Full Probabilistic Analysis Research Articles

Estimating metocean environments associated with extreme structural response to demonstrate the dangers of environmental contour methods

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution of the ocean environment and for wave–structure interaction, EVA provides a basis for full probabilistic design analysis. Alternatively, environmental contours provide an approximate approach to estimating structural integrity, without requiring structural knowledge. These contour methods also exploit statistical models, including EVA, but avoid the need for structural modelling by making what are believed to be conservative assumptions about the shape of the structural failure boundary in the environment space. These assumptions, however, may not always be appropriate, or may lead to unnecessary wasted resources from over design. We demonstrate a methodology for efficient fully probabilistic analysis of structural failure. From this, we estimate the joint conditional probability density of the environment (CDE), given the occurrence of an extreme structural response. We use CDE as a diagnostic to highlight the deficiencies of environmental contour methods for design; none of the IFORM environmental contours considered characterise CDE well for three example structures.

Service Life Design of Concrete Structures Made of High-Volume Limestone Powder Concrete—Case of the Carbonation-Induced Corrosion

One of the paths to CO2 emissions reduction in the concrete industry is to use low-clinker cements, providing at the same time the performance of concrete that is adequate for application in concrete structures. This paper explores the impact of the clinker replacement with high amounts of limestone powder (21–70% in the powder phase) on concrete carbonation resistance. To quantify this impact, the empirical relationship between the carbonation resistance and the compressive strength of the high-volume limestone powder concrete (HVLPC) was established. For that purpose, the regression analysis was applied on the experimental results collected from the published research. The service life analysis based on the full probabilistic approach was performed using the fib Model Code 2010 prediction model and proposed empirical relationship. The first-order reliability method (FORM) was applied to solve the limit state function of reinforcement depassivation with a reliability index equal to 1.3. The obtained minimum concrete cover depths were 40–110% higher compared to those prescribed in the current European standard EN 1992-1-1:2004 for indicative strength classes. Based on the full probabilistic analysis, recommended cover depths are given for all carbonation exposure classes, commonly applied concrete strength classes, and service lives of 50 and 100 years.

Rank-based Bayesian variable selection for genome-wide transcriptomic analyses.

Variable selection is crucial in high-dimensional omics-based analyses, since it is biologically reasonable to assume only a subset of non-noisy features contributes to the data structures. However, the task is particularly hard in an unsupervised setting, and a priori ad hoc variable selection is still a very frequent approach, despite the evident drawbacks and lack of reproducibility. We propose a Bayesian variable selection approach for rank-based unsupervised transcriptomic analysis. Making use of data rankings instead of the actual continuous measurements increases the robustness of conclusions when compared to classical statistical methods, and embedding variable selection into the inferential tasks allows complete reproducibility. Specifically, we develop a novel extension of the Bayesian Mallows model for variable selection that allows for a full probabilistic analysis, leading to coherent quantification of uncertainties. Simulation studies demonstrate the versatility and robustness of the proposed method in a variety of scenarios, as well as its superiority with respect to several competitors when varying the data dimension or data generating process. We use the novel approach to analyze genome-wide RNAseq gene expression data from ovarian cancer patients: several genes that affect cancer development are correctly detected in a completely unsupervised fashion, showing the usefulness of the method in the context of signature discovery for cancer genomics. Moreover, the possibility to also perform uncertainty quantification plays a key role in the subsequent biological investigation.

Quantitative Risk Analysis of Oil and Gas Fires and Explosions for FPSO Systems in China

The LH11-1 FPSO is an 80,000 t cylindrical structure that is responsible for the processing, storage, and offloading of process oil from existing and newly developed oilfields. In this paper, a full probabilistic analysis was developed based on very detailed CFD simulation results to evaluate ventilation, gas dispersion, explosion, and fire scenarios. A detailed fire and explosion risk analysis of LH11-1 FPSO was performed based on NORSOK Z-013 and FABIG Technical Note 11. The risk-based calculations were performed applying FLACS, KFX, and DNV GLEXPRESS Fire. Finally, the oil and gas dispersion, fire, and explosion consequence risks were calculated under the credible combination of leak frequency and leak location. By this probabilistic risk analysis, it was found that the west wind could generate optimal ventilation conditions for the topside process area of FPSO compared to other wind directions, while the hull region was poorly ventilated for all wind directions. The explosion risk analysis showed that the FPSO system would take no action in terms of explosion risk according to the acceptance criteria of 10−4 occ/year. Meanwhile, the fire risk analysis demonstrated that the PR1 first and second deck, PR2 first and second deck, process deck, offloading on starboard, and the base of the flare tower would have different impacts from the fire, and the PR1 first deck and PR2 first deck at the topside deck would be severely impacted regions.

Limit values of accelerated carbonation resistance to meet EC2 durability requirements

Although accelerated carbonation resistance has been extensively tested, there are no recommendations for the application of test results in codes of practice. The main objective of this study was to determine the limit values of accelerated carbonation resistance to satisfy the required service life of reinforced concrete structures with concrete covers as prescribed in EN 1992-1-1. The service life of 50 years was considered, as well as all carbonation exposure classes (from XC1 to XC4). A full probabilistic analysis was conducted using the fib-Bulletin 34 carbonation prediction model. Using the limit state function and a defined reliability index, the upper limits of the inverse effective carbonation resistance (R-1 ACC) for all exposure classes and in a function of concrete cover depth were determined. The determined values of R-1 ACC presented in this study represent the upper limit of the average value, as well as the maximum deviation of one sample in relation to this average value. Thus, a simple assessment of concrete quality is allowed in terms of carbonation resistance based on the accelerated carbonation depth measurements.

Full probabilistic analysis of random first‐order linear differential equations with Dirac delta impulses appearing in control

We study, from a probabilistic standpoint, first‐order impulsive linear differential equations, where all its parameters (initial condition and coefficients) are absolutely continuous random variables with a joint probability density function. We assume an infinite train of Dirac delta impulse applications at given time instants to control the model output. We take extensive advantage of the random variable transformation method to determine, first, an explicit expression for the probability density of the solution stochastic process, and secondly, of the random sequences for the maxima and minima. From these sequences, we determine the probability of stability of the solution stochastic process. This analysis is extended in the case that the application times are evenly spaced, via a period T, which is assumed to be a random variable. All the theoretical results are illustrated by means of several numerical examples, where we also perform a sensitivity analysis, via Sobol indexes, to highlight those model parameters that most explain the variability of the model response.

A full probabilistic analysis of a randomized kinetic model for reaction–deactivation of hydrogen peroxide decomposition with applications to real data

The classical kinetic equation has been broadly used to describe reaction and deactivation processes in chemistry. The mathematical formulation of this deterministic nonlinear differential equation depends on reaction and deactivation rate constants. In practice, these rates must be calculated via laboratory experiments, hence involving measurement errors. Therefore, it is more realistic to treat these rates as random variables rather than deterministic constants. This leads to the randomization of the kinetic equation, and hence its solution becomes a stochastic process. In this paper we address the probabilistic analysis of a randomized kinetic model to describe reaction and deactivation by catalase of hydrogen peroxide decomposition at a given initial concentration. In the first part of the paper, we determine closed-form expressions for the probability density functions of important quantities of the aforementioned chemical process (the fractional conversion of hydrogen peroxide, the time until a fixed quantity of this fractional conversion is reached and the activity of the catalase). These expressions are obtained by taking extensive advantage of the so called Random Variable Transformation technique. In the second part, we apply the theoretical results obtained in the first part together with the principle of maximum entropy to model the hydrogen peroxide decomposition and aspergillus niger catalase deactivation using real data excerpted from the recent literature. Our results show full agreement with previous reported analysis but having as additional benefit that they provide a more complete description of both model inputs and outputs since we take into account the intrinsic uncertainties involved in modelling process.

Reliability Verification of Existing RC Structures Using Partial Factors Approaches and Site-Specific Data

The assessment of an existing structure to determine its suitability for present and future use entails different sorts of problems than encountered when designing new structures. The differences revolve essentially around the nature of the information available. In existing structures, deteriorated or otherwise, the accuracy of the models used for such assessments can usually be improved by acquiring more data. The most accurate way to find actual load and resistance would be to conduct a probabilistic analysis using site data. This is a time-consuming process, however, calling for a working knowledge of probabilistic methods that may not be suited to everyday use by practising engineers. For this reason, in the past few years various studies have been conducted to develop assessment approaches, compatible with Eurocodes, which include the same verification format as normally applied for designing new structures. In this paper, the application of several of these approaches is illustrated by means of the reliability verification of one of the main beams of the reinforced concrete structure of an industrial building from the 1940s, recently transformed into a cultural centre. The obtained results are discussed and compared to the findings of a full probabilistic analysis.

Seismic reliability of axially loaded vertical piles

The reliability of single vertical pile foundations subjected to seismic loads is assessed and compared with the minimum acceptable reliability level for static load conditions mandated by the Canadian codes. The analysis is executed for a site with a mean shear-wave velocity of the top 30 m of the ground equal to 250 m/s subjected to the ground motion hazard of five Canadian cities. Using both a full probabilistic analysis and simplified probabilistic model, the results seem to indicate that the current design practice is unable to achieve the reliability target of the codes. The shortfall is particularly significant when the limiting pile settlement is relatively small. The calculated reliability level of small limiting settlements is impacted by the geotechnical variability, whereas the seismic hazard variability affects large pile limiting settlements. Finally, the simplified probabilistic model produces the same results as the full probabilistic model for large pile settlement and is a convenient tool to execute code calibration.

Probabilistic process simulation to predict process induced distortions of a composite frame

Within this work, an enhanced simulation strategy for predicting process-induced distortions and residual stresses of composite structures is developed, while taking into account probabilistic variations. The simulation strategy is demonstrated for a carbon fibre-reinforced frame of an aircraft fuselage. Based on a sequentially coupled temperature-displacement analysis, temperature and degree of cure distributions as well as stresses, strains, and distortions are determined. For the description of the reaction kinetic, a phenomenological-based model considering chemical and diffusion-controlled reactions is introduced. The mechanical material behavior is described by a viscoelastic material model depending on temperature, time, and degree of cure. Corresponding process-induced distortions and occurring residual stresses are calculated and analyzed. The results of the process-induced distortions are used to derive a compensated tooling design. To analyze the effect of statistical and systematic deviations of underlying process and material parameters, a procedure for a probabilistic process simulation is created. Based on a first sensitivity analysis, a design of experiment is performed over a specified parameter range. From this surrogate, models are derived to enable a full but efficient probabilistic analysis of spring-in angles and residual stresses at multiple frame positions. The effect of process parameter variations and fluctuation of inherent material properties on process-induced distortions is assessed. Moreover, the influence of different process cycles is shown. This allows to determine the expected range of the final part distortion and to derive the resulting tolerances during assembly. For validation of the probabilistic process simulation, several frames are manufactured at different process conditions, and frame geometries are measured by digital image correlation technique. The resulting part thicknesses, spring-in angles, and global frame distortions are determined. Finally, a comparison of measurements and probabilistic predictions is given, and results are evaluated with respect to main sensitivities.

Characterizing uncertain sea-level rise projections to support investment decisions.

Many institutions worldwide are considering how to include uncertainty about future changes in sea-levels and storm surges into their investment decisions regarding large capital infrastructures. Here we examine how to characterize deeply uncertain climate change projections to support such decisions using Robust Decision Making analysis. We address questions regarding how to confront the potential for future changes in low probability but large impact flooding events due to changes in sea-levels and storm surges. Such extreme events can affect investments in infrastructure but have proved difficult to consider in such decisions because of the deep uncertainty surrounding them. This study utilizes Robust Decision Making methods to address two questions applied to investment decisions at the Port of Los Angeles: (1) Under what future conditions would a Port of Los Angeles decision to harden its facilities against extreme flood scenarios at the next upgrade pass a cost-benefit test, and (2) Do sea-level rise projections and other information suggest such conditions are sufficiently likely to justify such an investment? We also compare and contrast the Robust Decision Making methods with a full probabilistic analysis. These two analysis frameworks result in similar investment recommendations for different idealized future sea-level projections, but provide different information to decision makers and envision different types of engagement with stakeholders. In particular, the full probabilistic analysis begins by aggregating the best scientific information into a single set of joint probability distributions, while the Robust Decision Making analysis identifies scenarios where a decision to invest in near-term response to extreme sea-level rise passes a cost-benefit test, and then assembles scientific information of differing levels of confidence to help decision makers judge whether or not these scenarios are sufficiently likely to justify making such investments. Results highlight the highly-localized and context dependent nature of applying Robust Decision Making methods to inform investment decisions.

Time-dependent seismic fragility curves for aging jacket-type offshore platforms subjected to earthquake ground motions

This paper assesses the seismic vulnerability of a recently designed jacket-type offshore platform through development of fragility curves and presents the formulation of time-dependent seismic fragility curves to capture the effects of ageing and deterioration on the seismic vulnerability of the representative platform. Among the various ageing processes, the corrosion deterioration of the structure is taken into account by applying a time-dependent model of corrosion deterioration of the tubular elements in the splash zone. Incremental dynamic analysis is performed on the initial uncorroded and corroded platforms considering soil–pile–structure interaction. A full probabilistic analysis is then performed to develop time-dependent seismic fragility curves for the immediate occupancy and collapse prevention limit states. Finally, a time variant cubic model is proposed to develop fragility curves at any point in time during platform’s service life, without need to perform a complete time-consuming fragility analyses. Results show substantial increase in probability of failure of the platform throughout its lifetime due to corrosion deterioration. The results also indicate that the time-dependent fragility curves can be used in offshore platforms to assess the seismic vulnerability of the structure and demonstrate the influence of various factors affecting the seismic vulnerability of the platform during its lifetime.

Performance of Fibre Reinforced Concrete Structures - Modelling of Damage and Reliability

Steel fibre reinforced concrete (FRC) has higher ductility, it can save amount of convention reinforcement, labour and in consequence costs of the structure. However, broader use of SFRC as construction material is limited among others by lack of design codes. According to the previous study, reliability and safety of ordinary reinforced engineering can be verified using non-linear finite element analysis and several safety formats that are proposed in fib Model Code 2010. In the presented paper, safety formats are applied for fibre reinforced structures such as tunnel lining precast segment and individual approaches are compared. As tensile and shear cracks or compressive crushing can develop in the fibre reinforced concrete under severe conditions, the design combining numerical and experimental investigations together with safety formats is appropriate method how to obtain safe and reliable structure. Finite element method and advanced material models taking into account FRC properties such as shape of tensile softening branch, high toughness and ductility are described in the paper. Since the variability of FRC material properties is rather high, full probabilistic analysis seems to be the most appropriate format for evaluation of structural performance, reliability and safety.

Cost-effectiveness and programmatic benefits of maternal vaccination against pertussis in England

Maternal pertussis immunisation was introduced during the pertussis resurgence in England in 2012 as a temporary measure to protect infants too young to be vaccinated. The programme was shown to be safe and highly effective. However, continuation of maternal vaccination as a routine programme requires a cost-effectiveness analysis. The estimated prevented disease burden among mothers and their infants was obtained assuming 89% (95% CI: 19%-99%) vaccine efficacy for mothers and 91% (95% CI: 84%-95%) for infants. Future incidence was projected based on the disease rates in 2010-2012, including the four-year cycle of low and high incidence years. Full probabilistic sensitivity analysis was performed for different scenarios. Assuming a vaccine coverage of 60%, there were 1650 prevented hospitalisations in infants (3.5% discounting, the first 10 years), including 55-60 deaths and ∼20,500 cases among mothers, of which around 1800 would be severe. The annual costs of the programme are £7.3 million assuming a price of £10 per dose and £9.4 million assuming £15 per dose. Using discounting of 3.5%, a 200 year time horizon and a price of £10 per dose (+£7.5 administration costs) only 25% of the iterations were below £30,000 per QALY. Using a 35% higher incidence resulted in 88% of the scenarios below this threshold. Assuming that the incidence remains at the level at the height of 2012, then the programme would be highly cost effective, with an ICER of £16,865 (£12,209-£25,976; price of £10 and 3.5%/3.5% discounting). Maternal vaccination is effective in preventing severe illness and deaths in infants but the cost-effectiveness of the programme is highly dependent on future incidence which is necessarily uncertain. However, the duration and magnitude of protection against transmission afforded by the current acellular vaccines is also uncertain as are the associated effects on future herd immunity. The direct protection offered by the maternal dose provides the only certain way of protecting vulnerable infants from birth.

Sparse multivariate function recovery with a small number of evaluations

In Kaltofen and Yang (2014) we give an algorithm based algebraic error-correcting decoding for multivariate sparse rational function interpolation from evaluations that can be numerically inaccurate and where several evaluations can have severe errors (“outliers”). Our 2014 algorithm can interpolate a sparse multivariate rational function from evaluations where the error rate 1/q is quite high, say q=5.For the algorithm with exact arithmetic and exact values at non-erroneous points, one avoids quadratic oversampling by using random evaluation points. Here we give the full probabilistic analysis for this fact, thus providing the missing proof to Theorem 2.1 in Section 2 of our ISSAC 2014 paper. Our argumentation already applies to our original 2007 sparse rational function interpolation algorithm (Kaltofen et al., 2007), where we have experimentally observed that for T unknown non-zero coefficients in a sparse candidate ansatz one only needs T+O(1) evaluations rather than O(T2) (cf. Candès and Tao sparse sensing), the latter of which we have proved in 2007. Here we prove that T+O(1) evaluations at random points indeed suffice.

Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii as well as to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Our main conclusions are: (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are key constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. [...]

Commentary: Priors, parameters, and probability: a bayesian perspective on sensitivity analysis.

Commentary: Priors, parameters, and probability: a bayesian perspective on sensitivity analysis.

The cost-effectiveness of a theory-based online health behaviour intervention for new university students: an economic evaluation.

BackgroundToo many young people engage in unhealthy behaviours such as eating unhealthily, being physically inactive, binge drinking and smoking. This study aimed to estimate the short-term and long-term cost-effectiveness of a theory-based online health behaviour intervention (“U@Uni”) in comparison with control in young people starting university.MethodsA costing analysis was conducted to estimate the full cost of U@Uni and the cost of U@Uni roll-out. The short-term cost-effectiveness of U@Uni was estimated using statistical analysis of 6-month cost and health-related quality of life data from the U@Uni randomised controlled trial. An economic modelling analysis combined evidence from the trial with published evidence of the effect of health behaviours on mortality risk and general population data on health behaviours, to estimate the lifetime cost-effectiveness of U@Uni in terms of incremental cost per QALY. Costs and effects were discounted at 1.5% per annum. A full probabilistic sensitivity analysis was conducted to account for uncertainty in model inputs and provide an estimate of the value of information for groups of important parameters.ResultsTo implement U@Uni for the randomised controlled trial was estimated to cost £292 per participant, whereas roll-out to another university was estimated to cost £19.71, both giving a QALY gain of 0.0128 per participant. The short-term (6-month) analysis suggested that U@Uni would not be cost-effective at a willingness-to-pay threshold of £20,000 per QALY (incremental cost per QALY gained = £243,926). When a lifetime horizon was adopted the results suggest that the full implementation of U@Uni is unlikely to be cost-effective, whereas the roll-out of U@Uni to another university is extremely likely to be cost-effective. The value of information analysis suggests that the most important drivers of decision uncertainty are uncertainties in the effect of U@Uni on health behaviours.ConclusionsThe study provides the first estimate of the costs and cost-effectiveness of an online health behaviour intervention targeted at new university students. The results suggest that the roll-out, but not the full implementation, of U@Uni would be a cost-effective decision for the UK Department of Health, given a lifetime perspective and a willingness-to pay threshold of £20,000 per QALY.Trial registrationCurrent Controlled Trials ISRCTN67684181.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2458-14-1011) contains supplementary material, which is available to authorized users.

Full-Probabilistic Analysis of Concrete Beams During Fire

Asimplified full-probabilistic calculation tool is developed which is capable of calculating the bending moment capacity of simply supported beams exposed to fire. It is found that the uncertainty with respect to the reduction factors for the material properties at elevated temperatures and the uncertainty with respect to the concrete cover have a negative effect on the safety level corresponding to the design value of the bending moment capacity calculated according to the Eurocode. Furthermore, the model allows an objective comparison of different design alternatives with respect to the safety level.

A Seismic Reliability Assessment of Reinforced Concrete Integral Bridges Subject to Corrosion

This paper seeks to determine the effect deterioration has on the seismic vulnerability of a 3 span integral concrete bridge. Traditionally it has been common to neglect the effects of deterioration when assessing the seismic vulnerability of bridges. However, since a lot of the bridges currently being assessed for retrofit are approaching the end of their design life, deterioration is often significant. Furthermore, since deterioration affects the main force resisting components of a bridge, it is reasonable to assume that it might affect its performance during an earthquake. For this paper, chloride induced corrosion of the reinforcing steel in the columns and in the deck has been considered. Corrosion is represented by a loss of steel cross section and strength. A 3 dimensional non-linear finite element model is created using the finite element platform Opensees. A full probabilistic analysis is conducted to develop time-dependent fragility curves. These fragility curves give the probability of reaching or exceeding a defined damage limit state, for a given ground motion intensity measure taken as Peak Ground Acceleration (PGA). This analysis accounts for variation in ground motion, material and corrosion parameters when assessing its overall seismic performance as well as the performance of its most critical components. The results of the study show that all components experience an increase in fragility with age, but that the columns are the most sensitive component to aging and dominate the system fragility for this bridge type.