Aircraft Robust Trajectory Optimization Using Nonintrusive Polynomial Chaos

Li, Xiang; Nair, Prasanth B.; Zhang, Zhigang; Gao, Lin; Gao, Chen

doi:10.2514/1.c032474

Cited by 47 publications

(42 citation statements)

References 26 publications

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“…Various approaches exist to determine a robust, optimized trajectory in the flight planning phase, i.e., before departure of the actual flight. Li et al [7] present a dynamic optimal control problem where stochastic equations are transferred to equivalent deterministic differential equations. However, uncertainties are represented by one variable, and large-scale problems are hard to compute.…”

Section: Trajectory Optimization With Forecast Uncertaintiesmentioning

confidence: 99%

In-Flight Aircraft Trajectory Optimization within Corridors Defined by Ensemble Weather Forecasts

et al. 2020

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Today, each flight is filed as a static route not later than one hour before departure. From there on, changes of the lateral route initiated by the pilot are only possible with air traffic control clearance and in the minority. Thus, the initially optimized trajectory of the flight plan is flown, although the optimization may already be based upon outdated weather data at take-off. Global weather data as those modeled by the Global Forecast System do, however, contain hints on forecast uncertainties itself, which is quantified by considering so-called ensemble forecast data. In this study, the variability in these weather parameter uncertainties is analyzed, before the trajectory optimization model TOMATO is applied to single trajectories considering the previously quantified uncertainties. TOMATO generates, based on the set of input data as provided by the ensembles, a 3D corridor encasing all resulting optimized trajectories. Assuming that this corridor is filed in addition to the initial flight plan, the optimum trajectory can be updated even during flight, as soon as updated weather forecasts are available. In return and as a compromise, flights would have to stay within the corridor to provide planning stability for Air Traffic Management compared to full free in-flight optimization. Although the corridor restricts the re-optimized trajectory, fuel savings of up to 1.1 %, compared to the initially filed flight, could be shown.

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Section: Trajectory Optimization With Forecast Uncertaintiesmentioning

confidence: 99%

In-Flight Aircraft Trajectory Optimization within Corridors Defined by Ensemble Weather Forecasts

et al. 2020

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“…, n x as a function of θ and φ for each design x d . Surrogate models have been shown to be useful for propagating uncertainties in various applications of design under uncertainty [19,[32][33][34]; in particular propagating mixed uncertainties by sampling surrogate models has been demonstrated to be effective [7,10]. These surrogate models can then be sampled as many times as required at small computational cost (assuming the computational expense of the simulation vastly outweighs evaluating the surrogate model).…”

Section: Surrogate Modeling For Computational Efficiencymentioning

confidence: 99%

Extending Horsetail Matching for Optimization Under Probabilistic, Interval, and Mixed Uncertainties

2018

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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 aero-structural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis.

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“…Once the coefficients are computed, sampling from the PCE generally has a lower computational cost than MC. PCE has been used in many fields for uncertainty quantification of computationally intensive models [37][38][39][40]. In orbital mechanics, PCE has been previously used for uncertainty propagation [41] and conjunction assessment [42,43].…”

Section: Introductionmentioning

confidence: 99%

Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions

Vittaldev

Russell

Linares

2016

Journal of Guidance, Control, and Dynamics

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Polynomial Chaos Expansion (PCE) and Gaussian Mixture Models (GMMs) are combined in a hybrid fashion to propagate state uncertainty for spacecraft with initial Gaussian errors. PCE models uncertainty by performing an expansion using orthogonal polynomials (OPs). The accuracy of PCE for a given problem can be improved by increasing the order of the OP expansion. The number of terms in the OP expansion increases factorially with dimensionality of the problem, thereby reducing the effectiveness of the PCE approach for problems of moderately high dimensionality. This paper shows a combination of GMM and PCE, GMM-PC as an alternative form of the multi-element PCE. GMM-PC reduces the overall order required to reach a desired accuracy. The initial distribution is converted to a GMM, and PCE is used to propagate the state uncertainty represented by each of the elements through the nonlinear dynamics. Splitting the initial distribution into a GMM reduces the size of the covariance associated with each new element thereby reducing the domain of approximation and allowing for lower order polynomials to be used. Several spacecraft uncertainty propagation examples are shown using GMM-PC. The resulting distributions are shown to

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Aircraft Robust Trajectory Optimization Using Nonintrusive Polynomial Chaos

Cited by 47 publications

References 26 publications

In-Flight Aircraft Trajectory Optimization within Corridors Defined by Ensemble Weather Forecasts

In-Flight Aircraft Trajectory Optimization within Corridors Defined by Ensemble Weather Forecasts

Extending Horsetail Matching for Optimization Under Probabilistic, Interval, and Mixed Uncertainties

Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions

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