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Significant reductions in environmental impact and operating costs are achievable when both aircraft configuration and operation are considered simultaneously at the early stages of aircraft design. The challenges with combining these disciplines are that the design space becomes larger, and each design evaluation requires coupled analyses. This paper presents a methodology in which a low-speed aerodynamic model and a trajectory simulation are integrated to study trades between aircraft performance, environmental impact, and cost. Four studies are conducted using this method to illustrate ways to reduce the environmental impacts of future airplanes in a future air-traffic system. First, a study of the departure procedure for the Boeing 747-200 shows that significant benefits are possible by modifying the current procedures without changing the aircraft. For instance, from the start of takeoff roll to 10,000 feet the following are mutually achievable: a 37% reduction in climb time, a 26% reduction in fuel consumption, a 26% reduction in 55 EPNdB noise exposure area, and a 2.6% reduction in operating costs. A second example analyzes trades between noise and operating cost and considers current noise taxation schemes. Then, the sensitivity of the takeoff and approach noise certification procedures are presented to show it is possible to simultaneously evaluate both configuration and operational changes. The results of these studies are that takeoff noise is insensitive to small configuration changes, but procedural modifications can have a significant impact. For approach, the noise can be significantly reduced through either configuration or procedural changes.

This paper introduces a computational strategy to determine optimal sets of sensor locations to support real-time operational decisions. We exploit unsupervised learning strategies (specifically self-organizing maps) to identify the most informative locations to place sensors. The sensor placement procedure is then combined with a Multi-Step-Reduced Order Modeling approach that exploits the low-dimensional map between the sparse sensed data and the decisions at hand. The approach is demonstrated for the real-time assessment of an unmanned aircraft wing panel undergoing structural degradation. For this application, we compare the optimal sets of sensor locations with random placements for a variety of sensor availabilities. By adopting our placement strategy, we achieve improvements in accuracy and robustness of capability predictions, even when measured data are sparse and cover less than 10% of the reference data., United States. Air Force. Office of Scientific Research (Grant FA9550-16-1-0108), SUTD-MIT International Design Centre (IDC)

Deciding how to represent and manage uncertainty is a vital part of designing complex systems. Widely used is a probabilistic approach—assigning a probability distribution to each uncertain variable. However, this presents the designer with the task of assuming or estimating these probability distributions from data; a task which is inevitably prone to error. This paper addresses this challenge by formulating a distributionally robust design optimization problem, and presents computationally ecient algorithms for solving the problem. In distributionally robust optimization (DRO) methods, the designer acknowledges that they are unable to exactly specify a probability distribution for the uncertain variables, and instead specifies a so-called ambiguity set of possible distributions. This paper uses an acoustic horn design problem to explore how the error incurred in estimating a probability distribution from data a↵ects the realized performance of designs found using a traditional multi-objective optimization under uncertainty. It is found that placing some importance on a risk reduction objective results in designs that are more robust to these errors, and thus have a better mean performance realized under the true distribution than if the designer were to focus all e↵orts on optimizing for mean performance alone. In contrast, the DRO approach is able to uncover designs that are not attainable using the multi-objective approach when given the same data. These DRO designs in some cases significantly outperform those designs found using the multi-objective approach., United States. Air Force. Office of Scientific Research (Grant FA9550-16-1-0108)

One important task of uncertainty quantification is propagating input uncertainties through a system of interest to quantify the uncertainties’ effects on the system outputs; however, numerical methods for uncertainty propagation are often based on Monte Carlo estimation, which can require large numbers of numerical simulations of the numerical model describing the system response to obtain estimates with acceptable accuracies. Thus, if the model is computationally expensive to evaluate, then Monte-Carlo-based uncertainty propagation methods can quickly become computationally intractable. We demonstrate that multifidelity methods can significantly speedup uncertainty propagation by leveraging low-cost low-fidelity models and establish accuracy guarantees by using occasional recourse to the expensive high-fidelity model. We focus on the multifidelity Monte Carlo method, which is a multifidelity approach that optimally distributes work among the models such that the mean-squared error of the multifidelity estimator is minimized for a given computational budget. The multifidelity Monte Carlo method is applicable to general types of low-fidelity models, including projection-based reduced models, data-fit surrogates, response surfaces, and simplified-physics models. We apply the multifidelity Monte Carlo method to a coupled aero-structural analysis of a wing and a flutter problem with a high-aspect-ratio wing. The low-fidelity models are data-fit surrogate models derived with standard procedures that are built in common software environments such as Matlab and numpy/scipy. Our results demonstrate speedups of orders of magnitude compared to using the high-fidelity model alone., United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Award FA9550-15-1-0038)

Digital Thread offers the opportunity to use information generated across the product lifecycle to design the next generation of products. In this paper, we introduce a mathematical methodology that establishes the data-driven design and decision problem associated with Digital Thread. Our objectives are twofold: 1) Provide a mathematical definition of Digital Thread in the context of conceptual and preliminary design and establish a methodology for how information along the Digital Thread enters into the design problem as well how design decisions affect the Digital Thread. 2) Develop a data-driven design method that incorporates data from different sources from across the product life cycle. We illustrate aspects of our methodology through an example design of a structural fiber-steered composite component., United States. Air Force. Office of Scientific Research (Grant FA9550-16-1-0108), SUTD-MIT International Design Centre (IDC)

This paper presents a multifidelity method for optimization under uncertainty for aerospace problems. In this work, the effectiveness of the method is demonstrated for the robust optimization of a tailless aircraft that is based on the Boeing Insitu ScanEagle. Aircraft design is often affected by uncertainties in manufacturing and operating conditions. Accounting for uncertainties during optimization ensures a robust design that is more likely to meet performance requirements. Designing robust systems can be computationally prohibitive due to the numerous evaluations of expensive-to-evaluate high-fidelity numerical models required to estimate system-level statistics at each optimization iteration. This work uses a multifidelity Monte Carlo approach to estimate the mean and the variance of the system outputs for robust optimization. The method uses control variates to exploit multiple fidelities and optimally allocates resources to different fidelities to minimize the variance in the estimates for a given budget. The results for the ScanEagle application show that the proposed multifidelity method achieves substantial speed-ups as compared to a regular Monte-Carlo-based robust optimization., United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (FA9550-15-1-0038)

Optimization requires the quantities of interest that define objective functions and constraints to be evaluated a large number of times. In aerospace engineering, these quantities of interest can be expensive to compute (e.g., numerically solving a set of partial differential equations), leading to a challenging optimization problem. Bayesian optimization (BO) is a class of algorithms for the global optimization of expensive-to-evaluate functions. BO leverages all past evaluations available to construct a surrogate model. This surrogate model is then used to select the next design to evaluate. This paper reviews two recent advances in BO that tackle the challenges of optimizing expensive functions and thus can enrich the optimization toolbox of the aerospace engineer. The first method addresses optimization problems subject to inequality constraints where a finite budget of evaluations is available, a common situation when dealing with expensive models (e.g., a limited time to conduct the optimization study or limited access to a supercomputer). This challenge is addressed via a lookahead BO algorithm that plans the sequence of designs to evaluate in order to maximize the improvement achieved, not only at the next iteration, but once the total budget is consumed. The second method demonstrates how sensitivity information, such as gradients computed with adjoint methods, can be incorporated into a BO algorithm. This algorithm exploits sensitivity information in two ways: first, to enhance the surrogate model, and second, to improve the selection of the next design to evaluate by accounting for future gradient evaluations. The benefits of the two methods are demonstrated on aerospace examples.

This paper presents a new approach for optimization under uncertainty in the presence of probabilistic, interval, and mixed uncertainties, avoiding the need to specify probability distributions on uncertain parameters when such information is not readily available. Existing approaches for optimization under these types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Here, horsetail matching is extended for use with these types of uncertainties to overcome some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems, the design of a wing using a low-fidelity coupled aerostructural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis.

This paper considers the e↵ects of uncertainty on multidisciplinary analysis estimates used in conceptual aircraft design. Specifically, the paper presents an analysis of the stability and control (S&C) characteristics of an illustrative Blended-Wing-Body (BWB) configuration using uncertain aerodynamic estimates. The S&C properties of a BWB are highly nonlinear, and as such pose a challenge for low-fidelity analysis techniques. By propagating bounds on uncertain aerodynamic data them through the analysis, bounds are derived for the resulting S&C limits. These estimates can then be used to guide future research and development e↵orts. Results demonstrate that even moderate uncertainty in estimating aerodynamic lift, drag, and moment coecients translates into large uncertainty in estimating the center of gravity limits, due to the highly nonlinear nature of the S&C model. The paper identifies directions for ongoing work using a multifidelity approach to address this issue., Boeing Company

Quantification and management of uncertainty are critical in the design of engineering systems, especially in the early stages of conceptual design. This paper presents an approach to defining budgets on the acceptable levels of uncertainty in design quantities of interest, such as the allowable risk in not meeting a critical design constraint and the allowable deviation in a system performance metric. A sensitivity-based method analyzes the effects of design decisions on satisfying those budgets, and a multi-objective optimization formulation permits the designer to explore the tradespace of uncertainty reduction activities while also accounting for a cost budget. For models that are computationally costly to evaluate, a surrogate modeling approach based on high dimensional model representation (HDMR) achieves efficient computation of the sensitivities. An example problem in aircraft conceptual design illustrates the approach., United States. National Aeronautics and Space Administration. Leading Edge Aeronautics Research Program (Grant NNX14AC73A), United States. Department of Energy. Applied Mathematics Program (Award DE-FG02-08ER2585), United States. Department of Energy. Applied Mathematics Program (Award DE-SC0009297)

Fixed point iteration is a common strategy to handle interdisciplinary coupling within a coupled multidisciplinary analysis. For each coupled analysis, this requires a large number of disciplinary high-fidelity simulations to resolve the interactions between different disciplines. When embedded within an uncertainty analysis loop (e.g., with Monte Carlo sampling over uncertain parameters) the number of high-fidelity disciplinary simulations quickly becomes prohibitive, since each sample requires a fixed point iteration and the uncertainty analysis typically involves thousands or even millions of samples. This paper develops a method for uncertainty analysis in feedback-coupled black-box systems that leverages adaptive surrogates to reduce the number of cases for which fixed point iteration is needed. The multifidelity coupled uncertainty propagation method is an iterative process that uses surrogates for approximating the coupling variables and adaptive sampling strategies to refine the surrogates. The adaptive sampling strategies explored in this work are residual error, information gain, and weighted information gain. The surrogate models are adapted in a way that does not compromise accuracy of the uncertainty analysis relative to the original coupled high-fidelity problem., United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Award FA9550-15-1-0038)

Designing and optimizing complex systems often requires numerous evaluations of a quantity of interest. This is typically achieved by querying potentially expensive numerical models in an optimization process. To alleviate the cost of optimization, surrogate models can be used in lieu of the original model, as they are cheaper to evaluate. In addition, different information sources with varying fidelity, such as numerical models, experimental results or historical data may be available to estimate the quantity of interest. This work proposes a strategy to adaptively construct and exploit a multifidelity surrogate when multiple information sources of varying fidelity are available. One of the distinguishing features of the proposed approach is the relaxation of the common assumption of hierarchical relationships among information sources. This is achieved by endowing the surrogate representation with uncertainty functions that can vary across the design space; this uncertainty quantifies the fidelity of the underlying information source. The resulting multifidelity surrogate is used in an optimization setting to identify the next design to evaluate, as well as to select the information sources with which to perform the evaluation, based on information source evaluation cost and fidelity. For an aerodynamic design example, the proposed strategy leverages multifidelity information to reduce the number of evaluations of the expensive information source needed during the optimization., United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550- 09-0613), Singapore-MIT Alliance Computational Engineering Programme