* Q. Zhong, Electrochemical Research Group, Shanghai University of Elec- tric Power, Key Laboratory of State Power Corporation of China, Shanghai, 200090 (P.R. China) M. Rohwerder Max-Planck-Institut fu ¨r Eisenforschung, Max-Planck-Str., 40237 Du ¨sseldorf (Germany) W. Chen, D. Liu Department of Chemistry and Chemical Engineering, Hunan University, Changsha, Hunan (P.R. China) Fuzzy cluster analysis constructed by numeric genetic algorithm (NGA) and its use in the evaluation of heterogeneity of temporarily protective oil coating Q. Zhong*, M. Rohwerder, W. Chen and D. Liu A fuzzy cluster analysis based on a numeric genetic algorithm (NGA) was applied for the study of the inhomogeneity of tempora- rily protective oil coating. Three different types of film behaviour can be assigned to the investigated temporarily protective coating: corrosive, protective and unstable. It is suggested that utilizing this method could evaluate the heterogeneity of temporarily protective oil coating more efficiently, precisely and more comprehensively. 1 Introduction Heterogeneous phenomena are familiar in electrochemical processes, such as localized corrosion, degradation of organic coatings, etc. Usually, single electrode set-ups are used for the investigation of such heterogeneous electrochemical systems, and the results obtained from such a single electrode set-up are averaged values. Obviously, this approach is not adequate for a comprehensive elucidation of heterogeneous systems. Furthermore, this leads to higher system error, less credibility and poor reproducibility. Unlike a single plate electrode, a wire beam electrode is a special multi-working electrode system, which consists of many microelectrodes (in general several hundreds). The dis- tribution of electrochemical parameters of heterogeneous sys- tems, such as corrosion potential, polarization resistance, etc., can be measured by using this type of electrode, and statistical information about theses parameters is directly obtained [1]. The feasibility of using a wire-beam electrode in studies of the electrochemical inhomogeneity of temporarily protective oil coating was successfully demonstrated, and it was shown that the reproducibility of electrochemical measurements by using the wire-beam electrode was greatly improved [2]. Wire beam electrodes have also been utilized for the study of many other heterogeneous systems [3 – 16] during the recent years. Along with the emerging of the wire beam electrode [11] system for studying and evaluating the electrochemical char- acteristics of heterogeneous systems, a large quantity of ex- perimental data could be obtained from this type of measure- ment system. In order to analyze these data obtained from wire beam electrodes more accurately, faster and more comprehen- sively, an effective classification method is needed for analyz- ing such inhomogeneous systems. Fuzzy cluster analysis is an effective tool for classifying large quantities of data, and up to now it has been widely and successfully utilized in agriculture, meteorology, environ- mental forecast etc. [17]. The aim of cluster analysis is the classification of objects according to similarities among them, and organizing data into groups. A cluster is a group of objects of more similarity to each other than to objects be- longing to other clusters. In metric spaces, similarity is often defined by means of distance based upon the length from a data vector to some prototypical object of the cluster (cluster centre). The prototypes are usually not known beforehand, and are sought by the clustering algorithm simultaneously with the partitioning of the data. Since clusters can formally be seen as subsets of the dataset, fuzzy clustering could be utilized for classification according to whether or not the sub- sets are fuzzy. Fuzzy clustering methods allow objects to be- long to several clusters simultaneously with different degrees of membership. The dataset (Z) is thus partitioned into fuzzy subsets. Objects on the boundaries between several classes are not forced to fully belong to one of the classes. In this paper, the clustering of quantitative data is considered. The data are observed electrochemical parameters. Each observation con- sists of n measured variables, grouped into an n-dimensional column vector Z k ¼ [z 1h ,z 2k , ...z nk ] T ,z k 2 Re n . A set of N ob- servations is denoted by Z ¼ {z k j k ¼ 1, 2, ..., N} and repre- sented as a n*N matrix. For example, in this paper, the data matrix is represented as a n*p matrix: 930 Zhong, Rohwerder, Chen and Liu Materials and Corrosion 2004, 55, No. 12 DOI: 10.1002/maco.200403802 F 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim