Over the past decade, classical probabilistic analysis has been a popular approach among the uncertainty quantification methods. As the complexity and performance requirements of a structural system are increased, the quantification of uncertainty becomes more complicated, and various forms of uncertainties should be taken into consideration. Because of the need to characterize the distribution of probability, classical probability theory may not be suitable for a large complex system such as an aircraft, in that our information is never complete because of lack of knowledge and statistical data. Evidence theory, also known as Dempster-Shafer theory, is proposed to handle the epistemic uncertainty that stems from lack of knowledge about a structural system. Evidence theory provides us with a useful tool for aleatory (random) and epistemic (subjective) uncertainties. An intermediate complexity wing example is used to evaluate the relevance of evidence theory to an uncertainty quantification problem for the preliminary design of airframe structures. Also, methods for efficient calculations in large-scale problems are discussed.
A design framework for rapid creation of feasible high-speed vehicle configurations is developed. High-speed vehicles operate under extreme mechanical and thermal operating conditions that require multidisciplinary analysis at multiple fidelity levels. For a conceptual design framework, the first step in developing vehicle configurations is a parameterized geometry which allows for multidisciplinary analysis. A new parameterized model was created from an existing generic high-speed vehicle that was previously developed in 2012. The parameterized model was developed in Engineering Sketch Pad and integrated with an analysis software using pyCAPS. For a preliminary study, an internal structure was developed for the generic vehicle and the vehicle was structurally analyzed with the vehicle surfaces optimized under aerodynamic pressure loading conditions.
Emulator embedded neural networks are a type of physics informed neural network which can leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network models can be trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty, leading to goal-oriented adaptive learning for more useful predictions of system response. While emulator embedded neural networks are scalable to high dimensional problems, they can require significant training costs, especially for ensembles of models, depending on the network structure and size of the data set. This can pose a computational challenge when conducting adaptive learning and design exploration of an aerospace system, especially if parallel training of multiple models is not implemented. In this work, a new type of emulator embedded neural network is developed using the rapid neural network paradigm. This involves initializing a neural network with randomly chosen weights and biases. Only the last layer's weights and biases are adjusted, using linear regression techniques such as Ridge regression or Lasso. This skips the lengthy gradient descent training process entirely, resulting in near-instantaneous creation of the emulator embedded neural network model. The proposed method is demonstrated on multiple analytical examples, as well as a preliminary aerospace design study of a generic hypersonic vehicle.
The design of thermal structures in the aerospace industry, including exhaust structures on embedded engine aircraft and hypersonic thermal protection systems, poses a number of complex design challenges that can be particularly well addressed using the material layout capabilities of structural topology optimization. However, no topology optimization methods are readily available with the necessary thermoelastic design capabilities as a significant portion of work in the topology optimization field is focused on cases of maximum stiffness design for structures subjected to externally applied mechanical loads. In addition, in the limited work on thermoelastic topology optimization, a direct treatment of thermal stresses, which are a primary consideration in thermal structures design, has not been demonstrated. Thus, in this paper, we present a method for the topology optimization of structures with combined mechanical and thermoelastic (temperature) loads that are subject to stress constraints. We present the necessary steps needed to address both the design-dependent thermal loads and accommodate the challenges of stress-based design criteria. A modern stress relaxation technique is utilized to remove the singularity phenomenon in stresses and the large number of constraints that result in the optimization problem are handled using a scaled aggregation technique that is shown to satisfy prescribed stress limits. Finally, the stress-based thermoelastic formulation is applied to two numerical example problems to demonstrate its effectiveness.
View Video Presentation: https://doi.org/10.2514/6.2021-3059.vid A new approach of unsupervised neural network-based kriging is proposed to capture non-stationary responses under uncertainty of a complex and high-dimensional system, such as a conceptual hypersonic vehicle. It is well known that typical kriging formulated with the assumption of stationarity of data variations fails to capture non-stationary system behaviors and having a large number of training samples causes numerical difficulties in kriging modeling, especially for high-dimensional aerospace systems. To address the computational challenges, the proposed approach uses unsupervised learning to cluster samples by localized spatial correlations of data variations. For each cluster, a kriging model is constructed by training a neural network model of correlation hyperparameters to capture non-stationary data variations. The predictions from the multiple kriging models are aggregated into a consensus prediction by using non-deterministic gaussian regression. The proposed method would enable us to 1) capture non-stationary system behaviors, 2) divide one large data set into multiple clusters with manageable sizes to avoid computational issues, 3) use parallel modeling of localized krigings for identified clusters, and 4) update local models adaptively and efficiently, instead of retraining the entire model. The proposed method is demonstrated with fundamental analytical examples, as well as a representative hypersonic vehicle design problem.
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