An important operational task for thermal turbines during run-up and run-down is to keep the stresses in the structural elements at a right level. This applies not only to their instantaneous values, but also to the impact of them on the engine lifetime. The turbine shaft is a particularly important element. The distribution of stresses depends on geometric characteristics of the shaft and its specific locations. This means a groove manufactured for fixing the rotor blades. The extreme stresses in this place occur during the start-up and the shaft heating to normal operating temperature. The process needs optimisation. Optimization tasks are multidisciplinary issues and can be carried out using different methods. In recent years, particular attention in optimisation has been paid to the use of artificial intelligence methods. Among them, a special role is assigned to genetic algorithms. The paper presents a genetic algorithm method to optimise the steam turbine shaft heating process during its start-up phase. The presented optimization task of this algorithm is to carry out the process of the shaft heating as soon as possible at the conditions of not exceeding the stresses at critical locations at any heating phase.
Consider the semilinear system defined by
x(i+1) = Ax(i) + f(x(i)), i≥ 0
x(0) = x0 ϵ ℜn
and the corresponding output signal y(i)=Cx(i), i ≥ 0, where A is a n x n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω in ℜp if the output signal (y(i))i associated to our system satisfies the condition y(i) in Ω, for every integer i ≥ 0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems (controlled and uncontrolled systems). Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.
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