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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.

Aerodynamic shape optimization of a hypersonic transport aircraft over a wide Mach-number range is challenging. The difficulty is not only associated with the large computational cost of high-fidelity CFD (computational fluid dynamics) simulations but also linked to the reasonable compromise between aerodynamic performances of aircraft at different speed ranges. This article proposes to use efficient global optimization based on surrogate models to address this type of problems. A RANS (Reynolds averaged Navier-Stokes) flow solver is adopted to evaluate objective and constraint functions; Kriging surrogate model combined with a parallel infill-sampling method and a multi-round strategy are employed to find the global optimum. First, a profile optimization with baseline airfoil of NACA64A-204 is conducted to achieve high lift-to-drag ratio ( L / D ) at both hypersonic ( Ma = 6.0 ) and transonic ( Ma = 0.8 ) regimes with up to 18 design variables, and significant improvement has been observed. Then, multi-objective wing optimizations of maximizing both hypersonic and transonic L / D s with up to 54 design variables are performed and multiple optimizations with various sets of weight coefficients are investigated. The optimized wings are further evaluated and compared with the baseline wing at the flow regimes from subsonic to hypersonic speeds. Results show that by using the optimized profile, hypersonic and transonic L / D s of a typical wing configuration are increased by 13.85% and 7.32%, respectively. After 3-D optimizations, the L / D s at hypersonic and transonic design points are further improved by 4.47% and 3.19%, respectively, and a better performance over a wide Mach-number range is obtained. It is shown that a multi-round surrogated-based optimization is feasible and effective for aerodynamic shape optimization of hypersonic transport aircrafts over a wide Mach-number range.

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 aims to develop an efficient global optimization method for design of transonic natural-laminar-flow (NLF) airfoils and wings, based on high-fidelity computational fluid dynamics (CFD) solver. The CFD solver features functionality of automatic transition prediction, by coupling Reynolds-averaged Navier-Stokes (RANS) equations with the linear-stability-theory-based dual e N method for Tollmien-Schlichting and crossflow instabilities. An A320-sized transonic NLF wing with a laminar supercritical airfoil is designed for cruise condition at Mach=0.74, Re=20 million, CL=0.515. In order to further improve the cruise efficiency, this NLF wing is optimized at higher Mach number of 0.75 via an in-house surrogate-based optimizer. The optimization is formulated as a drag minimization problem with constraints on lift, pitching moment and geometric thickness. Through only 130 CFD evaluations, 12.1 counts drag reduction is obtained, while all constraints are strictly satisfied. Further study shows that the drag reduction is contributed by both of shock-wave weakening and laminar-flow extension. On suction side, the favorable pressure gradient is maintained while shock wave is weakened; on pressure side, the crossflow (CF) instability is effectively suppressed and thereby the laminar flow region is dramatically extended. The improvement of aerodynamic performance is observed not only at design point but also over a certain range of off-design lift coefficients.

The efficiency of building a surrogate model for the output of a computer code can be dramatically improved via variable-fidelity surrogate modeling techniques. In this article, a hierarchical kriging model is proposed and used for variable-fidelity surrogate modeling problems. Here, hierarchical kriging refers to a surrogate model of a highfidelity function that uses a kriging model of a sampled lower-fidelity function as a model trend. As a consequence, the variation in the lower-fidelity data is mapped to the high-fidelity data, and a more accurate surrogate model for the high-fidelity function is obtained. A self-contained derivation of the hierarchical kriging model is presented. The proposed method is demonstrated with an analytical example and used for modeling the aerodynamic data of an RAE 2822 airfoil and an industrial transport aircraft configuration. The numerical examples show that it is efficient, accurate, and robust. It is also observed that hierarchical kriging provides a more reasonable mean-squared-error estimation than traditional cokriging. It can be applied to the efficient aerodynamic analysis and shape optimization of aircraft or any other research areas where computer codes of varying fidelity are in use.

As developing and integrating energy consumption detection system become more and more difficult, OPC technology is used to simplify the system. The integration of system can be improved largely and the development work can be decreased through OPC standard interface. Firstly, this paper introduces relative knowledge about OPC technology, and then realizes hardware and software development of energy consumption detection system in Shenyang large-scale public buildings. The result indicates that OPC can simplify system greatly and energy consumption data can be detected at real-time.

A hybrid airship denotes one kind of aircraft that combines the use of aerodynamic and buoyant lift. It is supposed to achieve the best combination of the high-speed characteristics of the airplane and the heavy-lifting capacity of the airship. In this work, an improved flight performance analysis method for a hybrid airship is proposed, aiming to provide a set of new formulas that are more suitable for a hybrid airship. The new formulas for analyzing the steady and accelerated performances of a hybrid airship are derived in a systematic way. The main advantage of the new formulas is that the relationship between the flight performances of a hybrid airship and airplane is indicated in a clearer and simpler expression. Base on the derivation, the theoretical comparisons are performed to show the advantage and disadvantage of the hybrid airship. An example of estimating flight performance of a model hybrid airship is presented to preliminarily demonstrate and evaluate the developed method, which shows a reasonable result.

An efficient method based on the surrogate-management framework has been excised to optimize the actuation parameters of active flow control over an airfoil via a synthetic jet. In this approach, sample points are chosen by the design of experiments method, and approximation models are built based on the sampled data obtained from unsteady Reynolds-averaged Navier―Stokes simulations. The accuracy of these approximation models is evaluated at some test points by comparing the approximated values with the accurate values obtained from unsteady Reynolds-averaged Navier―Stokes simulations. Three types of approximation models (quadratic response-surface model, kriging model, and radial-basis-function neutral network) are built from the same data set. The model with highest accuracy is chosen as the surrogate model to be used to replace the unsteady Reynolds-averaged Navier― Stokes analysis during optimization. The optimization objective is to maximize the lift coefficient of a NACA 0015 airfoil at given angles of attack (14 to 22°), with the jet momentum coefficient, nondimensional frequency, and jet angle being the design variables. The surrogate model is coupled with a simulated annealing genetic algorithm optimizer to efficiently obtain the global optimum. As a result of the optimization process, the lift coefficient at an angle of attack of 16° is increased by 16.9% and the corresponding drag is decreased by 13.4% with respect to the initial controlled flow. It is preliminarily shown that the presented method is efficient and applicable for optimization of active flow control via a synthetic jet.

In this paper, an efficient and accurate method based on the preconditioned advection upstream splitting method (AUSM) scheme is studied. Turkel’s preconditioning method in conjunction with the second-order finite-volume monotone upwind schemes for conservation laws (MUSCL)-type AUSMDV (a mixture of AUSMD and AUSMV where “D” and “V” denote a flux-difference splitting-biased scheme and flux-vector-splitting-biased one, respectively) and AUSM-up schemes based on the primitive variables is used to solve Navier–Stokes equations. These two schemes used in computational fluid dynamics with or without preconditioning methods are compared. The surface pressure distributions are compared with those calculated from a central difference scheme. The preconditioning method used in this paper obtains an improved convergence, stability, and the capability for the calculation of the low Mach number flows and transonic flows. The preconditioning high-resolution scheme strengthens thecapability of identifying discontinuities andreducingthe numerical dissipation.The presentmethod that combines the multigrid algorithm further accelerates the convergence. Flow-independent convergence rates of the method are also observed from the numerical results for the low Mach number flows. Nomenclature a = speed of sound Cd = drag coefficient Cl = lift coefficient Cp = pressure coefficient M = Mach number p = pressure u = component of velocity inx direction v = component of velocity iny direction w = component of velocity inz direction y=b = spanwise location � = density

[Abstract] Coupled aerodynamic and structural optimization is performed for the preliminary design of a high-subsonic transport-aircraft wing using surrogate models. The aerodynamic performance of wing/body combination in transonic flow is calculated with full-potential equation in conjunction with viscous correction method. Structural analysis is performed using finite-element method (FEM) to obtain stress and deform distribution. The span, taper ratio, sweep angle and linear twist angle are chosen as design variables that define the aerodynamic configuration of the wing. And another four representing thicknesses of spars and skin are selected as the design variables for structural discipline. After the aeroelastic analysis of the various candidate wings, the aerodynamic and structural performances are obtained such as the lift coefficient, the drag coefficient, and the deformation and equivalent stress of the wing. Based on these sample data, the approximation models for analyzing the aerodynamic and structural performances are established using surrogate models including quadratic response surface method (RSM), kriging model (KM) and radial-basis function (RBF) Network. The modeling accuracy is evaluated by numerical-error analysis. We aim to select the approximation models with best accuracy to replace the complicated and time-consuming analysis in optimization. It is found that KM and RSM has comparative high accuracy and both are more accurate than RBF. Multi-objective optimization for the supercritical wing is performed based on RSM, for maximizing lift-to-drag ratio and minimizing weight. And the optimization is constrained by lift, reference area, deform, equivalent stress. The performance of the optimal design is proven to be improved based on the initial design. And compared with the optimal design without considering aeroelastic effect, lift-to-drag ratio is increased by 5.77% and lift is increased by 19.55%. It is proven by practice that considering aeroelastic effect is necessary in priliminary design of aircraft when optimizing high-aspect-ratio wing.

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.

To work out route guidance in gigantic traffic network, the traffic information forecasting method based on Artificial Neural Network is studied in-depth and the time-varied road weight matrixes are constructed, which solve the problem of limitation in traditional and static road weight. The Parallel Genetic Algorithm (PGA) for optimal route choice is discussed in this paper and the corresponding genetic operator, mutation operator and the refresh way of the populations are also proposed. A method of Rectangle Restricted Searching Area (RRSA) which can reduce the searching area of PGA is presented. The problem of bad real-time and astringency of PGA existed in computing the optimal route in gigantic traffic network has also been solved using RRSA. To probe into the technology of the Route Guidance, a large number of experiments combined with the required analysis of the results have been carried on. It is indicated by simulation that the presented method of optimal route choice has achieved the accuracy, real-time and quick guidance in gigantic traffic network.

O VER the past decade, the hybrid method [coupling computational fluid dynamics (CFD) techniques with advanced analytic methods based on acoustic analogy, such as the Ffowcs Williams–Hawkings equation with penetrable data surface (FW–Hpds) method] has been successfully applied to predict the complicated acoustic field of helicopter rotors. The Ffowcs Williams–Hawkings (FW–H) equation [1], a rearrangement of Navier–Stokes equations by using generalfunction theory, provides an accurate theoretical model for describing the propagation of noise from a moving surface to the far field. The Farassat 1Amethod for solving the linear part of the FW–H equation was developed by Farassat and Succi [2]. It has been successfully applied in linear noise prediction [2,3] for more than 20 years. The Farassat 1A method predicts discrete frequency noise quite well, but it would run into complication when predicting nonlinear quadrupole noise of helicopter rotors, because the data surface is the blade itself and nonlinear effects are not included in the surface integral. To calculate the nonlinear noise [e.g., high-speed impulsive (HSI) noise], Farassat and Myers [4] derived the general form of the Kirchhoff equation and its solution (known as the Kirchhoff formulation) to describe the noise radiation from amoving surface. The data surface of the Kirchhoff formulation is fictitious and penetrable. The main benefit of the Kirchhoff method is that the nonlinear effect is accounted for by performing the integral on the data surface covering the nonlinear flow region. The Kirchhoff method coupled with the near-field CFD solution (called the CFD/ Kirchhoff method) has proven to be accurate and efficient when predicting impulsive noise. More recently, a new form of FW–H equation with a penetrable surface (called the FW–Hpds equation) was proposed by Crighton et al. [5] to improve the efficiency of solving the quadrupole noise. The method using a penetrable data surface for solving the FW–H equation with the Euler solution as input data was first implemented by di Francescantonio [6] for prediction of far-field noise from transonic helicopter rotors in hover. Brentner and Farassat [7] conducted an analytical comparison of the FW–Hpds method with the Kirchhoff method and concluded that the FW–Hpds method is more accurate and robust than the Kirchhoff method when the data surface is located in the nonlinear flow region. The FW–Hpds method rapidly showed promise in the studywork of a few researchers [7–10] when it was used for predicting the noise generated by helicopter rotors in hover and forward flight. More recently, Farassat and Casper [11] emphasized the role of analytical methods in computational aeroacoustics and recommended FW–Hpds as a very promising method for noise prediction of a complicated flowfield. To predict nonlinear noise generated by transonic rotors in hover, three-dimensional Euler equations were commonly used to consider the nonlinear effect related to shockwaves. To consider the influence of viscous effect in the near field and get more accurate information about noise sources, this paper uses Reynolds-Averaged Navier– Stokes (RANS) equations to model the nonlinear viscous flowfield near the rotor blades. The far-field noise is calculated by a retardedtime integral formula solving the FW–Hpds equation, with the solution of the RANS equations taken as input data.

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.

A modified advection upstream splitting method (AUSM-up) scheme is proposed to simulate the quasi-steady flow over rotary blades. Based on the chimera grid methodology, the cell centered finite-volume method (FVM) is used to solve the Reynolds-Averaged Navier-Stokes (RANS) equations described in the blade-attached rotational coordinate system with Spalart-Allmaras (S-A) and k-ω shear-stress-transport (SST) models for turbulence closure. In order to improve the computational efficiency, a full approximation storage (FAS) multi-grid technique combine with a Newton-like implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) scheme with viscous correction is utilized for time stepping. By adding the grid velocity into the cut-off Mach number Mco, a new AUSM-up scheme, named AUSM-up(R) scheme is developed and applied to a variety of different geometries, including helicopter rotors, horizontal axis wind turbine blades and low Reynolds number propellers. It is concluded that the new proposed scheme, AUSM-up(R) scheme, leads to higher resolution and more accurate solution, meanwhile the computational efficiency is almost equivalent to the commonly used Jameson’s central scheme.

The aim of the present study was to investigate the effects of RNA interference with prostaglandin-endoperoxide synthase 2 (COX‑2) gene on the proliferation and apoptosis of breast cancer MCF‑7 cells, as well as the underlying mechanism. The present study constructed the eukaryotic expression vector of the targeted COX‑2 gene, transfected the MCF‑7 cells and screened the stably expressed clone. Changes in the COX‑2 gene expression in breast cancer MCF‑7 cells prior to and following transfection were examined; the proliferation and apoptosis of MCF‑7 cells were analyzed. Furthermore, changes in the protein levels of survivin, B-cell lymphoma 2 (Bcl‑2) and Bcl-2-associated X (Bax) genes were detected. RNA interference mediated by a lentiviral expression vector significantly decreased the protein expression levels of the COX‑2 gene, and therefore, the proliferation and growth of breast cancer MCF‑7 cells was significantly suppressed and the apoptotic rate increased. Of note, the mRNA and protein expression levels of survivin and Bcl‑2 decreased, while those of Bax increased following COX-2 silencing. RNA interference markedly deactivated the COX‑2 gene, suppressed the proliferation of breast cancer MCF‑7 cells, and, to a certain extent, enhanced the induced spontaneous apoptosis, which is regulated by the Bax gene. These results provided evidence for the potential applications of RNA interference of the targeted COX‑2 gene in gene therapy for the treatment of breast cancer.

To investigate the potential use of miR-155 as novel breast cancer biomarker.There were 88 breast cancer patients underwent modified mastectomy and had detailed clinical follow-up information. Extracting RNA from the formalin-fixed paraffin embedded (FFPE) samples, miR-155 levels were quantified by real-time-PCR. miR-155 levels among clinico-pathological variables were accessed by Mann Whitney-U test. Overall survival curve was derived from Kaplan-Meier estimates and the curve was compared by Log-rank test. Cox regression analysis was used for multivariate analysis. All statistical tests were two-sided.Significantly higher miR-155 level was found in tumor tissue compared to paired normal tissue (t = 6.75, P = 0.000). A potential relationship between miR-155 levels and existing clinico-pathological parameters of breast cancer, such as menstrual status, tumor size, nodal involvement, stage of disease, hormone receptor status, HER-2 status, histological grade or tumor subtype was investigated. Up-regulated miR-155 level was observed in breast cancer with lymph node metastasis, pT3+4, advanced TNM stage, HER-2 positive and with vascular invasion (Z = -6.320 to -2.041, P = 0.000 to 0.041). When considering 2(-ΔCt) = 4.87 (median level) as cut-off value, patients with miR-155 up-regulation showed a positive association towards a shorter overall survival (χ(2) = 6.396, P = 0.011). In Cox multivariate analysis, miR-155 expression on FFPE was shown an inverse trend for outcomes of breast cancer (HR = 1.58, 95%CI: 0.87 - 3.16, P = 0.082).miR-155, as an oncomir, promotes lymph node involvement and vascular invasion and accompanies over-expressed HER-2 on breast cancer FFPE tissue. It suggests that miR-155 could predict the invasiveness.

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.

Design of airfoils specially tailored for wind turbine blades has dramatic influence on the performance of a wind turbine. The traditional way for wind turbine airfoil design is a kind of trial and error process. In order to improve the design efficiency was well as the performance of the design, numerical optimization methods coupling optimization algorithm with CFD codes in an automatic process chain are of great interest. This study is focused on the development of efficient numerical optimization design methods for wind turbine airfoils. The main feature is to use surrogate-based optimization. Surrogate-based optimization is very efficient and has the capability of finding global optima; it can be classified as the third-type optimization method other than the traditional gradient-based methods and gradient-free searching methods, such as evolutional algorithms. Optimization designs of FFA-W3-211, inverse design of NPU-WA-300 and realistic numerical optimization of NPU-WA-250 are exercised. Examples show that the developed methods are efficient and robust, with sufficient flexibility of handling both geometric and aerodynamic constraints, multi-points design and multi-objective design.

This paper summarizes recent progress in developing metamodels for efficiently predicting the aerodynamic loads acting on industrial aircraft configurations. We introduce a physics-based approach to reduced-order modeling based on proper orthogonal decomposition of snapshots of the full-order CFD model, and a mathematical approach to variable-fidelity modeling that aims at combining many low-fidelity CFD results with as few high-fidelity CFD results as possible using bridge functions and variants of Kriging and Cokriging. In both cases, the goal is to arrive at a model that can be used as an efficient surrogate to the original high-fidelity or full-order CFD model but with significantly less evaluation time and storage requirements. Both approaches are demonstrated on industrial aircraft configurations at subsonic and transonic flow conditions.

Surrogate modeling plays an increasingly important role in different areas of aerospace engineering, such as erodynamic shape optimization, aerodynamic data production, structural design, and multidisciplinary design optimization of aircraft or spacecraft. Cokriging provides an attractive alternative approach to conventional kriging to improve the efficiency of building a surrogate model. It was initially proposed and applied in the geostatistics community for the enhanced prediction of less intensively sampled primary variables of interest with the assistance of intensively sampled auxiliary variables. As the underlying theory of cokriging is that of two-variable or multivariable kriging, it can be regarded as a general extension of (one-variable) kriging to a model that is assisted by auxiliary variables or secondary information. In an attempt to apply cokriging to the surrogate modeling problems associated with deterministic computer experiments, this article is motivated by the development of an alternative cokriging method to address the challenge related to the construction of the covariance matrix of cokriging [7]. Earlier work done by other authors related to this study can be found in the statistical community. For example, Kennedy and O’Hagan (KOH) proposed an autoregressive model to calculate the covariances and crosscovariances in the covariance matrix and developed a Bayesian approach to predict the output from an expensive high-fidelity simulation code with the assistance of lower-fidelity simulation codes. This Bayesian approach is identical to a form of cokriging suitable for computer experiments. Later, Qian andWu proposed a similar method, in which a random function (Gaussian process model) was used to replace the constant multiplicative factor of KOH’s method to account for the nonlinear scale change. KOH’s method was applied to multifidelity analysis and design optimization in the context of aerospace engineering by Forrester et al. and Kuya et al. More recently, Zimmerman and Han proposed a cokriging method with simplified cross-correlation estimation. In this article, we propose an alternative approach for the construction of the cokriging covariance matrix and develop a more practical cokriging method in the context of surrogate-based analysis and optimization. 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.

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.

Gradient-based optimization using adjoint method has proved effective for automatic aerodynamic shape optimization via high-fidelity Computational Fluid Dynamics (CFD) methods. Past experience suggests that its optimization efficiency and robustness are crucially affected by the step size along a direction of descending. In this paper, a surrogate modeling method based on gradient-enhanced Kriging is exercised to determinate the step size of adjoint-based optimization and a routine for adjoint-based aerodynamic design has been proposed. Representative results are presented for the inverse design of a RAE 2822 airfoil. It is found that the efficiency as well as robustness of adjoint-based aerodynamic optimization can be dramatically improved. Nomenclature

A Variable-Fidelity Modeling (VFM) method has been developed as an efficient and accurate aerodynamic data modeling strategy. In this approach, a set of CFD methods with varying degrees of fidelity and computational expense is exercised to reduce the number of expensive high-fidelity computations. Kriging-based bridge functions are constructed to match the low- and high fidelity CFD data. The method is demonstrated by constructing a global approximation model of the aerodynamic coefficients of an RAE 2822 airfoil based on sampled data. The model is adaptively refined by inserting additional samples. It is shown that the method is promising for efficiently generating accurate aerodynamic models that can be used for the rapid prediction of aerodynamic data across the flight envelope.

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.

A fexible non-intrusive approach to parametric uncertainty quantifcation problems is developed, aimed at problems with many uncertain parameters, and for applications with a high cost of functional evaluations. It employs a Kriging response surface in the parameter space, augmented with gradients obtained from the adjoint of the deterministic equations. The Kriging correlation parameter optimization problem is solved using the Subplex algorithm, which is robust for noisy functionals, and whose effort typically increases only linearly with problem dimension. Integration over the resulting response surface to obtain statistical moments is performed using sparse grid techniques, which are designed to scale well with dimensionality. The efficiency and accuracy of the proposed method is compared with probabilistic collocation, direct application of sparse grid methods, and Monte-Carlo initially for model problems, and finally for a 2d compressible Navier-Stokes problem with a random geometry parameterized by 4 variables.

Hybrid airship denotes one kind of aircraft that combines the use of aerodynamic and buoyant lift. It is supposed to achieve the best combination of the high speed characteristics of the airplane and the heavy lifting capacity of the airship. In this work, an improved flight performance analysis method for hybrid airship is proposed, aiming to provide a set of new formulas that are more suitable for hybrid airship. The new formulas for analyzing the steady and accelerated performances of hybrid airship are derived out in a systematic way. The main advantage of the new formulas is that the relationship between the flight performances of hybrid airship and airplane is indicated in a clearer and simpler expression. Base on the derivation, it is concluded that the ratio of aerodynamic lift to the total lift, the effective power-to-weight ratio, the effective wing loading are three key parameters that affects the performances of hybrid airship. An example of designing a winged hybrid airship is presented to demonstrate and evaluate the developed method. Nomenclature C H = airship pressure height (The airship pressure height [1] is defined as the height at which the ballonets are fully deflated and is therefore the maximum height to which the airship can climb without overpressuring the envelope or venting gas) a ρ = gas density of air ( a,c ρ is the gas density of air at airship pressure height) h ρ = gas density of lifting gas ( h,c ρ is the gas density of lifting gas at airship pressure height) ship V = airship volume ' ship V = volume of the helium ballonet inside the airship ship

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.

In this paper, hierarchical clustering method is introduced for attribute discretization. It can determine automatically the significant clusters. First, the best classes for discretization are picked from scatter plots of several statistics. Moreover, these classes keep consistent with extracted clusters from dendrograms. By comparison, hierarchical clustering discretization method is typically more effective and advisable among several cluster algorithms with the defect inspection of wood veneer