Christine Q. Wu

Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents

For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.

Stability analysis via the concept of Lyapunov exponents: a case study in optimal controlled biped standing

Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency and satisfying the constraints between the biped feet and the ground. In this article, a proportional-derivative (PD) controller is proposed for a standing biped, which is simplified as a two-link inverted pendulum with one additional rigid foot-link. The genetic algorithm (GA) is used to search for the control gain meeting all three requirements. The stability analysis of such a deterministic biped control system is carried out using the concept of Lyapunov exponents (LEs), based on which, the system stability, where the disturbance comes from the initial states, and the structural stability, where the disturbance comes from the PD gains, are examined quantitively in terms of stability region. This article contributes to the biped balancing control, more significantly, the method shown in the studied case of biped provides a general framework of systematic stability analysis for certain deterministic nonlinear dynamical systems.

Integrated testing of standing balance and cognition: Test-retest reliability and construct validity

Balance and cognitive impairments which are common with aging often coexist, are prognostic of future adverse health events, including fall injuries. Consequently, dual-task assessment programs that simultaneously address both stability and cognition are important to consider in rehabilitation and benefit healthy aging. The objective of this study was to establish test-retest reliability and construct validity of a dual-task computer game-based platform (TGP) that integrates head tracking and cognitive tasks with balance activities. Thirty healthy, community-dwelling individuals median age 64 (range 60-67) were recruited from a certified Medical Fitness Facility. Participants performed a series of computerized head tracking and cognitive game tasks while standing on fixed and sponge surfaces. Testing was conducted on two occasions, one week apart. Moderate to high test retest reliability (ICC values of 0.55-0.75) was observed for all outcome measures representing balance, gaze performance, cognition, and dual-task performance. A significant increase in center of foot pressure (COP) excursion was observed during both head tracking and cognitive dual-task conditions. The results demonstrate the systems ability to reliably detect changes related to specific and integrated aspects of balance, gaze, and cognitive performance.

Using entropy measures to characterize human locomotion

Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

Lateral stability analysis of on-road vehicles using Lyapunov's direct method

Vehicle rollover may occur due to the yaw instability. Hence, the yaw stability analysis can help improve vehicle safety. In this paper, Lyapunovs direct method is applied to the lateral stability analysis of the non-linear vehicle model driven in a straight-line with constant longitudinal velocity, where the non-linearity of the model comes from the non-linear expression of the lateral tire forces. Two new Lyapunov functions are proposed. These functions do not explicitly depend on vehicle parameters and estimate the larger stability regions as compared with previous works.

Comparison of Four Friction Models: Feature Prediction

In this paper, we provide not only key knowledge for friction model selection among candidate models but also experimental friction features compared with numerical predictions reproduced by the candidate models. A motor-driven one-dimensional sliding block has been designed and fabricated in our lab to carry out a wide range of control tasks for the friction feature demonstrations and the parameter identifications of the candidate models. Besides the well-known static features such as break-away force and viscous friction, our setup experimentally demonstrates subtle dynamic features that characterize the physical behavior. The candidate models coupled with correct parameters experimentally obtained from our setup are taken to simulate the features of interest. The first part of this work briefly introduces the candidate friction models, the friction features of interest, and our experimental approach. The second part of this work is dedicated to the comparisons between the experimental features and the numerical model predictions. The discrepancies between the experimental features and the numerical model predictions help researchers to judge the accuracy of the models. The relation between the candidate model structures and their numerical friction feature predictions is investigated and discussed. A table that summarizes how to select the most optimal friction model among a variety of engineering applications is presented at the end of this paper. Such comprehensive comparisons have not been reported in previous literature.

A new load transfer index () with considering six degrees of freedom and its application in structural design and analysis

ABSTRACT Load paths analysis is important in design process of load bearing structures. U* index was introduced as the indicator of load paths based on finite element analysis. However, the U* index was only formulated based on three translational degrees of freedom (DOFs) without considering the rotational DOFs. Hence, the U* index cannot be used together with plate and shell theories, which are very important in engineering computations of thin-walled structures. A coupling issue in finite element analysis is that shell elements which are governed by plate and shell theories are invalid for U* calculations. This paper proposed a new load transfer index () with considering both translational and rotational DOFs (i.e. six DOFs). To demonstrate the effectiveness of the new index in structural design and analysis, a case study was performed to a complex thin-walled structure. The stiffness to mass ratio of the sample structure is raised by 18.3% based on the load transfer analysis using the new index.

Demonstration of the effectiveness of U*-based design criteria on vehicle structural design:

A basic function of vehicle structures is bearing the load. To design high efficient vehicle structures, it is crucial to know how the applied forces are transferred in the structure. The U* index was introduced as the indicator of the main load path in the structure. U*-based design criteria were developed to promote the ability of the U* index theory for vehicle structural design. However, the effectiveness of these U*-based design criteria on improving the structural performance is still unknown. In this paper, an improved design of a vehicle component was proposed based on the U* governed design criteria. Compared to the original design, the weight of the modified structure is reduced by 10% while the maximum displacement and stress are declined by 5% and 26%, respectively. The paper proves that the application of the U* driven design criteria can effectively increase the structural performance.

The Effects of Aging and Dual Tasking on Human Gait Complexity During Treadmill Walking: A Comparative Study Using Quantized Dynamical Entropy and Sample Entropy

Quantized dynamical entropy (QDE) has recently been proposed as a new measure to quantify the complexity of dynamical systems with the purpose of offering a better computational efficiency. This paper further investigates the viability of this method using five different human gait signals. These signals are recorded while normal walking and while performing secondary tasks among two age groups (young and older age groups). The results are compared with the outcomes of previously established sample entropy (SampEn) measure for the same signals. We also study how analyzing segmented and spatially and temporally normalized signal differs from analyzing whole data. Our findings show that human gait signals become more complex as people age and while they are cognitively loaded. Center of pressure (COP) displacement in mediolateral direction is the best signal for showing the gait changes. Moreover, the results suggest that by segmenting data, more information about intrastride dynamical features are obtained. Most importantly, QDE is shown to be a reliable measure for human gait complexity analysis.

Experimental validation of the U* index theory for load transfer analysis

Engineering structures are designed to transfer external loads to their supports. Therefore, it is necessary to study the pattern of load transfer. The U * index method has been introduced to follow the load path in the structure. The U * value at each point corresponds to its significance in the load carrying process. The U * index theory has been used as a new design approach in lightweight vehicle structures but there has not been any experimental validation of this theory. In this study, two experiments are presented to show that the U *index is a true indicator of load transfer in the structure and areas with higher U * index values indeed carry more load. The results also prove the insensitivity of the U * index to stress concentrations. This study presents the first experimental validation of the U * index theory which is important to this new approach for light-weight vehicle structural design.