Robust fault estimation of uncertain systems using an LMI‐based approach

General recent techniques in fault detection and isolation (FDI) are based on H_∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation‐based design methods. This article presents an LMI formulation to design full‐order and reduced‐order robust H_∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full‐order filter, which may be solved via recently developed LMI optimization techniques. For the reduced‐order FDI filter, the inequalities include a non‐convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd.     

Weathering of metapelites from the Quadrilátero Ferrífero mineral province,southeastern Brazil

Low-grade metamorphic rocks are known for their low mechanical strength and high weatherability. In the Quadrilátero Ferrífero, an important mineral province located in southeastern Brazil, this set of features results in frequent issues with mining and road slope instability, mainly associated with phyllites. Despite the significant iron ore production that occurs in this province, little is known about the geotechnical properties of the materials constituting the weathering front. Here, we report work aimed at investigating the changes in the basic properties of phyllites at four weathering grades. The methodology used included the field classification and mapping of four weathering grades in order to assess their spatial distribution on a road slope, as well as sampling for geological characterization by petrography and X-ray diffraction (XRD). In addition, the authors performed a physical characterization of all weathering grades, including index properties, mercury porosimetry, and strength data obtained with a Schmidt hammer both in the field and in the laboratory as well as using the point load test (PLT). Results showed the relevance of structural features such as discontinuities and metamorphic foliation observed in the weathering morphology in situ, with different weathering intensities occurring along the slope. Changes in the porosity and pore size distribution in the weathering front were nonlinear, as were resistance variations. The difficulty involved in performing the macroscopic identification of weathering grades due to the very fine texture of the rock as well as microstructural heterogeneities are likely causes of the observed variability in phyllite properties. This fundamental knowledge may aid the prediction of short-term and long-term scenarios for slope stability based on rock weatherability.