Multi-objective optimization for structural topology and control of piezoelectric smart truss with interval parameter considering non-probability reliability constraints

Based on First-order Taylor expansion in small parameter range and interval extension analysis of functions, both open-loop and closed-loop characteristics of the piezoelectric controlled truss with small interval parameters and the corresponding sensitivity are analyzed. The integration optimization model of structural topology and control for the controlled structures with interval parameters is established, where a risk index and a deviation penalty are employed to deal with the objective functions and non-probability reliability is also introduced for the uncertain constraint functions so as to transform the optimization problems with the interval parameter into the corresponding deterministic one under the equivalent risk index. The multi-objective genetic algorithm is chosen as the optimization method for the integration optimization. Some optimization strategies coupled with Genetic algorithm (GA), such as the examinations for individual validity, structural stability and system controllability are adopted to guide the optimization process efficiently. The results of numerical example show that many optimal individuals are obtained in the multi-objective optimization, i.e. a group of non-inferior solutions can be gotten. And the different values of parameters, such as risk index, deviation and reliability can make the optimal results different.