Model-based operational constraints for fluidised bed crystallisation.

Fluidised bed reactors are used for water softening in water treatment plants. Recent research shows that under current operation of reactors the crystallisation of calcium carbonate can be hampered. Until now the operational constraints on the fluidised bed have not been exactly known. Experiments were carried out to investigate the fluidisation behaviour of calcium carbonate pellets in water. The results of the fluidisation experiments are compared to two commonly used modelling approaches of Ergun and Richardon-Zaki. Using the experimental data the models are calibrated. The calibrated Richardson-Zaki model is used to determine operational constraints on pellet size at the bottom of the reactor and water flow through the reactor. The model-based constraints are compared to operational data of the Weesperkarspel full-scale treatment plant of Waternet (The Netherlands). It can be concluded that the current operation of the treatment plant violates the calculated constraints with consequences for effluent quality and corrective maintenance. By using models for determining the operation of the fluidised bed, the softening process can thus be improved.

Optimal flow distribution over multiple parallel pellet reactors: a model-based approach.

A drinking water treatment plant has a typical configuration of parallel lanes to provide safe drinking water 24 h a day. A new approach for optimising the production of drinking water treatment plants is proposed. This approach is applied to the softening process step and shows promising results in terms of cost reduction by optimising the water distribution over several parallel reactors. The proposed scheme relies on optimal model-based control of a single softening reactor and the use of a bypass.

Estimation of respiratory parameters via fuzzy clustering.

The results of monitoring respiratory parameters estimated from flow-pressure-volume measurements can be used to assess patients' pulmonary condition, to detect poor patient-ventilator interaction and consequently to optimize the ventilator settings. A new method is proposed to obtain detailed information about respiratory parameters without interfering with the expiration. By means of fuzzy clustering, the available data set is partitioned into fuzzy subsets that can be well approximated by linear regression models locally. Parameters of these models are then estimated by least-squares techniques. By analyzing the dependence of these local parameters on the location of the model in the flow-volume-pressure space, information on patients' pulmonary condition can be gained. The effectiveness of the proposed approaches is demonstrated by analyzing the dependence of the expiratory time constant on the volume in patients with chronic obstructive pulmonary disease (COPD) and patients without COPD.

Fuzzy relational classifier trained by fuzzy clustering.

A novel approach to nonlinear classification is presented, in the training phase of the classifier, the training data is first clustered in an unsupervised way by fuzzy c-means or a similar algorithm. The class labels are not used in this step. Then, a fuzzy relation between the clusters and the class identifiers is computed. This approach allows the number of prototypes to be independent of the number of actual classes. For the classification of unseen patterns, the membership degrees of the feature vector in the clusters are first computed by using the distance measure of the clustering algorithm. Then, the output fuzzy set is obtained by relational composition. This fuzzy set contains the membership degrees of the pattern in the given classes. A crisp decision is obtained by defuzzification, which gives either a single class or a "reject" decision, when a unique class cannot be selected based on the available information. The principle of the proposed method is demonstrated on an artificial data set and the applicability of the method is shown on the identification of live-stock from recorded sound sequences. The obtained results are compared with two other classifiers.

Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models.

The construction of interpretable Takagi-Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath-Geva (GG) algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the expectation-maximization (EM) identification of Gaussian mixture models. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.

Fuzzy modeling with multivariate membership functions: gray-box identification and control design.

A novel framework for fuzzy modeling and model-based control design is described. The fuzzy model is of the Takagi-Sugeno (TS) type with constant consequents. It uses multivariate antecedent membership functions obtained by Delaunay triangulation of their characteristic points. The number and position of these points are determined by an iterative insertion algorithm. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. Finally, methods for control design through linearization and inversion of this model are developed. The proposed techniques are demonstrated by means of two benchmark examples: identification of the well-known Box-Jenkins gas furnace and inverse model-based control of a pH process. The obtained results are compared with results from the literature.

Similarity measures in fuzzy rule base simplification.

In fuzzy rule-based models acquired from numerical data, redundancy may be present in the form of similar fuzzy sets that represent compatible concepts. This results in an unnecessarily complex and less transparent linguistic description of the system. By using a measure of similarity, a rule base simplification method is proposed that reduces the number of fuzzy sets in the model. Similar fuzzy sets are merged to create a common fuzzy set to replace them in the rule base. If the redundancy in the model is high, merging similar fuzzy sets might result in equal rules that also can be merged, thereby reducing the number of rules as well. The simplified rule base is computationally more efficient and linguistically more tractable. The approach has been successfully applied to fuzzy models of real world systems.