectively.The average electrical conductivity(EC)value is 354.4(μS/cm),and the extreme value is between 124.0 and 1247(μS/cm).Water is usually mineralized and presents nine types of water phase.The three principal components explain 84.42%of the total variance for 13 parameters.The factor F1(58.85%),the factor F2(16.88%)and the factor F3(8.69%)present for the majority of the total data set.In addition,multivariate statistical analysis confirmed the genetic relationship among aquifers and identified three main clusters.Clustering related to groundwater mineralization(F1),clustering related to oxide reduction and iron enrichment(F2),and clustering of groundwater pollution caused by nitrate and magnesium(F3).We found that agriculture,weathering activities and dissolution of geological materials promote the mineralization of groundwater.Groundwater quality in the Gao region is becoming less and less potable because of increasing salinity.

Rapid Analysis and Identification of Absorbed Components and Their Metabolites of Yuanhu Zhitong Dropping Pill in Rat Plasma and Brain Tissue Using UPLC-Q-TOF/MS with Multivariate Statistical Analysis

Objective To establish an effective approach for rapid and comprehensive analysis on the absorbed and metabolic components in rats after ig administration of Yuanhu Zhitong Dropping Pill（YHZT）. Methods Based on the combination of UPLC-Q-TOF/MS and multivariate statistical analysis, the absorbed prototype constituents and their metabolites in rat plasma were rapidly analyzed and identified, and the components absorbed into brain were further identified by comparing the extracted ion chromatograms（EICs） of control and brain tissue samples of dosed rats. Results A total of 38 YHZT-related xenobiotic compounds were detected and identified as the potential bioactive constituents in rat plasma, including 24 absorbed prototype constituents and 14 metabolites. In particular, of all prototype constituents, 14 were also detected in rat brain tissue, indicating that they could penetrate the blood-brain barrier and enter into brain. Conclusion An effective method is established and applied to analyze the potential bioactive constituents in YHZT, which provides a pathway to further investigate the pharmacological pattern and mechanism of YHZT.

Chemical comparison of dried rehmannia root and prepared rehmannia root by UPLC-TOF MS and HPLC-ELSD with multivariate statistical analysis

To identify the chemical differences which lead to the different therapeutic effects of dried rehmannia root(DRR)and prepared rehmannia root(PRR),we compared the chemical composition of decoctions of randomly purchased DRR and PRR using ultra performance liquid chromatography(UPLC)coupled with time-of-fight mass spectrometry and high performance liquid chromatography(HPLC)coupled with evaporative light scattering detection(ELSD)with the aid of multivariate statistical analysis.Both approaches clearly revealed compositional and quantitative differences between DRR and PRR.UPLC-MS data indicated stachyose,rehmaiono-side A(or rehmaionoside B),acteoside(or forsythiaside,or isoacteoside),6-O-coumaroylajugol(or 6-O-E-feruloylajugol,or 6-O-Z-feruloylajugol)as important discriminators between DRR and PRR decoctions.HPLC-ELSD analysis showed that the content of fructose in the decoctions of PRR was about four times greater than that of DRR(P<10^(-5)),while sucrose content in the decoctions of PRR was only about one seventh of that in DRR(P<0.01).Our results suggest that some compounds,such as fructose,stachyose and rehmaionoside,may be responsible for the differing therapeutic effects of DRR and PRR.Furthermore,improvements in quality control for PRR,which is currently lacking in the Chinese Pharmacopoeia,are recommended.

Combined Use of Multivariate Statistical Analysis and Hydrochemical Analysis for Groundwater Quality Evolution: A Case Study in North Chain Plain

Understanding the controlling factor of groundwater quality can enhance promoting sustainable development of groundwater resources. To this end, multivariate statistical analysis（MA） and hydrochemical analysis were introduced in this work. The results indicate that the canonical discriminant function with 7 parameters was established using the discriminant analysis（DA） method, which can afford 100% correct assignation according to the 3 different clusters（good water（GW）, poor water（PW）, and very poor water（VPW）） obtained from cluster analysis（CA）. According to factor analysis（FA）, 8 factors were extracted from 25 hydrochemical elements and account for 80.897% of the total data variance, suggesting that groundwater with higher concentrations of sodium, calcium, magnesium, chloride, and sulfate in southeastern study area are mainly affected by the natural process; the higher level of arsenic and chromium in groundwater extracted from northwestern part of study area are derived by industrial activities; domestic and agriculture sewage have important contribution to copper, iron, iodine, and phosphate in the northern study area. Therefore, this work can help identify the main controlling factor of groundwater quality in North China plain so as to make better and more informed decisions about how to achieve groundwater resources sustainable development.

Chemical comparison of Semen Euphorbiae and Semen Euphorbiae Pulveratum by UPLC-Q-TOF/MS coupled with multivariate statistical techniques

In the present study,we aimed to assess the chemical composition changes of Semen Euphorbiae(SE)and Semen Euphorbiae Pulveratum(SEP)by UPLC-Q-TOF/MS and multivariate statistical methods.The UPLC-Q-TOF/MS method and SIMCA-P software were used to analyze the changes of chemical components of SE and SEP based on PCA and PLS-DA multivariate statistical methods.A"component-target-disease"network model was constructed by Intelligent Platform for Life Sciences of traditional Chinese medicine(TCM)to predict potential related diseases.The differences of chemical composition were significant between SE and SEP.Under positive ion mode,the amounts of Euphorbia factor L2,L3,L7a,L8,L9 and lathyrol were obviously decreased after processing.Under negative ion mode,the amounts of aesculetin,bisaesculetin,ingenol and cetylic acid were increased obviously,while Euphorbia factor L1,L4 and L5 were decreased obviously after processing,and the components of euphobiasteroid,aesculetin,lathyrol and linoleic acid among the 14 differentiated compounds were closely related to the SE-related diseases through the"component-target-disease"network model.UPLC-Q-TOF/MS technology in combination with multivariate statistical methods had certain advantages in studying the complex changes of chemical composition before and after manufacturing pulveratum of SE.It provided a basis for clarifying the toxicity-attenuated mechanisms of SE manufacturing pulveratum,and laid the foundation for its further development and utilization.

Chemical Characteristics Combined with Bioactivity for Comprehensive Evaluation of Tumuxiang Based on HPLC-DAD and Multivariate Statistical Methods

Background: The dried roots of Inula helenium L.(IH) and Inula racemosa Hook f.(IR) are used commonly as folk medicine under the name of "tumuxiang(TMX)". Phenolic acid compounds and their derivatives, as main active constituents in IH and IR, exhibit prominent anti-inflammation effect.Objective: To develop a holistic method based on chemical characteristic and anti-inflammation effect for systematically evaluating the quality of twenty-seven TMX samples(including 18 IH samples and 9 IR samples) from different origins.Methods: HPLC fingerprints data of AL(Aucklandia lappa Decne.) whose dried root was similar with HR was added for classification analysis. The HPLC fingerprints of twenty-seven TMX samples and four AL samples were evaluated using hierarchical clustering analysis(HCA) and principle component analysis(PCA). The spectrum-efficacy model between HPLC fingerprints and anti-inflammatory activities was investigated by principal component regression(PCR) and partial least squares(PLS).Results: All samples were successfully divided into three main clusters and peaks 7, 9, 11, 22, 24 and 26 had a primary contribution to classify these medicinal herbs. The results were in accord with the appraisal results of herbs. The spectrum-efficacy relationship results indicated that citric acid, quinic acid, caffeic acid-β-D-glucopyranoside, chlorogenic acid, caffeic acid, 1,3-O-dicaffeoyl quinic acid, tianshic acid and 3β-Hydroxypterondontic acid had main contribution to anti-inflammatory activities.Conclusion: This comprehensive strategy was successfully used for identification of IH, IR and AL, which provided a reliable and adequate theoretical basis for the bioactivity relevant quality standards and studying the material basis of anti-inflammatory effect of TMX.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.