Erich-Peter Klement

FLEXFIS: A Variant for Incremental Learning of Takagi-Sugeno Fuzzy Systems

In this paper a new algorithm for the incremental learning of specific data-driven models, namely so-called Takagi-Sugeno fuzzy systems, is introduced. The new open-loop learning approach includes not only adaptation of linear parameters in fuzzy systems appearing in the rule consequents, but also sample mode adaptation of premise parameters appearing in the membership functions (i.e. fuzzy sets) together with a rule learning strategy. In this sense the proposed method is applicable for fast model training tasks in various industrial processes, whenever there is a demand of online system identification in order to apply models representing nonlinear system behaviors to system monitoring, online fault detection or open-loop control. An evaluation of the incremental learning algorithm is included at the end of the paper, where a comparison between conventional closed-loop modelling methods for fuzzy systems and the incremental learning method (also called adaptation in open-loop) demonstrated in this paper is made with respect to model qualities and computation time. This evaluation will be based on high dimensional data coming from an industrial measuring process as well as from a known source in the Internet, which should underline the usage of the new method for fast online identification tasks

Interpolation and extrapolation of fuzzy quantities – the multiple-dimensional case

Abstract This paper deals with the problem of rule interpolation and rule extrapolation for fuzzy and possibilistic systems. Such systems are used for representing and processing vague linguistic If-Then-rules, and they have been increasingly applied in the field of control engineering, pattern recognition and expert systems. The methodology of rule interpolation is required for deducing plausible conclusions from sparse (incomplete) rule bases. The interpolation/extrapolation method which was proposed for one-dimensional input space in [4] is extended in this paper to the general n-dimensional case by using the concept of aggregation operators. A characterization of the class of aggregation operators with which the extended method preserves all the nice features of the one- dimensional method is given.

Mathematical Analysis of Fuzzy Classifiers

We examine the principle capabilities and limits of fuzzy classifiers that are based on a finite set of fuzzy if-then rules like they are used for fuzzy controllers, except that the conclusion of a rule specifies a discrete class instead of a (fuzzy) real output value. Our results show that in the two-dimensional case, for classification problems whose solutions can only be solved approximately by crisp classification rules, very simple fuzzy rules provide an exact solution. However, in the multi-dimensional case, even for linear separable problems, max-min rules are not sufficient.

A fuzzy algorithm for pixel classification based on the discrepancy norm

A fuzzy method for a particular kind of pixel classification is proposed. It is one of the most important results in the development of an inspection system for a silk-screen printing process. The classification algorithm is applied to a reference image in the initial step of the printing process in order to obtain the regions which are to be checked by applying different criteria. Tight limitations in terms of computation speed have necessitated very specific, efficient methods which operate locally. These methods are motivated and discussed in detail.

Filtering of dynamic measurements in intelligent sensors for fault detection based on data-driven models

Increasing complexity of test benches and the widespread use of automatic calibration and optimization tools leads to tighter requirements on the data quality. For many applications, like engine test benches, there are too few physical information a priori to allow the use of classical fault detection methods. In this paper, we propose a structure which has been developed and tested for engine test benches, in which data-driven models are built dynamically from measurements and fault detection is carried out by using data-driven models as reference situation. To improve the performance of fault detection statements, signal analysis algorithms are applied in intelligent sensors to detect disturbances such as peaks or drifts in the dynamic signals.

Data mining using synergies between self-organizing maps and inductive learning of fuzzy rules

Identifying structures in large data sets raises a number of problems. On the one hand, many Methods cannot be applied to larger data sets, while, on the other hand, the results are often hard to interpret. We address these problems by a novel three-stage approach. First, we compute a small representation of the input data using a self-organizing map. This reduces the amount of data and allows us to create two-dimensional plots of the data. Then we use this preprocessed information to identify clusters of similarity. Finally, inductive learning methods are applied to generate sets of fuzzy descriptions of these clusters. This approach is applied to three case studies, including image data and real-world data sets. The results illustrate the generality and intuitiveness of the proposed method.

Cross-migrative triangular norms

We study the cross‐migrativity of triangular norms. The classes of continuous triangular norms, which are cross‐migrative with respect to some strict or nilpotent triangular norm, respectively, are completely characterized, as well as those which are cross‐migrative with respect to the greatest and smallest triangular norms, respectively. As a by‐product, parametric systems of equivalence relations on the classes of strict and nilpotent triangular norms are found.

Premise parameter estimation and adaptation in fuzzy systems with open-loop clustering methods

Clustering algorithms as unsupervised learning techniques are of fundamental importance in order to group any kind of recorded measurement data (in form of images, signals or physical values from sensors) into separate regions, also called clusters. This grouping is not only applied whenever a classification of feature vectors representing special attributes of the data set is required, but also in the case of approximating arbitrary relationships which possess an intense local (in the case of static processes) or time-variant (in the case of dynamic processes) behavior and therefore cannot be described with one closed analytical formula over the whole domain. In this paper first open-loop clustering methods are described, i.e. clustering methods which are able to adapt former generated clusters pointwise. Afterwards, a new approach for estimating and updating nonlinear parameters in Takagi-Sugeno fuzzy inference systems, i.e. premise parameters in the rules-antecedents, by applying open-loop clustering algorithms is stated together with the impact on the bias error and training time for up to 5-dimensional fuzzy models. Additionally; a detailed analysis of the method is given.

On the robustness of fault detection in reciprocating compressor valves

This paper examines robustness issues of fault detection methods for reciprocating compressor valves. The authors have previously proposed two independent fault detection approaches for reciprocating compressor valves. One method is based on vibration analysis of accelerometer data, the other one on analyzing pV diagrams. Based on real world data, experiments are conducted to conclude on the robustness of those methods. The data are manipulated in two ways: decreasing the sampling rate and adding noise. The results suggest that the method analyzing pV diagrams is very robust especially against downsampling, while the vibration analysis method is very sensitive if the sampling rate drops below a certain level. Additionally, a sequential probability ratio test is employed. The experiments show the capability of the test to increase the detection accuracy for both methods.

Detecting broken reciprocating compressor valves in the pV diagram

This paper presents a novel data-driven approach to detecting broken reciprocating compressor valves that is based on the idea that a broken valve will affect the shape of the pressure-volume (pV) diagram. This effect can be observed when the valves are closed. To avoid disturbances due to the load control, we concentrate on the expansion phase, linearized using the logarithmic pV diagram. The gradient of the expansion phase serves as an indicator of the fault state of the valves. Since the gradient is also affected by the pressure conditions, they are used as an additional indicator. After feature extraction, classification is done using support vector machines. The performance of the method was validated by analyzing real-world measurement data. Our results show a very high classification accuracy for varying compressor load and pressure conditions.