A data-centric approach to generative modelling for 3D-printed steel

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products.

Spatio-temporal Kriging of Lower Caribbean Wind Data

Planning of a wind farm location requires significant data. However, wind speed data sets in the lower Caribbean are usually incomplete. This paper considers imputation by spatio-temporal kriging using data from neighbouring locations. Temporal basis functions with spatial covariates are used to model diurnal wind speed cyclicity. The residual set of our spatio-temporal model is modelled as a Gaussian spatial random field. Fitted models may be used for spatial prediction as well as imputation. Examples of predictions are illustrated using two months of hourly data from eight Caribbean locations with prediction accuracy being assessed by cross validation and residuals.

Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.

Spatial Model for Corrosion in Ships and FPSOs

Corrosion in ship structures is influenced by a variety of factors that are varying in time and space. Existing corrosion models used in practice only partially address the spatial variability of the corrosion process. Typical estimations of corrosion parameters are based on averaging measurements over structural elements from different ships and operational conditions, without considering the variability among and within the elements. However, this variability is important when determining the necessary inspection coverage, and it may influence the reliability of the ship structure. We develop a probabilistic spatio-temporal corrosion model based on a hierarchical approach, which represents the spatial variability of the corrosion process. The model includes the hierarchical levels vessel – compartment – frame – structural element – plate element. At all levels, variables representing common influencing factors are introduced. Moreover, at the lowest level, which is the one of the plate element, the corrosion process is modeled as a spatial random field. For illustrative purposes, the model is trained through Bayesian analysis with measurement data from a group of tankers. In this application it is found that there is significant spatial dependence among corrosion processes in different parts of the ships, which the proposed hierarchical model can capture. Finally, it is demonstrated how this spatial dependence can be exploited when making inference on the future condition of the ships.