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The flapping motion has a great impact on the aerodynamic performance of flapping wings. In this paper, a surging motion is added to an airfoil performing pitching-plunging combined motion to figure out how it influences the lift performance and flow pattern of flapping airfoils. Firstly, the numerical methods are validated by a NACA0012 airfoil pitching case and a NACA0012 airfoil plunging case. Then, the E377m airfoil which has typical geometric characteristics of the bird-like airfoil is selected as the calculation model to study how phase differences φ1 between surging motion and plunging motion affect the aerodynamic performance of flapping airfoils. The results show that the airfoil with surging motion has comprehensively better lift performance and thrust performance than the airfoil without surging motion when 15°

Accurate prediction of tip vortices is crucial for predicting the hovering performance of a helicopter rotor. A new high-order scheme (we call it WENO-K) proposed by our research group is employed to minimize numerical dissipation and extended to numerical simulation of unsteady compressible viscous flows dominated by tip vortices over hovering rotors. WENO-K is referred to as an adaptively optimized WENO scheme with Gauss-Kriging reconstruction, and its advantage is to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities. Here WENO-K scheme is adopted to reconstruct left and right state values within the Roe Riemann solver updating the inviscid fluxes on a structured dynamic overset grid. To minimize the accuracy loss for high-order reconstruction on artificial boundaries of overset grid, a method of multilayer fringes is proposed to carry out interpolation between background grid and blade grid. Massively parallel computing considering automatic load balance on averagely partitioned overset grid is developed to reduce the wall-clock time of an unsteady simulation. Numerical results for Caradonna-Tung (C-T) rotor in hover at the conditions of subsonic and transonic tip Mach numbers show that the thrust coefficient error for the result of WENO-K scheme is no more than 3%. Compared with WENO-JS scheme, WENO-K scheme achieves about 40% improvement on accuracy of predicting rotor thrust with only 4.1% extra computational cost. More importantly, WENO-K scheme can capture more sophisticated unsteady flow structures and resolve tip vortices to a larger wake age with an increment of about 270° compared to WENO-JS scheme.

To improve robustness and efficiency of automatic transition prediction in aerodynamic design, a reduced model of linear stability analysis is usually adopted, such as eN-envelope or eN-database me...

Rotor noise is one of the most important reasons for restricting helicopter development; hence, the optimization design of rotor blade considering aeroacoustic and aerodynamic performance at the same time has always been the focus of research attention. For complex rotor design problems with a large number of design variables, the efficiency of the traditional Kriging model needs to be improved. Thus, Hierarchical Kriging (HK) model is employed in this study for rotor optimization design. By using the validated RANS solver and acoustic method based on the FW–Hpds equation, an efficient aerodynamic/aeroacoustic optimization method for high-dimensional problem of rotors in hover based on HK model is developed. By using present HK model and new infill-sampling criteria, the number of design variables is increased from less than 20–53. Results of two analytical function test cases show that the HK model is efficient and accurate in calculation. Subsequently, the helicopter rotor blade is optimally designed for aerodynamic/aeroacoustic performance in hover based on the HK model with high dimensional design variables. The objective function is adopted to improve the rotational noise characteristics by reducing the absolute peak of the acoustic pressure. In addition, the constraints of thrust, hover efficiency, solidity, and airfoils thickness are strictly satisfied. Optimization results show that the Kriging model finds the objective of reducing the noise by 2.87 dB after 248 iterations while the HK model does it only after 164 iterations. The optimization efficiency of the HK model is significantly higher than that of the traditional Kriging model. In the case analyzed, the HK model saves 35% of the time used by the Kriging model. Keywords: Aeroacoustics, Design optimization, FW-Hpds equation, Helicopter rotor, RANS equations

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation, with assistance of lower-fidelity and cheaper simulation(s). However, most existing works only incorporate “two” levels of fidelity, and thus efficiency improvement is very limited. In order to reduce the number of high-fidelity simulations as many as possible, there is a strong need to extend it to three or more fidelities. This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design. Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging (MHK), which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity. The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids, which are determined through a grid convergence study. First, sampling shapes are selected for each level of fidelity via technique of Design of Experiments (DoE). Then, CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective (e.g. CD) and constraint (e.g. CL, Cm) functions. Next, new samples are selected through infill-sampling criteria and the surrogate models are repetitively updated until a global optimum is found. The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows. The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method. Keywords: Aerodynamic shape optimization, Computational fluid dynamics, Hierarchical kriging, Kriging, Surrogate model

Expensive multiobjective optimization problem poses a big challenge. In many real-world engineering design problems, the time-consumed function evaluation is done by solving partial differential equations. The partial derivatives of a candidate solution can be calculated as a byproduct. Naturally, these problems can be solved more efficiently if gradient information is used. This paper proposes such a method, called MOEA/D-GEK, which combines MOEA/D and gradient-enhanced Kriging to solve expensive multiobjective problem. The gradient information is used for the construction of the Kriging model. Experimental studies on a set of test instances and a real-world aerodynamic design problem show high efficiency and effectiveness of our proposed method.

The method of aggregating a large number of constraints into one or few constraints has been successfully applied to wing structural design using gradient-based local optimization. However, numerical difficulties may occur in the case that the local curvatures of the aggregated constraint become extremely large and then ill-conditioned Hessian matrix may be yielded. This paper aims to test different methods of constraint aggregation within the framework of a gradient-free optimization, which makes use of cheap-to-evaluate surrogate models to find the global optimum. Three constraint aggregation approaches are investigated: the maximum constraint approach, the constant parameter Kreisselmeier-Steinhauser (KS) function, and the adaptive KS function. We also explore methods of aggregating constraints over the entire structure and within sub-domains. Examples of structural optimization and aero-structural optimization for a transport aircraft wing are employed and the results show that (1) the KS function with a larger constant parameter ρ can lead to better optimization results than the adaptive method, as the active constraints are approximated more accurately; (2) lumping the constraints within sub-domains instead of all together can improve the accuracy of the aggregated constraint and therefore helps find a better design. Finally, it is concluded from current test cases that the most efficient way of handling large-scale constraints for wing surrogate-based optimization is to aggregate constraints within sub-domains and with a relatively large constant parameter.

The efficient global optimization method (EGO) based on kriging surrogate model and expected improvement (EI) has received much attention for optimization of high-fidelity, expensive functions. However, when the standard EI method is directly applied to a variable-fidelity optimization (VFO) introducing assistance from cheap, low-fidelity functions via hierarchical kriging (HK) or cokriging, only high-fidelity samples can be chosen to update the variable-fidelity surrogate model. The theory of infilling low-fidelity samples towards the improvement of high-fidelity function is still a blank area. This article proposes a variable-fidelity EI (VF-EI) method that can adaptively select new samples of both low and high fidelity. Based on the theory of HK model, the EI of the high-fidelity function associated with adding low- and high-fidelity sample points are analytically derived, and the resulting VF-EI is a function of both the design variables x and the fidelity level l. Through maximizing the VF-EI, both the sample location and fidelity level of next numerical evaluation are determined, which in turn drives the optimization converging to the global optimum of high-fidelity function. The proposed VF-EI is verified by six analytical test cases and demonstrated by two engineering problems, including aerodynamic shape optimizations of RAE 2822 airfoil and ONERA M6 wing. The results show that it can remarkably improve the optimization efficiency and compares favorably to the existing methods.

Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES–RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES–RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

For real-world engineering design optimizations, it is of great significance to find approximate optimal designs with least number of expensive functional evaluations. This paper proposes to use a surrogate-based multi-objective evolutionary algorithm (SBMO) to address this type of problems. The basic idea is to decompose a multi-objective optimization problem into a number of scalar optimization subproblems and to optimize them simultaneously in a simple-to-implement manner, in which global surrogate models are used to enable full cooperation between subproblems. First, initial samples are selected by design of experiments and expensive simulations are conducted to evaluate them. Second, global surrogate models for objective (and constraint) functions are built through the sampled data and the optimization subproblems are solved simultaneously to suggest new samples. Third, the surrogate models are updated and the optimization proceeds to the next generation. This process is repeated until satisfactory Pareto-front solutions are found. Thanks to decomposition strategy, the infill-sampling criteria and constraint handling dedicated for a single-objective optimization can be directly used in a SBMO. The difference between SBMO and the existing methods such as MOEA/D-EGO is that a combined infill-sampling strategy and dedicated constraint handling are used. Benchmark test cases have demonstrated that SBMO is efficient, robust and has good capability of constraint handling. SBMO has been applied to multi-objective aerodynamic shape optimization of a transonic airfoil. It has been shown that SBMO is well suited for engineering design problems where expensive numerical simulations are employed.

The surrogate-assisted optimization algorithms (SAOAs) are very promising for solving computationally expensive optimization problems (EOPs). Generally, the performance of a SAOA is determined by the quality of its surrogate model and the infill sampling criterion. In this paper, we propose a radial basis function (RBF) assisted optimization algorithm with batch infill sampling criterion for solving EOPs (short for RBFBS). In RBFBS, the quality of RBF model is adjusted by choosing a good shape parameter via solving a sub-expensive hyperparameter optimization problem. Moreover, a batch infill sampling criterion that includes a bi-objective-based sampling approach and a single-objective-based sampling approach is proposed to get a batch of samples for expensive evaluation. The experimental results on various benchmark problems show that RBFBS is very promising for expensive optimization.

For a black box data-space exploration, classical DoE method prescribes a cluster of quasi-isotropic design points following a certain space-infill criterion, however the objective function behaves. Adding new points often disturbs the original spatial-infill properties, which restricts dimension-augmentation and reusability of data. Surrogate model based sequential design considers not only the spatial features of the design space but also the characteristic of the objective function. The latter may favor a highly anisotropic design for the sake of computational effort effectiveness, especially when highly informative samples are used. This work presents a high anisotropy design solution when derivative-assisted co-Kriging method is employed. Adaptation of this method has been proposed for the special case where only one single sample appears at certain dimensions. A 2-dimensional test function with distinctive spatial properties at each dimension is composed and used to assess the validity of the proposed method.

An adaptive finite-difference WENO method with Gauss-Kriging reconstruction (we call it WENO-K) is proposed to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities for hyperbolic system of conservation laws. The method adopts a kriging model with non-polynomial Gauss exponential function to obtain new reconstruction coefficients that contain a hyper-parameter. By adaptively optimizing the hyper-parameter and automatically identifying troubled cells using newly developed indicators, the accuracy in the smooth region is obviously improved. Compared with the classical WENO-JS method, the proposed WENO-K method provides more accurate reconstructions and sharper solution profiles near discontinuities. Furthermore, the WENO-K method is easy to implement in an existing classical WENO code with less than 13%∼16% of additional computational cost. Numerical results demonstrate that the proposed method outperforms the WENO-JS method for a broad range of problems. This method is supposed to be applied to other variants of WENO scheme and offers the potential of improving their accuracy.

With the development of smart city, the concept of smart development is integrated into the construction management, so as to promote the smart development of construction and improve the efficiency of construction management. This paper discusses the application prospect of GIS-BIM integration technology in construction schedule management, site material management and safety management of construction personnel. At the same time, it looks into the application trend of gis-bim integration technology and global wide area network, Internet of things, virtual reality and other emerging technologies in the integration of building construction management, so as to promote the intelligent and visual management development of gis-bim integration technology in building construction management.

The number of aerodynamic analysis in the design optimization of propeller has been reduced significantly by using the surrogate model, such as kriging. In this paper, a more efficient aerodynamic design optimization method of propeller is proposed by using the HK (hierarchical kriging) model. The high-fidelity model is defined as a RANS (Reynolds- Averaged Navier-Stokes) simulation for propeller and the low-fidelity model is defined as the results by blade-element/vortex theory. Initial samples are selected for two levels of fidelity via LHS (Latin Hypercube Sampling). The aerodynamic performance of varying fidelity is used to build variable-fidelity surrogate models for functions of objective (e.g. thrust) and constraint (e.g. shaft power). Infill sampling criteria, including MSP (minimizing of surrogate prediction), EI (expected improvement), PI (probability of improvement), LCB (lower-confidence bounding) and MSE (mean-squared error) are used to obtain new samples, and the surrogate models are repetitively updated until a global optimum is found. High-altitude propellers are optimized by the kriging model and hierarchical kriging model, respectively. Compared to kriging model, the number of RANS solving by the hierarchical kriging model is reduced 37.5%, and the optimization time is reduced 24.3%. The results have shown that the proposed design method for propeller can significantly improve the optimization efficiency.

Double-ended airfoils with round leading and trailing edges outperform conventional round-nose and sharp trailing-edge airfoils when used for the inboard part of a rigid coaxial rotor operating in forward flight, as reverse flow can occupy 80% surface of the retreating blade. However, aerodynamic design optimization for this kind of airfoils is challenging, since it is required to achieve drag reduction over a wider lift range in both forward and reverse flows but there is no method available currently. To address this problem, this article proposes an efficient hybrid inverse/optimization design method that combines inverse design and direct optimization within a surrogate-based optimization (SBO) framework. The weighted objective function consists of two components: prescribed pressure distributions and total drag. The resulting constrained optimization problem is solved by using kriging surrogate model and dedicated infill-sampling method. The proposed method is demonstrated by aerodynamic shape optimizations of a DBLN-526 airfoil and an elliptical airfoil and compared with direct optimization method. For DBLN-526 airfoil case, 7%–30% drag reduction is achieved in the range from zero lift to maximum lift and the optimum airfoil features better stall characteristics. For the case of elliptical airfoil of 40% thickness, significant drag reduction is achieved in both forward and reverse flows and the optimum airfoil features more robust aerodynamic performance at off-design Mach numbers. The results confirm that the proposed method outperforms the conventional direct optimization method and more practical for aerodynamic shape optimization of double-ended airfoils.

Aerodynamic shape optimization driven by high-fidelity computational fluid dynamics (CFD) simulations is still challenging, especially for complex aircraft configurations. The main difficulty is not only associated with the extremely large computational cost, but also related to the complicated design space with many local optima and a large number of design variables. Therefore, development of efficient global optimization algorithms is still of great interest. This study focuses on demonstrating surrogate-based optimization (SBO) for a wing-body configuration representative of a modern civil transport aircraft parameterized with as many as 80 design variables, while most previous SBO studies were limited to rather simple configurations with fewer parameters. The freeform deformation (FFD) method is used to control the shape of the wing. A Reynolds-averaged Navier-Stokes (RANS) flow solver is used to compute the aerodynamic coefficients at a set of initial sample points. Kriging is used to build a surrogate model for the drag coefficient, which is to be minimized, based on the initial samples. The surrogate model is iteratively refined based on different sample infill strategies. For 80 design variables, the SBO-type optimizer is shown to converge to an optimal shape with lower drag based on about 300 samples. Several studies are conducted on the influence of the resolution of the computational grid, the number and randomness of the initial samples, and the number of design variables on the final result.

Aiming at the error of same type sensors' data in household greenhouse environment, data-level fusion is used to reduce the error and obtain more accurate value of same type sensors' data. In order to improve the precision and reliability of data-level fusion, a weighting-coefficient construction method based on support degree and adaptive-weighted is proposed, which not only ensures the reliability of data fusion, but also makes the fusion result more stable. The accuracy of data fusion directly determines the precision and quality of greenhouse intelligent control. The experimental results show that the fusion result adopting the proposed method of this paper is superior to the result of traditional average-estimation fusion and data fusion based on support degree.

Variable-fidelity surrogate modeling offers an efficient way to generate aerodynamic data for aero-loads prediction based on a set of CFD methods with varying degree of fidelity and computational expense. In this paper, direct Gradient-Enhanced Kriging (GEK) and a newly developed Generalized Hybrid Bridge Function (GHBF) have been combined in order to improve the efficiency and accuracy of the existing Variable-Fidelity Modeling (VFM) approach. The new algorithms and features are demonstrated and evaluated for analytical functions and are subsequently used to construct a global surrogate model for the aerodynamic coefficients and drag polar of an RAE 2822 airfoil. It is shown that the gradient-enhanced GHBF proposed in this paper is very promising and can be used to significantly improve the efficiency, accuracy and robustness of VFM in the context of aero-loads prediction.

This paper presents the results of applying direct and surrogate-based optimization (SBO) algorithms to two-dimensional aerodynamic benchmark problems, both involving transonic flow, one invisvid and the other viscous. The direct optimization methods used in this study are the adjoint-based FUN3D and Stanford University Unstructured solvers. The SBO algorithms include the SurroOpt framework, which exploits approximation-based models, the multi-level optimization (MLO) algorithm, which relies on physics-based models, as well as the adjoint-enhanced MLO algorithm. The results demonstrate that direct optimization and the approximation-based methods are able to yield designs that are comparable to those obtained with high-dimensional shape parameterization methods. Physics-based SBO shows a rapid design improvement at a low computational cost compared to the direct and the approximation-based SBO techniques, which indicates that—for certain problems—derivative-free methods may be competitive to adjoint-based algorithms when embedded in surrogate-assisted frameworks. On the other hand, global search approaches, while more expensive, exhibit the potential to produce the best quality results.

Surrogate modeling plays an increasingly important role in multidisciplinary design optimization (MDO) associated with different areas of aerospace science and engineering. As a recent developed surrogate modeling method, support vector regression (SVR) has good capability of filtering numerical noise and is well suited for surrogate modeling problems with high nonlinearity. This work is focused on evaluation of SVR-based surrogate modeling method for the potential applications in aircraft conceptual design. Three numerical examples and an aerodynamic data prediction example are presented to show the accuracy of SVR for functions of varying complexity with and without numerical noises, and the key parameters of SVR model are studied. The SVR model is applied to the MDO problem of designing a general aviation airplane and good design result is obtained. The examples show that, SVR provides sufficient flexibility of switching between regression and interpolation, can filter noise and predict the functions well with a small number of samples, and is promising in aerodynamic data prediction and aircraft conceptual design.

Surrogate-based optimization (Queipo et al. 2005, Simpson et al. 2008) represents a class of optimization methodologies that make use of surrogate modeling techniques to quickly find the local or global optima. It provides us a novel optimization framework in which the conventional optimization algorithms, e.g. gradient-based or evolutionary algorithms are used for sub-optimization(s). Surrogate modeling techniques are of particular interest for engineering design when high-fidelity, thus expensive analysis codes (e.g. Computation Fluid Dynamics (CFD) or Computational Structural Dynamics (CSD)) are used. They can be used to greatly improve the design efficiency and be very helpful in finding global optima, filtering numerical noise, realizing parallel design optimization and integrating simulation codes of different disciplines into a process chain. Here the term “surrogate model” has the same meaning as “response surface model”, “metamodel”, “approximation model”, “emulator” etc. This chapter aims to give an overview of existing surrogate modeling techniques and issues about how to use them for optimization.

Cokriging is a statistical interpolation method for the enhanced prediction of a less intensively sampled primary variable of interest with assistance of intensively sampled auxiliary variables. In the geostatistics community it is referred to as two- or multi-variable kriging. In this paper, a new cokriging method is proposed and used for variable-fidelity surrogate modeling of aerodynamic data obtained with an expensive high-fidelity CFD code, assisted by data computed with cheaper lower-fidelity codes or by gradients computed with an adjoint version of the high-fidelity CFD code, or both. A self-contained derivation as well as the numerical implementation of this new cokriging method is presented and the comparison with the autoregressive model of Kennedy and O’Hagan is discussed. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil based on sampled CFD data. The numerical examples show that it is efficient, robust and practical for the surrogate modeling of aerodynamic data based on a set of CFD methods with varying degrees of fidelity and computational expense. It can potentially be applied in the efficient CFD-based aerodynamic analysis and design optimization of aircraft.

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.

[Abstract] A hybrid method for computational prediction of aeroacoustic noise from a helicopter rotor in forward flight is presented and investigated. This method is a combination of URNS (Unsteady Reynolds-averaged Naiver-Stokes) Method and FWHpds(Ffowcs Williams-Hawkings equation with Penetrable Data Surface) method. The aerodynamic flowfield near rotor blades is calculated by solving URNS equations with a cellcentered finite-volume scheme. The URNS equations are solved on a moving overset grid system that allows for prescribed pitching and flapping motion of rotor blades. The far-field noise is predicted by using the method based on Ffowcs Williams-Hawkings equation with penetrable data surface (FW-Hpds) covering the nonlinear flow region. The computed results are compared with experimental data and reasonably good agreement has been achieved. The results are also compared with that of Euler/FW-Hpds method. This comparison shows that the present method based on URNS equations is more accurate for the prediction of High-Speed Impulsive (HSI) noise and Blade-Vortex Interaction (BVI) noise generated by helicopter rotor in forward flight.