Statistical Characterization of Morphodynamic Signals Using Wavelet Analysis

Morphodynamic and hydrodynamic properties are concomitantly part of the entire dynamic of river systems and commonly present both temporal and spatial persistent variability. Therefore, the study of both river morphodynamic signals (e.g. bed forms and meandering and anabranching river morphometrics) and hydrodynamic signals (e.g. velocity fields, sediment concentrations) requires both temporal and spatial multi-scale signal representations. The present research is focused on the former type of signals and it is a first attempt to discriminate such signals and, subsequently, develop the theoretical background to link these processes at different spatial and temporal scales and determine the scales that have more influence on river evolution. The main contribution of this study are: [1] to design a methodology to discriminate bed form features (e.g. bars, dunes and ripples) via the combined application of robust spline filters and one-dimensional continuous wavelet transforms, allowing the quantitative recognition of bed form hierarchies. The methodology was tested by using synthetic bed form signals and subsequently applied to the analysis of bed form features from the Parana River, Argentina. [2] To develop a methodology for the statistical analysis of the spatial distribution of meandering rivers morphometrics by coupling the capabilities of one-dimensional wavelet transforms, principal component analysis and Frechet distance. A universal river classification method is also proposed. [3] To perform a novel study of the planimetric configuration of confluences in tropical free meandering rivers located in the upper Amazon catchment. River confluences in tropical environments represent areas where biota is concentrated; therefore, a better understanding and characterization of these features has a particular importance for the Amazonian ecosystem. [4] To evaluate the potential of two-dimensional wavelet transforms in the analysis of bed form features. The broader impact will be an improved understanding of river morphodynamics of the upper Amazon River for practical applications such as navigability. Furthermore, the project will provide an updated statistical analysis of the meandering rivers dynamics for practical applications, including erosion control, river ecology, and habitat restoration. The developed statistical tool will be included as an application of the RVR Meander platform (www.rvrmeander.org), which is a broadly used software for river restoration

Development of chatter threshold boundary for milling of metals

This study reports on a novel experimental method for the prediction of chatter based on the chaos theory. The variation of Poincaré sections of the reconstructed phase space attractor is able to identify the transition of the milling system from a stable to an unstable condition, continuously during the milling process. Two mathematical tools are used to measure the variation of Poincaré sections they being; image correlation and a designed regression model. Image correlation uses Poincaré sections as a pattern and the computation of Pearson’s coefficient assists to develop a chatter threshold boundary. Titanium is the main material in this research, as chatter is more applicable during cutting of titanium due to its specific mechanical properties. Moreover, the method is used in detection of chatter during milling of stainless steel and aluminum in order to demonstrate the method can detect chatter during cutting of other metals. The new method can be used to detect chatter on-line, as it is independent of the cutting parameters and dynamics of the milling process, and can be integrated in the cutting machines. The method does not need expensive equipment and complex process, so it can be easily used in normal production workshop environment. A regression model computes the trend of changes in the Poincaré sections and gives a numerical output value to define the boundary between the stable and unstable state of the milling process. These mathematical tools can be used in expert software to monitor the milling process on-line and detect the onset of chatter