The proposed study develops a framework that accurately captures and models input and output variables for multidisciplinary systems in order to mitigate the computational cost when uncertainties are involved. Under this framework, the dimension of the random input variables is reduced depending on the degree of correlation calculated by an entropy based correlation coefficient (e). According to the obtained value of e, the dimension is truncated by two different methods. First feature extraction methods, namely Principal Component Analysis and the Auto-Encoder algorithm, are utilized when the input variables are highly correlated. In contrast, the Independent Features Test is implemented as the feature selection method if the correlation is too low to select a critical subset of model features. An Artificial Neural Network, including a Probabilistic Neural Network, is integrated into the framework to correctly capture the complex response behavior of the multidisciplinary system with low computational cost. The efficacy of the proposed method is demonstrated with electro-mechanical engineering examples, including a solder joint and a stretchable patch antenna.
Strain gauges based on the micro-strip patch antenna have been increasingly employed in structural health monitoring. However, the lower bandwidth, influenced by the antenna’s geometric properties, limits efficiency of the antenna when major strain, creating drastic variation of the resonant frequency, is applied. The performance of the antenna cannot be guaranteed without also considering the substrate’s varying thickness, caused by manual fabrication and printing procedure. However, all such considerations lead to an increase of multivariate design variables, that in turn, increase uncertainty and computational costs. Thus, the proposed research develops a framework that accurately models the geometric variables of the antenna and efficiently reduces the multivariate dimensions that draw uncertainty preventing accurate system reliability estimation. In the proposed framework, a dimension reduction method is thoroughly conducted by utilizing a critical decision criterion depending on the degree of correlation. Specifically, artificial neural network and probabilistic neural network are employed to correctly estimate the variability of complex system responses. Furthermore, an optimal design of the stretchable patch antenna is developed. This design will allow frequency shifts under tensile strain and still remain within reliable frequency ranges. The proposed approach is beneficial to the process of capturing and managing antenna design variables. The presented example clearly demonstrates the advantage of the obtained optimal design of the stretchable patch antenna compared to an ultra-wideband radar system that often requires complicated design processes and high computational costs.
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.
The design of strongly coupled multidisciplinary engineering systems is challenging since it is characterized by the complex interaction of different disciplines. Such complexity cannot be easily captured by explicit analytical solutions, which motivates the development of surrogate modeling. It enables the prediction of the systems’ behavior without analytical formulations. Among existing surrogate modeling techniques, deep learning has gained significant interest because of the flexibility of non-linear formulation and applicability to data-driven analysis. Notably, the convolution neural networks-based deep surrogate model augments the precision of prediction and estimation of system behavior once image-based inputs representing physical experiments and simulation are employed. Nevertheless, the feasibility of the deep surrogate model is often flawed due to the miserable correlation representation between design parameters and the corresponding responses. Massive training costs also degrade the performance of the predictive model. To address those issues, this research proposes a physics-informed artificial image (PiAI) that incubates geometry-informed CAD, location-clarified filter, and essential simulation conditions, which augments the prediction credibility. Moreover, in lieu of employing multimodalities or multiple image channels, the proposed method employs a unimodal-based single image input to increase computational efficiency. The proposed framework’s efficacy and applicability are addressed in practical engineering design applications: cantilever beam and stretchable strain sensor.
As the trend of miniaturization of electronic components has grown, demands for advanced microelectronics packaging development have also increased. At the same time, however, this trend raises concerns of unreliable assembly processes that are caused by defective packaging interconnections. In particular, the defects can be induced by non-coplanarity and unpredictable structural deformation of interconnections. When a slope of the die exceeds a certain degree, connectivity between components in the package may fail, which results in warpage or electrical power loss. To control this issue, thermo-compression bonding has been developed to globally apply heat and pressure into the die while the substrate is maintained at a low stage temperature. Therefore, in order to effectively handle these issues, strongly coupled thermal and structural analysis is inevitable. In this research, a simulation-based optimal design of thermo-compression bonding is developed to achieve better packaging reliability in the time transient domain. The proposed framework clearly demonstrates how the multivariate uncertain parameters can be generated. Also, it suggests how the multivariate uncertainty can be propagated through the classification approach, i.e., artificial neural network. The classification approach is then utilized to estimate the reliability of the system. The efficacy of the proposed framework is demonstrated with a practical example of an advanced packaging system which is utilized in actual commercial products. Ultimately, this study demonstrates how the strong coupling optimization method can be utilized in the actual packaging system.
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