A new dependency-aware interval arithmetic is presented and its algebraic system is investigated.

A decision feedback equalizer, transceiver, and method are provided, the equalizer having at least one comparator, the at least one comparator comprising a first stage, comprising a main branch having two track switches with a resistive load, an offset cancellation branch, a plurality of tap branches with transistor sizes smaller than the main branch, in which previous decisions of the equalizer are mixed with the tap weights using current-mode switching, and a cross coupled latch branch; and a second stage, comprising a comparator module for making decisions based on the outputs of the first stage and a clock input, and a plurality of flip-flops for storing the output of the comparator module.

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Blade tip timing (BTT) includes a number of uncertainties that discourage its use. One of the main ones is the shift in the equilibrium position of the blade tip due to steady (non-oscillatory) bending and/or twisting of the blade, and axial movement of the bladed disk (blisk)-shaft system. This results in a shift in the effective measurement position of the probe relative to the blade chord, resulting in errors in the tip vibration measurement which can translate to a huge error in the corresponding stress estimate, which relies on calibration against finite element (FE) models. Previous experimentally validated research by the authors introduced a method for quantifying steady movement of a single type (axial, lean, or untwist), using BTT data from not more than two probes. In this paper, a development of the previous method is presented that provides a solution for the case of simultaneous types of blade steady movements. Additional probes are used for determining the direction, but these can be placed at any angular positions. The developed method is validated using a BTT simulator of a blisk, and accurate results obtained. The simultaneous axial and lean movements can be accurately determined when the untwist is negligible, and an uncertainty level can be specified when the untwist is not negligible. The untwist itself can be calculated accurately in all cases of simultaneous movements. Guidelines for the use of the method in different scenarios are provided.