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Modeling forms the basis for optimal control of complex technical processes in the context of industry 4.0 development and, hence, for high product quality as well as efficient production. For the mechanical joining process of self-pierce riveting with 11 input and 5 output variables, two modeling approaches based on (1) experimental data and (2) FEM computer simulation are outlined and performed. A physical modeling approach is ruled out due to the high problem dimensionality and complex nonlinear dynamic relationships between input and output variables. Alternatively, data-based approaches lead to Artificial Intelligence (AI) model designs. The experimental approach is cost- and resource-consuming; therefore, only a relatively small data set can be collected. Here, we present results from experimental trials that serve as representatives and are generalized by a description with high-dimensional parametric membership functions (fuzzification). The fuzzification procedure is also applied to the FEM computer simulation results. In principle, it can provide an arbitrarily large database. However, consequently, time- and computational effort increase considerably. Both data sets form the basis for parallel model building using the AI method of local fuzzy pattern models, which can be used to describe highly nonlinear input-output relationships by error-minimizing partitioning. Finally, the comparison of the results of the two modeling approaches is outlined. Finally, a coupled modeling strategy and future model adaptation are proposed.

In this paper we introduce a new fuzzy system using adaptive fuzzy pattern classification (AFPC) for data-based online evolvement. The fuzzy pattern concept represents an efficient tool for handling uncertainty in multi-dimensional data streams and combines powerful performance, flexibility and meaningful interpretability within one consistent framework. We outline AFPC for non-linear, multi-dimensional transition processes, namely, for the identification of lane change intention in car driving. While lane changes are rare, they are highly safety-relevant transition processes, showing high fuzziness and large individual and inter-individual variations (e.g., in lane change duration). The method employs a combined knowledge- and data-based approach, and the underlying fuzzy potential membership function concept models expert knowledge, closely mirroring human cognition. The design of AFPC comprises (I) an initial training phase (off-line and supervised), which generates a meaningful start-classifier, (II) an online application phase, and finally (III) an evolvement phase (online and unsupervised). Here we consider parametric and structural adaptations and discuss prospects and future challenges. Furthermore, we present specific modeling results for such online data from a real driving study. Next-generation advanced driver assistance systems, as well as autonomously driven vehicles need to evolve, in terms of parameters and structure, based on online real-time data. AFPC presents an efficient tool for application in this area and others (e.g., medicine).

Modelle dienen der Speicherung von Wissen und als Basis fur Entscheidungen. Sie finden Anwendung in unterschiedlichsten Bereichen wie Technik, Medizin, Wirtschaft, Psychologie, Umwelt oder Verkehr. Gerade fur komplexe Zusammenhange sind Verfahren, die auf interpretierbaren Mustern beruhen, hoch flexibel und adaptiv. Die Theorie der Fuzzy Sets hat nun das Potenzial, gleitende Ubergange zwischen den Mustern zu beschreiben und damit realitatsnahe Modelle zu entwerfen. In dem Beitrag wird speziell die Fuzzy-Pattern-Klassifikation ausgefuhrt, die eine parametrische Zugehorigkeitsfunktion nutzt, mit der Muster auch in hochdimensionalen Merkmalsraumen beschrieben werden konnen. An zwei aktuellen, deutlich unterschiedlichen Anwendungen wird beispielhaft gezeigt, wie das gleiche Modellierungskonzept in humanwissenschaftlichen (psychologischen) und in technischen Bereichen einsetzbar ist. Konkret handelt es sich zum einen um den Einsatz linguistischer Antwortskalen in Fragebogenaktionen und zum anderen um die Zeitreihen-Prognose (konkret des fluktuierenden Energieertrags von Photovoltaikanlagen). Es ist Anliegen, hierbei zumindest exemplarisch den fundamentalen Charakter und damit auch die Transdisziplinaritat der Fuzzy Theorie zu zeigen.

The article describes a general two-step procedure for the numerical translation of vague linguistic terms (LTs). The suggested procedure consists of empirical and model components, including (1) participants' estimates of numerical values corresponding to verbal terms and (2) modeling of the empirical data using fuzzy membership functions (MFs), respectively. The procedure is outlined in two studies for data from N = 89 and N = 109 participants, who were asked to estimate numbers corresponding to 11 verbal frequency expressions (e.g., sometimes). Positions and shapes of the resulting MFs varied considerably in symmetry, vagueness, and overlap and are indicative of the different meanings of the vague frequency expressions. Words were not distributed equidistantly across the numerical scale. This has important implications for the many questionnaires that use verbal rating scales, which consist of frequency expressions and operate on the premise of equidistance. These results are discussed for an exemplar questionnaire (COPSOQ). Furthermore, the variation of the number of prompted LTs (5 vs. 11) showed no influence on the words' interpretations.

In some nonstationary time series, where a global model is neither available nor applicable, we may observe recurring patterns that can be extracted to create several local models instead. This article proposes knowledge-based short-time prediction methods for multivariate streaming time series that rely on the early recognition of such local patterns. A parametric fuzzy model for patterns is presented, along with an online, classification-based recognition procedure, which will introduce the notion of evolving classification results. Subsequently, two options are discussed to predict time series employing the fuzzified pattern knowledge, accompanied by an example. Special emphasis is placed on comprehensible models and methods, as well as a seamless interface to data mining algorithms.

Kurzfassung In diesem Beitrag wird ein methodischer Ansatz für den Fuzzy Abgleich von Anforderungsvektoren mit Beschreibungsvektoren der Kompetenzzellen in hierarchielosen Produktionsnetzen vorgestellt. Als Entscheidungssystem dient dabei ein so genannter Fuzzy Pattern-Klassifikator, der als Knoten innerhalb eines Klassifikatornetzwerks eine Teilbewertung für die Auswahl von Kompetenzzellen bei einer gegebenen Anforderung liefert. Die Vorgehensweise wird beispielhaft anhand des Partialmodells der Logistik-Kompetenzzelle demonstriert.

Kurzfassung In diesem Beitrag wird eine Methode zur Implementierung unscharfer Informationen in Kompetenzzellenmodelle vorgestellt. Dabei wird die bisher existierende und auf scharfen Beschreibungsparametern basierende Modellierung von Kompetenzzellen in hierarchielosen Netzen so erweitert, dass die beschreibenden Merkmale durch unscharfe (Fuzzy) Größen ergänzt bzw. bereits existierende scharfe Größen fuzzifiziert werden. Damit wird die Voraussetzung geschaffen, eine Modellierung von Gruppen ähnlicher Kompetenzzellen durch Fuzzy Pattern Klassifikatoren vorzunehmen. Diese liefern eine Teilbewertung für die Auswahl geeigneter Kompetenzzellen bei einer gegebenen Anforderung. Die Vorgehensweise wird beispielhaft anhand des Partialmodells der Fertigungs-Kompetenzzelle demonstriert.

In connection with the efficiency of already known adaptive systems there are questions referring to stabilization and the speed of adaption. For those the solutions very often are only unsufficient compromises. An essential difficulty occurs e.g. with MRAS because of the appearance of instabilities due to the nonlinear adaption feedback. The parameter-searching and -estimating with MIAS requires a great expanditure for calculating especially with high ranged systems, so that the adaption processes are retarded

This article contributes to clustering and fuzzy modelling of data such that specific characteristics of each datum can be incorporated. Particularly, each object may exhibit an individual area of influence in its feature space, for which it is representative. For such objects, a similarity measure is introduced, which is used to modify common clustering algorithms to take each object’s extent into account when finding clusters. A real-world example demonstrates the practical usability of the presented methods, which deliver results in accordance to findings of experts in that field.

The paper describes a general two-step procedure for the numerical translation of linguistic terms using parametric fuzzy potential membership functions. In an empirical study 121 participants estimated numerical values that correspond to 13 verbal probability expressions. Among the estimates are the most typical numerical equivalent and the minimal and maximal values that just correspond to the given linguistic terms. These values serve as foundation for the proposed fuzzy approach. Positions and shapes of the resulting membership functions suggest that the verbal probability expressions are not distributed equidistantly along the probability scale and vary considerably in symmetry, vagueness and overlap. Therefore we recommend the proposed empirical procedure and fuzzy approach for future investigations and applications in the area of decision support.

A modeling method is suggested in this paper, which permits building multidimensional fuzzy models of time series consisting of fuzzy prototypes. These models have to be trained in a so-called period of learning and are suitable for short, medium and long range forecasts. The prediction of an incomplete time series is based on fuzzy classification to the prototypes. The results are grades of membership. In principle, these grades and further courses of prototypes are used to forecast the time series.

It is always impressive to watch an experienced specialist master difficult and complex situations. The real problems are very different but the characteristics of the action are similar: acquiring a flood of information, concentrating on the essential, evaluating and reaching a purpuseful decision. The expert often cant explain his decision making process. Doubtlessly, his knowledge and experiences about the functional connections are very important. However his ability to compare the present situation with typical examples leads to a strategy in a more effective way. This intellectual process means an immense reduction from a lot of information to a few pattern.