Variable Complexity Modeling Research Articles

Multi-Fidelity Aerodynamic Data Fusion with a Deep Neural Network Modeling Method

To generate more high-quality aerodynamic data using the information provided by different fidelity data, where low-fidelity aerodynamic data provides the trend information and high-fidelity aerodynamic data provides value information, we applied a deep neural network (DNN) algorithm to fuse the information of multi-fidelity aerodynamic data. We discuss the relationships between the low-fidelity and high-fidelity data, and then we describe the proposed architecture for an aerodynamic data fusion model. The architecture consists of three fully-connected neural networks that are employed to approximate low-fidelity data, and the linear part and nonlinear part of correlation for the low- and high-fidelity data, respectively. To test the proposed multi-fidelity aerodynamic data fusion method, we calculated Euler and Navier–Stokes simulations for a typical airfoil at various Mach numbers and angles of attack to obtain the aerodynamic coefficients as low- and high-fidelity data. A fusion model of the longitudinal coefficients of lift and drag was constructed with the proposed method. For comparisons, variable complexity modeling and cokriging models were also built. The accuracy spread between the predicted value and true value was discussed for both the training and test data of the three different methods. We calculated the root mean square error and average relative deviation to demonstrate the performance of the three different methods. The fusion result of the proposed method was satisfactory on the test case, and showed a better performance compared with the other two traditional methods presented. The results provide evidence that the method proposed in this paper can be useful in dealing with the multi-fidelity aerodynamic data fusion problem.

Multi-disciplinary design optimization with variable complexity modeling for a stratosphere airship

This paper proposes a hybrid architecture based on Multi-disciplinary Design Optimization (MDO) with the Variable Complexity Modeling (VCM) method, to solve the problem of general design optimization for a stratosphere airship. Firstly, MDO based on the Concurrent SubSpace Optimization (CSSO) strategy is improved for handling the subsystem coupling problem in stratosphere airship design which contains aerodynamics, structure, and energy. Secondly, the VCM method based on the surrogate model is presented for reducing the computational complexity in high-fidelity modeling without loss of accuracy. Moreover, the global-to-local optimization strategy is added to the architecture to enhance the process. Finally, the result gives a prominent stratosphere airship general solution that validates the feasibility and efficiency of the optimization architecture. Besides, a sensitivity analysis is conducted to outline the critical impact upon stratosphere airship design.

Optimization Strategy for a Shrouded Turbine Blade Using Variable-Complexity Modeling Methodology

This paper presents the development of a collaborative optimization framework in combination with a variable-complexity modeling technique for the multidisciplinary coupling analysis and design of a shrouded turbine blade. The multidisciplinary optimization design of the shrouded turbine blade involves a high-fidelity detailed computational model and medium-fidelity models, which can become prohibitively expensive. In this investigation, a variable-complexity modeling methodology is introduced, where low-fidelity models and a scaling function are used to approximate the medium- and high-fidelity models through the optimizers in an inner-loop optimization to reduce computational expense. The optimization framework developed includes the collaborative optimization process, parametric modeling of the shrouded turbine blade, fluid–structure interaction solver using arbitrary Lagrangian–Eulerian formulation, an adaptive hexahedral structure mesh generator by establishing virtual blocks and parametric fixed points, and a variable-complexity modeling method combining the multiplicative and additive corrections to manage three levels of fidelity models. On the shrouded turbine-blade design problem, it achieves a feasible optimizer only calling nine high-fidelity analyses. Response surface model variation and cross-validation tests are performed to verify the predictive power of the response surface model in the multidisciplinary design optimization process of the shrouded turbine blade.

Conceptual Design Optimization of Tensairity Girder Using Variable Complexity Modeling Method

Tensairity girder is a light weight inflatable fabric structural concept which can be used in road emergency transportation. It uses low pressure air to stabilize compression elements against buckling. With the purpose of obtaining the comprehensive target of minimum deflection and weight under ultimate load, the cross-section and the inner pressure of tensairity girder was optimized in this paper. The Variable Complexity Modeling (VCM) method was used in this paper combining the Kriging approximate method with the Finite Element Analysis (FEA) method, which was implemented by ABAQUS. In the Kriging method, the sample points of the surrogate model were outlined by Design of Experiment (DOE) technique based on Optimal Latin Hypercube. The optimization framework was constructed in iSIGHT with a global optimization method, Multi-Island Genetic Algorithm (MIGA), followed by a local optimization method, Sequential Quadratic Program (SQP). The result of the optimization gives a prominent conceptual design of the tensairity girder, which approves the solution architecture of VCM is feasible and efficient. Furthermore, a useful trend of sensitivity between optimization variables and responses was performed to guide future design. It was proved that the inner pressure is the key parameter to balance the maximum Von Mises stress and deflection on tensairity girder, and the parameters of cross section impact the mass of tensairity girder obviously.

A modified variable complexity modeling for efficient multidisciplinary aircraft conceptual design

This paper describes a modified variable complexity modeling (MVCM) framework that uses a neural network to replace the Taylor series after several warm-up iterations. The MVCM framework with an additive scaling function is most efficient in terms of high-fidelity function evaluation savings compared with traditional variable complexity modeling (VCM) among multiplicative and hybrid scaling functions. The MVCM framework achieves 59.1 and 68.6 % savings in high-fidelity function evaluations for one-dimensionally and two-dimensionally constrained problems, respectively, compared with the VCM method. The MVCM framework provides a larger trust region than the VCM due to the global behavior of neural networks. The MVCM solution also converges closely to the high-fidelity function. The MVCM framework is integrated with an in-house low-fidelity aircraft design synthesis program and a high-fidelity analysis (AADL3D) for the conceptual design of multidisciplinary regional jet aircraft (RJA) to enhance the optimal RJA configuration compared with low-fidelity analysis results. The optimal RJA wing configuration using the MVCM framework provides more realistic and reasonable configurations compared to the results of low-fidelity analysis with a short turnaround time.

A Simulation on The Approximate Optimization for Crash Analysis by using The Variable Complexity Modeling.

A Simulation on The Approximate Optimization for Crash Analysis by using The Variable Complexity Modeling.

High-Speed Civil Transport Design Space Exploration Using Aerodynamic Response Surface Approximations

A method has been developed to generate and use polynomial approximations to the range and cruise drag components in a highly constrained, multidisciplinary design optimization of a high-speed civil transport (HSCT) cone guration. The method improves optimization performance by eliminating the numerical noise present in the analyses through the use of response surface methodology. In this implementation quadratic polynomials are e t within variable bounds to data gathered from a series of numerical analyses of different aircraft designs. Because the HSCT optimization process contains noise and suffers from a nonconvex design space even when noise is e ltered out, multiple optimization runs are performed from different starting points with and without the response surface models in order to evaluate both their effectiveness as surrogate functions and as a design exploration tool. The alternative method used is variable complexity modeling (VCM). It is shown that response surface methodology facilitates design space exploration, allowing improvements in terms of both convergence performance and computational effort when multiple starting points are required, although using VCM usually produces better e nal designs.

Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper selectively surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates.

Response Surface Models Combining Linear and Euler Aerodynamics for Supersonic Transport Design

A method has been developed to efficiently implement supersonic aerodynamic predictions from Euler solutions into a highly constrained, muItidisciplinary design optimization of a High-Speed Civil Transport. The method alleviates the large computational burden associated with performing computational fluid dynamics analyses through the use of variable-complexity modeling techniques, response surface (RS) methodologies, and coarse-grained parallel computing. Using information gained from lower-fidelity aerodynamic models, reduced-term RS models representing a correction to the linear theory RS model predictions are constructed using Euler solutions. Studies into 5-, 10-, 15-, and 20-variable design problems show that accurate results can be obtained with the reduced-term models at a fraction of the cost of creating the full-term quadratic RS models. Specifically, a savings of 255 CPU hours out of 392 CPU hours required to create the full-term RS model is obtained for the 20-variable problem on a single 75MHz IP21 processor of a Silicon Graphics, Inc. Power Challenge.

A Coarse-Grained Parallel Variable-Complexity Multidisciplinary Optimization Paradigm

Modem aerospace vehicle design requires the interac tion of multiple disciplines, traditionally processed in a sequential order. Multidisciplinary optimization (MDO), a formal methodology for the integration of these disci plines, is evolving toward methods capable of replacing the traditional sequential methodology of aerospace vehi cle design by concurrent algorithms, with both an overall gain in product performance and a decrease in design time. A parallel MDO paradigm using variable-complexity modeling and multipoint response surface approxima tions is presented here for the particular instance of the design of a high-speed civil transport (HSCT). This para digm interleaves the disciplines at one level of complexity and processes them hierarchically at another level of complexity, achieving parallelism within disciplines rather than across disciplines. A master-slave paradigm manages a coarse-grained parallelism of the analysis and optimization codes required by the disciplines showing reasonable speedups and efficiencies on an Intel Paragon.