_Article_  
**Integration of Dimension Reduction and Uncertainty Quantification in Designing Stretchable Strain Gauge Sensor**  
**[PERSON]****1**, **[PERSON]****2**, **[PERSON]****3,* and [PERSON]****1,*  
1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; [EMAIL_ADDRESS]  
2 Department of Mechanical Engineering, TOBB University of Economics and Technology, 06560 Ankara, Turkey; [EMAIL_ADDRESS]  
3 School of Mechanical Engineering, Chung-Ang University, Seoul 06974, Korea  
* Correspondence: [EMAIL_ADDRESS] (H-J.C.); [EMAIL_ADDRESS] (S-K.C.); Tel.: +82-2-820-5787 (H-J.C.); +1-404-894-9218 (S-K.C.)  
Received: 29 November 2019; Accepted: 13 January 2020; Published: 16 January 2020  
**Abstract: Interests in strain gauge sensors employing stretchable patch antenna have escalated in the area of structural health monitoring, because the malleable sensor is sensitive to capturing strain variation in any shape of structure. However, owing to the narrow frequency bandwidth of the patch antenna, the operation quality of the strain sensor is not often assured under structural deformation, which creates unpredictable frequency shifts. Geometric properties of the stretchable antenna also severely regulate the performance of the sensor. Especially rugged substrate created by printing procedure and manual fabrication derives multivariate design variables. Such design variables intensify the computational burden and uncertainties that impede reliable analysis of the strain sensor. In this research, therefore, a framework is proposed not only to comprehensively capture the sensor's geometric design variables, but also to effectively reduce the multivariate dimensions. The geometric uncertainties are characterized based on the measurements from real specimens and a Gaussian copula is used to represent them with the correlations. A dimension reduction process with a clear decision criterion by entropy-based correlation coefficient dwindles uncertainties that inhibit precise system reliability assessment. After handling the uncertainties, an artificial neural network-based surrogate model predicts the system responses, and a probabilistic neural network derives a precise estimation of the variability of complicated system behavior. To elicit better performance of the stretchable antenna-based strain sensor, a shape optimization process is then executed by developing an optimal design of the strain sensor, which can resolve the issue of the frequency shift in the narrow bandwidth. Compared with the conventional rigid antenna-based strain sensors, the proposed design brings flexible shape adjustment that enables the resonance frequency to be maintained in reliable frequency bandwidth and antenna performance to be maximized under deformation. Hence, the efficacy of the proposed design framework that employs uncertainty characterization, dimension reduction, and machine learning-based behavior prediction is epitomized by the stretchable antenna-based strain sensor.**  
**Keywords: stretchable antenna-based strain sensor; structural optimization; structural health monitoring; dimension reduction; entropy-based correlation coefficient; multidisciplinary design and analysis; uncertainty-integrated and machine learning-based surrogate modeling**