Variable-Fidelity Simulation Models and Sparse Gradient Updates for Cost-Efficient Optimization of Compact Antenna Input Characteristics

Abstract

Design of antennas for the Internet of Things (IoT) applications requires taking into account several performance figures, both electrical (e.g., impedance matching) and field (gain, radiation pattern), but also physical constraints, primarily concerning size limitation. Fulfillment of stringent specifications necessitates the development of topologically complex structures described by a large number of geometry parameters that need tuning. Conventional optimization procedures are typically too expensive when the antenna is evaluated using high-fidelity electromagnetic (EM) analysis, otherwise required to ensure accuracy. This paper proposes a novel surrogate-assisted optimization algorithm for computationally efficient design optimization of antenna structures. In the paper, the optimization of antenna input characteristic is presented, specifically, minimization of the antenna reflection coefficient in a given bandwidth. Our methodology involves variable-fidelity EM simulations as well as a dedicated procedure to reduce the cost of estimating the antenna response gradients. The latter is based on monitoring the variations of the antenna response sensitivities along the optimization path. The procedure suppresses the finite-differentiation-based sensitivity updates for variables that exhibit stable gradient behavior. The proposed algorithm is validated using three compact wideband antennas and demonstrated to outperform both the conventional trust region algorithm and the pattern search procedure, as well as surrogate-based procedures while retaining acceptable design quality.

Microwave systems design centering exploiting space mapping technology and modified trust region algorithm

“…8. Update the quadratic model using the updating formulas (12)- (16), then set k = k + 1, and go to Step 3. 9.…”

“…Recently, the algorithmic acceleration of TR routines through sparse Jacobian matrix updates are presented. 15,16 Regarding microwave systems design centering, there is another big challenge, besides the aforementioned difficulties. In any EM-based system, to get only one value of the yield function at a given deign point, a computationally expensive full-wave electromagnetic simulator is to be invoked many times, at the generated sample points.…”

Antenna Modeling Using Variable-Fidelity EM Simulations and Constrained Co-Kriging

“…Expediting design procedures that require repetitive references to the EM model has been the subject of extensive research over the recent years. Available solutions include incorporation of adjoint sensitivities into gradientbased routines [11], [12], algorithmic improvements of conventional methods (e.g., suppression of finite-differentiation sensitivity updates [13], [14]), exploring response features (e.g., [15], [16]), or utilization of surrogate models, both physics-based (space mapping [17], manifold mapping [18], adaptive response scaling [19]) and data-driven (response surfaces [20], kriging [21], neural networks [22]), as well as machine learning techniques [23], [24].…”

Improved-Efficacy Optimization of Compact Microwave Passives by Means of Frequency-Related Regularization

“…Given the aforementioned challenges, it is no surprise that the development of methods for accelerating EM-driven design procedures has been widely researched over the last decades. The available techniques include gradient-based routines expedited by adjoint sensitivities [32], [33] or sparse Jacobian updates [34], [35], as well as surrogate-assisted algorithms involving approximation models [36]- [38] and variable-fidelity simulations [39]- [41]. A representative example of the latter is space mapping [42] widely used in microwave engineering [43].…”