The objective of this work was threefold: 1) to assess how local dynamic spinal stability is affected by various factors including: the personal lift-assist device (PLAD), different loads when lifting, and prolonged repetitive work; 2) to establish the between-day reproducibility of local dynamic stability and kinematic variability measures; and 3) to directly compare local dynamic spinal stability to quasi-static mechanical spinal stability. The first study was an investigation into the effects of the PLAD on local dynamic spinal stability during repetitive lifting. Short- (λmax-s) and long-term (λmax-l) maximum finite-time Lyapunov exponents were calculated from measured trunk kinematics to assess stability. PLAD use did not change λmax-s, but significantly reduced λmax-l; indicating increased local dynamic spinal stability when lifting with the device. The second study was a report on the effects of lifting two different loads (0% and 10% maximum back strength) on local dynamic spinal stability and kinematic variability, expressed as the mean standard deviation (MeanSD) across cycles. It was determined that increasing the load that was lifted significantly reduced λmax-s, but not λmax-l or MeanSD. Thus, as muscular and moment demands increased with load so did subjects’ spinal stability. The third study was designed to look at changes in local dynamic spinal stability and kinematic variability resulting from 1.5 hours of repetitive automotive manufacturing work, as well as the between-day reproducibility of the measures. Operators performed a repetitive dynamic trunk flexion task immediately pre- and post-shift, as well as at the same pre-shift time on the following day. Despite significant increases in back pain scores, operators were able to maintain their stability and variability post-shift. Moreover, λmax-s was the most reproducible measure. The final study was structured to directly compare lumbar spine rotational stiffness (quasi-static mechanical spinal stability), calculated with an EMG-driven biomechanical model, to local dynamic spine stability, during a series of dynamic lifting challenges. Results suggest that spine rotational stiffness and local dynamic stability are positively associated, as they provided similar information when lifting rate was controlled. However, both models provide unique information and future research is required to fully understand their relationship. In general, the results of these studies illustrate the potential for Lyapunov analyses of kinematic data to be used to assess local dynamic spinal stability in a variety of situations. / Thesis (Ph.D, Kinesiology & Health Studies) -- Queen's University, 2012-07-31 15:34:01.804

Balance control is important for biped standing. Due to the time-varying control bounds induced by the foot constraints, and the lack of tools for analyzing stability of highly nonlinear systems, it is extremely difficult to design balance control strategies for a standing biped with a rigorous stability analysis in spite of large efforts. In this thesis, three important issues are fully considered for a standing biped: maintaining the postural stability, minimizing the energy consumption and satisfying the constraints between the biped feet and the ground. Both the theoretical and the experimental studies on the constrained and energy-efficient control are carried out systematically using the genetic algorithm (GA). The stability for the proposed balancing system is thoroughly investigated using the concept of Lyapunov exponents. On the other hand, the controlled standing biped is characterized by high nonlinearity and great complexity. For systems with such features, in general the Lyapunov exponents are hard to be estimated using the model-based method. Meanwhile the biped is supposed to be stabilized at the upright posture, indicating that the system should possess negative Lyapunov exponents only. However the accuracy of negative exponents is usually poor if following the traditional time-series-based methods. As it is nontrivial to examine the system stability for bipedal robots, the numerical accuracy of the estimated Lyapunov exponents is extremely demanding. In this research, two novel approaches are proposed based upon system approximation using different types of Radial-Basis-Function (RBF) networks. Both the proposed methods can estimate the exponents reliably with straightforward algorithms, yet no mathematical model is required in any newly developed method. The efficacies of both methods are demonstrated through a linear quadratic regulator (LQR) balancing system for a standing biped, as well as several other dynamical systems. The thesis as a whole, has set up a framework for developing more sophisticated controllers in more complex movement for robot models with less conservative assumptions. The systematic stability analysis shown in this thesis has a great potential for many other engineering systems.

Thesis (PhD) - Swinburne University of Technology, Centre for Molecular Simulation - 2007. / Dissertation submitted in fulfilment of requirements for the degree Doctor of Philosophy, Centre for Molecular Simulation, Faculty of Information and Communication Technologies, Swinburne University of Technology, 2007. Typescript. Includes bibliographical references (p. 151-161).

Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Description based on contents viewed Feb. 12, 2009; title from PDF t.p. Includes bibliographical references (p. 75-77).

Thesis (M.S.)--Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaves 144-146).

Vehicle yaw stabilization and rollover prevention are two key factors in safety of vehicles. Designing a controller that can address both of the above safety concerns is of interest. In addition, it is essential that the performance of such a controller is evaluated properly. This can be done using a proper stability analysis. The above research problem is challenging for two reasons. First, maintaining both of the objectives, yaw stabilization and rollover mitigation, is contradictory at some instances, specifically when the vehicle is close to the verge of wheel lift-off. Second, the complexity of the dynamics of vehicle systems, which mostly arises from tire dynamics, makes the problems of controller design and stability analysis more challenging. In this Ph.D. thesis, a novel method for stability analysis of dynamical systems using the concept of Lyapunov exponents is proposed. The proposed method for stability analysis does not have the limitations of the current methods, and more specifically, can identify boundaries of the whole stability regions of attractors in a dynamical system. Furthermore, this method is computationally efficient and can be applied to general forms of nonlinear systems. The proposed stability analysis scheme is applied to the closed loop systems of ground vehicles with T-S fuzzy controllers for the purpose of evaluating and comparing the performance of the systems. The T-S fuzzy controllers integrate yaw stabilization and rollover avoidance. The ground vehicles that are studied in this research consist of torsionally flexible and torsionally rigid vehicles, which have differences in their dynamics because of the torsional compliance in their frames. The torsional compliance plays an important role in the dynamics, specifically for long vehicles, leading to different rollover indexes in the front and rear axles of the vehicles. The T-S fuzzy controllers are capable of prioritizing the contradictory objectives, and capturing all the essential complexities of dynamics of the systems. / February 2016

abstract: There are many inconsistencies in the literature regarding how to estimate the Lyapunov Exponent (LyE) for gait. In the last decade, many papers have been published using Lyapunov Exponents to determine differences between young healthy and elderly adults and healthy and frail older adults. However, the differences in methodologies of data collection, input parameters, and algorithms used for the LyE calculation has led to conflicting numerical values for the literature to build upon. Without a unified methodology for calculating the LyE, researchers can only look at the trends found in studies. For instance, LyE is generally lower for young adults compared to elderly adults, but these values cannot be correlated across studies to create a classifier for individuals that are healthy or at-risk of falling. These issues could potentially be solved by standardizing the process of computing the LyE. This dissertation examined several hurdles that must be overcome to create a standardized method of calculating the LyE for gait data when collected with an accelerometer. In each of the following investigations, both the Rosenstein et al. and Wolf et al. algorithms as well as three normalization methods were applied in order to understand the extent at which these factors affect the LyE. First, the a priori parameters of time delay and embedding dimension which are required for phase space reconstruction were investigated. This study found that the time delay can be standardized to a value of 10 and that an embedding dimension of 5 or 7 should be used for the Rosenstein and Wolf algorithm respectively. Next, the effect of data length on the LyE was examined using 30 to 1300 strides of gait data. This analysis found that comparisons across papers are only possible when similar amounts of data are used but comparing across normalization methods is not recommended. And finally, the reliability and minimum required number of strides for each of the 6 algorithm-normalization method combinations in both young healthy and elderly adults was evaluated. This research found that the Rosenstein algorithm was more reliable and required fewer strides for the calculation of the LyE for an accelerometer. / Dissertation/Thesis / Appendix A / Doctoral Dissertation Biomedical Engineering 2019

The objective of this thesis is to develop a novel methodology of fractional stochastic dynamics to study stochastic stability of viscoelastic systems under stochastic loadings. Numerous structures in civil engineering are driven by dynamic forces, such as seismic and wind loads, which can be described satisfactorily only by using probabilistic models, such as white noise processes, real noise processes, or bounded noise processes. Viscoelastic materials exhibit time-dependent stress relaxation and creep; it has been shown that fractional calculus provide a unique and powerful mathematical tool to model such a hereditary property. Investigation of stochastic stability of viscoelastic systems with fractional calculus frequently leads to a parametrized family of fractional stochastic differential equations of motion. Parametric excitation may cause parametric resonance or instability, which is more dangerous than ordinary resonance as it is characterized by exponential growth of the response amplitudes even in the presence of damping. The Lyapunov exponents and moment Lyapunov exponents provide not only the information about stability or instability of stochastic systems, but also how rapidly the response grows or diminishes with time. Lyapunov exponents characterizes sample stability or instability. However, this sample stability cannot assure the moment stability. Hence, to obtain a complete picture of the dynamic stability, it is important to study both the top Lyapunov exponent and the moment Lyapunov exponent. Unfortunately, it is very difficult to obtain the accurate values of theses two exponents. One has to resort to numerical and approximate approaches. The main contributions of this thesis are: (1) A new numerical simulation method is proposed to determine moment Lyapunov exponents of fractional stochastic systems, in which three steps are involved: discretization of fractional derivatives, numerical solution of the fractional equation, and an algorithm for calculating Lyapunov exponents from small data sets. (2) Higher-order stochastic averaging method is developed and applied to investigate stochastic stability of fractional viscoelastic single-degree-of-freedom structures under white noise, real noise, or bounded noise excitation. (3) For two-degree-of-freedom coupled non-gyroscopic and gyroscopic viscoelastic systems under random excitation, the Stratonovich equations of motion are set up, and then decoupled into four-dimensional Ito stochastic differential equations, by making use of the method of stochastic averaging for the non-viscoelastic terms and the method of Larionov for viscoelastic terms. An elegant scheme for formulating the eigenvalue problems is presented by using Khasminskii and Wedig’s mathematical transformations from the decoupled Ito equations. Moment Lyapunov exponents are approximately determined by solving the eigenvalue problems through Fourier series expansion. Stability boundaries, critical excitations, and stability index are obtained. The effects of various parameters on the stochastic stability of the system are discussed. Parametric resonances are studied in detail. Approximate analytical results are confirmed by numerical simulations.

Four aspects of the dynamics of continuous-time dynamical systems are studied in this work. The relationship between the Lyapunov exponents of the original system and the Lyapunov exponents of induced Poincare maps is examined. The behavior of these Poincare maps as discriminators of chaos from noise is explored, and the possible Poissonian statistics generated at rarely visited surfaces are studied.

QC 20100414