Fault detection and identification using a Kullback-Leibler divergence based multi-block principal component analysis and bayesian inference

Considering the huge number of variables in plant-wide process monitoring and complex relationships (linear, nonlinear, partial correlation, or independence) among these variables, multivariate statistical process monitoring (MSPM) performance may be deteriorated especially by the independent variables. Meanwhile, whether related variables keep high concordance during the variation process is still a question. Under this circumstance, a multi-block technology based on mathematical statistics method, Kullback-Leibler Divergence, is proposed to put the variables having similar statistical characteristics into the same block, and then build principal component analysis (PCA) models in each low-dimensional subspace. Bayesian inference is also employed to combine the monitoring results from each sub-block into the final monitoring statistics. Additionally, a novel fault diagnosis approach is developed for fault identification. The superiority of the proposed method is demonstrated by applications on a simple simulated multivariate process and the Tennessee Eastman benchmark process.     

Granger Causality Testing in Mixed‐Frequency VARs with Possibly (Co)Integrated Processes

We analyze Granger causality (GC) testing in mixed‐frequency vector autoregressions (MF‐VARs) with possibly integrated or cointegrated time series. It is well known that conducting inference on a set of parameters is dependent on knowing the correct (co)integration order of the processes involved. Corresponding tests are, however, known to often suffer from size distortions and/or a loss of power. Our approach works for MF variables that are stationary, integrated of an arbitrary order, or cointegrated. As it only requires the estimation of a MF‐VAR in levels with appropriately adjusted lag length, after which GC tests can be conducted using simple standard Wald tests, it is of great practical appeal. In addition, we show that the presence of non‐stationary and trivially cointegrated high‐frequency regressors leads to standard distributions when testing for causality on a subset of parameters, sometimes even without any need to augment the VAR order. Monte Carlo simulations and two applications involving the oil price and consumer prices as well as GDP and industrial production in Germany illustrate our approach.     

Small scale flame-spread testing to BS 476 part 7

An apparatus based on the BS 476 Part 7 small scale flame-spread specification, which has evolved over a number of years, is described. Many changes from the original simple gas/air furnace have been introduced, which have led to the development of a very useful flame-spread test apparatus where all known variables are precisely controlled. The work has shown that the radiometers described in the standard do not monitor all the variables which affect flame-spread results, and reported problems of reproducibility and variation on the large scale test, may be due to inadequate control of the furnace. The significance of the results is that the use of gas/air radian panels as the basis for flame-spread tests needs to be re-examined. All parameters should be carefully controlled and the entire procedure, particularly regarding the use of pilot ignition sources, needs to be reconsidered. There is an increasing need for test methods which assess materials at radiation intensities beyond that given by small ignition sources. The type of flame-spread apparatus described in the paper may help fulfil this important requirement.     

A Two Level Fractional Factorial Design to Test the Effect of Oil Sands Composition and Process Water Chemistry on Bitumen Recovery from Model Systems

To overcome the compositional variability inherent to natural oil sands we use extraction tests with model oil sands (MOS) systems in a systematic, experimental design study. Eight significant variables from screening tests in earlier work are tested here. Namely, concentrations of bitumen, silica fines, sodium kaolinite, illite and montmorillonite. In addition, we tested different concentrations of Ca²⁺, Mg²⁺, and Na⁺ in the synthetic process water used with bitumen separation tests. A two level, fractional factorial experimental design allowed testing of the selected variables using only 16 runs. In addition, sodium hydroxide was added as a ninth variable and four repeat tests allowed evaluation of precision. The resulting bitumen recovery model explained 94% of the data variation. The associated parameter estimates were in general agreement with previous experimental observations and with actual operational experience.     

Statistical methods for comparing GPC curves

The possibilities of comparing the GPC curves of two or more polymers were studied, and the method of “distinguished points” (DPs) is suggested for this purpose. The features of these DP values as random variables were investigated. According to the experimental results they meet the requirements of the statistical tests applied in this text. In order to indicate the significant deviation or the agreement of the DP values of GPC curves of two polymers, the sequential U and t tests are suggested, because with these methods the number of the necessary parallel measurements is considerably decreased, and one can also decide on the magnitude of the variation on must be able to detect, while in the case of more than two polymers the methods of the analysis of variance can be utilized. The molecular weight ranges in which significant differences occur can also be determined. The described methods were tested by materials of known molecular weight distributions.     

Group sequential testing in dental clinical trials with longitudinal data on multiple outcome variables

In this article, methods are proposed for design and analysis of clinical trials that gather longitudinal data on multiple outcome variables. A valid test of the null hypothesis of no treatment group differences can be obtained for any choice of a working alternative hypothesis and a working covariance matrix for the outcome variables. Increased power can be achieved by accurate modeling of the true treatment effect and covariance structure. Implementation of the procedure is simple using existing software for generalized estimating equations. The procedure is an extension of the 'derived variable' technique (univariate analysis applied to a linear combination of the outcome variables) and also of O'Brien's generalized least squares test. The procedure is extended to allow sequential testing using an arbitrary division of the total type I error rate among repeated hypothesis tests. The methods are illustrated by the design of a study on the safety of dental amalgam fillings, which served as the motivation for the research.     

MULTICOMPONENT WAVE PROPAGATION: ATTAINMENT OF COHERENCE FROM ARBITRARY STARTING CONDITIONS†

The method of characteristics is used to prove the coherence principle, namely, that an arbitrary starting variation embedded between sufficiently large regions of constant state is resolved into coherent (simple)waves, which become separated by new regions of constant state. It is furthermore shown that this principle allows the directions of change of dependent variables to be immediately predicted within entirely noncoherent situations.     

Calculation of the phase envelope of multicomponent mixtures with the bead spring method

A robust numerical scheme for the calculation of constant composition (isoplethic) phase diagrams of complex multicomponent mixtures is presented. The scheme refers to the sequential calculation of the phase envelope of a mixture by guiding the estimation for the equilibrium curve via the introduction of a “spring” that sets the slope value of the modified tangent plane distance with respect to either temperature or pressure. A simple variation of the proposed method allows direct estimation of the Cricondentherm and/or Cricondenbar points, thus avoiding the calculation of the entire phase diagram. Extensive tests of the proposed scheme for different types of phase diagrams, using both cubic and higher‐order equations of state are presented. © 2015 American Institute of Chemical Engineers AIChE J, 62: 868–879, 2016     

Definition of a practical multi-criteria procedure for selecting the best coagulant in a chemically assisted primary sedimentation process for the treatment of urban wastewater

Chemically assisted primary sedimentation (CAPS) or chemically enhanced primary treatment (CEPT) consists of adding chemicals in order to increase the coagulation, flocculation and sedimentation of raw wastewater. Over the last twenty years, the use of CAPS has increased due to the development of better coagulants and flocculation enhancers, stricter standards as well as the need for low-energy treatment technologies, especially in developing countries. This paper defines a very simple multi-criteria procedure to be used in order to select the best combination of coagulant and dose when using jar tests. It is based on the adoption of the following 5 criteria: COD percentage removal, sludge volume after 2 h, coagulant dose, coagulant cost, pH percentage variation. The mathematical affordability of the procedure was tested by comparing it with the well known analytic hierarchy process.     

Fault detection based on polygon area statistics of transformation matrix identified from combined moving window data

Principal component analysis (PCA) has been widely used in monitoring industrial processes, but it is still necessary to make improvements in having a timely and effective access to variation information. It is known that the transformation matrix generated from real-time PCA model indicates inner relations between original variables and new produced components, so this matrix would be different when modeling data deviate due to the change of the operating condition. Based on this theory, this paper proposes a novel real-time monitoring approach which utilizes polygon area method to measure the variation degree of the transformation matrices and then constructs a statistic for monitoring purpose. The on-line data are collected through a combined moving window (CMW), containing both normal and monitored data. To evaluate the performance of the proposed method, a simple numerical simulation, the CSTR process and the classic Tennessee Eastman process are employed for illustration, with some PCA-based methods used for comparison.     

Inferential sensor for on-line monitoring of ammonium bisulfate formation temperature in coal-fired power plants

As a byproduct of the selective catalytic reduction system, ammonium bisulfate could lead to frequent unit outages by forming sticky deposits on the surface of air preheaters and heat rate deterioration in coal-fired power plants. Field tests were carried out to investigate the variation of ammonium bisulfate formation temperature at a coal-fired unit, retrofit with an on-line ammonium bisulfate probe. Two inferential sensor models are proposed in this paper. One is based on adaptive principle component analysis, to infer the ammonium bisulfate formation temperature from real process variables, using a linear interpolation approach suitable for control schemes. The other approach is a support vector regression based model, implemented to give predicted value directly from the input variables, while on-line data are unavailable. Model results indicate that both models can properly represent the inherent relationships between the selected input variables and ammonium bisulfate formation temperature. The adaptive principle component analysis model can be easily included in a selective catalytic reduction control loop and give high resolution predicted data, especially when the continuous analyzer is available. The support vector regression model can serve as a useful backup and replacement model, when the hard sensor is faulty or unavailable.     

Temperature-dependent mechanical properties and constitutive equation of cellulose nitrate

The strain-time response under tensile loading (creep tests) and the stress strain response under constant tensile stress rate (proportional loading tests) have been evaluated at 4 temperatures 20, 45, 55, and 65°C, for samples of cellulose nitrate. A time-dependent constitutive equation (or stress-strain relation) for the nonlinear visco-elastic material is deduced from invariant theory with a hypothesis of a creep potential. The procedure for determining the seven material constants involved in the deduced constitutive equation is described for the creep and proportional loading tests and the variation of these constants with temperature is presented. The deduced constitutive equation gives good agreement with the actual observations for the creep and proportional loading tests, independent of the values of temperature, creep stress, or stress rate.     

Residuals‐based tests for the null of no‐cointegration: an Analytical comparison

Abstract. This article studies the asymptotic distribution of five residuals‐based tests for the null of no‐cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares (GLS)‐detrended variables. The local asymptotic power of the tests is shown to be a function of Brownian motion and Ornstein–Uhlenbeck processes, depending on a single nuisance parameter, which is determined by the correlation at frequency zero of the errors of the cointegration regression with the shocks to the right‐hand side variables. The tests are compared in terms of power in large and small samples. It is shown that, while no significant improvement can be achieved by using unit root tests other than the OLS detrended t‐test originally proposed by Engle and Granger (1987), the power of GLS residuals tests can be higher than the power of system tests for some values of the nuisance parameter.     

Effect of Resin System Parameters on Resin Transfer Molding of Vinyl Ester Based Composites—A Statistically Designed Study

Although the area of composites has advanced significantly over the past three decades, there is still a lack of understanding as to the coupling between materials and processing variables, especially as related to the use of resin systems in emerging processes such as resin transfer molding (RTM). As materials are tailored through the use of additives to resin systems, intricate fiber architectures, and the use of specific processing parameters, the need for a thorough understanding of the effect of minor variations in the materials system and the ultimate need for process control techniques increases. The current investigation is aimed at developing an understanding of variation in performance in three similar vinyl ester resin based composite systems as a function of mold release agent concentration, presence of a wetting/dispersion agent, and preform tool temperature. It is seen that the concentration of mold release agent has a significant influence on performance, which can be correlated with results of dynamic mechanical analysis tests. The importance of using statistically based studies to determine optimum settings and overall variation in performance is emphasized. This approach is favored over the use of an n[sgrave] approach, which gives the user a means of controlling quality based on postproduction control rather than through the selection of settings that are insensitive to variation in the quality of incoming material process changes. The achievement of quality through control of material and process variables is important not only for the cost-efficient production of composite parts but also for the fabrication of large parts such as would be needed for civil infrastructure applications (bridge decks, piers, etc.), where postproduction rejection would result in significant losses.     

PREDICTION OF THERMAL CONDUCTIVITY AND VISCOSITY FOR SOME FLUIDS IN THE NEAR-CRITICAL REGION

The objective of this work was to develop general, simple and accurate expressions to predict the peculiar behavior of thermal conductivity and viscosity in the near-critical region. Expressions were determined for (a) variation of thermal conductivity as a function of temperature and density or pressure for carbon dioxide, water, and ammonia, and for (b) variation of viscosity as a function of temperature and density or pressure for carbon dioxide, water, and nitrogen. The predicted results based on the developed expressions showed a very good agreement with the available thermal conductivity experimental data and an excellent agreement with the available viscosity experimental data     

Analysis of Factors Influencing Colour Matching in Package Dyeing

Automated dyeing can be successfully accomplished only if all the variables that affect the final colour are held within limits that keep the accumulated effect on colour within acceptable tolerances. The number of variables is large and the magnitude of the effect of each factor on colour must be assessed in order to determine the degree of process control to be imposed on each factor to meet any prescribed standard of colour matching. A comprehensive investigation of the many variables, using a statistical factorial type of design (termed skeleton factorial design), is described. These designs reduce the experimental work to reasonable proportions and enable simple estimates to be made of the effect of each factor. Colour variations were assessed instrumentally and translated into colour-difference terms using a uniform colour-difference co-ordinate system. Simulation work assessed the colour variation consequent upon random variation of groups of factors with given standard deviation. From this work, it was possible to construct limits of accuracy that had to be maintained, at each relevant process, to achieve dye lots that were within the prescribed tolerances at the end of each automated dyeing cycle.     

High-density polyethylene melt elasticity—some anomalous observations on the effects of molecular structure

The die swell behavior of polymeric melts is a manifestation of melt elasticity of these materials and is of considerable commercial as well as fundamental importance. Hence, knowledge of the effect of such molecular variables as molecular weight (MW) and molecular weight distribution (MWD) on melt elasticity is important from both commercial and basic rheological points of view. The effect of these variables on melt elasticity of broad-distribution polymers in the shear rate region of commercial interest is not unambiguously known, with most published theory and experiment being applicable to the low-shear behavior of narrow-distribution polymers and blends thereof. There is indication that die swell increases with increasing MW and broadening MWD. However, the current investigation of carefully characterized broad-distribution HDPE materials prepared specifically to examine the effects of various molecular variables on melt elasticity does not support this contention and, in fact, provides consistent evidence for the opposite result, i.e., decreasing die swell with increasing MW or broadening distribution. The various samples studies were prepared by fractionation removal or addition of component molecular species or by polymerization designed to provide systematic variation of molecular species or by polymerization designed to provide systematic variation of molecular parameters. Overall MWD's of the samples were characterized, and die swell behavior was determined at 200°C over a wide shear rate region in a high L/D capillary both with and without annealing of extrudates. The results are presented showing effects of specific molecular variables.     

Mechanical properties of rigid thermoplastic foams—Part I: Experimental considerations

The through-thickness variation in the porosity of structural foam material is known to result in different “material properties” when mechanics based on homogeneous materials is used to interpret data from standard tensile and bend tests. Unresolved issues relating to structural design include the specification of the most useful test specimen, the identification of useful material properties, and the application of these properties to part design and analysis. This paper develops procedures for determining the mechanical properties of rigid thermoplastic structural foams, and for the application of these properties to the design of load-bearing components. Rather than molded specimens, it is suggested that specimens cut from large, edge-gated plates be used for determining mechanical properties of structural foams. By modeling foams as continuous but nonhomogeneous materials, it is shown that data from simple tensile and flexural tests can be used in structural analysis to systematically account for the through-thickness variation of material properties.     

Study of coal and coke ignition in fluidized beds

Ignition tests were conducted with delayed and fluid petroleum cokes, a high volatile bituminous coal and their blends in bench- and pilot-scale fluidized bed combustors. In the bench-scale FBC tests, a visual inspection ignition criterion was developed based on the ‘CO–CO₂’ profiles obtained as a function of time and bed temperature. In the pilot-scale unit, the rapid increase in SO₂ levels was used as the indicator of fuel ignition. In addition to the fluidized bed ignition tests, thermogravimetric analysis (TGA) measurements were made on all fuels and their chars. The results showed that, while the fluid coke (which has the lowest volatile content) was the most difficult to ignite, ignition was not a simple function of volatile content. Further, different test methods and ignition criteria demonstrated significantly different ignition temperatures, with the largest variation arising between bench- and pilot-scale equipment. Finally, tests on mixtures of petroleum coke and coal showed that there was no interaction between these two fuels, and that the coke ignited only when it achieved its own ignition temperature.