arXiv subjects

Daniel Straub

Publications and source records attributed to Daniel Straub.

At least 37 records · Page 2Linked to original sources

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

A metric for assessing and optimizing data-driven prognostic algorithms for predictive maintenance

Prognostic Health Management aims to predict the Remaining Useful Life (RUL) of degrading components/systems utilizing monitoring data. These RUL predictions form the basis for optimizing maintenance planning in a Predictive Maintenance (PdM) paradigm. We here propose a metric for assessing data-driven prognostic algorithms based on their impact on downstream PdM decisions. The metric is defined in association with a decision setting and a corresponding PdM policy. We consider two typical PdM decision settings, namely component ordering and/or replacement planning, for which we investigate and improve PdM policies that are commonly utilized in the literature. All policies are evaluated via the data-based estimation of the long-run expected maintenance cost per unit time, using monitored run-to-failure experiments. The policy evaluation enables the estimation of the proposed metric. We employ the metric as an objective function for optimizing heuristic PdM policies and algorithms' hyperparameters. The effect of different PdM policies on the metric is initially investigated through a theoretical numerical example. Subsequently, we employ four data-driven prognostic algorithms on a simulated turbofan engine degradation problem, and investigate the joint effect of prognostic algorithm and PdM policy on the metric, resulting in a decision-oriented performance assessment of these algorithms.

stat.AP↗

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↗

arXiv2023

POMDP inference and robust solution via deep reinforcement learning: An application to railway optimal maintenance

Partially Observable Markov Decision Processes (POMDPs) can model complex sequential decision-making problems under stochastic and uncertain environments. A main reason hindering their broad adoption in real-world applications is the lack of availability of a suitable POMDP model or a simulator thereof. Available solution algorithms, such as Reinforcement Learning (RL), require the knowledge of the transition dynamics and the observation generating process, which are often unknown and non-trivial to infer. In this work, we propose a combined framework for inference and robust solution of POMDPs via deep RL. First, all transition and observation model parameters are jointly inferred via Markov Chain Monte Carlo sampling of a hidden Markov model, which is conditioned on actions, in order to recover full posterior distributions from the available data. The POMDP with uncertain parameters is then solved via deep RL techniques with the parameter distributions incorporated into the solution via domain randomization, in order to develop solutions that are robust to model uncertainty. As a further contribution, we compare the use of transformers and long short-term memory networks, which constitute model-free RL solutions, with a model-based/model-free hybrid approach. We apply these methods to the real-world problem of optimal maintenance planning for railway assets.

cs.LG↗

arXiv2023

Variance-based reliability sensitivity with dependent inputs using failure samples

Reliability sensitivity analysis is concerned with measuring the influence of a system's uncertain input parameters on its probability of failure. Statistically dependent inputs present a challenge in both computing and interpreting these sensitivity indices; such dependencies require discerning between variable interactions produced by the probabilistic model describing the system inputs and the computational model describing the system itself. To accomplish such a separation of effects in the context of reliability sensitivity analysis we extend on an idea originally proposed by Mara and Tarantola (2012) for model outputs unrelated to rare events. We compute the independent (influence via computational model) and full (influence via both computational and probabilistic model) contributions of all inputs to the variance of the indicator function of the rare event. We compute this full set of variance-based sensitivity indices of the rare event indicator using a single set of failure samples. This is possible by considering $d$ different hierarchically structured isoprobabilistic transformations of this set of failure samples from the original $d$-dimensional space of dependent inputs to standard-normal space. The approach facilitates computing the full set of variance-based reliability sensitivity indices with a single set of failure samples obtained as the byproduct of a single run of a sample-based rare event estimation method. That is, no additional evaluations of the computational model are required. We demonstrate the approach on a test function and two engineering problems.

stat.AP↗

arXiv2022

Bridging POMDPs and Bayesian decision making for robust maintenance planning under model uncertainty: An application to railway systems

Structural Health Monitoring (SHM) describes a process for inferring quantifiable metrics of structural condition, which can serve as input to support decisions on the operation and maintenance of infrastructure assets. Given the long lifespan of critical structures, this problem can be cast as a sequential decision making problem over prescribed horizons. Partially Observable Markov Decision Processes (POMDPs) offer a formal framework to solve the underlying optimal planning task. However, two issues can undermine the POMDP solutions. Firstly, the need for a model that can adequately describe the evolution of the structural condition under deterioration or corrective actions and, secondly, the non-trivial task of recovery of the observation process parameters from available monitoring data. Despite these potential challenges, the adopted POMDP models do not typically account for uncertainty on model parameters, leading to solutions which can be unrealistically confident. In this work, we address both key issues. We present a framework to estimate POMDP transition and observation model parameters directly from available data, via Markov Chain Monte Carlo (MCMC) sampling of a Hidden Markov Model (HMM) conditioned on actions. The MCMC inference estimates distributions of the involved model parameters. We then form and solve the POMDP problem by exploiting the inferred distributions, to derive solutions that are robust to model uncertainty. We successfully apply our approach on maintenance planning for railway track assets on the basis of a "fractal value" indicator, which is computed from actual railway monitoring data.

cs.AI↗

arXiv2022

Bayesian improved cross entropy method for network reliability assessment

We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.

stat.AP↗

arXiv2022

A framework for quantifying the value of vibration-based structural health monitoring

The difficulty in quantifying the benefit of Structural Health Monitoring (SHM) for decision support is one of the bottlenecks to an extensive adoption of SHM on real-world structures. In this paper, we present a framework for such a quantification of the value of vibration-based SHM, which can be flexibly applied to different use cases. These cover SHM-based decisions at different time scales, from near-real time diagnostics to the prognosis of slowly evolving deterioration processes over the lifetime of a structure. The framework includes an advanced model of the SHM system. It employs a Bayesian filter for the tasks of sequential joint deterioration state-parameter estimation and structural reliability updating, using continuously identified modal and intermittent visual inspection data. It also includes a realistic model of the inspection and maintenance decisions throughout the structural life-cycle. On this basis, the Value of SHM is quantified by the difference in expected total life-cycle costs with and without the SHM. We investigate the framework through application on a numerical model of a two-span bridge system, subjected to gradual and shock deterioration, as well as to changing environmental conditions, over its lifetime. The results show that this framework can be used as an a-priori decision support tool to inform the decision on whether or not to install a vibration-based SHM system on a structure, for a wide range of SHM use cases.

stat.AP↗

arXiv2022

On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an off-line (batch) or an on-line (recursive) Bayesian framework. With a focus on the quantification of the full parameter uncertainty, we review, adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model is used to approximate the posterior distribution within the resampling process in all three filters. Two numerical examples serve as the basis for a comparative assessment of off-line and on-line Bayesian estimation of time-invariant deterioration model parameters. The first case study considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential crack monitoring measurements. The second high-dimensional, linear, Gaussian case study employs a random field to model corrosion deterioration across a beam, which is updated with sequential measurements from sensors. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.

stat.CO↗

arXiv2022

Sequential active learning of low-dimensional model representations for reliability analysis

To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modelling termed partial least squares-driven polynomial chaos expansion (PLS-PCE) to render such problems feasible. Standalone surrogate models typically perform poorly for reliability analysis. Therefore, in a previous work, we have used PLS-PCEs to reconstruct the intermediate densities of a sequential importance sampling approach to reliability analysis. Here, we extend this approach with an active learning procedure that allows for improved error control at each importance sampling level. To this end, we formulate an estimate of the combined estimation error for both the subspace identified in the dimension reduction step and surrogate model constructed therein. With this, it is possible to adapt the design of experiments so as to optimally learn the subspace representation and the surrogate model constructed therein. The approach is gradient-free and thus can be directly applied to black box-type models. We demonstrate the performance of this approach with a series of low- (2 dimensions) to high- (869 dimensions) dimensional example problems featuring a number of well-known caveats for reliability methods besides high dimensions and expensive computational models: strongly nonlinear limit-state functions, multiple relevant failure regions and small probabilities of failure.

stat.CO↗

arXiv2022

Certified Dimension Reduction for Bayesian Updating with the Cross-Entropy Method

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is updated with the observations to compute the posterior parameter distribution. Solving for the posterior distribution can be challenging when, e.g., prior and posterior significantly differ from one another and/or the parameter space is high-dimensional. We use a sequence of importance sampling measures that arise by tempering the likelihood to approach inverse problems exhibiting a significant distance between prior and posterior. Each importance sampling measure is identified by cross-entropy minimization as proposed in the context of Bayesian inverse problems in Engel et al. (2021). To efficiently address problems with high-dimensional parameter spaces we set up the minimization procedure in a low-dimensional subspace of the original parameter space. The principal idea is to analyse the spectrum of the second-moment matrix of the gradient of the log-likelihood function to identify a suitable subspace. Following Zahm et al. (2021), an upper bound on the Kullback-Leibler-divergence between full-dimensional and subspace posterior is provided, which can be utilized to determine the effective dimension of the inverse problem corresponding to a prescribed approximation error bound. We suggest heuristic criteria for optimally selecting the number of model and model gradient evaluations in each iteration of the importance sampling sequence. We investigate the performance of this approach using examples from engineering mechanics set in various parameter space dimensions.

stat.CO↗

arXiv2022

A unifying review of NDE models towards optimal decision support

Non-destructive evaluation (NDE) inspections are an integral part of asset integrity management. The relationship between the condition of interest and the quantity measured by NDE is described with probabilistic models such as PoD or ROC curves. These models are used to assess the quality of the information provided by NDE systems, which is affected by factors such as the experience of the inspector, environmental conditions, ease of access, and the precision of the measurement device. In this paper, we review existing probabilistic models of NDE andshow how they are connected within a unifying framework. This frameworkprovides insights into how these models should be learned, calibrated, and applied. We investigate and highlighthow the choice of the model can affect the maintenance decisions taken on the basis of NDE results. In addition, we analyze the impact of experimental design on the performance of a given NDE system in a decision-making context.

stat.AP↗

arXiv2021

Decision-theoretic reliability sensitivity

We propose and discuss sensitivity metrics for reliability analysis, which are based on the value of information. These metrics are easier to interpret than other existing sensitivity metrics in the context of a specific decision and they are applicable to any type of reliability assessment, including those with dependent inputs. We develop computational strategies that enable efficient evaluation of these metrics, in some scenarios without additional runs of the deterministic model. The metrics are investigated by application to numerical examples.

math.OC↗

arXiv2021

Value of information from vibration-based structural health monitoring extracted via Bayesian model updating

Quantifying the value of the information extracted from a structural health monitoring (SHM) system is an important step towards convincing decision makers to implement these systems. We quantify this value by adaptation of the Bayesian decision analysis framework. In contrast to previous works, we model in detail the entire process of data generation to processing, model updating and reliability calculation, and investigate it on a deteriorating bridge system. The framework assumes that dynamic response data are obtained in a sequential fashion from deployed accelerometers, subsequently processed by an output-only operational modal analysis scheme for identifying the system's modal characteristics. We employ a classical Bayesian model updating methodology to sequentially learn the deterioration and estimate the structural damage evolution over time. This leads to sequential updating of the structural reliability, which constitutes the basis for a preposterior Bayesian decision analysis. Alternative actions are defined and a heuristic-based approach is employed for the life-cycle optimization. By solving the preposterior Bayesian decision analysis, one is able to quantify the benefit of the availability of long-term SHM vibrational data. Numerical investigations show that this framework can provide quantitative measures on the optimality of an SHM system in a specific decision context.

stat.AP↗

arXiv2021

Optimal adaptive inspection and maintenance planning for deteriorating structural systems

Optimizing inspection and maintenance (I&M) plans for a large deteriorating structure is a computationally challenging task, in particular if one considers interdependences among its components. This is due to the sheer number of possible decision alternatives over the lifetime of the structure and the uncertainty surrounding the deterioration processes, the structural performance and the outcomes of inspection and maintenance actions. To address this challenge, Luque and Straub (2019) proposed a heuristic approach in which I&M plans for structural systems are defined through a set of simple decision rules. Here, we formalize the optimization of these decision rules and extend the approach to enable adaptive planning. The initially optimal I&M plan is successively adapted throughout the service life, based on past inspection and monitoring results. The proposed methodology uses stochastic deterioration models and accounts for the interdependence among structural components. The heuristic-based adaptive planning is illustrated for a structural frame subjected to fatigue.

eess.SY↗

arXiv2020

Cross-entropy-based importance sampling with failure-informed dimension reduction for rare event simulation

The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model. Importance sampling with the cross-entropy method offers an efficient way to address such problems provided that a suitable parametric family of biasing densities is employed. Although some existing parametric distribution families are designed to perform efficiently in high dimensions, their applicability within the cross-entropy method is limited to problems with dimension of O(1e2). In this work, rather than directly building sampling densities in high dimensions, we focus on identifying the intrinsic low-dimensional structure of the rare event simulation problem. To this end, we exploit a connection between rare event simulation and Bayesian inverse problems. This allows us to adapt dimension reduction techniques from Bayesian inference to construct new, effectively low-dimensional, biasing distributions within the cross-entropy method. In particular, we employ the approach in [47], as it enables control of the error in the approximation of the optimal biasing distribution. We illustrate our method using two standard high-dimensional reliability benchmark problems and one structural mechanics application involving random fields.

stat.CO↗

arXiv2019

Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines

The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series representation through retaining only the most important basis terms. In this work, we present a novel sparse Bayesian learning technique for obtaining sparse Polynomial Chaos expansions which is based on a Relevance Vector Machine model and is trained using Variational Inference. The methodology shows great potential in high-dimensional data-driven settings using relatively few data points and achieves user-controlled sparse levels that are comparable to other methods such as compressive sensing. The proposed approach is illustrated on two numerical examples, a synthetic response function that is explored for validation purposes and a low-carbon steel plate with random Young's modulus and random loading, which is modeled by stochastic finite element with 38 input random variables.

stat.ML↗

arXiv2012

Bayesian Network Enhanced with Structural Reliability Methods: Application

The enhanced Bayesian network (eBN) methodology described in the companion paper facilitates the assessment of reliability and risk of engineering systems when information about the system evolves in time. We present the application of the eBN (a) to the assessment of the life-cycle reliability of a structural system, (b) to the optimization of a decision on performing measurements in that structural system, and (c) to the risk assessment of an infrastructure system subject to natural hazards and deterioration of constituent structures. In all applications, observations of system performances or the hazards are made at various points in time and the eBN efficiently includes these observations in the analysis to provide an updated probabilistic model of the system at all times.

stat.AP↗