Abstract: 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 to-pology with a densely arranged layout that exploits a combination of high- and low-impedance transmission line sections. All relevant dimensions of the struc-ture are simultaneously optimized in order to explicitly reduce the coupler size while maintaining equal power split at the operating frequency of 1 GHz and suf-ficient bandwidth for return loss and isolation characteristics. Acceptable levels of electrical performance are ensured by using a penalty function approach. Two de-signs with footprints of 350 mm2 and 360 mm2 have been designed and experi-mentally 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.

Abstract: Probability of detection (POD) is used for reliability analysis of nondestructive testing systems. POD is determined by experiments, but it can be enhanced by information through physics-based simulation models and model-assisted probability of detection (MAPOD) methods. Due to time-consuming evaluations of the physics-based models and a large random input parameter space, MAPOD analysis can be impractical to complete in a timely manner. In this paper, we use stochastic polynomial chaos expansions (PCE) in place of the true model to accelerate the MAPOD analysis. In particular, we use state-of-the-art least-angle regression method and hyperbolic sparse technique to construct the PCE. The proposed method is demonstrated on a spherically-void-defect benchmark problem developed by the World Federal Nondestructive Evaluation Center. In this work, the benchmark problem is setup with two random input parameters. The results show that accurate MAPOD analysis obtained with the proposed approach. Moreover, the proposed framework requires around 100 samples for the convergence on the statistical moments, whereas direct Monte Carlo sampling (MCS) with the true model needs over 10,000 samples, and MCS with the deterministic Kriging model does not converge due to its inability to accurately represent the true model.

Abstract: We present an efficient way to solve the Bethe-Salpeter equation (BSE), which is developed to model collective excitation of electron-hole pairs in molecules and solids. The BSE is an eigenvalue problem. The Bethe--Salpeter Hamiltonian matrix to be diagonalized requires at least $O(N_e^5)$ operations with a large pre-constant to construct, where $N_e$ is proportional to the number of electrons in the system, in a conventional approach. This can be extremely costly for large systems. Our approach is based on using the interpolative separable density fitting (ISDF) technique to construct low-rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. This approach allows us to reduce the complexity of the Hamiltonian construction to $O(N_e^3)$ with a much smaller pre-constant. We implement this ISDF method for the BSE calculations under the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. We show that the ISDF based BSE calculations in molecules and solids can produce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.

Abstract: 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.