To adapt to the new requirement of the developing flatness control theory and technology, cubic patterns were introduced on the basis of the traditional linear, quadratic and quartic flatness basic patterns. Linear, q...
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To adapt to the new requirement of the developing flatness control theory and technology, cubic patterns were introduced on the basis of the traditional linear, quadratic and quartic flatness basic patterns. Linear, quadratic, cubic and quartic Legendre orthogonal polynomials were adopted to express the flatness basic patterns. In order to over- come the defects live in the existent recognition methods based on fuzzy, neural network and supportvector regres- sion （SVR） theory, a novel flatnesspatternrecognition method based on leastsquaressupportvectorregression （LS-SVR） was proposed. On this basis, for the purpose of determining the hyper-parameters of LS-SVR effectively and enhan- cing the recognition accuracy and generalization performance of the model, particle swarm optimization algorithm with leave-one-out （LOO） error as fitness function was adopted. To overcome the disadvantage of high computational complexity of naive cross-validation algorithm, a novel fast cross-validation algorithm was introduced to calculate the LOO error of LDSVR. Results of experiments on flatness data calculated by theory and a 900HC cold-rolling mill practically measured flatness signals demonstrate that the proposed approach can distinguish the types and define the magnitudes of the flatness defects effectively with high accuracy, high speed and strong generalization ability.
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