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Statistical approach to Control Performance Assessment (CPA) is of great practical importance. This is particularly visible in process industry, where there are many PID loops. They are often assessed with measures derived from the Gaussian probabilistic density function. Standard deviation, variance, skewness or kurtosis form the majority of applied indexes. The review of data originating from process industry shows, however, to the contrary, that these signals have rather non-Gaussian properties and are mostly characterized by fat-tailed distribution disable the ability. Investigations show that strong disturbances may significantly disable the capacity of proper assessment. Standard measures often fail in such cases. It is shown that non-Gaussian measures can help with this problem. Various disturbances are tested and compared. Results show that fat-tailed distributions are an interesting alternative. They are less sensitive to disturbance shadowing and still make possible loop dynamic assessment. [ABSTRACT FROM AUTHOR]

Letbe open with. We characterize the setshaving the following property: for every real analytic functionfonwith Taylor expansionat zero, the seriesis also the Taylor expansion at zero of some real analytic function on. This result gives a characterization of the idempotents in the algebraof Hadamard-type operators on the space of all real analytic functions, i.e. operators with all monomials being eigenvectors. In many cases, we also describe the multiplicative functionals onand the (continuous) algebra homomorphisms. We show that the algebrais never locally m-convex and in many cases it is not a Q-algebra. [ABSTRACT FROM AUTHOR]

This paper presents an application of the L-moments and L-moment ratio diagrams (LMRD) to the analysis of hydrological data at regional (country) scale. Existing research focuses on two main areas of the analysis: statistical analysis using LMRD and regression analysis. Further research mixes both approaches applying regression analysis to L-moments. Another direction of the research is clustering of the climatic and physiographic catchment properties and its validation using LMRD. However, LMRD plots can be separately used as the clustering domain. It is proposed to decompose the features into some classes, and than present these results on the LMRD. Such plots constitute the source for the clustering. Obtained clusters are then validated against k-means clustering performed in the LMRD diagram domain. Results show that statistical L-moments analysis can be improved with data mining clustering algorithms. Such combination delivers a new perspective for the interpretation of the results. It is shown that clustering in the LMRD domain is consistent with the K-means clustering. It is anther argument showing that L-moments diagrams can be considered as a very powerful and informative tool for hydrologists enabling the comparison on the regional basis with respect to various catchment properties. The method is validated on data consisting of daily river flow data from 290 gauges covering entire Poland. [ABSTRACT FROM AUTHOR]