Reliability Based Optimization of Composite Laminates for Frequency Constraint

The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

Application of Conservative Surrogate to Reliability Based Vehicle Design for Crashworthiness

Surrogate models are commonly used for approximation of large computationally expensive vehicle crash simulation to facilitate rapid design space exploration and optimization. Unfortunately, the optimum design based on surrogates may turn out to be infeasible after running finite element crash simulation due to the surrogate errors. To meet this challenge, conservative strategy of surrogate modeling through compensating fitting errors was used for reliability based design optimization of vehicle structures for crashworthiness and weight reduction. The critical crash responses were constructed by unbiased kriging models, and conservative surrogates were obtained via adding safety margin to estimate the crash responses conservatively. The benefits of using conservative surrogates for reliability based design optimization were investigated in the context of constraint feasibility of the optimum designs through a mathematical example and a case study on vehicle crashworthiness design. The results demonstrate that optimization based on conservative surrogate helps to achieve the feasible optimum design, showing more attractive for reliability based design optimization in engineering applications.

A Polynomial Chaos Expansion Trust Region Method for Robust Optimization

Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of the objective function and the constraints.In a previous work,the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion.This paper extends the proposed method to the case of the robust optimization.The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region.This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration(single loop method).Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function,the proposed method can handle any approximation order and any choice for the robust measures.Some numerical experiments based on finite element functions are performed to show the efficiency of the method.