Model order reduction based on trajectory piecewise linearization (TPWL) is a beneficial technique for approximating nonlinear models. One efficient method for building projection matrix in TPWL reduction is by aggregation of projection matrices of linearization points (LPs). However, in this method, the size of projection matrix will also grow up by increasing the number of LPs, which yield the increment of the size of reduced model. In other words, the size of reduced model will depend on the number of LPs. In this paper, we will address this issue and propose two new strategies for obviating this problem. Contrarily to former works in TPWL modeling, we established a model via TWPL based on output weighting of parallel linear models. Then, we proposed two reduction strategies for suggested TPWL model. The first algorithm inspires from former works in this field but in a parallel structure that enable segregation of projection matrices whereas the second algorithm remedies the problem by considering the high-order TPWL model as a unit linear model and reduces this model like a linear model but uses back projection method for constructing different outputs. The efficiency of methods is shown by comparison with former TPWL methods through vast simulations.
Optimal irrigation allocation and reservoir operation are essential in combating water scarcity in arid and semi-arid regions like Iran. Due to the huge number of decision variables in a reservoir-farm system, the inseparable nature of the crop yield function and the large variety of constraints, a genetic algorithm (GA) and harmony search (HS) are employed in the current paper to construct an integrated reservoir-farm system (IRFS). This integrated model can take into account crop sensitivity to water stress in order to maximize the net benefit of crops and to optimize crop areas and irrigation scheduling. This methodology is applied to the multi-crop Aharchay irrigation system downstream of Sattarkhan Dam. The outputs include the optimal values of the cultivated area, irrigation depth, and water release from the reservoir in 10-day periods. The results showed the speed of convergence, the optimal value of the total benefit and the slightly greater yield values of the HS algorithm compared to those of the GA. Both models also resulted in higher benefit amounts compared to the real and attainable benefit in the region. Finally, regarding the speed of convergence to the maximum value of the objective function, the HS algorithm demonstrated more promising results than the GA in the current case of interest.
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