Johannes A. Roubos

Learning fuzzy classification rules from labeled data

The automatic design of fuzzy rule-based classification systems based on labeled data is considered. It is recognized that both classification performance and interpretability are of major importance and effort is made to keep the resulting rule bases small and comprehensible. For this purpose, an iterative approach for developing fuzzy classifiers is proposed. The initial model is derived from the data and subsequently, feature selection and rule-base simplification are applied to reduce the model, while a genetic algorithm is used for parameter optimization. An application to the Wine data classification problem is shown.

Data-driven generation of compact, accurate, and linguistically sound fuzzy classifiers based on a decision-tree initialization

Abstract The data-driven identification of fuzzy rule-based classifiers for high-dimensional problems is addressed. A binary decision-tree-based initialization of fuzzy classifiers is proposed for the selection of the relevant features and effective initial partitioning of the input domains of the fuzzy system. Fuzzy classifiers have more flexible decision boundaries than decision trees (DTs) and can therefore be more parsimonious. Hence, the decision tree initialized fuzzy classifier is reduced in an iterative scheme by means of similarity-driven rule-reduction. To improve classification performance of the reduced fuzzy system, a genetic algorithm with a multiobjective criterion searching for both redundancy and accuracy is applied. The proposed approach is studied for (i) an artificial problem, (ii) the Wisconsin Breast Cancer classification problem, and (iii) a summary of results is given for a set of well-known classification problems available from the Internet: Iris, Ionospehere, Glass, Pima, and Wine data.

Fuzzy model-based predictive control using Takagi–Sugeno models

Abstract Nonlinear model-based predictive control (MBPC) in multi-input multi-output (MIMO) process control is attractive for industry. However, two main problems need to be considered: (i) obtaining a good nonlinear model of the process, and (ii) applying the model for control purposes. In this paper, recent work focusing on the use of Takagi–Sugeno fuzzy models in combination with MBPC is described. First, the fuzzy model-identification of MIMO processes is given. The process model is derived from input–output data by means of product-space fuzzy clustering. The MIMO model is represented as a set of coupled multi-input, single-output (MISO) models. Next, the Takagi–Sugeno fuzzy model is used in combination with MBPC. The critical element in nonlinear MBPC is the optimization routine which is nonconvex and thus difficult to solve. Two methods to deal with this problem are developed: (i) a branch-and-bound method with iterative grid-size reduction, and (ii) control based on a local linear model. Both methods have been tested and evaluated with a simulated laboratory setup for a MIMO liquid level process with two inputs and four outputs.

Identification of MIMO systems by input-output TS fuzzy models

A number of techniques have been introduced to construct fuzzy models from measured data. Most attention has been focused on multiple-input, single-output (MISO) systems. This article concentrates on the identification of multiple-input multiple-output (MIMO) systems by means of product-space fuzzy clustering with adaptive distance measure (the Gustafson-Kessel algorithm). The MIMO model is represented as a set of coupled input-output MISO models of the Takagi-Sugeno type. Knowledge of the physical structure can easily be incorporated in the structure of the model. Software implementation in the form of a MATLAB toolbox is briefly described. A simulation example of four cascaded tanks is given.

A Quantitative Approach to Characterizing Cell Lysis Caused by Mechanical Agitation of Streptomyces clavuligerus

Streptomyces clavuligerusis a commercially important actinomycete that is used to produce clavulanic acid, a β‐lactamase inhibitor. Observations during 10 batch cultivations with S. clavuligerus on defined media have led to the finding that the organism is very sensitive to shear when grown in batch cultures with increasing stirrer speed. The stirrer speed was increased to keep the dissolved oxygen level above 50% air saturation. A quantitative approach based on the calculation of elemental balances and a simple mathematical model is proposed to characterize the biomass lysis. Finally, a linear relation between biomass yield and observed specific growth rate is determined. Results show that cell lysis occurs at a high degradation rate, e.g., μmax = 0.16 h−1 and kd = 0.07 h−1, when the gassed power input increases above 1.1, 1.7, or 2.0 kW/m3, respectively, depending on the medium composition. The overall biomass yield on substrate is dramatically reduced in all experiments (>30%).

Clavulanic acid degradation in Streptomyces clavuligerus fed-batch cultivations.

Clavulanic acid (CA) is an important antibiotic that is produced by Streptomyces clavuligerus. CA is unstable and product degradation has turned out to have a major impact on product titers in fed‐batch cultivations. Three different types of experiments have been used to elucidate CA degradation under fed‐batch cultivation conditions. First, the influence of individual medium compounds was examined. Second, degradation was monitored during the exponential growth phase in batch cultivations. Third, CA degradation was studied in the supernatant of samples taken during a fed‐batch. In addition, data from six fed‐batch cultivations were studied to derive information about CA degradation during the production phase. These cultivations were based on a mineral medium, containing glycerol, glutamate, ammonium, and phosphate as the main nutrients. The ammonium concentration had a large influence on the degradation rate constant. In addition, either changes in the substrate availability or high concentrations of ammonium or glycerol cause a major increase in the degradation rate constant. Finally, a linear and a fuzzy logic model were made to predict CA degradation rates in these fed‐batches.

Predictive control by local linearization of a Takagi-Sugeno fuzzy model

Linear model based predictive control (MBPC) has many advantages but also drawbacks over nonlinear MBPC. In this paper a possibility of using linear MBPC to control nonlinear systems is investigated. Takagi-Sugeno fuzzy models are chosen as the model structure. Local linear models can be derived from the linear rule consequents in a straightforward way. For each sample time a local linear model is calculated and used to calculate the next incremental control action using linear MBPC. This receding horizon controller is used in the IMC scheme to correct for model mismatch. Two simulation examples are given: a SISO liquid level process and a MIMO liquid level process with two inputs and four outputs.

Compact TS-fuzzy models through clustering and OLS plus FIS model reduction

Identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy models of the Takagi-Sugeno (TS) type may be a good choice to describe such systems; however, in many cases these become soon complex. We propose a three-step method to obtain compact TS-models that can be effectively used to represent complex systems: 1) a new fuzzy clustering method is proposed for identification of compact TS-models; 2) the most relevant consequent variables of the TS-model are selected by an orthogonal least squares (OLS) method based on the obtained clusters; and 3) for selection of relevant antecedent variables, a new method is proposed based on Fishers interclass separability (FIS) criterion. The overall approach is demonstrated by means of the MPG (miles per gallon) nonlinear regression benchmark. Results are compared with those obtained by standard linear, neuro-fuzzy and advanced fuzzy clustering-based identification tools.

Comments on the benchmarks in "A proposal for improving the accuracy of Linguistic Modeling" and related articles

In the above paper by Cordon and Herrara (IEEE Trans. Fuzzy Syst., vol. 8, p. 335-44, 2000), the so-called accurate linguistic modeling (ALM) method was proposed to improve the accuracy of linguistic fuzzy models. A number of examples are given to demonstrate the benefits of the approach. We show that: 1) these examples are not suitable as benchmarks or demonstrators of nonlinear modeling techniques and 2) better results can be obtained by using both standard regression tools as well as other fuzzy modeling techniques. We argue that benchmark examples that are used in articles to demonstrate the effectiveness of fuzzy modeling techniques should be selected with great care. Critical analysis of the results should be made and linear models should be regarded as a lower bound on the acceptable performance.

A Semi-Stoichiometric Model for a Streptomyces Fed-Batch Cultivation with Multiple Feeds

Abstract A semi-stoichiometric model has been developed for the clavulanic acid (CA) production by Streptomyces clavuligerus in a fed-batch process on a chemically defined medium. Six fed-batch cultivations were performed with a similar batch medium containing glycerol, glutamate, ammonium and phosphate. Product formation is induced by a stationary phase, and continued within a phosphate limited growth phase by feeding glycerol, phosphate and glutamate and/or ammonium with constant feed rates, or with a varying ammonium addition rate when it is used for pH control. The process can be described well by a stoichiometric model and constant CA production rates for the different metabolic conditions. Only one kinetic function was necessary in the model, i.e., to describe the glutamate uptake rate. The stoichiometric coefficients are estimated from the data and the model parameters are fine-tuned by a genetic algorithm. A fairly simple but accurate model with closed mass balances is obtained.