This work compares methods to compute confidence bands in a validation task of a vehicle single-track model. The confidence bands are computed from time series by naïve method, Gaussian process regression and heteroscedastic and non-stationary Gaussian process regression. The simulation model considers the epistemic uncertainty of the vehicle mass parameter by Latin hypercube sampling. The validation procedure compares all stochastically simulated time series of the vehicle yaw rate with the confidence band of the reference data. The model is marked as valid if the yaw rate for each time step is within the confidence band of the reference data. The data was challenging due to noise and time-varying variance and smoothness. Due to required data pre-processing and the high sensitivity to noise in the reference data, the naïve method has generated unusable confidence bands and cannot be recommended for similar validation tasks. Gaussian process regression solved the problem of noise sensitivity, but was not able to model the time-varying length scale of the reference data. Therefore, heteroscedastic and non-stationary Gaussian process regression is proposed to calculate accurate confidence bands of time-varying and noisy reference data for the validation of dynamic models by a confidence band approach.

这项工作比较了在车辆单轨模型的验证任务中计算置信带的方法。置信带是通过朴素方法，高斯过程回归以及异方差和非平稳高斯过程回归从时间序列中计算出来的。该仿真模型通过拉丁超立方体采样考虑了车辆质量参数的认知不确定性。验证过程将车辆横摆率的所有随机模拟时间序列与参考数据的置信带进行比较。如果每个时间步的偏航率在参考数据的置信带内，则将模型标记为有效。由于噪声，时变方差和平滑度，数据具有挑战性。由于需要进行数据预处理以及对参考数据中的噪声高度敏感，天真的方法已生成了无法使用的置信带，因此不建议将其用于类似的验证任务。高斯过程回归解决了噪声敏感度的问题，但无法对参考数据的时变长度尺度进行建模。因此，提出了异方差和非平稳高斯过程回归来计算时变和嘈杂参考数据的准确置信带，以通过置信带方法验证动态模型。