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In recent years, multi-layered hierarchical compositions of the well-known and widely used Gaussian process models called deep Gaussian processes are finding use in the approximation of black-box functions. In this paper, the performance of deep Gaussian process models is empirically evaluated and compared against the well-established Gaussian process models with a special emphasis on engineering problems. The work draws conclusions through detailed comparisons in terms of metrics such as computational training cost, data requirement, predictive error, and robustness to the choice of the initial design of experiments. Additionally, the viability and robustness of Deep Gaussian process models for applications on practical engineering problems are analyzed through sensitivity to hyperparameters and scalability with respect to the input space dimensionality respectively. Finally, the models are also compared in an adaptive construction setting, where they are built sequentially by selecting points that maximize posterior variance. Experiments are conducted on canonical test functions with varying input dimensions, an engineering test function, and a practical transonic airfoil test case with a high-dimensional input space. The experiments suggest that deep Gaussian process models outperform traditional Gaussian process models in terms of accuracy at the cost of incurring a significantly higher computational expense for the training procedure. The sensitivity studies indicate that inducing points is the most important hyperparameter that affects deep Gaussian process performance and training time. This work empirically shows that deep Gaussian processes are promising candidates for problems that are known to be nonlinear, high-dimensional, and when limited training data is available.

Deep Gaussian process (DGP) models are multi-layered hierarchical generalizations of the well-known Gaussian process (GP) models widely used to construct surrogate models of aerodynamic quantities of interest. Combining the desirable features of GP models and deep neural networks (DNN), DGP models are known to perform well when training data is scarce and the behavior of the system response is highly non-stationary. In this paper, the performance of DGP models is evaluated against GP models. Detailed comparisons are made and conclusions are drawn in terms of training time, data requirements, predictive error, and robustness to choice of training design of experiments, among other metrics. Additionally, sensitivity and scalability analyses are conducted for the DGP models to evaluate their usability. Finally, an adaptive construction of both models is presented, where the models are built sequentially by selecting points that maximize posterior variance. Several experiments are conducted with canonical test functions at varying input dimensions and a viscous transonic airfoil test case at 42 input dimensions. The experiments suggest that DGP models outperform traditional GP models in terms of accuracy but incur higher computational costs for training.

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In recent years, hybrid airships have been identified as promising alternatives for high altitude, long endurance missions. In this study, a design methodology to study the feasibility of a winged hybrid airship powered by solar energy is presented. The proposed methodology involves five disciplines of the airship, viz., geometry, aerodynamics, environment, energy and structures that have been coupled in order to develop an optimum design which incorporates the maximum advantages of the modules. A total of fourteen design variables have been finalized, which are required to carry out the sizing of the envelope, wing, and solar panel layout. The Particle Swarm Optimization (PSO) algorithm is implemented to carry out optimization of a user-defined fitness function for given user-defined operating conditions. The optimization study is subjected to general constraints of weight balance and energy balance. Optimal solutions have been obtained for two different configurations. These are—conventional airship and winged hybrid airship. The solutions have been obtained for four different days of the year, in order to analyse any potential benefits and pitfalls of the two configurations for the varying conditions over the course of one year. The results obtained are generally found to be in excellent agreement with the imposed constraints. The winged hybrid airship configuration was found to have offered no significant benefits in comparison to the conventional configuration. The analysis of the key parameters and data values readily supports this conclusion.

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