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Time series motifs are approximately repeated patterns found within the data. Such motifs have utility for many data mining algorithms, including rule-discovery, novelty-detection, summarization and clustering. Since the formalization of the problem and the introduction of efficient linear time algorithms, motif discovery has been successfully applied to many domains, including medicine, motion capture, robotics and meteorology.In this work we show that most previous applications of time series motifs have been severely limited by the definition's brittleness to even slight changes of uniform scaling, the speed at which the patterns develop. We introduce a new algorithm that allows discovery of time series motifs with invariance to uniform scaling, and show that it produces objectively superior results in several important domains. Apart from being more general than all other motif discovery algorithms, a further contribution of our work is that it is simpler than previous approaches, in particular we have drastically reduced the number of parameters that need to be specified.

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Armor layers of mound breakwaters are usually designed with empirical formulas based on small-scale tests in non-breaking wave conditions. However, most rubble mound breakwaters are constructed in the depth-induced breaking zone, where they must withstand design storms having some percentage of large waves breaking before reaching the structure; in these cases, the design formulas for non-breaking wave conditions are not fully valid. To characterize double-layer rock armor damage in breaking wave conditions, 2D physical model tests were carried out with a bottom slope m=1/50. In order to develop a simple method to determine the wave parameters in the depth-induced breaking zone, experimental wave measurements were compared to the numerical estimations given by the SwanOne model. An analysis was conducted to select the best characteristic wave height to estimate rock armor damage when dealing with depth-induced breaking waves; the spectral significant wave height, H m0 , estimated at a distance of 3h s seaward from the structure toe, was found to be the most adequate. 2 A new hydraulic stability formula is proposed for double-layer rock armors in breaking wave conditions, considering the observed potential 6-power relationship between the equivalent dimensionless armor damage and the H m0 at 3h s seaward distance from the structure toe.

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The toe berm is a relevant design element when rubble mound breakwaters are built on steep sea bottoms in breaking conditions. Different design formulas can be found in the literature to predict the damage caused to submerged toe berms placed on gentle bottom slopes. However, these formulas are not valid for very shallow waters in combination with steep sea bottoms where toe berms receive the full force of breaking waves. To guarantee breakwater stability in these conditions, new design formulas are needed for toe berms. To this end, physical model tests were carried out and data were analyzed to characterize rock toe berm stability in very shallow water and with a bottom slope m = 1/10. Based on test results, a new formula was developed with three parameters to estimate the nominal diameter (D n50 ) of the toe berm rocks:water depth at the toe (h s ), deep water significant wave height (H s0 ) and deep water wave length (L 0p ).

Elsevier Molines, J.; Medina Folgado, JR. (2015). Calibration of overtopping roughness factors for concrete armor units in non-breaking conditions using the CLASH database. Coastal Engineering. 96:62-70.

No abstract