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.

Bearing Remaining Useful Life Prediction Based on a Scaled Health Indicator and a LSTM Model with Attention Mechanism

Rotor systems are of considerable importance in most modern industrial machinery, and the evaluation of the working conditions and longevity of their core component—the rolling bearing—has gained considerable research interest. In this study, a scale-normalized bearing health indicator based on the improved phase space warping (PSW) and hidden Markov model regression was established. This indicator was then used as the input for the encoder–decoder LSTM neural network with an attention mechanism to predict the rolling bearing RUL. Experiments show that compared with traditional health indicators such as kurtosis and root mean square (RMS), this scale-normalized bearing health indicator directly indicates the actual damage degree of the bearing, thereby enabling the LSTM model to predict RUL of the bearing more accurately.

Fatigue Detection Using Phase-Space Warping

A novel application of phase-space warping (PSW) method to detect fatigue in the musculoskeletal system is presented. Experimental kinematic, force, and physiological signals are used to produce a fatigue metric. The metric is produced using time-delay embedding and PSW methods. The results showed that by using force and kinematic signals, an overall estimate of the muscle group state can be achieved. Further, when using electromyography (EMG) signals the fatigue metric can be used as a tool to evaluate muscles activation and load sharing patterns for individual muscles. The presented method will allow for fatigue evolution measurement outside a laboratory environment, which open doors to applications such as tracking the physical state of players during competition, workers in a plant, and patients undergoing in-home rehabilitation.

Dynamical Analysis of Sawing Motion Tracks Muscle Fatigue Evolution

Both for civilian and military applications, tracking and identifying muscle fatigue—usually caused by continuous, repetitive motion over a finite period of time—is of great importance. The muscle fatigue process is very difficult to track due to its hidden nature. Invasive procedures are often needed to measure fatigue. Here, easily obtainable noninvasive kinematic measurements are used to extract muscle fatigue related trends associated with a sawing motion. The methodology is derived from dynamical systems based fatigue identification in engineered systems. Ten right-handed subjects perform sawing motion until voluntary exhaustion. Three sets of joint kinematic angles are measured from the elbow, wrist, and shoulder. Fatigue is identified in two steps: (1) phase space warping based feature vectors are estimated from kinematic time series; and (2) smooth orthogonal decomposition (SOD) is used to extract fatigue related trends from these features. SOD-based trends are compared against independently obtained fatigue markers estimated from the mean and median frequencies of electrography (EMG) signals of individual muscles. SOD-based trends from elbow and shoulder kinematics adequately capature fatigue in the triceps muscle estimated from the EMG measurements. These same kinematic angles show little fatigue information in the flexor/extensor carpi radialis (not directly engaged in sawing motion). The methodology used here shows great potential in tracking individual muscle fatigue evolution using only motion kinematics data.

Tracking Muscle Fatigue Markers Through Nonlinear and Multivariate Analysis of Motion Kinematics

Both athletes and soldiers subject their body to extensive prolonged movements at the price of completing their tasks. The purpose of his study is to show that phase space warping (PSW) concept and smooth orthogonal decomposition (SOD) can be used to extract muscle fatigue related information from easily obtainable and noninvasive movement kinematics data. Two experimental setups are considered: load carrying soldiers walking on a treadmill and subjects performing a sawing motion. PSW and SOD based fatigue related trends are compared against local muscle fatigue markers obtained from surface electromyography (sEMG) measurements. In particular, a decrease in the mean power frequencies (MNF) or median power frequencies (MDF) of the sEMGs are used to indicate the onset of muscle fatigue, since a muscle fatigue causes a shift in the power spectrum of sEMG to lower frequencies.