Statistical properties of acoustic emission signals from metal cutting processes

Acoustic Emission (AE) data from single point turning machining are analysed in this paper in order to gain a greater insight of the signal statistical properties for Tool Condition Monitoring (TCM) applications. A statistical analysis of the time series data amplitude and root mean square (RMS) value at various tool wear levels are performed, �nding that ageing features can be revealed in all cases from the observed experimental histograms. In particular, AE data amplitudes are shown to be distributed with a power-law behaviour above a cross-over value. An analytic model for the RMS values probability density function (pdf) is obtained resorting to the Jaynes' maximum entropy principle (MEp); novel technique of constraining the modelling function under few fractional moments, instead of a greater amount of ordinary moments, leads to well-tailored functions for experimental histograms.Comment: 16 pages, 7 figure

Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected values of the program variables, which is insufficient to recover the full probabilistic program behaviour. We present a method to automatically generate moment-based invariants of a subclass of probabilistic programs, called Prob-solvable loops, with polynomial assignments over random variables and parametrised distributions. We combine methods from symbolic summation and statistics to derive invariants as valid properties over higher-order moments, such as expected values or variances, of program variables. We successfully evaluated our work on several examples where full automation for computing higher-order moments and invariants over program variables was not yet possible