Three-Level Mixed-Effects Location Scale Model With Modeling Random Scale Variance

In this dissertation, we propose a three-level mixed-effects random location scale model with modeling random scale variance (RL-RSS model). This model allows covariates to influence both error variance and random scale variance through a log-linear representation. The error variance varies across subjects through a subject-level normally distributed random scale effect, above and beyond the contribution of covariates on error variance. The subject-level random scale effect and random location effect are allowed to correlate with each other. Parameter estimation was based on the combination of maximum marginal likelihood (MML) method and Empirical Bayes (EB) method. An iterative Newton-Raphson solution was used to maximize the log likelihood, and multi-dimensional Gauss-Hermite quadrature is used to numerically approximate integral values. An SAS program via PROC NLMIXED using adaptive quadrature was developed to fit the proposed model. The data from Ecological Momentary Assessment (EMA) Adolescent Smoking Study are used to illustrate the application of the proposed model. In this study, a three-level clustering data structure, level-1 smoking events/occasions nested within level-2 waves nested within level-3 subjects, was used in the data analysis. The proposed RL-RSS model was fit to the data. Simulation process was carried out to validate the accuracy and reliability of the proposed three-level RL-RSS model. The simulation results show that RL-RSS resolves the intercept over-estimation of random scale variance occurring in the simple mixed-effect random location scale model

Non-linear control approaches for active railway suspensions

This thesis studies various linear and non-linear control approaches for active railway suspensions. The aim of the study is to improve the system performance of active secondary suspensions in response to different track features. The primary motivation for active suspension on railway vehicles is to improve suspension performance and thereby run faster or provide a better ride quality. The problem of discriminating between the random track and deterministic track input is a fundamental problem for the design of active secondary suspensions on railway vehicle. The basic requirement of an active suspension system is to improve the ride quality without increasing the suspension deflection unacceptably when the vehicle negotiates on both straight track and deterministic track features. This thesis presents and compares different control strategies of active suspension systems for railway vehicles. Firstly, a number of linear approaches for filtering the absolute velocity signal are theoretically examined in order to optimise the trade-off between the random and deterministic input requirements. What can be achieved with linear filters is initially determined. This is quantified by the degradation in the straight track ride quality needed to restrict the maximum deflection to an acceptable level as a vehicle traverses the transition to a typical railway gradient, and a range of filter types, frequencies and absolute damping rates are assessed in order to explore the boundary of what can be achieved through linear means. Secondly, some nonlinear Kalman-Filter methods are investigated to further improve the suspension performance. Finally, a comparison between linear and non-linear strategies is studied

State estimation error response of subsystem 1 in interconnected system 2.

State estimation error response of subsystem 1 in interconnected system 2.</p

Fault estimation error response of subsystem 1 in interconnected system 1.

Fault estimation error response of subsystem 1 in interconnected system 1.</p

State estimation error response of subsystem 2 in interconnected system 1.

State estimation error response of subsystem 2 in interconnected system 1.</p

Fault estimation error response of subsystem 2 in interconnected system 1.

Fault estimation error response of subsystem 2 in interconnected system 1.</p

S1 File -

In this research, a class of nonlinear interconnected systems with sensor faults were investigated and an estimation method was proposed for system sensor faults based on the theory of system state reconstruction. Considering sensor fault vectors in nonlinear interconnected systems, this method constructed a generalized nonlinear interconnected system, whose state was designed by augmenting the original system state and fault vectors, which provides a foundation for fault estimation of nonlinear interconnected systems. An augmented observer was developed by equivalent transformation of generalized interconnected system, so as to realize robust estimations of sensor faults in interconnected systems. This estimation method took into account the effect of external disturbance of the system on fault estimation and estimated the convergence speed of error system; the developed method also considered the convenience of solving the gain matrix of the augmented observer, which was beneficial to the realization of sensor fault estimation in interconnected system. The sensor estimation method proposed in the paper has the advantages of robustness in fault estimation,rapidity in error convergence, and convenience in solving the gain matrix. Finally, the state and sensor fault estimation errors of two interconnected systems can both approach 0 within 10 seconds, thus achieving the purpose of fault estimation. Two simulation experiments verified the effectiveness of the proposed fault estimation method and provided a reference for the fault estimation method of nonlinear interconnected systems with disturbance.</div

Fault estimation error response of subsystem 1 in interconnected system 2.

Fault estimation error response of subsystem 1 in interconnected system 2.</p

Fault estimation error response of subsystem 2 in interconnected system 2.

Fault estimation error response of subsystem 2 in interconnected system 2.</p

State estimation error response of subsystem 2 in interconnected system 2.

State estimation error response of subsystem 2 in interconnected system 2.</p