Showing papers by "Robert Babuska published in 2004"

Effective optimization for fuzzy model predictive control

Abstract: This paper addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, time-consuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For long-range predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a high-purity distillation column.

Input selection for nonlinear regression models

Abstract: A simple and effective method for the selection of significant inputs in nonlinear regression models is proposed. Given a set of input-output data and an initial superset of potential inputs, the relevant inputs are selected by checking whether after deleting a particular input, the data set is still consistent with the basic property of a function. In order to be able to handle real-valued and noisy data in a sensible manner, fuzzy clustering is first applied. The obtained clusters are compared by using a similarity measure in order to find inconsistencies within the data. Several examples using simulated and real-world data sets are presented to demonstrate the effectiveness of the algorithm.

Integrated operation of drinking water treatment plant at Amsterdam water supply

Abstract: Water treatment plants are in general robust and designs are based on the performance of individual processes with pre-set boundary conditions. It is assumed that an integral approach of the entire treatment plant can lead to more efficient operation. Taking into account the developments in sensoring, automation and computation, it is a challenge to improve quality and reliability of the treatment plants and to make maximal use of the installed infrastructure, postponing new investments. At Amsterdam Water Supply (AWS), the first steps have been taken to come to an integral dynamic model of the total water treatment plant and the use of this model as an instrument for integral control. The parameters influencing the performance of the water treatment process will be incorporated in an overall model evaluating the goal factors quality (good, constant and reliable), quantity, costs, environmental impact (low residuals level), redundancy and flexibility. For several individual processes at AWS models have already been developed during the last few years, like models for the ozone process, biological activated carbon filtration and pellet softening. For the final calibration and validation pilot reactors are automated and on-line data are collected. Criteria for evaluation are developed to realise an optimal control of the individual processes in interaction with the goal factors of the total treatment process.

FUZZSAM - visualization of fuzzy clustering results by modified Sammon mapping

Abstract: Since in practical data mining problems high-dimensional data are clustered, the resulting clusters are high-dimensional geometrical objects, which are difficult to analyze and interpret. Cluster validity measures try to solve this problem by providing a single numerical value. As a low dimensional graphical representation of the clusters could be much more informative than such a single value, this paper proposes a new tool for the visualization of fuzzy clustering results. By using the basic properties of fuzzy clustering algorithms, this new tool maps the cluster centers and the data such that the distances between the clusters and the data-points are preserved. During the iterative mapping process, the algorithm uses the membership values of the data and minimizes an objective function similar to the original clustering algorithm. Comparing to the original Sammon mapping not only reliable cluster shapes are obtained but the numerical complexity of the algorithm is also drastically reduced. The algorithm has been applied to several data sets and the numerical results show performance superior to principal component analysis and the classical Sammon mapping based projection. The examples demonstrate that proposed FUZZSAMM algorithm is a useful tool in user-guided clustering.

Structure selection for nonlinear models with mixed discrete and continuous inputs: a comparative study

Abstract: A comparison of two methods for selecting inputs in nonlinear models with mixed discrete (categorical) and continuous variables is presented. Both methods assume that an initial superset of potential regressors is given along with a set of data. In the first approach, the relevant inputs are selected by a model-free search algorithm using fuzzy clustering to quantize continuous data into subsets. The second approach employs regression trees as an induction algorithm 'wrapped' within a search method. The results obtained for two simulation examples and one real-world data set show that the fuzzy clustering-based method performs more consistently in selecting the model structure. Moreover, this method is much faster then the wrapper approach.

Fuzzy clustering for selecting structure of nonlinear models with mixed discrete and continuous inputs

Abstract: A method for selecting regressors in nonlinear models with mixed discrete (categorical) and continuous inputs is proposed. Given a set of input-output data and an initial superset of potential inputs, the relevant inputs are selected by a model-free search algorithm. Fuzzy clustering is used to quantize continuous data into subsets that can be handled in a similar way as discrete data. Two simulation examples and one real-world data set are included to illustrate the performance of the proposed method and compare it with the performance of regression trees. For small to medium size problems (up to 15 candidate inputs), the proposed method works effectively. For larger problems, the computational load becomes too high.

State-space reconstruction and prediction of chaotic time series based on fuzzy clustering

Abstract: Selecting the embedding dimension of a dynamic system is a key step toward the analysis and prediction of nonlinear and chaotic time-series. This paper proposes a clustering-based algorithm for this purpose. The clustering is applied in the reconstructed space defined by the lagged output variables. The intrinsic dimension of the reconstructed space is then estimated based on the analysis of the eigenvalues of the fuzzy cluster covariance matrices, while the correct embedding dimension is inferred from the prediction performance of the local models of the clusters. The main advantage of the proposed solution is that three tasks are simultaneously solved during clustering: selection of the embedding dimension, estimation of the intrinsic dimension, and identification of a model that can be used for prediction.

Fuzzy Clustering for Selecting Nonlinear Models with Mixed Continuous Inputs

Abstract: A method for selecting regressors in nonlinear models with mixed discrete (categorical) and continuous inputs is proposed. Given a set of input-output data and an initial superset of potential inputs, the relevant inputs are selected by a model-free search algorithm. Fuzzy clustering is used to quantize continuous data into subsets that can be handled in a similar way as discrete data. Two simulation example5 and one reai-world data set are included to illustrite the performance of the proposed method and compare it with the performance of regression trees. For small to medium size problems (up to 15 candidate inputs), the proposed method works effectively. For larger problems, the computational load becomes too high.