Joel A. Levitt

A polynomial-algebraic method for non-stationary TARMA signal analysis—part I: the method

Abstract Time-dependent autoregressive moving-average (TARMA) models, with parameters belonging to a subspace spanned by pre-defined time-domain functions, offer appropriate representation for a fairly wide class of non-stationary signals. The methods available for their estimation have, however, been limited to the subclass of pure autoregressive (TAR) models. In this paper, a polynomial-algebraic (P-A) method for the estimation of mixed TARMA models is introduced. The method is based upon a skew polynomial operator algebra, through which the AR and MA polynomial operators are related to the model’s inverse function, and through which appropriate filtering operations, essential for the construction of a restricted quadratic approximation of the prediction error (PE) criterion, are introduced. The P-A method is characterized by low computational complexity, no need for initial guess parameter values, and avoidance of local extrema problems associated with PE optimization. The performance characteristics of the P-A method are assessed via numerically synthesized non-stationary signals, while PE-based model refinement is also examined. A first application of the non-stationary TARMA approach and the P-A method to the problem of modeling and prediction of an actual non-stationary engineering signal is also presented, and critical comparisons with non-stationary ARIMA (integrated ARMA) and conventional ARMA methods made. The paper is divided into two parts. The polynomial-algebraic method is introduced in the first, whereas its application to the non-stationary modeling and prediction of an automotive active suspension power consumption signal paradigm is presented in the second.

Nonlinear system identification of hydraulic actuator. Friction dynamics using a Hammerstein model

We present two Hammerstein-type models for parametric system identification of the lip seal friction process in a hydraulic actuator. Adaptive algorithms with least squares criteria are derived, and the performances of the two models are evaluated using experimental results.

A polynomial-algebraic method for non-stationary TARMA signal analysis—part II: application to modeling and prediction of power consumption in automobile active suspension systems

Time dependent AutoregRessive Moving Average (TARMA) models, with parameters belonging to a sub-space spanned by time-domain functions, offer appropriate representation for a fairly wide class of non-stationary signals. Yet, their estimation is difficult, due to problems related to local extrema and the need for accurate initial guess parameter values. In this paper a Polynomial-Algebraic (P-A) TARMA estimation method is introduced. The P-A method achieves low computational complexity while eliminating the need for initial guess parameter values and avoiding local extrema problems. Its performance is demonstrated via Monte Carlo simulations.

Physically Based Modeling of Reciprocating Lip Seal Friction

Lip seal friction under constant speed sliding is modeled as the sum of three physically based components: (I) viscous shear loss in the lubricant; (2) hysteresis losses due to roughness-imposed deformation of the seal material, and (3) hysteresis losses due to deformation caused by varying intermolecular forces at the sliding interface. Increasingly thick hydrodynamic films progressively reduce contributions of the roughness and intermolecular components. Peaks in friction expected from these two components are smaller, occurring at lower sliding speed, than in dry rubber friction. Model simulations capture friction trends with temperature, hydraulic pressure, seal material, lubricant viscosity and shaft roughness.

Nonlinear system identification of hydraulic actuator friction dynamics using a finite-state memory model

We present a finite-state memory model for parametric system identification of the lip seal friction process in a hydraulic actuator. The performance of the finite-state memory model is compared with two Hammerstein type models using experimental results.

Modeling and Identification of Lubricated Polymer Friction Dynamics

A systematic approach is proposed to model the dynamics of lubricated polymer friction. It starts with the development of a physical model to describe the fundamental mechanisms of the friction. The physical model then serves as the basic structure for the development of a complex model able to capture a wider spectrum of the deterministic and stochastic dynamics of friction. To assess the accuracy of the complex model, two estimation algorithms are formulated to estimate the unknown parameters in the model and to test the model against experimental data. One algorithm is based on the maximum likelihood principle to estimate the constant parameters for stationary friction dynamics, and the other based on the extended Kalman filter to estimate the time-varying parameters for nonstationary friction dynamics. The model and the algorithms are all validated through experiments.

Nonstationary signal estimation using time-varying ARMA models

A parametric approach for the estimation of nonstationary signals is presented. The approach is based on time-varying autoregressive moving average (TARMA) signal representations. The TARMA model coefficients vary in a deterministically organized way and are estimated using a novel fully linear parameter estimation method. The estimation algorithm is based on the properties of the TARMA models that allow their manipulations using operations restricted to the time domain. It is shown that the estimation method is computationally simple, overcomes local extrema problems associated with nonlinear search procedures, and eliminates the need for initial guesses of the parameter values.<<ETX>>