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  • Multi-objective optimization of structures topology by genetic algorithms
    Publication . Madeira, JFA; Rodrigues, H.; Pina, Heitor
    This work develops a computational model for topology optimization of linear elastic structures for situations where more than one objective function is required, each one of them with a different optimal solution. The method is thus developed for multi-objective optimization problems and is based on Genetic Algorithms. Its purpose is to evolve an evenly distributed group of solutions (population) to obtain the optimum Pareto set for the given problem. To reduce computational effort, optimal solutions of each of the single-objective problems are introduced in the initial population. Two numerical examples are presented and discussed to assess the method.
    2005-01Journal article Restricted access Show more
  • Does independent component analysis play a role in unmixing hyperspectral data?
    Publication . Nascimento, Jose; Bioucas-Dias, José M.
    Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.
    2005-01Journal article Restricted access Show more