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An Uncertainty Model Of Approximating The Analytical Solution To The Real Case In The Field Of Stress Prediction

Gutiérrez R., Ramírez M., Olmeda E., Díaz V.

Metrology and Measurement Systems

2015

Vol. 22, nr 3

429--442

Deterministic mechanics has been extensively used by engineers as they needed models that could predict the behavior of designed structures and components. However, modern engineering is now shifting to a new approach where the uncertainty analysis of the model inputs enables to obtain more accurate results. This paper presents an application of this new approach in the field of the stress analysis. In this case, a two-dimensional stress elasticity model is compared with the experimental stress results of five different size tubes measured with resistive strain gages. Theoretical and experimental uncertainties have been calculated by means of the Monte Carlo method and a weighted least square algorithm, respectively. The paper proposes that the analytical engineering models have to integrate an uncertainty component considering the uncertainties of the input data and phenomena observed during the test, that are difficult to adapt in the analytical model. The prediction will be thus improved, the theoretical result being much closer to the real case.

Exponential estimates of a class of time-delay nonlinear systems with convex representations

Ramírez M., Villafuerte R., González T., Bernal M.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 4

815--826

This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.