Pentti Minkkinen

Adaptive Fuzzy C-Means clustering in process monitoring

Abstract Quite often, quality control models fail because, e.g., the mean values are changing continuously. These kinds of changes, e.g., process drifts due to seasonal fluctuations, are common in an activated sludge waste-water treatment plant in Finland. Different Fuzzy C-Means (FCM) clustering algorithms were tested in order to cope with these kinds of seasonal effects. Firstly, a Principal Component Analysis (PCA) model was constructed in order to visualize the data set and reduce the dimensionality of the problem. Then, score values of the PCA were used in the FCM. The cluster centers represented the different process conditions (winter and summer seasons). Different algorithms were used to update the cluster centers or to give them some flexibility. The testing of different FCM algorithms was carried out by using a separate test set. The adaptive and the flexible FCM algorithms were compared to the basic non-adaptive FCM. For both cases, modifications are proposed and a simple strategy for updating the cluster centers is given.

Wavelet-PLS regression models for both exploratory data analysis and process monitoring

Two novel approaches are presented which take into account the collinearity among variables and the different phenomena occurring at different scales. This is achieved by combining partial least squares (PLS) and multiresolution analysis (MRA). In this work the two novel approaches are interconnected. First, a standard exploratory PLS model is scrutinized with MRA. In this way, different events at different scales and latent variables are recognized. In this case, especially periodic seasonal fluctuations and long‐term drifting introduce problems. These low‐frequency variations mask and interfere with the detection of small and moderate‐level transient phenomena. As a result, the confidence limits become too wide. This relatively common problem caused by autocorrelated measurements can be avoided by detrending. In practice, this is realized by using fixed‐size moving windows and by detrending these windows. Based on the MRA of the standard model, the second PLS model for process monitoring is constructed based on the filtered measurements. This filtering is done by removing the low‐frequency scales representing low‐frequency components, such as seasonal fluctuations and other long‐term variations, prior to standard PLS modeling. For these particular data the results are shown to be superior compared to a conventional PLS model based on the non‐filtered measurements. Often, model updating is necessary owing to non‐stationary characteristics of the process and variables. As a big advantage, this new approach seems to remove any further need for model updating, at least in this particular case. This is because the presented approach removes low‐frequency fluctuations and results in a more stationary filtered data set that is more suitable for monitoring. Copyright

Partial least squares modeling of an activated sludge plant: A case study

Abstract Many variables are normally measured in an activated sludge waste water treatment plant. Some of them are strongly cross-correlated. Partial least squares (PLS) and principal component analysis (PCA) have been widely used with these kind of processes because they both can be used with redundant data sets. In PLS, variable interactions can be visualized by loading weights and object groupings by scores. The aim of this paper was to utilize PLS and auto-correlation function in modeling the multivariate process. Loadings, loading weights, scores, MLR-type regression coefficients and auto-correlation functions were used to study the model. PLS results were visualized and it was shown how these results can be used to get a more profound look into the process. Sometimes it is rather difficult to find out corresponding phenomena behind latent variables, but almost in every case one can easily isolate the disturbance and find out, i.e., variables which are deviating strongly from the normal operating conditions.

Multivariate data analysis of key pollutants in sewage samples: a case study

Waste water treatment plants often need detailed information about the sources and levels of pollutants in sewage in order to maintain stable process conditions and to achieve permitted levels for hazardous compounds in their effluents. A high content of pollutants is usually traceable to industrial inputs. In this study the main objective was to study the factors affecting the composition of sewage of domestic origin. Sixty-five domestic sewage samples collected during 9 months at eight different sites in Melbourne, Australia, were analyzed for 83 chemical variables. The data set also included two samples of combined domestic/industrial wastewaters, seven samples from waste water treatment plant influent streams and five domestic water supply samples. The data was studied with multivariate data analysis methods; principal component analysis (PCA) and partial least squares (PLS). With multivariate methods, effects of lifestyle of residents, day of the week and sampling time or weather on the pollutant levels could be determined.

Principal component analysis, contribution plots and feature weights in the monitoring of sequential process data from a paper machine's wet end.

Abstract Data collected from a paper mill using a WIC-100 process analyzer was divided into six classes, each representing a different kind of paper grade or quality. Each of the six classes were modeled separately by principal component analysis (PCA). The score values of the calibration data, together with the corresponding confidence limits and the trajectory of the current data, are used to visualize the state of the process. For each of the classes, two collective multivariate control charts have been used to describe the state of the process. The first one of these charts is calculated from the residuals and the second one is based on the Mahalanobis distance of the score values. Both of these charts can be traced back to the original variables. Multivariate control charts and biplots have been applied together with the contribution plots and the feature weights in order to detect any process problems and to isolate the deviating variables. The results have been verified by using parallel coordinates. These methods are useful in detecting and isolating the various types of changes that may occur in the wet end process of a paper machine. The concept of contribution map has also been introduced. In this context, Bonferroni bounds have been used as decision rules for plotting points (warnings) on the contribution map.

Determination of acid value, hydroxyl value and water content in reactions between dicarboxylic acids and diols using near-infrared spectroscopy and non-linear partial least squares regression

Abstract A predictive calibration model based on non-linear partial least squares (PLS) regression was developed to describe the relationship between the near-infrared (NIR) reflectance spectra and the acid value, hydroxyl value and water, content in polyesterification of dicarboxylic acids with diols. Two dicarboxylic acids and six diols were tested in different combinations with one dicarboxylic acid and one diol at a time. The polyesterifications were carried out isothermally in a laboratory scale semi-batch reactor at temperatures between 140–190 °C. NIR spectrometry offers a fast in-line method for monitoring and controlling the polyesterification reaction. A predictive model which relates all the NIR spectra and the measured acid values was developed. The calibration of the NIR spectra and the hydroxyl value succeeded in experiments where the hydroxyl value was determined. The measured water content and the NIR spectra could not be calibrated with the same model for different dicarboxylic acid and diol combinations. Principal component analysis (PCA) was used to classify the NIR spectra. The spectra could be classified according to the dicarboxylic acid and diol used in the experiment.

A combined approach of partial least squares and fuzzy c-means clustering for the monitoring of an activated-sludge waste-water treatment plant

Abstract In this paper, a combined approach of partial least squares (PLS) and fuzzy c-means (FCM) clustering for the monitoring of an activated-sludge waste-water treatment plant is presented. Their properties are also investigated. Both methods were applied together in process monitoring. PLS was used for extracting the most useful information from the control and process variables in order to predict a response variable, namely the diluted sludge volume index. Score values were used in FCM, which utilizes the principle of an object belonging to several classes at the same time instead of just one class. The memberships of each of the classes are defined by the membership values. Corresponding membership plots were used to help in the interpretation of the score plots. Short-term changes were considered to be disturbances and long-term changes due to drifting.

Evaluation of the fundamental sampling error in the sampling of particulate solids

Abstract Chemical analysis is a multi-stage process, which starts with primary sampling and ends with evaluation of the resuts. Especially in trace analysis and microanalysis of solid materials, sampling can far outweigh all other sources of error. For estimating the reliability of complete analytical procedures, a method is needed which can be used to estimate the errors made in the primary and the secondary sampling and sample preparation steps. Based on Gys theory of sampling, a computer program (SAMPEX) was written for the solution of practical sampling problems. The method involves the estimation of the sampling constant, C. For well-characterized materials, C can be estimated from the material properties. If the necessary material properties are difficult to estimate, C can be evaluated experimentally. The program can be used to solve the following problems: minimum sample size for a tolerated relative standard deviation of the fundamental sampling error; relative size for a tolerated for a given sample size; maximum particle size of the material for a specified standard deviation and sample size; balanced design of a multi-stage sampling and sample-reduction process; and sampling for particle size determination.

Modeling of activated sludge plants treatment efficiency with PLSR: a process analytical case study

Abstract The most common waste water purification method within Finnish pulp and paper industry is activated sludge method. Activated sludge method is a complex biological process, where several physical, chemical, and microbiological mechanisms simultaneously affect the purification result. There are tens of processes and control parameters determined at the plants. However, the parameter sets do not include any parameters describing the special features of the industrial influent nor any parameters directly describing microbial composition of the sludge. Thus there seems to be an obvious need for new parameters. As a part of a cooperation project empirical data sets from three pulp and paper mills were studied with multivariate methods. The main interest was focused on the information covered by the presently measured process and control parameters and their capability to predict purification result or approaching bulking state. The descriptor variables for PLSR models were selected by using a forward stepwise procedure with cross-validation criteria. As conclusion of PLSR modeling, the parameters included most of the information needed to predict the approaching process drift, which was caused by sludge bulking. However, the models for purification efficiency or for effluent quality indicated an obvious lack of relevant information. The average purification result could still be predicted.

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH2PO4 and Na2HPO4,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.