Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

Reliability of vegetation community information derived using decorana ordination and fuzzy c-means clustering

Descriptions of vegetation communities are often based on vague semantic terms describing species presence and dominance. For this reason, some researchers advocate the use of fuzzy sets in the statistical classification of plant species data into communities. In this study, spatially referenced vegetation abundance values collected from Greek phrygana were analysed by ordination (DECORANA), and classified on the resulting axes using fuzzy c-means to yield a point data-set representing local memberships in characteristic plant communities. The fuzzy clusters matched vegetation communities noted in the field, which tended to grade into one another, rather than occupying discrete patches. The fuzzy set representation of the community exploited the strengths of detrended correspondence analysis while retaining richer information than a TWINSPAN classification of the same data. Thus, in the absence of phytosociological benchmarks, meaningful and manageable habitat information could be derived from complex, multivariate species data. We also analysed the influence of the reliability of different surveyors' field observations by multiple sampling at a selected sample location. We show that the impact of surveyor error was more severe in the Boolean than the fuzzy classification. © 2007 Springer.

Prediction of PM10 concentrations using Fuzzy c-Means and ANN

Salamanca has been considered among the most polluted cities in Mexico. The vehicular park, the industry and the emissions produced by agriculture, as well as orography and climatic characteristics have propitiated the increment in pollutant concentration of Particulate Matter less than 10 μg/m3 in diameter (PM10). In this work, a Multilayer Perceptron Neural Network has been used to make the prediction of an hour ahead of pollutant concentration. A database used to train the Neural Network corresponds to historical time series of meteorological variables (wind speed, wind direction, temperature and relative humidity) and air pollutant concentrations of PM10. Before the prediction, Fuzzy c-Means clustering algorithm have been implemented in order to find relationship among pollutant and meteorological variables. These relationship help us to get additional information that will be used for predicting. Our experiments with the proposed system show the importance of this set of meteorological variables on the prediction of PM10 pollutant concentrations and the neural network efficiency. The performance estimation is determined using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results shown that the information obtained in the clustering step allows a prediction of an hour ahead, with data from past 2 hours

Uma nova forma de calcular os centros dos Clusters em algoritmos de agrupamento tipo fuzzy c-means

Clustering data is a very important task in data mining, image processing and pattern recognition problems. One of the most popular clustering algorithms is the Fuzzy C-Means (FCM). This thesis proposes to implement a new way of calculating the cluster centers in the procedure of FCM algorithm which are called ckMeans, and in some variants of FCM, in particular, here we apply it for those variants that use other distances. The goal of this change is to reduce the number of iterations and processing time of these algorithms without affecting the quality of the partition, or even to improve the number of correct classifications in some cases. Also, we developed an algorithm based on ckMeans to manipulate interval data considering interval membership degrees. This algorithm allows the representation of data without converting interval data into punctual ones, as it happens to other extensions of FCM that deal with interval data. In order to validate the proposed methodologies it was made a comparison between a clustering for ckMeans, K-Means and FCM algorithms (since the algorithm proposed in this paper to calculate the centers is similar to the K-Means) considering three different distances. We used several known databases. In this case, the results of Interval ckMeans were compared with the results of other clustering algorithms when applied to an interval database with minimum and maximum temperature of the month for a given year, referring to 37 cities distributed across continents

Novos métodos determinísticos para gerar centros iniciais dos grupos no algoritmo fuzzy C-Means e variantes

Data clustering is applied to various fields such as data mining, image processing and pattern recognition technique. Clustering algorithms splits a data set into clusters such that elements within the same cluster have a high degree of similarity, while elements belonging to different clusters have a high degree of dissimilarity. The Fuzzy C-Means Algorithm (FCM) is a fuzzy clustering algorithm most used and discussed in the literature. The performance of the FCM is strongly affected by the selection of the initial centers of the clusters. Therefore, the choice of a good set of initial cluster centers is very important for the performance of the algorithm. However, in FCM, the choice of initial centers is made randomly, making it difficult to find a good set. This paper proposes three new methods to obtain initial cluster centers, deterministically, the FCM algorithm, and can also be used in variants of the FCM. In this work these initialization methods were applied in variant ckMeans.With the proposed methods, we intend to obtain a set of initial centers which are close to the real cluster centers. With these new approaches startup if you want to reduce the number of iterations to converge these algorithms and processing time without affecting the quality of the cluster or even improve the quality in some cases. Accordingly, cluster validation indices were used to measure the quality of the clusters obtained by the modified FCM and ckMeans algorithms with the proposed initialization methods when applied to various data sets

ANN and Fuzzy c-Means applied to environmental pollution prediction

Salamanca, situated in center of Mexico is among the cities which suffer most from the air pollution in Mexico. The vehicular park and the industry, as well as orography and climatic characteristics have propitiated the increment in pollutant concentration of Sulphur Dioxide (SO2). In this work, a Multilayer Perceptron Neural Network has been used to make the prediction of an hour ahead of pollutant concentration. A database used to train the Neural Network corresponds to historical time series of meteorological variables and air pollutant concentrations of SO2. Before the prediction, Fuzzy c-Means and K-means clustering algorithms have been implemented in order to find relationship among pollutant and meteorological variables. Our experiments with the proposed system show the importance of this set of meteorological variables on the prediction of SO2 pollutant concentrations and the neural network efficiency. The performance estimation is determined using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results showed that the information obtained in the clustering step allows a prediction of an hour ahead, with data from past 2 hours.

Fuzzy c-means variants for medical image segmentation

Segmentation is an important step in many medical imaging applications and a variety of image segmentation techniques exist. One group of segmentation algorithms is based on clustering concepts. In this article we investigate several fuzzy c-means based clustering algorithms and their application to medical image segmentation. In particular we evaluate the conventional hard c-means (HCM) and fuzzy c-means (FCM) approaches as well as three computationally more efficient derivatives of fuzzy c-means: fast FCM with random sampling, fast generalised FCM, and a new anisotropic mean shift based FCM. © 2010 by IJTS, ISDER.

SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

Management zones using fuzzy clustering based on spatial-temporal variability of soil and corn yield

Clustering soil and crop data can be used as a basis for the definition of management zones because the data are grouped into clusters based on the similar interaction of these variables. Therefore, the objective of this study was to identify management zones using fuzzy c-means clustering analysis based on the spatial and temporal variability of soil attributes and corn yield. The study site (18 by 250-m in size) was located in Jaboticabal, São Paulo/Brazil. Corn yield was measured in one hundred 4.5 by 10-m cells along four parallel transects (25 observations per transect) over five growing seasons between 2001 and 2010. Soil chemical and physical attributes were measured. SAS procedure MIXED was used to identify which variable(s) most influenced the spatial variability of corn yield over the five study years. Basis saturation (BS) was the variable that better related to corn yield, thus, semivariograms models were fitted for BS and corn yield and then, data values were krigged. Management Zone Analyst software was used to carry out the fuzzy c-means clustering algorithm. The optimum number of management zones can change over time, as well as the degree of agreement between the BS and corn yield management zone maps. Thus, it is very important take into account the temporal variability of crop yield and soil attributes to delineate management zones accurately.

An evolving possibilistic fuzzy modeling approach for value-at-risk estimation

Market risk exposure plays a key role for nancial institutions risk management. A possible measure for this exposure is to evaluate losses likely to incurwhen the price of the portfolio's assets declines using Value-at-Risk (VaR) estimates, one of the most prominent measure of nancial downside market risk. This paper suggests an evolving possibilistic fuzzy modeling approach for VaR estimation. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling, which employs memberships and typicalities to update clusters and creates new clusters based on a statistical control distance-based criteria. ePFM also uses an utility measure to evaluate the quality of the current cluster structure. Computational experiments consider data of the main global equity market indexes of United States, London, Germany, Spain and Brazil from January 2000 to December 2012 for VaR estimation using ePFM, traditional VaR benchmarks such as Historical Simulation, GARCH, EWMA, and Extreme Value Theory and state of the art evolving approaches. The results show that ePFM is a potential candidate for VaR modeling, with better performance than alternative approaches.

A fuzzy approach to texture segmentation

The texture segmentation techniques are diversified by the existence of several approaches. In this paper, we propose fuzzy features for the segmentation of texture image. For this purpose, a membership function is constructed to represent the effect of the neighboring pixels on the current pixel in a window. Using these membership function values, we find a feature by weighted average method for the current pixel. This is repeated for all pixels in the window treating each time one pixel as the current pixel. Using these fuzzy based features, we derive three descriptors such as maximum, entropy, and energy for each window. To segment the texture image, the modified mountain clustering that is unsupervised and fuzzy c-means clustering have been used. The performance of the proposed features is compared with that of fractal features.

A framework for extreme-event control in wastewater treatment

In this paper an approach to extreme event control in wastewater treatment plant operation by use of automatic supervisory control is discussed. The framework presented is based on the fact that different operational conditions manifest themselves as clusters in a multivariate measurement space. These clusters are identified and linked to specific and corresponding events by use of principal component analysis and fuzzy c-means clustering. A reduced system model is assigned to each type of extreme event and used to calculate appropriate local controller set points. In earlier work we have shown that this approach is applicable to wastewater treatment control using look-up tables to determine current set points. In this work we focus on the automatic determination of appropriate set points by use of steady state and dynamic predictions. The performance of a relatively simple steady-state supervisory controller is compared with that of a model predictive supervisory controller. Also, a look-up table approach is included in the comparison, as it provides a simple and robust alternative to the steady-state and model predictive controllers, The methodology is illustrated in a simulation study.

Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the RodriguesTriple Junction in the Indian Ocean were studied applying classical statistical methods(fuzzy c-means clustering, linear mixing model, principal component analysis) for theextraction of endmembers and evaluating the spatial and temporal variation ofgeochemical signals. Three main factors of sedimentation were expected by the marinegeologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. Thedisplay of fuzzy membership values and/or factor scores versus depth providedconsistent results for two factors only; the ultra-basic component could not beidentified. The reason for this may be that only traditional statistical methods wereapplied, i.e. the untransformed components were used and the cosine-theta coefficient assimilarity measure.During the last decade considerable progress in compositional data analysis was madeand many case studies were published using new tools for exploratory analysis of thesedata. Therefore it makes sense to check if the application of suitable data transformations,reduction of the D-part simplex to two or three factors and visualinterpretation of the factor scores would lead to a revision of earlier results and toanswers to open questions . In this paper we follow the lines of a paper of R. Tolosana-Delgado et al. (2005) starting with a problem-oriented interpretation of the biplotscattergram, extracting compositional factors, ilr-transformation of the components andvisualization of the factor scores in a spatial context: The compositional factors will beplotted versus depth (time) of the core samples in order to facilitate the identification ofthe expected sources of the sedimentary process.Kew words: compositional data analysis, biplot, deep sea sediments