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Machine learning (ML) classifiers serve as essential tools facilitating classification and prediction across various domains. The performance of these algorithms should be known to ensure their reliable application. In certain fields, receiver operating characteristic and precision-recall curves are frequently employed to assess machine learning algorithms without accounting for the impact of process parameters. However, it may be essential to evaluate the performance of these algorithms in relation to such parameters. As a performance evaluation metric capable of considering the effects of process parameters, this paper uses a modified probability of detection (POD) approach to assess the reliability of ML-based algorithms. As an example, the POD-based approach is employed to assess ML models used for predicting the lane changing behavior of a vehicle driver. The time remaining to the predicted (and therefore unknown) lane changing event is considered as process parameter. The hit/miss approach to POD is taken here and modified by considering the probability of lane changing derived from ML algorithms at each time step, and obtaining the final result of the analysis accordingly. This improves the reliability of results compared to the standard hit/miss approach, which considers the outcome of the classifiers as either 0 or 1, while also simplifying evaluation compared to the \^a versus a approach. Performance evaluation results of the proposed approach are compared with those obtained with the standard hit/miss approach and a pre-developed \^a versus a approach to validate the effectiveness of the proposed method. The comparison shows that this method provides an averaging conservative behavior with the advantage of enhancing the reliability of the hit/miss approach to POD while retaining its simplicity., Comment: Manuscript: 8 pages, 6 figures, 4 tables

In conditional automation, the automated driving system assumes full control and only issues a takeover request to a human driver to resume driving in critical situations. Previous studies have concluded that the time budget required by drivers to resume driving after a takeover request varies with situations and different takeover variables. However, no comprehensive generalized approaches for estimating in advance the time budget required by drivers to takeover have been provided. In this contribution, fixed (7 s) and variable time budgets (6 s, 5 s, and 4 s) with and without visual imagery assistance were investigated for suitability in three takeover scenarios using performance measures such as average lateral displacement. The results indicate that 7 s is suitable for two of the studied scenarios based on their characteristics. Using the obtained results and known relations between takeover variables, a mathematical formula for estimating takeover request time budget is proposed. The proposed formula integrates individual stimulus response time, driving experience, scenario specific requirements and allows increased safety for takeover maneuvers. Furthermore, the visual imagery resulted in increased takeover time which invariably increases the time budget. Thus the time demand of the visualized information if applicable (such as visual imagery) should be included in the time budget., Comment: Manuscript: 12 pages, 12 figures, 7 tables

Using data sources beyond the Automatic Identification System to represent the context a vessel is navigating in and consequently improve situation awareness is still rare in machine learning approaches to vessel trajectory prediction (VTP). In inland shipping, where vessel movement is constrained within fairways, navigational context information is indispensable. In this contribution targeting inland VTP, Gaussian Mixture Models (GMMs) are applied, on a fused dataset of AIS and discharge measurements, to generate multi-modal distribution curves, capturing typical lateral vessel positioning in the fairway and dislocation speeds along the waterway. By sampling the probability density curves of the GMMs, feature vectors are derived which are used, together with spatio-temporal vessel features and fairway geometries, as input to a VTP transformer model. The incorporation of these distribution features of both the current and forthcoming navigation context improves prediction accuracy. The superiority of the model over a previously proposed transformer model for inland VTP is shown. The novelty lies in the provision of preprocessed, statistics-based features representing the conditioned spatial context, rather than relying on the model to extract relevant features for the VTP task from contextual data. Oversimplification of the complexity of inland navigation patterns by assuming a single typical route or selecting specific clusters prior to model application is avoided by giving the model access to the entire distribution information. The methodology's generalizability is demonstrated through the usage of data of 3 distinct river sections. It can be integrated into an interaction-aware prediction framework, where insights into the positioning of the actual vessel behavior in the overall distribution at the current location and discharge can enhance trajectory prediction accuracy., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Physics-related and model-based vessel trajectory prediction is highly accurate but requires specific knowledge of the vessel under consideration which is not always practical. Machine learning-based trajectory prediction models do not require expert knowledge, but rely on the implicit knowledge extracted from massive amounts of data. Several deep learning (DL) methods for vessel trajectory prediction have recently been suggested. The DL models developed typically only process information about the (dis)location of vessels defined with respect to a global reference system. In the context of inland navigation, this can be problematic, since without knowledge of the limited navigable space, irrealistic trajectories are likely to be determined. If spatial constraintes are introduced, e.g., by implementing an additional submodule to process map data, however, overall complexity increases. Instead of processing the vessel displacement information on the one hand and the spatial information on the other hand, the paper proposes the merging of both information. Here, fairway-related and navigation-related displacement information are used directly. In this way, the previously proposed context-sensitive Classification Transformer (CSCT) shows an improved spatial awareness. Additionally, the CSCT is adapted to assess the model uncertainty by enabling dropout during inference. This approach is trained on different inland waterways to analyze its generalizability. As the improved CSCT obtains lower prediction errors and enables to estimate the trustworthiness of each prediction, it is more suitable for safety-critical applications in inland navigation than previously developed models.

Accurate vessel trajectory prediction is necessary for save and efficient navigation. Deep learning-based prediction models, esp. encoder-decoders, are rarely applied to inland navigation specifically. Approaches from the maritime domain cannot directly be transferred to river navigation due to specific driving behavior influencing factors. Different encoder-decoder architectures, including a transformer encoder-decoder, are compared herein for predicting the next positions of inland vessels, given not only spatio-temporal information from AIS, but also river specific features. The results show that the reformulation of the regression task as classification problem and the inclusion of river specific features yield the lowest displacement errors. The standard LSTM encoder-decoder outperforms the transformer encoder-decoder for the data considered, but is computationally more expensive. In this study for the first time a transformer-based encoder-decoder model is applied to the problem of predicting the ship trajectory. Here, a feature vector using the river-specific context of navigation input parameters is established. Future studies can built on the proposed models, investigate the improvement of the computationally more efficient transformer, e.g. through further hyper-parameter optimization, and use additional river-specific information in the context representation to further increase prediction accuracy.

Autonomous transportation systems such as road vehicles or vessels require the consideration of the static and dynamic environment to dislocate without collision. Anticipating the behavior of an agent in a given situation is required to adequately react to it in time. Developing deep learning-based models has become the dominant approach to motion prediction recently. The social environment is often considered through a CNN-LSTM-based sub-module processing a $\textit{social tensor}$ that includes information of the past trajectory of surrounding agents. For the proposed transformer-based trajectory prediction model, an alternative, computationally more efficient social tensor definition and processing is suggested. It considers the interdependencies between target and surrounding agents at each time step directly instead of relying on information of last hidden LSTM states of individually processed agents. A transformer-based sub-module, the Social Tensor Transformer, is integrated into the overall prediction model. It is responsible for enriching the target agent's dislocation features with social interaction information obtained from the social tensor. For the awareness of spatial limitations, dislocation features are defined in relation to the navigable area. This replaces additional, computationally expensive map processing sub-modules. An ablation study shows, that for longer prediction horizons, the deviation of the predicted trajectory from the ground truth is lower compared to a spatially and socially agnostic model. Even if the performance gain from a spatial-only to a spatial and social context-sensitive model is small in terms of common error measures, by visualizing the results it can be shown that the proposed model in fact is able to predict reactions to surrounding agents and explicitely allows an interpretable behavior.

In complex and unknown processes, global models are initially generated over the entire experimental space, but they often fail to provide accurate predictions in local areas. Recognizing this limitation, this study addresses the need for models that effectively represent both global and local experimental spaces. It introduces a novel machine learning (ML) approach: Polynomial Chaos Expanded Gaussian Process (PCEGP), leveraging polynomial chaos expansion (PCE) to calculate input-dependent hyperparameters of the Gaussian process (GP). This approach provides a mathematically interpretable method that incorporates non-stationary covariance functions and heteroscedastic noise estimation to generate locally adapted models. The model performance is compared to different algorithms in benchmark tests for regression tasks. The results demonstrate low prediction errors of the PCEGP in these benchmark applications, highlighting model performance that is often competitive with or superior to previous methods. A key advantage of the presented model is the transparency and traceability in the calculation of hyperparameters and model predictions., Comment: Manuscript: 20 pages, 4 figures, 7 tables

Dynamic fluctuations in the wind field to which a wind turbine (WT) is exposed to are responsible for fatigue loads on its components. To reduce structural loads in WTs, advanced control schemes have been proposed. In recent years, prognosis-based lifetime control of WTs has become increasingly important. In this approach, the prognostic controller gains are adapted based on the stateof-health (SOH) of the WT component to achieve the desired lifetime. However, stochastic wind dynamics complicates estimation of the SOH of a WT. More recently, robust controllers have been combined with real-time damage evaluation models to meet prognosis objectives. Most rely on model-based online load cycle counting algorithms to determine fatigue damage, with analytical models providing the degradation estimate. However, most use load measurements that are either unreliable or unavailable in commercial WTs, limiting their practicality. In this contribution, a hybrid prognosis scheme combining data-driven load prediction and model-based damage estimation models for robust lifetime control of commercial WTs is proposed. A data-driven support vector machine (SVM) regression model is trained using loading data obtained from dynamic simulations using a {\mu}-synthesis robust disturbance accommodating controller (RDAC). The regression model uses available WT measurements to predict tower load. Based on this prediction, an online rain-flow counting (RFC) damage evaluation model estimates the damage level and lifetime of the tower. The RDAC controller gains are dynamically adapted to achieve a predefined damage limit and lifetime. The proposed approach is evaluated on a 5 MW reference WT and its performance is compared with a model-based prognosis scheme using ideal WT tower measurement. Results demonstrate the efficacy of the proposed approach to control the fatigue lifetime in WT components., Comment: Manuscript: 19 pages, 7 figures, 5 tables