arXiv subjects

Erik Frisk

Publications and source records attributed to Erik Frisk.

At least 19 recordsLinked to original sources

arXiv2026

SurvCF(t): Counterfactual Explanations for Survival Analysis in Predictive Maintenance Multivariate Time Series Data

Predictive maintenance relies on accurate Remaining Useful Life estimation, often formulated using survival analysis over multivariate time-series data. While modern deep survival models achieve strong predictive performance, their black-box nature limits their use in safety-critical settings where actionable insight is required. In this work, we introduce \textit{SurvCF(t)}, the first framework for generating counterfactual explanations for survival models operating on time-series data. \textit{SurvCF(t)} identifies minimal, plausible, and temporally consistent changes to an asset's operational history that increase its predicted life time, framing explanation as a constrained optimization problem combining validity, proximity, sparsity, and plausibility. We evaluate the method on multiple benchmarks, including C-MAPSS, N-CMAPSS, and a real-world case study of the Scania Component\_X dataset, demonstrating its ability to produce actionable and interpretable interventions. Our results show that \textit{SurvCF(t)} bridges the gap between survival prediction and prescriptive maintenance, enabling explainable and decision-oriented AI for maintenance strategies.

cs.LG↗

arXiv2026

Vessel Trajectory Prediction using COLREGs-aware Optimal Planning

This paper presents a trajectory prediction method for marine vessels based on optimal planning. Crude initial trajectories respecting static obstacles are first generated using A*-search to provide a feasible warm start. In the second step, a numerical optimizer is used to ensure COLREG compliance. The prediction problem is posed as sequential trajectory planning from the perspective of each surrounding vessel, requiring only their current positions, velocities, and intended destinations as input. As the latter is included in AIS messages, this enables faster predictions than learning-based methods that typically require longer data histories. The proposed method is validated using real-world scenarios constructed from AIS data.

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arXiv2026

Unveiling Transferability in Trajectory Prediction via Latent Scene Embeddings

The growing availability of trajectory datasets has fueled major advances in data-driven motion prediction. Yet, models trained on one dataset often fail to generalize beyond their training domain as a result of differences in scene layouts, agent behaviors, and sensing conditions. A framework that learns latent representations of datasets and quantifies their similarity using distributional metrics is presented. This large-scale study covers 24 major datasets, including the most widely used motion-prediction benchmarks, and shows that the resulting transferability scores strongly correlate with cross-dataset model performance. The results provide practical guidance for dataset selection, pretraining, and large-scale foundation models for motion prediction, paving the way toward more generalizable and robust predictive systems.

cs.CV↗

arXiv2026

Grid-Constrained Smart Charging of Large EV Fleets: Comparative Study of Sequential DP and a Full Fleet Solver

This paper presents a comparative optimization framework for smart charging of electrified vehicle fleets. Using heuristic sequential dynamic programming (SeqDP), the framework minimizes electricity costs while adhering to constraints related to the power grid, charging infrastructure, vehicle availability, and simple considerations of battery aging. Based on real-world operational data, the model incorporates discrete energy states, time-varying tariffs, and state-of-charge (SoC) targets to deliver a scalable and cost-effective solution. Classical DP approach suffers from exponential computational complexity as the problem size increases. This becomes particularly problematic when conducting monthly-scale analyses aimed at minimizing peak power demand across all vehicles. The extended time horizon, coupled with multi-state decision-making, renders exact optimization impractical at larger scales. To address this, a heuristic method is employed to enable systematic aggregation and tractable computation for the Non-Linear Programming (NLP) problem. Rather than seeking a globally optimal solution, this study focuses on a time-efficient smart charging strategy that aims to minimize energy cost while flattening the overall power profile. In this context, a sequential heuristic DP approach is proposed. Its performance is evaluated against a full-fleet solver using Gurobi, a widely used commercial solver in both academia and industry. The proposed algorithm achieves a reduction of the overall cost and peak power by more than 90% compared to uncontrolled schedules. Its relative cost remains within 9\% of the optimal values obtained from the full-fleet solver, and its relative peak-power deviation stays below 15% for larger fleets.

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arXiv2026

Inverse-dynamics observer design for a linear single-track vehicle model with distributed tire dynamics

Accurate estimation of the vehicle's sideslip angle and tire forces is essential for enhancing safety and handling performances in unknown driving scenarios. To this end, the present paper proposes an innovative observer that combines a linear single-track model with a distributed representation of the tires and information collected from standard sensors. In particular, by adopting a comprehensive representation of the tires in terms of hyperbolic partial differential equations (PDEs), the proposed estimation strategy exploits dynamical inversion to reconstruct the lumped and distributed vehicle states solely from yaw rate and lateral acceleration measurements. Simulation results demonstrate the effectiveness of the observer in estimating the sideslip angle and tire forces even in the presence of noise and model uncertainties.

eess.SY↗

arXiv2026

Lateral tracking control of all-wheel steering vehicles with intelligent tires

The accurate characterization of tire dynamics is critical for advancing control strategies in autonomous road vehicles, as tire behavior significantly influences handling and stability through the generation of forces and moments at the tire-road interface. Smart tire technologies have emerged as a promising tool for sensing key variables such as road friction, tire pressure, and wear states, and for estimating kinematic and dynamic states like vehicle speed and tire forces. However, most existing estimation and control algorithms rely on empirical correlations or machine learning approaches, which require extensive calibration and can be sensitive to variations in operating conditions. In contrast, model-based techniques, which leverage infinite-dimensional representations of tire dynamics using partial differential equations (PDEs), offer a more robust approach. This paper proposes a novel model-based, output-feedback lateral tracking control strategy for all-wheel steering vehicles that integrates distributed tire dynamics with smart tire technologies. The primary contributions include the suppression of micro-shimmy phenomena at low speeds and path-following via force control, achieved through the estimation of tire slip angles, vehicle kinematics, and lateral tire forces. The proposed controller and observer are based on formulations using ODE-PDE systems, representing rigid body dynamics and distributed tire behavior. This work marks the first rigorous control strategy for vehicular systems equipped with distributed tire representations in conjunction with smart tire technologies.

eess.SY↗

arXiv2026

First-order friction models with bristle dynamics: lumped and distributed formulations

Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate the design of control and estimation algorithms. However, many rate-dependent formulations are built on empirical considerations, whereas physical derivations may offer greater interpretability. In this context, starting from fundamental physical principles, this paper introduces a novel class of first-order dynamic friction models that approximate the dynamics of a bristle element by inverting the friction characteristic. Amongst the developed models, a specific formulation closely resembling the LuGre model is derived using a simple rheological equation for the bristle element. This model is rigorously analyzed in terms of stability and passivity -- important properties that support the synthesis of observers and controllers. Furthermore, a distributed version, formulated as a hyperbolic partial differential equation (PDE), is presented, which enables the modeling of frictional processes commonly encountered in rolling contact phenomena. The tribological behavior of the proposed description is evaluated through classical experiments and validated against the response predicted by the LuGre model, revealing both notable similarities and key differences.

eess.SY↗

arXiv2026

Stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics via singular perturbation analysis

This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial differential equations (PDEs). Motivated by the long-standing practice of neglecting transient tire dynamics in vehicle modeling and control, a rigorous justification is provided for such simplifications using singular perturbation theory. A perturbation parameter, defined as the ratio between a characteristic rolling contact length and the vehicle's longitudinal speed, is introduced to formalize the time-scale separation between rigid-body motion and tire dynamics. For sufficiently small values of this parameter, it is demonstrated that standard finite-dimensional techniques can be applied to analyze the local stability of equilibria and to design stabilizing controllers. Whilst the proposed controllers build on classical approaches, the novelty of this work lies in establishing the first singular perturbation framework for ODE-PDE vehicle models with distributed tire dynamics, providing a theoretical justification for their quasi-static reduction and for the use of finite-dimensional tools for analysis and control design.

eess.SY↗

arXiv2026

Passivity-exploiting stabilization of semilinear single-track vehicle models with distributed tire friction dynamics

This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial differential equations (PDEs). A passivity-exploiting backstepping design is presented, which leverages the strict dissipativity properties of the PDE subsystem to achieve exponential stabilization of the considered ODE-PDE interconnection around a prescribed equilibrium. Sufficient conditions for local well-posedness and exponential convergence are derived by constructing a Lyapunov functional combining the lumped and distributed states. Both state-feedback and output-feedback controllers are synthesized, the latter relying on a cascaded observer. The theoretical results are corroborated with numerical simulations, considering non-ideal scenarios and accounting for external disturbances and uncertainties. Simulation results confirm that the proposed control strategy can effectively and robustly stabilize oversteer vehicles at high speeds, demonstrating the relevance of the approach for improving the safety and performance in automotive applications.

eess.SY↗

arXiv2026

Linear viscoelastic rheological FrBD models

In [1], a new modeling paradigm for developing rate-and-state-dependent, control-oriented friction models was introduced. The framework, termed Friction with Bristle Dynamics (FrBD), combines nonlinear analytical expressions for the friction coefficient with constitutive equations for bristle-like elements. Within the FrBD framework, this letter introduces two novel formulations based on the two most general linear viscoelastic models for solids: the Generalized Maxwell (GM) and Generalized Kelvin-Voigt (GKV) elements. Both are analyzed in terms of boundedness and passivity, revealing that these properties are satisfied for any physically meaningful parametrization. An application of passivity for control design is also illustrated, considering an example from robotics. The findings of this letter systematically integrate rate-and-state dynamic friction models with linear viscoelasticity.

eess.SY↗

arXiv2026

Boundary adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction

This paper presents an adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction characteristics parameterized by a matrix of unknown coefficients appearing in the nonlinear (and possibly non-smooth) PDE source terms. Under appropriate assumptions of forward completeness and boundary sensing, an adaptive observer is synthesized to simultaneously estimate the lumped and distributed states, as well as the uncertain friction parameters, using only boundary measurements. The observer combines a finite-dimensional parameter estimator with an infinite-dimensional description of the state error dynamics, and achieves exponential convergence under persistent excitation. The effectiveness of the proposed design is demonstrated in simulation by considering a relevant example borrowed from road vehicle dynamics.

eess.SY↗

arXiv2026

Semilinear single-track vehicle models with distributed tyre friction dynamics

This paper introduces a novel family of single-track vehicle models that incorporate a distributed representation of transient tyre dynamics, whilst simultaneously accounting for nonlinear effects induced by friction. The core of the proposed framework is represented by the distributed Friction with Bristle Dynamics (FrBD) model, which unifies and extends classical formulations such as Dahl and LuGre by describing the rolling contact process as a spatially distributed system governed by semilinear partial differential equations (PDEs). This model is systematically integrated into a single-track vehicle framework, where the resulting semilinear ODE-PDE interconnection captures the interaction between lateral vehicle motion and tyre deformation. Two main variants are considered: one with rigid tyre carcass and another with flexible carcass, each admitting a compact state-space representation. Local and global well-posedness properties for the coupled system are established rigorously, highlighting the dissipative and physically consistent properties of the distributed FrBD model. A linearisation procedure is also presented, enabling spectral analysis and transfer function derivation, and potentially facilitating the synthesis of controllers and observers. Numerical simulations demonstrate the model's capability to capture micro-shimmy oscillations and transient lateral responses to advanced steering manoeuvres. The proposed formulation advances the state-of-the-art in vehicle dynamics modelling by providing a physically grounded, mathematically rigorous, and computationally tractable approach to incorporating transient tyre behaviour in lateral vehicle dynamics, when accounting for the effect of limited friction.

cs.RO↗

arXiv2025

Behavior-Aware Online Prediction of Obstacle Occupancy using Zonotopes

Predicting the motion of surrounding vehicles is key to safe autonomous driving, especially in unstructured environments without prior information. This paper proposes a novel online method to accurately predict the occupancy sets of surrounding vehicles based solely on motion observations. The approach is divided into two stages: first, an Extended Kalman Filter and a Linear Programming (LP) problem are used to estimate a compact zonotopic set of control actions; then, a reachability analysis propagates this set to predict future occupancy. The effectiveness of the method has been validated through simulations in an urban environment, showing accurate and compact predictions without relying on prior assumptions or prior training data.

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arXiv2025

Probabilistic Machine Learning for Uncertainty-Aware Diagnosis of Industrial Systems

Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks, these models often struggle with the evaluation of their confidence. This matter is particularly important in consistency-based diagnosis where decision logic is highly sensitive to false alarms. To address this challenge, this work presents a diagnostic framework that uses ensemble probabilistic machine learning to improve diagnostic characteristics of data driven consistency based diagnosis by quantifying and automating the prediction uncertainty. The proposed method is evaluated across several case studies using both ablation and comparative analyses, showing consistent improvements across a range of diagnostic metrics.

cs.LG↗

arXiv2025

Two-dimensional time-to-collision measures for articulated vehicles: predicting sideswipe and rear-end collisions

Time-to-collision is a commonly employed measure for rear-end collision prediction. However, its conventional formulation, which assumes constant speed and heading, is incapable of identifying sideswipe collisions. A two-dimensional extension has been proposed to incorporate lateral interactions with passenger cars, yet it assumes identical, fixed headings and does not accommodate articulated vehicles such as tractor-semitrailers. In this paper, the existing formulation for the car is first refined to incorporate differences in vehicle heading. Subsequently, new two-dimensional time-to-collision measures are proposed for articulated vehicles: TTC$_{\mathrm{2D}}^{\mathrm{AV}}$ and modified TTC$_{\mathrm{2D}}^{\mathrm{AV}}$. These measures employ constant-speed and constant-acceleration assumptions and are analogous to their one-dimensional counterparts: time-to-collision and modified time-to-collision. The proposed measures are assessed in CARLA using randomly generated cut-in scenarios simulated with a tractor-semitrailer model, incorporating a range of trailer lengths. A short analysis is also conducted to test the measures in a roundabout and tight turn. The analyses demonstrate that the proposed measures substantially improve the detection of sideswipe collisions while maintaining a comparable level of performance to existing measures in detecting rear-end collisions. Across 30 simulated scenarios, they correctly identify 14 of 15 sideswipe collisions, compared with 7 of 15 identified by the existing formulation. Moreover, the mean prediction error for sideswipe collisions is reduced by approximately 20% compared to the existing formulation.

cs.RO↗

arXiv2024

Uncertainty-Aware Decision-Making and Planning for Autonomous Forced Merging

In this paper, we develop an uncertainty-aware decision-making and motion-planning method for an autonomous ego vehicle in forced merging scenarios, considering the motion uncertainty of surrounding vehicles. The method dynamically captures the uncertainty of surrounding vehicles by online estimation of their acceleration bounds, enabling a reactive but rapid understanding of the uncertainty characteristics of the surrounding vehicles. By leveraging these estimated bounds, a non-conservative forward occupancy of surrounding vehicles is predicted over a horizon, which is incorporated in both the decision-making process and the motion-planning strategy, to enhance the resilience and safety of the planned reference trajectory. The method successfully fulfills the tasks in challenging forced merging scenarios, and the properties are illustrated by comparison with several alternative approaches.

cs.RO↗

arXiv2024

The LiU-ICE Benchmark -- An Industrial Fault Diagnosis Case Study

This paper presents the LiU-ICE fault diagnosis benchmark. The purpose of the benchmark is to support fault diagnosis research by providing data and a model of an industrially relevant system. Data has been collected from an internal combustion engine test bench operated in both nominal and faulty modes. A state-of-the-art model of the air path through an internal combustion engine with unknown parameters is provided. This benchmark has previously been used in a competition at the 12th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes (Safe Process) 2024, Ferrara, Italy.

eess.SY↗

arXiv2024

Toward Unified Practices in Trajectory Prediction Research on Bird's-Eye-View Datasets

The availability of high-quality datasets is crucial for the development of behavior prediction algorithms in autonomous vehicles. This paper highlights the need to standardize the use of certain datasets for motion forecasting research to simplify comparative analysis and proposes a set of tools and practices to achieve this. Drawing on extensive experience and a comprehensive review of current literature, we summarize our proposals for preprocessing, visualization, and evaluation in the form of an open-sourced toolbox designed for researchers working on trajectory prediction problems. The clear specification of necessary preprocessing steps and evaluation metrics is intended to alleviate development efforts and facilitate the comparison of results across different studies. The toolbox is available at: https://github.com/westny/dronalize.

cs.RO↗