Minimum Model Error Research Articles

Two-Dimensional Models of Boundary and Mixed Friction at a Line Contact

Two-dimensional dynamic friction models at a lubricated line contact, operating in boundary and mixed lubrication regimes, are developed. The friction coefficient is shown to be a function of the sliding velocity and the instantaneous separation of the sliding bodies, normal to the sliding direction. The models are based on unsteady friction experiments carried out under constant normal loads and under time-varying sliding velocities. The normal motions at the sliding contact were detected indirectly by contact resistance measurements. The contact resistance is related to the theoretical central film thickness for smooth surfaces. An advanced system identification technique (Minimum Model Error) is implemented to identify the most important terms in a number of nonlinear friction models. Two friction models are then nondimensionalized and parameterized. The validity and range of application of the models are then tested, by comparing them with experiments and with selected models proposed by other researchers.

Estimation of model error for nonlinear system identification

Algorithms are presented for estimation of deterministic model error in the assumed models of nonlinear discrete and continuous time systems. The explicit model error time histories are parameterised using least squares method. The parameterised models relative to the true model explain the deterministic deficiency in the chosen models, in the sense of minimum model error. The algorithms have appealing features of extended Kalman filter. The numerical simulation results are obtained by implementing the algorithms in PC MATLAB. >

Riccati solution for the minimum model error algorithm

Riccati solution for the minimum model error algorithm

An experimental study of nonlinear dynamic system identification

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both digital simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Existence and uniqueness proof for the minimum model error optimal estimation algorithm

A general solution to the jump-discontinuous two-point boundary value problem (TPBVP) of the minimum model error is presented. Its existence and uniqueness are then proved.

Minimum model error estimation for poorly modeled dynamic systems

A novel strategy (which we call minimum model error'* estimation) for postexperiment optimal state estimation of discretely measured dynamic systems is developed and illustrated for a simple example. The method is especially appropriate for postexperiment estimation of dynamic systems whose presumed state governing equations are known to contain, or are suspected of containing, errors. The hew method accounts for errors in the system dynamic model equations in a rigorous manner. Specifically, the dynamic model error terms in the proposed method do not require the usual Kalman filter-smoother process noise assumptions of zero-mean, symmetrically distributed random disturbances, nor do they require representation by assumed parameterized time series (such as Fourier series); Instead, the dynamic model error terms require no prior assumptions other than piecewise continuity. Estimates of the state histories, as well as the dynamic model errors, are Obtained as part of the solution of a two-point boundary value problem. The state estimates are continuous and optimal in a global sense, yet the algorithm processes the measurements sequentially. The example demonstrates the method and shows it to be quite accurate for state estimation of a poorly modeled dynamic system.