## 1 Introduction
In the computer-based design and analysis of stretchable antennas for a strain gauge, usually, an assumption of uniform thickness is made to reduce design complexity and computational burden. However, if the randomness corresponding to the thickness is overlooked, reliable response assessment of the MSP antenna-based strain sensor can be impeded. As already proven by various simulations and measurements [15; 16; 17; 18; 19; 20], although the analysis of the non-uniform substrate-based antenna is always more complicated than that of constant substrate-based antenna, it involves better reliability predictions as the approach corresponding to the uneven substrate represents the real environment. Thus, it is absolutely imperative to examine the thickness variation to improve the reliability of the antenna-based sensor. Unfortunately, however, considering the roughness would bring extremely increased computational costs as well as total number of design variables (DVs). It is indispensable to capture and propagate all possible critical variables and the corresponding uncertainties to ensure that the system is reliable, but such an approach would incur high dimensions of DVs, increasing computational complexity [21]. Furthermore, once the DVs are contaminated by the immensely correlated random behavior, the extravagant variables obstruct the reliability of the performance estimation [22; 23]. To eliminate these issues, a rigorous design of stretchable electronics based on efficient capturing and modeling of correlated and high dimensional random variables is required [24]. Therefore, this study proposed a dimension reduction (DR) framework to effectively manage uncertainties especially occurring for the substrate thickness. In the framework, a Gaussian copula is utilized [25] to precisely model the intricacy of DVs. The intricacy can be described by a joint distribution that consists of manifold marginal distributions. After modeling the geometric uncertainties, a clear guideline engaging the entropy-based correlation coefficient was exploited to suggest a better decision between feature extraction and selection. Through the guideline, engineers can embrace a competent choice of an efficient DR method based on multivariate data properties. In accordance with the entropy-based correlation coefficient, two DR methods, particularly feature extraction and feature selection, diminish the overabundance of the DVs. Specifically, the performance of two feature extraction methods (principal component analysis (PCA) [26] and auto-encoder (AE) [27]) are evaluated to identify the one that gives the best predictions, while feature selection employs independent features test (IFT) [28]. Details will be addressed in the following sections. The second drawback is about the narrow bandwidth, which often fails to warrant the operation of the MSP antenna for measuring strain. In general, information transferred by a radio frequency system is only trustworthy within the desired frequency bandwidth. Owing to the unforeseen structural deformation that produces extreme frequency shifts, the stretchable strain sensor cannot perform stable detection when the frequency deviates from an allowable bandwidth. To handle this issue,  
Figure 1: Stretchable antenna. (**a**) The antenna (dark color) and the polydimethylsiloxane (PDMS) substrate (light color); (**b**) scratched surface of the substrate observed by FEI Quanta 250 scanning electron microscope (SEM) device. manifold solutions have been proposed. Specifically, the ultra-wideband (UWB) wireless system is used to facilitate multiple broadband and a high data rate, which enlarges the range for frequency activity [29]. However, the solution is not convincing owing to the complicated design process, power limitation, and standardization. Other approaches engaging optimization techniques also exist, but most have focused on sizing adjustment of the antenna [30].