Dynamic spatio-temporal models integrating physics for extreme environmental processes

Though accident data have been collected across industries, they may inherently contain uncertainty of randomness and fuzziness which in turn leads to misleading interpretation of the analysis. To handle the issue of uncertainty within accident data, the present work proposes a rough set theory (RST)-based approach to provide rule-based solution to the industry to minimize the number of accidents at work. Using RST and RST-based rule generation algorithm Learning by Example Module: Version 2 (LEM2), 279 important rules are extracted from the accident data obtained from an integrated steel industry to analyze the incident outcomes (injury, near miss and property damage). The results of the proposed methodology explore some of the important findings which are useful for the industry perspective. Therefore, the RST-based approach can be effective and efficient as well because of its potential to produce good results in the presence of uncertainty in data.

We present a novel method for predicting the performance of an object recognition approach in the presence of data uncertainty, occlusion and clutter. The recognition approach uses a vote-based decision criterion, which selects the object/pose hypothesis that has the maximum number of consistent features (votes) with the scene data. The prediction method determines a fundamental, optimistic, limit on achievable performance by any vote-based recognition system. It captures the structural similarity between model objects, which is a fundamental factor in determining the recognition performance. Given a bound on data uncertainty, we determine the structural similarity between every pair of model objects. This is done by computing the number of consistent features between the two objects as a function of the relative transformation between them. Similarity information is then used, along with statistical models for data distortion, to estimate the probability of correct recognition (PCR) as a function of occlusion and clutter rates. The method is validated by comparing predicted PCR plots with ones that are obtained experimentally.

Ground motion models (GMMs) are the key element of probabilistic seismic hazard assessment (PSHA). These models predict an earthquake ground motion intensity measure as a function of some independent variables that represent the earthquake source, path and site effects. The latter one can substantially influence the PSHA results since they are critical factors affecting the amplitude, frequency content, and duration of seismic waves. In regions with different geological characteristics, therefore, site effects should be appropriately accounted for in GMMs and thus PSHA. This is the case for southwest Iceland where due to its distinct geological characteristics (e.g., lava layers interbedded with sedimentary deposits), site-specific amplification varies significantly across different geological units, particularly at higher frequencies. In this study we develop a new set of GMMs with frequency-dependent site amplification factors for four site categories (i.e., hard rock, rock, lava, and stiff soil) in Iceland. We use advanced Bayesian hierarchical modeling (BHM). The BHM framework reduces uncertainty and enhances the reliability of predictions. The models also benefit from the inclusion of site-specific parameters, such as frequency-dependent amplification factors, which account for Iceland’s unique geological conditions. Moreover, due to the limited strong-motion data in Iceland, particularly for larger magnitudes, developing GMMs with all the essential terms such as magnitude saturation, magnitude-dependent distance scaling and inelastic attenuation terms, is challenging. In this regard, the Bayesian statistical approach can be particularly useful as it allows taking prior information about the model parameters into account and adding it to the information in the likelihood that stems from the observed data. This study utilized 83 strong-motion records from six strike-slip earthquakes (*Mw* 5.1–6.5), recorded at 34 seismic stations across diverse geological settings. In GMMs, uncertainty in the median prediction values is epistemic which depends on the GMM’s functional form. To consider the epistemic uncertainty therefore, we take different functional forms as those used and proposed in Kowsari et al. (2020), with a new functional form specifically calibrated to Icelandic strong-motions that incorporates depth-dependent magnitude scaling and frequency-independent site effects to improve the applicability of GMMs in Iceland. Later, this epistemic uncertainty can be taken into account in PSHA using either a backbone or logic tree approach. The Bayesian hierarchical ground motion models (BH-GMMs) developed in this study consider the attenuation of BH-GMMs for peak ground acceleration (*PGA*) at four site classes along with the observed Icelandic strong-motions for different magnitudes (*Mw* 5.2, *Mw* 6.4, *Mw* 7.2). The results indicated the capability of BH-GMMs to effectively capture the attenuation of *PGA* with distance for varying magnitudes. Moreover, the attenuation trends of observed PGAs, align closely with the model predictions for each geological unit, underscoring the importance of incorporating site-specific amplification in PSHA. The distinction in amplification behaviors, particularly at higher frequencies, provides critical insights into the interaction between seismic waves and geological units. This study highlights the critical role of local geological conditions in shaping seismic responses and sets a benchmark for future research in seismic hazard assessment, particularly in regions with complex geological and seismic environments like Southwest Iceland. Kowsari M, Sonnemann T, Halldorsson B, Hrafnkelsson B, Snæbjörnsson JÞ, Jónsson S. Bayesian Inference of Empirical Ground Motion Models to Pseudo-Spectral Accelerations of South Iceland Seismic Zone Earthquakes based on Informative Priors. Soil Dyn Earthq Eng 2020;132:106075. https://doi.org/10.1016/j.soildyn.2020.106075.

In this brief, a hierarchical Bayesian network modeling framework is formulated for large-scale process monitoring and decision making, which includes a basic layer and a functional layer. First, the whole process is decomposed into different units, where local Bayesian networks are constructed, providing monitoring information and decision-making capability for the upper layer. The network structure is determined automatically based on the process data in each local unit of the basic layer. Then, through incorporating the topological structure of the process, a functional Bayesian network is further constructed to infer the information from the basic layer, which can be customized according to user demands, such as fault detection, fault diagnosis, and classification of operating status. The performance of the proposed method is evaluated through a benchmark process.

Microstructure modelling quantifies subvoxel tissue features by combining an MRI acquisition with a mathematical model, which is typically fitted voxel-by-voxel with least-squares (LSQ) minimisation to give voxelwise maps of microstructural quantities such as diffusivity and compartmental fractions. Such approaches are susceptible to voxelwise noise, which can lead to erroneous values in parameter maps. Hierarchical Bayesian modelling (HBM) can address this limitation but has only been demonstrated for simple models. We previously derived an HBM approach for an arbitrary microstructure model with flexible parameter constraints, utilising a Markov chain Monte Carlo algorithm for parameter estimation; here, the method is demonstrated and evaluated using simulated and human data for two previously unexplored diffusion MRI techniques, namely, diffusion kurtosis imaging and blood-brain barrier filter exchange imaging. When compared with LSQ minimisation, HBM increased the accuracy, precision, contrast-to-noise ratio and parameter map quality in both simulated and human data. HBM was also able to resolve local parameter variations associated with white matter lesions in a small sample of cerebral small vessel disease subjects, which were obscured by high noise levels in the LSQ-derived parameter maps. Finally, a noise sensitivity assessment in simulations showed that HBM improved the contrast-to-noise ratio and parameter map quality even at low signal-to-noise ratios. This generalised HBM framework can improve parameter estimation for more complex diffusion MRI microstructural models that extend beyond linear combinations of exponentials.

SummaryReliable methods to downscale species distributions from coarse to fine grain (equivalent to resolution or support) hold great potential benefit for ecology and conservation. Existing methods have been based on partially unrealistic assumptions and yield mixed results.Here, we introduce a novel and simple approach for downscaling species distribution models based on a hierarchicalBayesian modelling (HBM) framework. Our approach treats putative (unknown) fine‐grain presences/absences as latent variables, which are modelled as a function of observed fine‐grain environmental variables and constrained by observed coarse‐grain presences/absences using logistic regression. The aim is to produce downscaled fine‐grain probabilities of species occurrence that (1) closely resemble the probabilities produced by a logistic model parameterized with the observed fine‐grain data (the ‘reference model’) and (2) are improvements over conventional downscaling methods. We additionally test how fine‐grain occupancy based on power‐law scale‐area relationships modifies the downscaling results. We test our approach on 127 bird species from the San Diego breeding atlas data surveyed at 5 km grain.TheHBMapproach provides unbiased fine‐grain probabilities of occurrence whilst the conventional methods (direct approach, point sampling) consistently over‐predict occurrence probabilities. Incorporation of the downscaled occupancy further improves reliability of the models, but only in cases when the fine‐grain occupancy is estimated accurately.Summing predictions across grid cells and species,HBMs provide better estimates of fine‐grain species richness than conventional methods. They also provide better estimates of fine‐grain occupancy (prevalence).The presentedHBM‐based downscaling approach offers improved predictions of fine‐grain presence and absence compared with existing methods. The combination of theBayesian approach with key macroecological relationships (specifically, the scale‐area relationship) offers a promising general basis for downscaling distributions that may be extended, for example, using generalized linear or additive models. These approaches enable integrative predictions of spatial biodiversity patterns at fine grains.

Hierarchical Bayesian modelling for spatial analysis of the number of avalanche occurrences at the scale of the township

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

The near-shore ocean ecosystem is influenced by catchment runoff. The Great Barrier Reef has been experiencing significant water quality deterioration over the past 150 years, due in part to agricultural intensification and urban settlement in adjacent catchments (Thorburn et al., 2013). There is a need for us to understand the influences of catchment characteristics on stream water quality, with an aim to mitigate and manage the water quality issue in the terrestrial stream runoff derived from the adjacent Great Barrier Reef catchments. The event-based water quality monitoring data set from the Paddock to Reef Integrated Monitoring Program across six Natural Management Regions provides a potential opportunity to develop a data-driven understanding of catchment characteristics affecting water quality at the catchment scale. This requires a robust and reliable modelling tool to relate the monitoring data to anthropogenic and natural processes. In this study, monitoring data of Total Suspended Solids (TSS) and dissolved Oxidised Nitrogen (NOX) from 32 sites across the Great Barrier Reef catchments are selected as case study constituents due to the high risk they pose to reef health when exported from catchments to the receiving marine environment. Also, these two constituents have distinct biogeochemical processes in catchments. Specifically, TSS is typically conserved (although mobilized and deposited) while travelling through river systems; while NOX can be potentially processed and removed from the system altogether. A Bayesian hierarchical linear modelling framework is adopted, due to its ability to borrow strength among sites, allowing information to be transferred across space, and due to its ability to provide uncertainty of the predictions. The Bayesian hierarchical linear regression model in this study is developed to evaluate the significance of various catchment characteristics (e.g., land uses, catchment topography and geology) on spatial variation in water quality. The main findings of this study are listed as follows, • Sites located in the Burdekin and Fitzroy Natural Management Regions tend to have greater TSS concentrations, illustrated by the modelled site-specific spatial random effects (deviation from the overall average concentration). Additionally, grazing and dry land agriculture land uses are positively correlated with the spatial random effect on TSS. The complexity of interaction between different catchment characteristics (e.g., land use and topography) can potentially result in a negative spatial random effect on TSS, which is reduced in the relatively steeper Great Barrier Reef catchments with a denser stream network. • Sugar cane is one of the most significant NOX contributors according to the modelling results, likely partially due to the excessive application of fertilizers; however, conservation land use has limited effect on NOX removal, indicating denitrification process alone may not be sufficient to remove NOX. The modelling results demonstrate different land management strategies are required for the purpose of reducing different constituents. This work will provide scientific insights for water quality management at the catchment scale.

We develop a space‐time Bayesian hierarchical modeling (BHM) framework for two flood risk attributes—seasonal daily maximum flow and the number of events that exceed a threshold during a season (NEETM)—at a suite of gauge locations on a river network. The model uses generalized extreme value (GEV) and Poisson distributions as marginals for these flood attributes with non‐stationary parameters. The rate parameters of the Poisson distribution and location, scale, and shape parameters of the GEV are modeled as linear functions of suitable covariates. Gaussian copulas are applied to capture the spatial dependence. The best covariates are selected using the Watanabe‐Akaike information criterion (WAIC). The modeling framework results in the posterior distribution of the flood attributes at all the gauges and various lead times. We demonstrate the utility of this modeling framework to forecast the flood risk attributes during the summer peak monsoon season (July‐August) at five gauges in the Narmada River basin (NRB) of West‐Central India for several lead times (0–3 months). As potential covariates, we consider climate indices such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Pacific Warm Pool Region (PWPR) from antecedent seasons, which have shown strong teleconnections with the Indian monsoon. We also include new indices related to the East Pacific and West Indian Ocean regions depending on the lead times. We show useful long lead skill from this modeling approach which has a strong potential to enable robust risk‐based flood mitigation and adaptation strategies 3 months before flood occurrences.

Surveillance systems are commonly used to provide early warning detection or to assess an impact of an intervention/policy. Traditionally, the methodological and conceptual frameworks for surveillance have been designed for infectious diseases, but the rising burden of non-communicable diseases (NCDs) worldwide suggests a pressing need for surveillance strategies to detect unusual patterns in the data and to help unveil important risk factors in this setting. Surveillance methods need to be able to detect meaningful departures from expectation and exploit dependencies within such data to produce unbiased estimates of risk as well as future forecasts. This has led to the increasing development of a range of space-time methods specifically designed for NCD surveillance. We present an overview of recent advances in spatiotemporal disease surveillance for NCDs, using hierarchically specified models. This provides a coherent framework for modelling complex data structures, dealing with data sparsity, exploiting dependencies between data sources and propagating the inherent uncertainties present in both the data and the modelling process. We then focus on three commonly used models within the Bayesian Hierarchical Model (BHM) framework and, through a simulation study, we compare their performance. We also discuss some challenges faced by researchers when dealing with NCD surveillance, including how to account for false detection and the modifiable areal unit problem. Finally, we consider how to use and interpret the complex models, how model selection may vary depending on the intended user group and how best to communicate results to stakeholders and the general public.

Production forecasting in unconventional reservoir systems is an important problem for the industry. While "averaging" observed production profiles is often used to construct type wells, model-based methods have significant advantages, including observance of basic fluid-flow principles. Model-based approaches for type well construction involve using analytical and numerical models for a representative well in a group of wells. Scaling factors are used to apply the model to the rest of the wells in the group. However, there is uncertainty in the estimates of these scaling factors that is not accounted for when we use point estimates. In this work, we calculate the uncertainty in the scaling factors in a group of analog wells. We then account for this uncertainty in the estimation of the P10, P50 and P90 type wells within the group of analog wells, using a Bayesian hierarchical model. We select a group of analog wells and fit a model to a representative well in the group. We then calculate the scaling factor for each well in the group as a probability distribution. We pool these distributions to estimate the variation in scaling factors between different wells. This represents the uncertainty in the scaling factors across the group. We translate this into uncertainty in the production rate profile across the group. Finally, we generate P10, P50 and P90 production profiles from the distribution. These represent type wells for the group of analog wells. We show that our technique is superior to point estimates of scaling factors traditionally used in the industry, due to pooling of distributions. Point estimates ignore possible variation in the scaling factor due to noise and presence of outliers. We show that this could accumulate and have a significant impact on the estimated type well. This propagates to the calculation of estimated ultimate recovery. We validate our method with simulated data, with and without added noise. Forecasting production for producing wells and estimating production on proved undeveloped reserves are problems of engineering and economic importance. Existing methods using empirical averaging of production profiles or point estimates for scaling factors fail to use information on the uncertainty of the scaling factors. By discarding this information, we discard uncertainty that could influence reserves estimates. We present a method that incorporates this uncertainty into the analysis transparently. Our method can also be used to pool uncertainty across various well groups.

In recent years, the demand to provide best-estimate predictions with confident bounds is increasing for the nuclear reactor performance and safety analysis. The Organisation for Economic Co-operation and Development Nuclear Energy Agency has been developing an international benchmark of the light water reactor (LWR) uncertainty analysis in modeling (UAM) for the examination of uncertainty quantification and propagation methodologies with various modeling and simulation code systems. The objective of the present work is to develop an uncertainty propagation mechanism based on the stochastic sampling method by taking into account the uncertainties of both basic nuclear data and fuel modeling parameters in the simulation of pressurized water reactors (PWRs) that can be incorporated in the conventional LWR simulation approach. More specifically, the Three Mile Island Unit 1–related exercises from the LWR-UAM benchmark have been modeled using the coupled TRACE/PARCS code system in the three-dimensional core representation. The input uncertainties of the neutronics simulation include few-group cross sections and kinetics parameters generated using the Sampler/Polaris sequence of SCALE 6.2.1. Several heat transfer–related variables for the fuel modeling were considered as sources of input uncertainty of the thermal-hydraulics simulations, including the thermal conductivity of fuel and cladding, fuel heat capacity, and the gap conductance. Dakota was used to sample input parameters of the coupled code system and to perform the uncertainty analysis. Two types of simulations were conducted: steady-state calculation at hot full-power condition and transient scenario initiated by the spatially asymmetric rod ejection accident. Quantities of interest for the steady-state calculation, including core multiplication factor and power peaking factors, were calculated with associated uncertainties. For transient calculations, best-estimate plus uncertainty results of the time evolution of core reactivity, core power, and peak fuel temperature were generated and analyzed. The Wilks’ formula was used to determine the necessary sample size to achieve a 95% confidence of the 95% limit of output quantities of interest. Although the uncertainty propagation and quantification method presented in this paper was developed for PWRs, it could be in general applicable to the multiphysics uncertainty quantification of other types of LWR cores.

In this study, the role of self‐validated computing for solving the energy hub‐scheduling problem in the presence of multiple and heterogeneous sources of data uncertainties is explored and a new solution paradigm based on affine arithmetic is conceptualised. The benefits deriving from the application of this methodology are analysed in details, and several numerical results are presented and discussed.

Based on the recent approach of Bertsimas and Sim (2004, 2003) to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. We exploit the binary nature of the optimization problem in proving our results. A discussion on the cost of ignoring uncertainty is also included.