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Daniel Straub

Publications and source records attributed to Daniel Straub.

At least 19 recordsLinked to original sources
arXiv2026

Branching out: Prognostics-Based Replacement Policies for Series Systems

We propose a hybrid planning method for deriving prognostics-based predictive maintenance policies. The method accounts for the available decision options, the information on the future state of the system provided by a prognostic model, and the costs of the underlying renewal-reward process. It results in policies defined by only a few parameters, which can be determined based on theoretical considerations or by optimization from run-to-failure data. We demonstrate the potential of the method in two separate predictive maintenance decision settings: preventive replacement and preventive ordering. Numerical investigations show that the derived policies rival the performance of optimized benchmark policies, while being significantly more efficient and robust against overfitting.

math.OC↗
arXiv2026

A Hierarchical Bayesian Framework for Model-based Prognostics

In prognostics and health management (PHM) of engineered systems, maintenance decisions are ideally informed by predictions of a system's remaining useful life (RUL) based on operational data. Model-based prognostics algorithms rely on a parametric model of the system degradation process. The model parameters are learned from real-time operational data collected on the system. However, there can be valuable information in data from similar systems or components, which is not typically utilized in PHM. In this contribution, we propose a hierarchical Bayesian modeling (HBM) framework for PHM that integrates both operational data and run-to-failure data from similar systems or components. The HBM framework utilizes hyperparameter distributions learned from data of similar systems or components as priors. It enables efficient updates of predictions as more information becomes available, allowing for increasingly accurate assessments of the degradation process and its associated variability. The effectiveness of the proposed framework is demonstrated through two experimental applications involving real-world data from crack growth and lithium battery degradation. Results show significant improvements in RUL prediction accuracy and demonstrate how the framework facilitates uncertainty management through predictive distributions.

stat.ME↗
arXiv2025

Emergent Cooperative Driving Strategies for Stop-and-Go Wave Mitigation via Multi-Agent Reinforcement Learning

Stop-and-go waves in traffic flow pose a persistent challenge, compromising safety, efficiency, and environmental sustainability. This paper introduces a novel mitigation strategy discovered through training multi-agent deep reinforcement learning (DRL) agents in a simulated ring-road environment. The agents autonomously develop a cooperative driving policy, where most vehicles maintain minimal headways to maximize throughput, while a single "buffer" vehicle adopts a larger headway to absorb perturbations and prevent wave propagation. This strategy enhances stability without sacrificing overall flow. We further demonstrate that adapting this cooperative strategy to classical car-following models, such as the Intelligent Driver Model (IDM), yields improved stability and traffic efficiency. Furthermore, we show within a parametrised linear framework, that the cooperative strategy can optimise system performance under stability constraints. Our findings offer promising insights for future autonomous vehicle systems and highway management.

physics.soc-ph↗
arXiv2025

Leaf It to Renewal: Improved Predictive Maintenance Policies via Renewal Theory and Decision Trees

We propose a hybrid planning method for deriving prognostics-based predictive maintenance policies. The method accounts for the available decision options, the information on the future state of the system provided by a prognostic model, and the costs of the underlying renewal-reward process. It results in policies defined by only a few parameters, which can be determined based on theoretical considerations or by optimization from run-to-failure data. We demonstrate the potential of the method in two separate predictive maintenance decision settings: preventive replacement and preventive ordering. Numerical investigations show that the derived policies rival the performance of optimized benchmark policies, while being significantly more efficient and robust against overfitting.

math.OC↗
arXiv2025

Sensitivity measures for engineering and environmental decision support

Information value, a measure for decision sensitivity, can provide essential information in engineering and environmental assessments. It quantifies the potential for improved decision-making when reducing uncertainty in specific inputs. By contrast to other sensitivity measures, it admits not only a relative ranking of input factors but also an absolute interpretation through statements like ''Eliminating the uncertainty in factor $A$ has an expected value of $5000$ Euro''. In this paper, we present a comprehensive overview of the information value by presenting the theory and methods in view of their application to engineering and environmental assessments. We show how one should differentiate between aleatory and epistemic uncertainty in the analysis. Furthermore, we introduce the evaluation of the information value in applications where the decision is described by a continuous parameter. The paper concludes with two real-life applications of the information value to highlight its power in supporting decision-making in engineering and environmental applications.

stat.AP↗
arXiv2025

Near-real-time ship grounding damage assessment using Bayesian networks

In a post-grounding event, the rapid assessment of hull girder residual strength is crucial for making informed decisions, such as determining whether the vessel can safely reach the closest yard. One of the primary challenges in this assessment is the uncertainty in the estimation of the extent of structural damage. Although classification societies have developed rapid response damage assessment tools, primarily relying on 2D Smith-based models, these tools are based on deterministic methods and conservative estimates of damage extent. To enhance this assessment, we propose a probabilistic framework for rapid grounding damage assessment of ship structures using Bayesian networks (BNs). The proposed BN model integrates multiple information sources, including underwater inspection results, hydrostatic and bathymetric data, crashworthiness models, and hydraulic models for flooding and oil spill monitoring. By systematically incorporating these parameters and their associated uncertainties within a causal framework, the BN allows for dynamic updates as new evidence emerges during an incident. Two case studies demonstrate the effectiveness of this methodology, highlighting its potential as a practical decision support tool to improve operational safety during grounding events. The results indicate that combining models with on-site observations can even replace costly underwater inspections.

stat.AP↗
arXiv2025

A novel stratified sampler with unbalanced refinement for network reliability assessment

We investigate stratified sampling in the context of network reliability assessment. We propose an unbalanced stratum refinement procedure, which operates on a partition of network components into clusters and the number of failed components within each cluster. The size of each refined stratum and the associated conditional failure probability, collectively termed failure signatures, can be calculated and estimated using the conditional Bernoulli model. The estimator is further improved by determining the minimum number of component failure $i^*$ to reach system failure and then by considering only strata with at least $i^*$ failed components. We propose a heuristic but practicable approximation of the optimal sample size for all strata, assuming a coherent network performance function. The efficiency of the proposed stratified sampler with unbalanced refinement (SSuR) is demonstrated through two network reliability problems.

stat.ME↗
arXiv2025

Safety integrity framework for automated driving

This paper describes the comprehensive safety framework that underpinned the development, release process, and regulatory approval of BMW's first SAE Level 3 Automated Driving System. The framework combines established qualitative and quantitative methods from the fields of Systems Engineering, Engineering Risk Analysis, Bayesian Data Analysis, Design of Experiments, and Statistical Learning in a novel manner. The approach systematically minimizes the risks associated with hardware and software faults, performance limitations, and insufficient specifications to an acceptable level that achieves a Positive Risk Balance. At the core of the framework is the systematic identification and quantification of uncertainties associated with hazard scenarios and the redundantly designed system based on designed experiments, field data, and expert knowledge. The residual risk of the system is then estimated through Stochastic Simulation and evaluated by Sensitivity Analysis. By integrating these advanced analytical techniques into the V-Model, the framework fulfills, unifies, and complements existing automotive safety standards. It therefore provides a comprehensive, rigorous, and transparent safety assurance process for the development and deployment of Automated Driving Systems.

cs.RO↗
arXiv2025

Deep Belief Markov Models for POMDP Inference

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The POMDP framework allows for modeling and solving sequential decision-making problems under observation uncertainty. In complex, high-dimensional, partially observable environments, existing methods for inference based on exact computations (e.g., via Bayes' theorem) or sampling algorithms do not scale well. Furthermore, ground truth states may not be available for learning the exact transition dynamics. DBMMs extend deep Markov models into the partially observable decision-making framework and allow efficient belief inference entirely based on available observation data via variational inference methods. By leveraging the potency of neural networks, DBMMs can infer and simulate non-linear relationships in the system dynamics and naturally scale to problems with high dimensionality and discrete or continuous variables. In addition, neural network parameters can be dynamically updated efficiently based on data availability. DBMMs can thus be used to infer a belief variable, thus enabling the derivation of POMDP solutions over the belief space. We evaluate the efficacy of the proposed methodology by evaluating the capability of model-formulation agnostic inference of DBMMs in benchmark problems that include discrete and continuous variables.

cs.LG↗
arXiv2025

Convex Is Back: Solving Belief MDPs With Convexity-Informed Deep Reinforcement Learning

We present a novel method for Deep Reinforcement Learning (DRL), incorporating the convex property of the value function over the belief space in Partially Observable Markov Decision Processes (POMDPs). We introduce hard- and soft-enforced convexity as two different approaches, and compare their performance against standard DRL on two well-known POMDP environments, namely the Tiger and FieldVisionRockSample problems. Our findings show that including the convexity feature can substantially increase performance of the agents, as well as increase robustness over the hyperparameter space, especially when testing on out-of-distribution domains. The source code for this work can be found at https://github.com/Dakout/Convex_DRL.

cs.LG↗
arXiv2024

Probabilistic digital twins for geotechnical design and construction

The digital twin approach has gained recognition as a promising solution to the challenges faced by the Architecture, Engineering, Construction, Operations, and Management (AECOM) industries. However, its broader application across AECOM sectors remains limited. One significant obstacle is that traditional digital twins rely on deterministic models, which require deterministic input parameters. This limits their accuracy, as they do not account for the substantial uncertainties inherent in AECOM projects. These uncertainties are particularly pronounced in geotechnical design and construction. To address this challenge, we propose a Probabilistic Digital Twin (PDT) framework that extends traditional digital twin methodologies by incorporating uncertainties, and is tailored to the requirements of geotechnical design and construction. The PDT framework provides a structured approach to integrating all sources of uncertainty, including aleatoric, data, model, and prediction uncertainties, and propagates them throughout the entire modeling process. To ensure that site-specific conditions are accurately reflected as additional information is obtained, the PDT leverages Bayesian methods for model updating. The effectiveness of the probabilistic digital twin framework is showcased through an application to a highway foundation construction project, demonstrating its potential to improve decision-making and project outcomes in the face of significant uncertainties.

stat.AP↗
arXiv2024

Enhanced sequential directional importance sampling for structural reliability analysis

Sequential directional importance sampling (SDIS) is an efficient adaptive simulation method for estimating failure probabilities. It expresses the failure probability as the product of a group of integrals that are easy to estimate, wherein the first one is estimated with Monte Carlo simulation (MCS), and all the subsequent ones are estimated with directional importance sampling. In this work, we propose an enhanced SDIS method for structural reliability analysis. We discuss the efficiency of MCS for estimating the first integral in standard SDIS and propose using Subset Simulation as an alternative method. Additionally, we propose a Kriging-based active learning algorithm tailored to identify multiple roots in certain important directions within a specificed search interval. The performance of the enhanced SDIS is demonstrated through various complex benchmark problems. The results show that the enhanced SDIS is a versatile reliability analysis method that can efficiently and robustly solve challenging reliability problems

stat.ME↗
arXiv2024

Branch-and-bound algorithm for efficient reliability analysis of general coherent systems

Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event, which can be re-used when the input probability distributions change over time or when new data is available. However, existing branch-and-bound algorithms can handle only a limited set of system performance functions, mostly network connectivity and maximum flow. Furthermore, they run redundant analyses on component vector states whose system state can be inferred from previous analysis results. This study addresses these limitations by proposing branch and bound for reliability analysis of general coherent systems} (BRC) algorithm: an algorithm that automatically finds minimal representations of failure/survival events of general coherent systems. Computational efficiency is attained by dynamically inferring importance of component events from hitherto obtained results. We demonstrate advantages of the BRC method as a real-time risk management tool by application to the Eastern Massachusetts highway benchmark network.

math.OC↗
arXiv2024

State Space Kriging model for emulating complex nonlinear dynamical systems under stochastic excitation

We present a new surrogate model for emulating the behavior of complex nonlinear dynamical systems with external stochastic excitation. The model represents the system dynamics in state space form through a sparse Kriging model. The resulting surrogate model is termed state space Kriging (S2K) model. Sparsity in the Kriging model is achieved by selecting an informative training subset from the observed time histories of the state vector and its derivative with respect to time. We propose a tailored technique for designing the training time histories of state vector and its derivative, aimed at enhancing the robustness of the S2K prediction. We validate the performance of the S2K model with various benchmarks. The results show that S2K yields accurate prediction of complex nonlinear dynamical systems under stochastic excitation with only a few training time histories of state vector.

math.DS↗
arXiv2024

FORM-based global reliability sensitivity analysis of systems with multiple failure modes

Global variance-based reliability sensitivity indices arise from a variance decomposition of the indicator function describing the failure event. The first-order indices reflect the main effect of each variable on the variance of the failure event and can be used for variable prioritization; the total-effect indices represent the total effect of each variable, including its interaction with other variables, and can be used for variable fixing. This contribution derives expressions for the variance-based reliability indices of systems with multiple failure modes that are based on the first-order reliability method (FORM). The derived expressions are a function of the FORM results and, hence, do not require additional expensive model evaluations. They do involve the evaluation of multinormal integrals, for which effective solutions are available. We demonstrate that the derived expressions enable an accurate estimation of variance-based reliability sensitivities for general system problems to which FORM is applicable.

stat.ME↗
arXiv2024

Monitoring-Supported Value Generation for Managing Structures and Infrastructure Systems

To maximize its value, the design, development and implementation of Structural Health Monitoring (SHM) should focus on its role in facilitating decision support. In this position paper, we offer perspectives on the synergy between SHM and decision-making. We propose a classification of SHM use cases aligning with various dimensions that are closely linked to the respective decision contexts. The types of decisions that have to be supported by the SHM system within these settings are discussed along with the corresponding challenges. We provide an overview of different classes of models that are required for integrating SHM in the decision-making process to support management and operation and maintenance of structures and infrastructure systems. Fundamental decision-theoretic principles and state-of-the-art methods for optimizing maintenance and operational decision-making under uncertainty are briefly discussed. Finally, we offer a viewpoint on the appropriate course of action for quantifying, validating and maximizing the added value generated by SHM. This work aspires to synthesize the different perspectives of the SHM, Prognostic Health Management (PHM), and reliability communities, and deliver a roadmap towards monitoring-based decision support.

cs.CY↗
arXiv2023

An investigation of belief-free DRL and MCTS for inspection and maintenance planning

We propose a novel Deep Reinforcement Learning (DRL) architecture for sequential decision processes under uncertainty, as encountered in inspection and maintenance (I&M) planning. Unlike other DRL algorithms for (I&M) planning, the proposed +RQN architecture dispenses with computing the belief state and directly handles erroneous observations instead. We apply the algorithm to a basic I&M planning problem for a one-component system subject to deterioration. In addition, we investigate the performance of Monte Carlo tree search for the I&M problem and compare it to the +RQN. The comparison includes a statistical analysis of the two methods' resulting policies, as well as their visualization in the belief space.

cs.AI↗
arXiv2023

Bayesian improved cross entropy method with categorical mixture models

We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture as the parametric family to capture the dependence among network components. At each iteration of the BiCE method, the mixture parameters are updated through the weighted maximum a posteriori (MAP) estimate, which mitigates the overfitting issue of the standard improved cross entropy (iCE) method through a novel balanced prior, and we propose a generalized version of the expectation-maximization (EM) algorithm to approximate this weighted MAP estimate. The resulting importance sampling distribution is proved to be unbiased. For choosing a proper number of components $K$ in the mixture, we compute the Bayesian information criterion (BIC) of each candidate $K$ as a by-product of the generalized EM algorithm. The performance of the proposed method is investigated through a simple illustration, a benchmark study, and a practical application. In all these numerical examples, the BiCE method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.

stat.ME↗