Domenic Di Francesco

In pipelines, pressure vessels and various other steel structures, the remaining thickness of a corroding ligament can be measured directly and repeatedly over time. Statistical analysis of these measurements is a common approach for estimating the rate of corrosion growth, where the uncertainties associated with the inspection activity are taken into account. An additional source of variability in such calculations is the epistemic uncertainty associated with the limited number of measurements that are available to engineers at any point in time. Traditional methods face challenges in fitting models to limited or missing datasets. In such cases, deterministic upper bound values, as recommended in industrial guidance, are sometimes assumed for the purpose of integrity management planning. In this paper, Bayesian inference is proposed as a means for representing available information in consistency with evidence. This, in turn, facilitates decision support in the context of risk-informed integrity management. Aggregating inspection data from multiple locations does not account for the possible variability between the locations, and creating fully independent models can result in excessive levels of uncertainty at locations with limited data. Engineers intuitively acknowledge that the areas with more sites of corrosion should, to some extent, inform estimates of growth rates in other locations. Bayesian multi-level (hierarchical) models provide a mathematical basis for achieving this by means of the appropriate pooling of information, based on the homogeneity of the data. Included in this paper is an outline of the process of fitting a Bayesian multi-level model and a discussion of the benefits and challenges of pooling inspection data between distinct locations, using example calculations and simulated data.

Engineers use semi-empirical models of complex degradation phenomena to manage the integrity of structural systems. Historically, the intended application of these models has been to perform deterministic calculations to demonstrate that failure is not expected. However, as integrity management systems are increasingly optimised decision makers require quantified likelihoods of events such as failure to help ensure that maintenance investments are completed where and when they are worthwhile. In the probabilistic application of degradation models, inherent and un-quantified conservatism can lead to ineffective risk management. Bayesian analysis can be used to fit semi-empirical degradation models to existing test data (and can be updated if new data is available) such that the variability within, and the inter-dependency between all model parameters is quantified. This includes model uncertainty parameters. In this paper, an SN curve and a two-stage Paris Law model have been fitted using Markov Chain Monte Carlo sampling. The benefits and challenges associated with this approach are discussed in the context of existing standards and guidelines developed for industry. Posterior predictive sampling is used to demonstrate how the models can be used to produce results that are fully compatible with a Bayesian decision analysis.

Engineers perform fatigue assessments to support structural integrity management. Given that the purpose of these calculations is linked to problems of decision making under various sources of uncertainty, probabilistic methods are often more useful than deterministic alternatives. Guidance on the direct probabilistic application of procedures in existing industrial standards is currently limited and dependencies between marginal probabilistic models are generally not considered, despite their potential significance being acknowledged. This paper proposes the use of Bayesian data analysis as a flexible and intuitive approach to coherently and consistently account for uncertainty and dependency in fatigue crack growth rate models. Various Bayesian models are established and presented, based on the same data as the existing models in BS 7910 (a widely used industrial standard). The models are compared in terms of their out of sample predictive accuracy, using methods with a basis in information theory and cross-validation. The Bayesian models exhibit an improved performance, with the most accurate predictions resulting from multi-level (hierarchical) models, which account for variation between constituent test datasets and partially pool information.

All engineering structures degrade or become damaged in service to some extent. Information collection activities, such as inspection or structural health monitoring can reduce uncertainty in probabilistic models of structural condition. By linking the information that they provide to the improved integrity management strategies that they facilitate, their expected value can be quantified. This value of information can be obtained using Bayesian decision analysis. In this work an extended value of information model is presented that accounts for the risk associated with exposure to a hazardous environment. By evaluating this risk on the same scale as the risk of structural failure, the relationship between the expected quality of information and the number of staff-hours in a hazardous environment (such as an offshore oil and gas platform) is investigated. An example case study identifies the requirements regarding the precision, bias, and reliability of information from autonomous or remote inspection methods, for them to be considered as an optimal risk management strategy.

Attempts to formalize inspection and monitoring strategies in industry have struggled to combine evidence from multiple sources (including subject matter expertise) in a mathematically coherent way. The perceived requirement for large amounts of data are often cited as the reason that quantitative risk-based inspection is incompatible with the sparse and imperfect information that is typically available to structural integrity engineers. Current industrial guidance is also limited in its methods of distinguishing quality of inspections, as this is typically based on simplified (qualitative) heuristics. In this paper, Bayesian multi-level (partial pooling) models are proposed as a flexible and transparent method of combining imperfect and incomplete information, to support decision-making regarding the integrity management of in-service structures. This work builds on the established theoretical framework for computing the expected value of information, by allowing for partial pooling between inspection measurements (or groups of measurements). This method is demonstrated for a simulated example of a structure with active corrosion in multiple locations, which acknowledges that the data will be associated with some precision, bias, and reliability. Quantifying the extent to which an inspection of one location can reduce uncertainty in damage models at remote locations has been shown to influence many aspects of the expected value of an inspection. These results are considered in the context of the current challenges in risk based structural integrity management.