Bounded error identification exploiting a-priori information on noise whiteness and noise/output correlation
In this paper we consider the problem of set-membership identification of nonlinear polynomial output error models, where output measurements are affected by bounded additive noise known to enjoy certain peculiar properties like whiteness and uncorrelation with the noiseless output sequence. More precisely, we propose an original approach to compute the so-called parameter uncertainty intervals by properly taking into account all the available a-priori information about the model structure and the properties of the noise. Parameters bounds are obtained by computing the solution to a set of polynomial optimization problems, where the decision variable are suitably selected and constrained in order to enforce the available a-priori information on the noise properties. Convex relaxation techniques are exploited to solve the formulated optimization problem. A simulation example is reported in order to show the effectiveness of the proposed approach.
Abstract The paper describes the application of a range of solution procedures to simple tie-bar models involving softening ‘stress-strain’ relationships. It illustrates the difficulties that can be encountered as a result of the associated localizations, ‘bifurcations’, and alternative equilibrium states. As a result of this study, a new solution procedure is tentatively proposed which requires the computer program to distinguish between ‘limit points’ and ‘bifurcations’. Once the latter has been detected, the solution is steered towards the ‘stable’ equilibrium path by adding to the current displacements a component of the eigenmode associated with the lowest eigenvector.