Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plates Using Genetic Algorithms

Shape control of adaptive structures using piezoelectric actuators has found a wide range of applications in recent years. In this paper, the problem of finding optimal distribution of piezoelectric actuators and corresponding actuation voltages for static shape control of a plate is formulated as a multi-objective optimization problem. The two conflicting objectives considered are minimization of input control energy and minimization of mean square deviation between the desired and actuated shapes with constraints on the maximum number of actuators and maximum induced stresses. A shear lag model of the smart plate structure is created, and the optimization problem is solved using an evolutionary multi-objective optimization algorithm: nondominated sorting genetic algorithm-II. Pareto-optimal solutions are obtained for different case studies. Further, the obtained solutions are verified by comparing them with the single-objective optimization solutions. Attainment surface based performance evaluation of the proposed optimization algorithm has been carried out.

[1]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[2]  Mohammad R. Akbarzadeh-Totonchi,et al.  Genetic Quantum Algorithm for Voltage and Pattern Design of Piezoelectric Actuator , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[3]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[4]  Arthur W. Leissa,et al.  Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[5]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[6]  J. Dias Rodrigues,et al.  The application of genetic algorithms for shape control with piezoelectric patches—an experimental comparison , 2004 .

[7]  Rex K. Kincaid.  Minimizing distortion in truss structures - A comparison of simulated annealing and TABU search , 1991 .

[8]  Jose Mathew,et al.  Finite Element Modeling of Piezoelectric Actuators for Active Flow Control Applications , 2001 .

[9]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

[10]  Joshua D. Knowles.  A summary-attainment-surface plotting method for visualizing the performance of stochastic multiobjective optimizers , 2005, 5th International Conference on Intelligent Systems Design and Applications (ISDA'05).

[11]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

[12]  Liyong Tong,et al.  Energy Optimization in Local Shape Control of Structures with Nonlinear Peizoelectric Actuators , 2005 .

[13]  Grant P. Steven,et al.  A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures , 2000 .

[14]  László P. Kollár,et al.  Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified , 1994 .