![]() Other works rely on local searches that introduce linear segments iteratively until satisfying a stopping criterion. In order to reduce the chance of yielding a local minimum, genetic algorithms have been proposed for clustering. However, fuzzy clustering is dependent on the initial parameters and can reach a local minimum. Akin to the previous technique, a fuzzy clustering strategy is developed in to represent a nonlinear system with a piecewise-linear model. This work attempts to mitigate undesirable effects of clustering, particularly the influence of outliers and the synthesis of subpotimal approximations. Some techniques are based on point clustering, such as -means, which has found applications in nonlinear dynamic systems and control. ![]() Īlthough many works in the literature are dedicated to piecewise linearization, few of them address the problem of generating piecewise-linear models which is often delegated to the scientist or engineer. In optimization, nonlinear problems can be recast as a mixed-integer linear programming (MILP) problem, which is then solved with MILP algorithms. In petroleum engineering, the fluid flow from an oil well and the pressure drop in a pipeline can be approximated with a piecewise-linear function. Piecewise-linear functions are widely used to approximate functions for which only sample points are known and to model nonlinear functions. Of the production function of gas-lifted oil wells. Derived from recursive formulations, the algorithms are applied to the approximation To ensure continuity, and a generalization of these models for stochastic functions whose data points are The models include piecewise-linearįunctions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies This paper presents a range of piecewise-linear models and algorithms to aidĮngineers to find an approximation that fits best their applications. Piecewise-linear functions can approximate nonlinear and unknown functions for which only sample
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