Uncertainty-Based Optimization Method And Its Application In Aircraft Design

There are many uncertainties enconuntered in both the aircraft manufacturing process and its subsequent flight operation. The physical properties of materials are uncertain. Manufacturing errors produce an aerodynamic shape and structural dimensions different from the original design. Furthermore, the load on the aircraft is not constant during operation. Fuel is consumed continually during cruise, thus fight parameters keep changing. After an aircraft has been produced, some parameters sometimes need to be adjusted for a new type. If these uncertainties are considered in the conceptual design process, the aircraft's performance will be robust and reliable. Therefore, this paper conducts systemic research on robust optimization and reliability-based optimization, and their application to aircraft design. The main contributions are the following:1)Based on analysis and review of the existing theory of optimization under uncertainty, this paper points out that uncertainty analysis based on surrogate model is a potential and practical way to solve this problem, especially for the situations where time-consuming software, such as computational fluid dynamics and finite element analysis software, has to be used.2)A sequential global surrogate model is proposed. Its accuracy is very high, and its computational cost is moderate. The number of total sampling points is controlled by a strategy of adding sampling points in the design space sequentially. Meanwhile, the requirements for global and local accuracies are satisfied. A mathematical example verifies that accuracy of the sequential global surrogate model is very high, and it can be applied to the robust optimization for practical engineering designs.3)The robust optimization, based on the proposed sequential global surrogate model, is applied to aircraft conceptual design and airfoil design. The results of conceptual design for a passenger jet indicate that the constraints are satisfied with a much higher possibility after optimization under uncertainty, i.e., the risk decreases. The aerodynamic performance of transonic airfoil is sensitive to fight conditions. After an optimization considering operation variations and manufacturing errors, the objective drag coefficient of the airfoil is insensitive to the uncertainties, and the constraint of the pitch moment coefficient is still satisfied under the uncertainties.4)A reliability analysis method based on SVM (Support Vector Machine) and MPP (Most Probable Point) is proposed. SVM is employed to create a surrogate model of the limit-state function at the MPP. The gradient information at the MPP is also used in the process. It guarantees that the surrogate model passes through the MPP and that the surrogate model is tangent to the limit-state function at the MPP. Then Importance Sampling is used to calculate the probability of failure with the surrogate model. The examples demonstrate that the proposed method is more accurate than the FORM, more efficient than the direct Monte Carlo simulation, and more robust than the Important Sampling method.5)The SORA (Sequential Optimization and Reliability Assessment) and reliability method based on SVM are integrated. The SORA decoupled the traditional double loop reliability optimization into a single loop strategy. This advantage of SORA is taken and reliability analysis based on SVM is used to amend the error from linear approximation for limit state function in SORA. This method improves the accuracy of reliability assessment. A cantilever beam example indicates that this optimization strategy is accurate and its computational cost is moderate.6)The reliability optimization based on SORA and improved SVM is applied to the design of wing structure. It is considered that properties of materials are uncertain, errors exist in the manufacture and assembly process, and that loads are not constant. The proposed reliability-based optimization is applied to a simplified wing structure design under these uncertainties. Results demonstrate that the weight of the wing is reduced, and that both deterministic and probabilistic constraints are satisfied.