Robustness of Optimal Design Solutions to Reduce Vibration Transmission in a Lightweight 2-D Structure, Part I: Geometric Design

Abstract

A two-dimensional lightweight cantilever structure is studied, comprising 40 rigidly joined beams, of which the geometry is optimized to reduce vibration transmission over a given bandwidth. In this paper, the optimization is achieved by using genetic algorithms. Ten optimized design candidates were achieved for each of three cases resulting from minimizing an objective function (the vibration transmission between two points on the structure) which is calculated (i) using a single frequency, (ii) the frequency average over a narrow bandwidth, and (iii) the frequency average over a broad frequency range. All the candidates show performance improvements and normally the best performance is taken to be the best candidate. This paper then considers the sensitivity of each optimal candidate to small changes in the geometry of the structure. If the performance of a structure is too sensitive to perturbations its practical application is limited or may not be realizable in practice. The robustness of the optimized candidates is studied in order to "nd those candidates which are least sensitive to changing design parameters. This is achieved by perturbing the positions of the joints by an ensemble of sets of random numbers. The statistical e!ect on the objective function is investigated, and some candidates are seen to be more robust to such perturbations than others and generally the greater the bandwidth over which the structure is optimized the more robust the design. A selection criterion is then applied which enables the best candidates to be identi"ed on grounds of both nominal optimized performance and robustness. Finally, the advantage of using genetic algorithms over traditional &&hill-climbing'' optimization methods is shown, on the grounds of both nominal performance and robustness.

Comparison of the Effectiveness of Minimizing Cost Function Parameters for Active Control of Vibrational Energy Transmission in a Lightly Damped Structure

“…In this paper the number of possible actuator combinations is relatively small and an exhaustive search is feasible. The method of determination of the optimal actuator positions is not given here, but the authors have previously detailed the exhaustive search method used to "nd the best actuator positions for one of the cost functions considered here [7]. This paper is organized as follows: Section 2 details the two-dimensional (2-D) structure considered and presents an overview of the application of active vibration control systems to the structure.…”

“…Brennan et al [6] show that the best power measurement strategy can depend upon the nature of the problem. The application of feedforward active control is used here, its application to the structure considered here was discussed in reference [7], where the advantage of using an energy-based cost function over one based on velocities at a point was also given.…”

Total Internal Reflection-Based High Efficiency Grating Design for a Metal-Free Polarizing Filter Applications Using Hybrid Optimization Procedure

“…This two-step procedure allows saving the computation time to find the global minimum. To employ GA, the fitness function can be expressed as [13,14] …”

“…In recent years, hybrid optimization techniques are provided to improve the search performance and reduce the computational complexity of design [12,13]. Anthony employed the robustness issues and genetic algorithm (GA) to produce optimal solutions for two-dimensional structural applications [14]. Fang et al used the hybrid genetic algorithm for a zoom optics application [15].…”

“…In accordance with the TIR-based grating condition, it might be a big obstacle to obtain the optimum grating parameters, , , and . For this case, a stochastic approach can be employed, but it costs time and a question remains if a solution is a global minimum or not [12][13][14][15][16][17][18]. In recent years, hybrid optimization techniques are provided to improve the search performance and reduce the computational complexity of design [12,13].…”