Geometry-Informed Optimal Parameter Selection for Phase Space Warping with Application to Early Fatigue Damage Detection in 3D-Printed Beams

Phase space warping (PSW) methodology reconstructs a non-stationary hidden process from quasi-stationary observable dynamics, where these two coupled dynamical processes have disparate time scales. PSW has been applied to multivariate damage identification and tracking, biomechanics, and manifold characterization in nonlinear dynamical systems. However, its theory is not clearly connected to its practice. Furthermore, there is no associated sampling theory or guidelines for optimal parameter selection to estimate the hidden dynamics reliably. This paper focuses on a geometrical interpretation of PSW that coherently bridges its theory and practice by providing the needed theoretical insights and explaining practical constraints. The corresponding algorithm's parameter space is explored to provide reliable and accurate estimates of the PSW function guided by the obtained geometrical properties and insights. Numerical examples of a nonlinear hierarchical dynamical system with various hidden processes and observable dynamics are used to guide the parameter selection for the PSW algorithm. Parameter selection guidelines are obtained through global sensitivity analysis to the estimation accuracy of the simulation results. The established guidelines are used to extract fatigue damage evolution in 3D-printed beams from experimentally obtained vibration data. The obtained results show how the PSW-based fatigue tracking can be used for early fatigue damage detection.

Heuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm

Bjånes DA, Fisher LE, Gaunt RA, Weber DJHeuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm. bioRxiv First published May 21, 2020. Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing.NEW & NOTEWORTHYHSST incorporates known neurophysiological priors of extracellular neural recordings while simultaneously taking advantage of powerful abstract mathematical tools. Rather than simply selecting free parameters prior to running a sorting algorithm, HSST executes a sorting algorithm across a range of input parameters, using heuristic metrics to detect which spike-sorting output is most physiologically plausible. This novel approach enables unsupervised spike-sorting exceeding the performance of previous methods, thereby enabling the processing of large data sets with confidence.