Qualitative Representation of Trends (QRT): Extended method for identification of consecutive inflection points

In this paper a methodology for extraction of qualitative descriptions of data series is extended for proper inflection point recognition. The original method allows the extraction of qualitative information such as the sign of the first and second derivatives of the assumed signals underlying univariate noisy time series. However, it is not able to handle consecutive inflection points, i.e. inflection points which follow each other in time with no minimum or maximum in between them. To improve this method for proper assessment of inflection points, the original method is compared with three modifications of the original method. One of the alternatives based on repeated application of Witkin's stability criterion delivers better results for both identification of the qualitative descriptions and the locations in time of extrema and inflection points. Furthermore, the same modified method is shown to deliver the best fault diagnosis performance in a benchmark batch fermentation study. Furthermore, the same modified method is shown to deliver the best fault diagnosis performance in a benchmark batch fermentation study.