Ensemble Of Surrogate Models For Lightweight Design Of Autobody Structure

Simulation-based design optimization is widely used in design of complex systems building upon the successful development of finite element techniques. Take automotive industry for example, it is a critical problem to reduce the weight to improve fuel efficiency and meet the gas emission requirement; this is an urgent problem for both traditional gasoline and fuel cell vehicles. Meanwhile, the lightweight vehicle should maintain, or achieve better performance in crashworthiness, stiffness, modal and noise, vibration, harshness (NVH) performance, etc. The above problem is widely recognized as a multi-disciplinary, multi-variable, and multi-constraint optimization problem. In practice, integrating structural optimization directly with expensive finite element simulations is generally infeasible since optimization search typically requires thousands or even millions of simulations on crashworthiness and NVH performance,. As a consequence, there is a growing interest in using surrogate model or metamodel to approximate the complicated highly nonlinear behaviors to manage the complexity in analysis and optimization for weight reduction of autobody.Although surrogate based design optimization is considered as one of the efficient approaches to dealing with complex engineering problems, inaccuracy in metamodeling may result in misleading design solutions.The dissertation concentrates on improving the quality of metamodeling techniques. An approach for constructing the ensemble of surrogates is proposed to provide better approximation of autobody structural responses. A strategy for sequential sampling is presented for ensemble of surrogates to improve its accuracy further. As a refinement, conservative prediction for constraints is put forward to ensure the actual constraint feasibility of the approximated solution. A lightweight design method based on ensemble of multiple surrogates is finally presented, followed by an industrial case study for weight reduction of autobody of fuel cell vehicle. The main research tasks and the corresponding conclusions from this dissertation are summarized as follows: (1) Study on the ensemble of surrogatesSeveral individual surrogates are investigated in terms of prediction capability, such as polynomial response surface, radial basis function, Kriging and support vector regression. A new scheme for weights selection is proposed based on cross validation error, and the ensemble of surrogates are constructed through the weighted average method. The scope of application for ensemble of surrogates is discussed and the influence of the number of individual surrogates is also researched. By using a large amount of test functions and engineering cases, it is shown that the new weights selection method is more effective when compared with the currently existing weights selection methods and individual surrogates. It is also demonstrated that the prediction capability of the ensembled surrogates is the best when the number of individual surrogates is from 3 to 5. In conclusion, ensemble of surrogates is an effective approach for metamodeling on autobody structural responses, which possesses high dimensionality, high nonlinearity and small sampling points.(2) Sequential sampling strategy for ensemble of surrogatesBased on the weights of individual surrogates and its prediction errors with ensemble of surrogates, an index of weighted standard deviation is proposed to represent the metamodel uncertainty for ensemble of surrogates. It has been demonstrated that the proposedhe index is highly correlated with the actual errors of ensemble of surrogates. A sequential sampling strategy is proposed to improve the accuracy of the ensembled surrogates by iteratively adding sample points with the maximum weighted standard deviations. We demonstrate the advantages of this strategy using analytical problems and one engineering problem. It is noted that the index of the weighted standard deviation is more useful for a qualitative identification rather than quantitative on the metamodel uncertainty. It is also shown that the sequential sampling strategy can effectively improve the prediction of ensemble of surrogates in the region of high uncertainty, especially for high dimensional and high nonlinear responses.(3) Conservative prediction of surrogates for constrained optimizationThe methodology of conservative prediction of surrogates is proposed by employing the concept of safety margin. An approach for estimating the safety margins under a given conservativeness level is proposed based on the cumulative distribution function obtained in cross validation. The method helps compensate surrogate errors to push the constrain boundary towards the feasible domain. Furthemore, a strategy for sequentially updating the conservativeness level is developed to decrease the safety margins effectively. The ensemble of surrogates, safety margins, and the scheme for updating the safety margin in surrogate based optimization are applied to lightweight design of vehicle structures under crashworthiness. The proposed techniques resulted in more feasible solutions and achieved more weight reduction within a limited number of optimization cycles, showing great potential for surrogate based design optimization in real engineering problems.(4) Method on lightweight design of autobody and industrial application based on ensemble of surrogatesA method for lightweight design of autobody is proposed by integrating the ensemble of surrogates, sequential sampling strategy, and conservative surrogates for constraint function. The framework and the detail flowchart of ensemble of surrogates-based method for lightweight design of autobody are presented. An industrial application is studied to verify the feasibility of the proposed framework, where multidisciplinary optimization of autobody for a fuel cell vehicle is conducted considering various types of crash scenarios, including full-overlap frontal crash, 40% overlap frontal crash with deformable barrier, side impact, and rear impact, stiffness and modal frequency of body-in-white, and NVH.Design optimization for autobody is a complex, multi-disciplinary, multi-variable, and multi-constraint problem. This dissertation studies the ensemble of surrogates,its sequential sampling strategy, and conservative surrogates, in an attempt to construct more accurate surrogate models for autobody structural responses with high nonlinearity and to ensure the actual constraint feasibility of the approximate solution. The research aims for providing better surrogate models for lightweight design of autobody, as well as guiding and improving the process of lightweight autobody development, towards the end goal of improving the R&D capability of vehicle lightweight design.