Xiaosong Du

Application of Multifidelity Optimization Techniques to Benchmark Aerodynamic Design Problems

Two-dimensional benchmark cases involving lift-constrained drag minimization in inviscid and viscous transonic flows are solved using derivative-free multi-fidelity optimization algorithms (space mapping and manifold mapping) and are compared with direct gradient-based optimization algorithms using adjoint sensitivities and trust regions. With 8 B-spline design variables, the multi-fidelity algorithms yield optimized shapes comparable to the shapes obtained by the direct algorithms but at a fraction of the cost. In particular for the inviscid case, the multi-fidelity algorithms needed less than 150 equivalent high-fidelity model evaluations (only flow solutions) taking approximately 460 minutes on a HPC with 32 processors, whereas the direct algorithm needed 391 high-fidelity model evaluations (flow and adjoint) taking approximately 4,494 minutes on the same HPC. For the viscous case, the multi-fidelity algorithms yield an optimized shape using less than 125 equivalent high-fidelity evaluations taking approximately 17.4 hours on the HPC. The direct algorithm was unsuccessful in optimizing the baseline shape in this case. A simple variation of surrogate-based optimization, the sequential approximate optimization (SAO), is utilized to optimize the twist distribution of a rectangular unswept wing in inviscid flow. Using 3 Bspline design variables, the SAO algorithm is able to obtain an optimized design with a nearelliptic section lift distribution. The total optimization cost is 22 high-fidelity model evaluations or approximately 42.5 hours on a HPC with 32 processors.

Model-assisted probability of detection of flaws in aluminum blocks using polynomial chaos expansions

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination withmodel-assisted POD (MAPOD) methods. With the development of advanced physics-basedmethods, such as ultrasonic NDTtesting, the empirical information,needed for POD methods, can bereduced. However, performing accurate numerical simulationscan be prohibitivelytimeconsuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through thephysics-basedsimulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using nonintrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary leastsquares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw inanaluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation modelfor this case,which is the UTSim2 model.

Surrogate modeling of ultrasonic simulations using data-driven methods

Ultrasonic testing (UT) is used to detect internal flaws in materials and to characterize material properties. In many applications, computational simulations are an important part of the inspection-design and analysis processes. Having fast surrogate models for UT simulations is key for enabling efficient inverse analysis and model-assisted probability of detection (MAPOD). In many cases, it is impractical to perform the aforementioned tasks in a timely manner using current simulation models directly. Fast surrogate models can make these processes computationally tractable. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to integrate data-driven methods (here, kriging interpolation with variable-fidelity models to construct an accurate and fast surrogate model. These techniques are investigated using test cases involving UT simulations of solid components immersed in a water bath during the in...

Model-Assisted Probability of Detection for Structural Health Monitoring of Flat Plates

The paper presents a computational framework for assessing quantitatively the detection capability of structural health monitoring (SHM) systems for flat plates. The detection capability is quantified using the probability of detection (POD) metric, developed within the area of nondestructive testing, which accounts for the variability of the uncertain system parameters and describes the detection accuracy using confidence bounds. SHM provides the capability of continuously monitoring the structural integrity using multiple sensors placed sensibly on the structure. It is important that the SHM can reliably and accurately detect damage when it occurs. The proposed computational framework models the structural behavior of flat plate using a spring-mass system with a lumped mass at each sensor location. The quantity of interest is the degree of damage of the plate, which is defined in this work as the difference in the strain field of a damaged plate with respect to the strain field of the healthy plate. The computational framework determines the POD based on the degree of damage of the plate for a given loading condition. The proposed approach is demonstrated on a numerical example of a flat plate with two sides fixed and a load acting normal to the surface. The POD is estimated for two uncertain parameters, the plate thickness and the modulus of elasticity of the material, and a damage located in one spot of the plate. The results show that the POD is close to zero for small loads, but increases quickly with increasing loads.

Stochastic-Expansions-Based Model-Assisted Probability of Detection Analysis of the Spherically-Void-Defect Benchmark Problem

Probability of detection (POD) is used for reliability analysis in nondestructive testing (NDT) area. Traditionally, it is determined by experimental tests, while it can be enhanced by physics-based simulation models, which is called model-assisted probability of detection (MAPOD). However, accurate physics-based models are usually expensive in time. In this paper, we implement a type of stochastic polynomial chaos expansions (PCE), as alternative of actual physics-based model for the MAPOD calculation. State-of-the-art least-angle regression method and hyperbolic sparse technique are integrated within PCE construction. The proposed method is tested on a spherically-void-defect benchmark problem, developed by the World Federal Nondestructive Evaluation Center. The benchmark problem is added with two uncertainty parameters, where the PCE model usually requires about 100 sample points for the convergence on statistical moments, while direct Monte Carlo method needs more than 10000 samples, and Kriging based Monte Carlo method is oscillating. With about 100 sample points, PCE model can reduce root mean square error to be within 1% standard deviation of test points, while Kriging model cannot reach that level of accuracy even with 200 sample points.

Explicit Size-Reduction-Oriented Design of a Compact Microstrip Rat-Race Coupler Using Surrogate-Based Optimization Methods

In this paper, an explicit size reduction of a compact rat-race coupler implemented in a microstrip technology is considered. The coupler circuit features a simple topology with a densely arranged layout that exploits a combination of high- and low-impedance transmission line sections. All relevant dimensions of the structure are simultaneously optimized in order to explicitly reduce the coupler size while maintaining equal power split at the operating frequency of 1 GHz and sufficient bandwidth for return loss and isolation characteristics. Acceptable levels of electrical performance are ensured by using a penalty function approach. Two designs with footprints of 350 mm2 and 360 mm2 have been designed and experimentally validated. The latter structure is characterized by 27% bandwidth. For the sake of computational efficiency, surrogate-based optimization principles are utilized. In particular, we employ an iterative construction and re-optimization of the surrogate model involving a suitably corrected low-fidelity representation of the coupler structure. This permits rapid optimization at the cost corresponding to a handful of evaluations of the high-fidelity coupler model.

Expedite Design of Variable-Topology Broadband Hybrid Couplers for Size Reduction Using Surrogate-Based Optimization and Co-Simulation Coarse Models

Abstract In this paper, we discuss a computationally efficient approach to expedite design optimization of broadband hybrid couplers occupying a minimized substrate area. Structure size reduction is achieved here by decomposing an original coupler circuit into low- and high-impedance components and replacing them with electrically equivalent slow-wave lines with reduced physical dimensions. The main challenge is reliable design of computationally demanding low-impedance slow-wave structures that feature a quasi-periodic circuit topology for wideband operation. Our goal is to determine an adequate number of recurrent unit elements as well as to adjust their designable parameters so that the coupler footprint area is minimal. The proposed method involves using surrogate-based optimization with a reconfigurable co-simulation coarse model as the key component enabling design process acceleration. The latter model is composed in Keysight ADS circuit simulator from multiple EM-evaluated data blocks of the slow-wave unit element and theory-based feeding line models. The embedded optimization algorithm is a trust-region-based gradient search with coarse model Jacobian estimation. We exploit a penalty function approach to ensure that the electrical conditions for the slow-wave lines are accordingly satisfied, apart from explicitly minimizing the area of the coupler. The effectiveness of the proposed technique is demonstrated through a design example of two-section 3-dB branch-line coupler. For the given example, we obtain nine circuit design solutions that correspond to the compact couplers whose multi-element slow-wave lines are composed of unit cells ranging from two to ten.

Airfoil Design Under Uncertainty Using Non-Intrusive Polynomial Chaos Theory and Utility Functions

Abstract Fast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated for the design of airfoil shapes under uncertainty. The proposed approach is illustrated on a numerical example of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable. The results show that compared with the standard problem formulation the proposed approach yields more robust designs. In other words, the designs obtained by the proposed approach are less sensitive to variations in the uncertain variables than those obtained with the standard problem formulation.

Pareto Ranking Bisection Algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces.

Abstract A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.