Projection Pursuit Gaussian Process Regression

A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is high. Gaussian process models with additive correlation functions are scalable to dimensionality, but they are very restrictive as they only work for additive functions. In this work, we consider a projection pursuit model, in which the nonparametric part is driven by an additive Gaussian process regression. The dimension of the additive function is chosen to be higher than the original input dimension. We show that this dimension expansion can help approximate more complex functions. A gradient descent algorithm is proposed to maximize the likelihood function. Simulation studies show that the proposed method outperforms the traditional Gaussian process models

Silent and Efficient Supersonic Bi-Directional Flying Wing

The supersonic bi-directional (SBiDir) flying wing (FW) concept has a great potential to achieve low sonic boom with high supersonic aerodynamic performance due to removal of performance conflict between high speed and low speed by rotating goo in flight. This NIAC Phase 1 research has achieved three objectives: 2) prove the concept based on simulation that it can achieve very low boom with smooth Sine wave ground over-pressure signature and excellent aerodynamic efficiency; 3) conduct trade study to correlate the geometric parameters with sonic boom and aerodynamic performance for further automated design optimization in Phase II. The design methodology developed in Phase I includes three parts: 1) an advanced geometry model, which can vary airfoil meanline angle distribution to control the expansion and shock waves on the airplane surface to mitigate sonic boom and improve aerodynamic efficiency. 2) a validated CFD procedure to resolve near field flow with accurate shock strength. The sonic boom propagation from near field to far field ground is simulated by NASA NF Boom code. The surface friction drag prediction is based on fiat plate correlation adopted by Seebass and supported by the experimental study of Winter and Smith, which is on the conservative side and is more reliable than CFD RANS simulation. 3) a mission analysis tool based on Corke's model that provides design requirements and constraints of supersonic airplanes for range, payload, volume, size, weight, etc. The design mission target is a supersonic transport with cruise Mach number 1.6, 100 passengers, and 4000nm range. The trade study has several very important findings: 1) The far field ground sonic boom signature is directly related to the smoothness of the flow on the airplane surface. The meanline angle distribution is a very effective control methodology to mitigate surface shock and expansion wave strength, and mitigating compression wave coalescing by achieving smooth loading distribution chord-wise. Compared with a linear meanline angle distribution, a design using nonlinear and non-monotonic meanline angle distribution is able to reduce the sonic boom ground loudness by over 20dBP1. The design achieves sonic boom ground loudness less than 70dBP1 and aerodynamic dynamic efficiency 1/D of 8.4. 2) Decreasing sweep angle within the Mach cone will increase 1/D as well as sonic boom. A design with variable sweep from 84 at the very leading edge to 68 at the tip achieves an extraordinarily high 1/D of 10.4 at Mach number 1.6 due to the low wave drag. If no sonic boom constraint is attached, SBiDir-FW concept still has a lot of room to increase the 1/D. 3) The round leading edge and trailing edge under high sweep angle are beneficial to improve aerodynamic performance, sonic boom, and to increase volume of the airplane. 4) Subsonic performance is benefited greatly from the high slenderness of supersonic configuration after rotating goo. A design with excellent supersonic aspect ratio of 0.44, 1/D of 8.g, gives an extraordinary subsonic aspect ration of 10 and 1/D of 1g.7. Two configurations are designed in details to install internal seats, landing gears, and engine installation to demonstrate the feasibility of SBiDir-FW configuration to accommodate all the required volume for realistic airplane. Here we emphasize that the qualitative findings in Phase I are very encouraging, more important than the quantitative results. Qualitative findings give the understanding of physics and provide the path to achieve the ultimate high performance design. The promising quantitative results achieved in Phase I need to be confirmed by wind tunnel testing in Phase II and ultimately proved by flight test. The other important step forward will be made to study the rotation transition from both CFD unsteady simulation and wind tunnel testing

Data-Efficient Design and Analysis Methodologies for Computer and Physical Experiments

Data science for experimentation, including the rapidly growing area of the design and analysis of computer experiments, aims to use statistical approaches to collect and analyze (physical or virtual) experimental responses and facilitate decision-making. The cost for each run of an experiment can be expensive. This dissertation proposes novel data-efficient methodologies to tackle three different challenges in this field. The first two are regarding computer experiments, and the third one is regarding physical experiments. The first work aims to reconstruct the input-output relationship (surrogate model) given by the computer code via scattered evaluations with small sizes based on Gaussian process regression. Traditional isotropic Gaussian process models suffer from the curse of dimensionality when the input dimension is relatively high given limited data points. Gaussian process models with additive correlation functions are scalable to dimensionality, but they are more restrictive as they only work for additive functions. In the first work, we consider a projection pursuit model in which the nonparametric part is driven by an additive Gaussian process regression. We choose the dimension of the additive function higher than the original input dimension and call this strategy “dimension expansion”. We show that dimension expansion can help approximate more complex functions. A gradient descent algorithm is proposed for model training based on the maximum likelihood estimation. Simulation studies show that the proposed method outperforms the traditional Gaussian process models. The second work focuses on the designs of experiments (DoE) of multi-fidelity computer experiments with fixed budget. We consider the autoregressive Gaussian process model and the optimal nested design that maximizes the prediction accuracy subject to the budget constraint. An approximate solution is identified through the idea of multilevel approximation and recent error bounds of Gaussian process regression. The proposed (approximately) optimal designs admit a simple analytical form. We prove that, to achieve the same prediction accuracy, the proposed optimal multi-fidelity design requires much lower computational cost than any single-fidelity design in the asymptotic sense. The last work is proposed to model complex experiments when the distributions of training and testing input features are different (referred to as domain adaptation). In this work, we propose a novel transfer learning algorithm called Renewing Iterative Self-labeling Domain Adaptation (Re-ISDA) to tackle the domain adaptation problem. The learning problem is formulated as a dynamic programming model, and the latter is then solved by an efficient greedy algorithm by adding a renewing step to the original ISDA algorithm. This renewing step helps avoid a potential issue of the ISDA that the possible mis-labeled samples by a weak predictor in the initial stage of the iterative learning can cause serious harm to the subsequent learning process. Numerical studies show that the proposed method outperforms prevailing transfer learning methods. The proposed method also achieves high prediction accuracy for a cervical spine motion problem

Boundary Layer Loss Mechanism and Justification of Wall Functions for Turbulence Modeling

The AIAA Aerospace Sciences Meeting is the first major multidisciplinary event of the year for aerospace scientists and engineers from around the world to share and disseminate scientific knowledge and research results with a view toward new technologies for aerospace systems. The wide range of topics includes aircraft design, applied aerodynamics, atmospheric flight mechanics, design engineering, education, fluid dynamics, ground testing, history, homeland security, multidisciplinary design optimization, plasmadynamics and lasers, software systems, space exploration, systems engineering, thermophysics, and much more. A paper on Boundary Layer Loss Mechanism and Justification of Wall Functions for Turbulence Modeling presented at the 2004 Aerospace Sciences Meeting

Investigation of Mixed Micro-Compressor Casing Treatment Using Non-Matching Mesh Interface

Abstract In this paper, a non conservative interpolation boundary condition, for the non-matching mesh blocks, was developed and validated for the micro compressor casing treatment. The conservative variables were interpolated in the halo layers of non-matching mesh interface using Finite Element Method (FEM) type linear interpolation shape functions, instead of using overset grids. Using this new boundary condition, the effect of casing treatment on stall margin and compressor performance is investigated for a mixed flow type micro-compressor. The computed compressor performance map for the casing treatment case is compared with the experimental results and shows good agreement except in the region close to stall. With the application of the casing treatment, improvement in the stall margin is observed without the loss of efficiency over the operating range

Distortion elimination for serpentine duct at various Mach numbers using co-flow jet active flow control

This paper numerically investigates Co-flow Jet (CFJ) active flow control (AFC) for eliminating the AGARD M2129 serpentine inlet distortion with throat Mach number (Mth) varying from 0.42 to 0.79. The configuration was optimized at design Mth of 0.79 in a prior study. The current objective is to investigate the CFJ S-duct performance at off-design Mth with the fixed geometry. The high-order FASIP in-house code is used to conduct 3D Reynolds Averaged Navier-Stokes (RANS) simulation with the one-equation Spalart-Allmaras (S-A) turbulence model. The CFD simulation is well validated with the experiment of AGARD test cases in the studied Mach numbers. Results show that CFJ virtually eliminates the flow distortion for all the studied Mth. However, the off design Mth have lower energy efficiency. At the design Mth, CFJ requires the lowest power coefficient (Pc) to eliminate the flow separation and distortion. The exergy analysis indicates that CFJ S-duct at the design Mth has the highest system energy efficiency with the EIPR (ratio of exergy increase to the power required) exceeding 1. At the off-design Mth, EIPR is lower than 1 because the shifts of separation-onset spot and adverse-pressure-gradient region make CFJ injection and suction no longer at the most efficient location. This leads to the rising of the CFJ power coefficient even though the actual power is less. Nevertheless, the overall system is still very efficient at off-design Mth for the CFJ S-duct with the CFJ energy expenditure recovered by 72%, 90%, 96% for Mth of 0.42, 0.55, and 0.69, respectively