A probabilistic model for aircraft in climb using monotonic functional Gaussian process emulators
A probabilistic model for aircraft in climb using monotonic functional Gaussian process emulators
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DOI：
10.1098/rspa.2022.0607
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Nick Pepper;Marc Thomas;George De Ath;Enrico Oliver;R. Cannon;R. Everson;T. Dodwell
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文献类型：
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作者：
Nick Pepper;Marc Thomas;George De Ath;Enrico Oliver;R. Cannon;R. Everson;T. Dodwell
确保垂直间隔是在拥挤空域中保持飞机之间安全间隔的关键手段。飞机轨迹是在存在重大认知不确定性的情况下建模的，导致观察到的轨迹与确定性模型的预测之间存在差异，阻碍了确保安全分离的规划任务。本文提出了一种概率模型，用于模拟飞机爬升时的轨迹，并对预测轨迹的不确定性进行界定。单调的泛函表示利用了雷达观测中的时空相关性。通过使用高斯过程仿真器，将爬升过程参数化为函数输出的特征被直接映射到函数输出，从而提供快速近似，同时确保所产生的轨迹是单调的。该模型作为飞机爬升的概率数字孪生模型，以工业上广泛使用的确定性模型飞机数据为基础。当应用于看不见的测试数据集时，发现概率模型提供的平均预测以平均绝对误差衡量的准确率提高了20.56%，数据驱动的可信区间的准确率提高了9.54%。
Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper, a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian process emulators, features that parameterize the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against the base of aircraft data, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 20.56% more accurate, as measured by the mean absolute error, with data-driven credible intervals that were9.54% sharper.