Distribution Of Model Parameters Research Articles

Parameter estimation for allometric trophic network models: A variational Bayesian inverse problem approach

Abstract Differential equation models are powerful tools for predicting biological systems, capable of projecting far into the future and incorporating data recorded at arbitrary times. However, estimating these models' parameters from observations can be challenging because numerical methods are often required to approximate their solution. An example of such a model is the allometric trophic network model, for which studies considering its inverse problem are limited, particularly in the Bayesian framework. Here we develop a variational Bayesian method for parameter inference of the allometric trophic network model and explore how accurately we can recover its parameter values. We represent the model as a Bayesian neural network, which combines an artificial neural network with Bayesian inference, using a surrogate for the posterior distribution of model parameters, and train this model by evolutionary optimization to avoid potentially costly computation of the gradient with respect to the model parameters. Using synthetic data, we compare the accuracy of this variational inference to ordinary least squares estimation. To reduce the number of estimated parameters, we focus on the inference of functional response parameters. Our variational Bayesian method yields parameter estimates that are comparable to the ordinary least squares results in terms of accuracy. The method provides a promising approach for including uncertainty quantification in parameter estimation, which the simple ordinary least squares approach as it is does not address. Regardless of the method, potential multimodality of the inference problem is nonetheless important to keep in mind. The present study suggests a technique for parameter inference of ordinary differential equation models in the Bayesian context. We propose the method especially for validation of the allometric trophic network model against empirical data.

Model-Based Clustering of Categorical Data Based on the Hamming Distance

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components. Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Prognosis of reflective pavement cracking development with Bayesian updating and surrogate models

ABSTRACT The main objective of this study is to establish an integrated prognostic method for predicting the development of thermal-induced reflective cracking in asphalt overlay on concrete pavement. The integrated prognosis process for crack growth is developed on the modified Paris’ law and includes three steps: (1) calculation of J-integral; (2) Bayesian updating of crack growth parameters and (3) prediction of remaining life. Finite element modelling (FEM) was conducted to calculate J-integrals at different crack depths and cold weather conditions. A surrogate model was built based on the original Kriging method and it shows high accuracy in predicting J-integrals from maximum air temperature, temperature drop and crack depth. The Bayesian updating process starts from the laboratory-measured distribution of fracture model parameters (A and n) in Paris’ Law and converges to the true values to match the measured crack depths at different loading cycles from field inspection. On the other hand, the consideration of material damage in asphalt overlay avoids over-estimation of remaining loading cycles for reflective cracking to reach the pavement surface. Further study is recommended to accurately assess in-situ pavement modulus and detect crack depth over concrete joints for implementation of the proposed prognostics method.

Multiwavelength Study of Extreme High-energy Peaked BL Lac Source 1ES 0229+200 Using Ultraviolet, X-Ray, and γ-Ray Observations

We present a comprehensive analysis of the broadband spectral energy distribution (SED) of the extreme high-energy peaked BL Lac source, 1ES 0229+200. Our study utilizes near-simultaneous data collected at various epochs between 2017 September and 2021 August (MJD 58119−59365) from different instruments, including AstroSat−UVIT, Soft X-ray focusing Telescope, LAXPC, Swift−UVOT, Fermi-LAT, and MAGIC. We investigate the one-zone synchrotron and synchrotron self-Compton (SSC) model, employing diverse particle distributions such as the log parabola, broken power law, power law with a maximum electron energy γ, energy-dependent diffusion (EDD), and energy-dependent acceleration (EDA) models to fit the broadband SED of the source. Our findings indicate that both peaks in the SED are well described by the one-zone SSC model across all particle distribution models. We estimate the jet power for different particle distributions. The estimated jet power for broken power law particle distributions is found to be on the order of 1047 (1044) erg s−1 for a minimum electron energy γmin ∼10 (104). However, for intrinsically curved particle energy distributions (e.g., log parabola, EDD, and EDA models), the estimated jet power is ∼1044 erg s−1. The SED fitting at five epochs enables us to explore the correlation between the derived spectral parameters of various particle distribution models. Notably, the observed correlations are inconsistent with the predictions in the power-law with a maximum γ model, although the EDD and EDA models yield the correlations as expected. Moreover, the estimated physical parameter values are consistent with the model assumptions.

Hematocrits of red blood cell units increase during storage due to changes in mean corpuscular volume, impacting outcomes of red cell exchange procedures

Abstract Introduction Hematocrits of red blood cell (RBC) units are generally not measured by blood centers or transfusion services. Red blood cell exchange (RCE) is commonly used to treat sickle cell disease, and a key parameter needed in RCE is the average hematocrit of RBC units. However, there is no consensus on the average hematocrit to use or how it is affected by storage. The goal of our study is to determine the average hematocrit of RBC units by measuring hematologic parameters RBC units during storage and performing statistical modeling of hematocrit changes over time. Methods We sampled aliquots of leukoreduced RBC units in AS-1 (n=10) using the Terumo TSCD-II Sterile Tubing Welder to sterilely collect ~15mL of RBCs in transfer-pack containers. Aliquots were collected weekly from Day 7 to Day 42 of storage. Complete blood counts were performed using the Sysmex XN-3100 Hematology Analyzer. We statistically modeled changes in RBC units during storage by utilizing Bayesian multilevel linear regression models, allowing for capturing effects at the individual RBC-unit level. Posterior distributions of model parameters were estimated and processed using Stan and the rethinking and rstan packages in R. Posterior distributions are summarized with posterior means and 95%-credible intervals in parentheses. Model selection was done by calculating Akaike weights using the widely applicable information criterion (WAIC) to signify statistical support for each model. Results Multilevel linear regression models of hematologic parameters as a function of storage time were developed. Hematocrits increased with a posterior mean of 1.4% (0.98–1.75%) per week of storage, with posterior mean hematocrits of: 61.9% (60.2–63.6%) on Day 7, 63.9% (61.5–66.4%) on Day 21, and 66.0% (62.8–69.7%) on Day 42. These results indicate that a single average cannot be used for RBC units since hematocrits dramatically increase during storage. Mean corpuscular volume (MCV) increased with a posterior mean of 2.31 fL (1.4–3.71) per week whereas hemoglobin remained stable with a posterior mean increase of 0.008 g/dL (-0.016–0.031) per week. Using these results, we subsequently developed a multilevel regression model of hematocrit as a function of MCV. The model using MCV (WAIC=100.2, weight=100%) was favored over the model using time (WAIC=120.0, weight=0%), suggesting that changes in MCV are driving the increasing hematocrits. Conclusion Our study is the first to leverage Bayesian statistics to carefully quantify the average hematocrits of RBC units during storage time and to demonstrate that increasing hematocrits are caused by changes in MCV. These results indicate that transfusion protocols must consider the age of RBC units for RCE calculations, and provisions (e.g., requiring use of fresh units for RCE) may help minimize the variability in post-exchange testing. Moreover, our findings suggest that transfusion services should regularly measure hematocrits of RBC units in their inventory.

Optimum noise mechanism for differentially private queries in discrete finite sets

The differential privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this emphasis tends to neglect the crucial considerations of response accuracy and utility, especially in the context of categorical or discrete numerical database queries, where the parameters defining the noise distribution are finite and could be chosen optimally. This paper addresses this gap by introducing a novel framework for designing an optimal noise probability mass function (PMF) tailored to discrete and finite query sets. Our approach considers the modulo summation of random noise as the DP mechanism, aiming to present a tractable solution that not only satisfies privacy constraints but also minimizes query distortion. Unlike existing approaches focused solely on meeting privacy constraints, our framework seeks to optimize the noise distribution under an arbitrary (ϵ,δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\epsilon , \\delta )$$\\end{document} constraint, thereby enhancing the accuracy and utility of the response. We demonstrate that the optimal PMF can be obtained through solving a mixed-integer linear program. Additionally, closed-form solutions for the optimal PMF are provided, minimizing the probability of error for two specific cases. Numerical experiments highlight the superior performance of our proposed optimal mechanisms compared to state-of-the-art methods. This paper contributes to the DP literature by presenting a clear and systematic approach to designing noise mechanisms that not only satisfy privacy requirements but also optimize query distortion. The framework introduced here opens avenues for improved privacy-preserving database queries, offering significant enhancements in response accuracy and utility.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

A Comparative Study of Single-Chain and Multi-Chain MCMC Algorithms for Bayesian Model Updating-Based Structural Damage Detection

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

General Population Mortality Adjustment in Survival Extrapolation of Cancer Trials: Exploring Plausibility and Implications for Cost-Effectiveness Analyses in HER2-Positive Breast Cancer in Sweden.

In economic evaluations of novel therapies, assessing lifetime effects based on trial data often necessitates survival extrapolation, with the choice of model affecting outcomes. The aim of this study was to assess accuracy and variability between alternative approaches to survival extrapolation. Data on HER2-positive breast cancer patients from the Swedish National Breast Cancer Register were used to fit standard parametric distribution (SPD) models and excess hazard (EH) models adjusting the survival projections based on general population mortality (GPM). Models were fitted using 6-y data for stage I and II, 4-y data for stage III, and 2-y data for stage IV cancer reflecting an early data cutoff while maintaining sufficient events for comparison of model estimates with actual long-term outcomes. We compared model projections of 15-y survival and restricted mean survival time (RMST) to 15-y registry data and explored the variability between models in extrapolations of long-term survival. Among 11,224 patients compared with the observed registry 15-y RMST estimates across the disease stages, EH cure models provided the most accurate estimates in patients with stage I to III cancer, whereas EH models without cure most closely matched survival in patients with stage IV cancer, in which cure assumption was less plausible. The Akaike information criterion-averaged model projections varied as follows: -8.2% to +5.3% for SPD models, -4.9% to +5.2% for the EH model without a cure assumption, and -19.3% to -0.2% for the EH model with a cure assumption. EH models significantly reduced between-model variance in the predicted RMSTs over a 50-y time horizon compared with SPD models. EH models may be considered as alternatives to SPD models to produce more accurate and plausible survival extrapolation that accounts for general population mortality. Excess hazard (EH) methods have been suggested as an approach to incorporate background mortality rates in economic evaluation using survival extrapolation.We highlight that EH models with or without a cure assumption can produce more accurate survival projections and significantly reduce between-model variability in comparison with standard parametric distribution models across cancer stages.EH models may be a preferred modeling method to reduce model uncertainty in health economic modeling since models that would otherwise have produced implausible extrapolations are constrained by the EH framework.Reduced uncertainty in economic evaluations will enhance the application of evidence-based health care decision making.

Statistical analysis of the ground deformation of Vulcanian explosions at Sakurajima volcano, Japan

The forecast of pulsatory explosions during volcanic unrest periods is an essential issue for the assessment and mitigation of volcanic hazards. Although various precursors are detectable through geophysical and geochemical monitoring, difficulties remain in precisely constraining possible scenarios. A probabilistic approach is effective in assessing risk while considering various uncertainties. Sakurajima volcano characterized by frequent Vulcanian activity is one of the suitable fields for the probabilistic forecast of pulsatory explosions. Their inflation-deflation patterns of ground deformation related to Vulcanian explosions are useful for evaluating the imminence and size of the next event. The large database obtained from its vigorous activity can contribute to statistical analysis. In this study, aiming the probabilistic forecast of the timing and size of explosions, we investigated the duration of inflation and volume changes at the pressure source using strain records of over 5000 events of Sakurajima volcano. Then, a stochastic model was estimated to explain the distribution of these events. The log-logistic distribution was found to be an appropriate model for data distribution, indicating the presence of competing processes, such as pressurization and depressurization, in the conduit. The model parameters of the log-logistic distribution temporally fluctuated reflecting the volcanic activity, especially increasing the magma supply from a deep region. We also suggested a methodology to constrain the probabilities of the likely timing and size of an imminent explosion using real-time strain monitoring and an estimated model distribution. Although some improvements would be needed for practical forecasting, our approach could be useful in predicting possible ash hazards.

Bayesian modeling and optimization for split-plot experiments with multiple responses

In many industrial processes, cost or time constraints make some input variables harder to change or control than others. An appropriate experimental design method is restricted randomization, which results in split-plot experiments. Empirical models that connect multiple quality characteristics with input variables play a crucial role in robust parameter design for split-plot experiments. At present, many modeling methods typically adopt the single response model for analyzing industrial processes in the split-plot experiments without considering correlation among multiple responses, correlation among whole plots, and uncertainty of model parameters. However, ignoring these issues can lead to poor product or process design. To solve these issues, this paper suggests a novel Bayesian modeling and optimization approach. We first construct a Bayesian multi-response linear mixed-effects model and obtain the posterior distribution for model parameters by employing Bayesian theorem. Then, the Gibbs sampling procedure is employed for the estimation of model parameters. Finally, the overall weighted desirability optimization function meeting the specification is developed to avoid acquiring ideal input settings with outliers. A simulation and an engineering case study demonstrate the validity of the proposed method. In comparison to existing methods, the optimization results given the proposed method are more robust and reliable.

Optimization of distribution function and model parameters for molecular communication via diffusion with OtoO approximation

The analysis is generally conducted in stationary receiver and transmitter models in a diffusion environment for the fundamental Molecular communication (MOC) models. However, a mobile MOC model is employed in this study, deviating from the existing literature. This mobile MOC model considers the mobility of all variables in the diffusion environment, including the transmitter, receiver, and molecules. Firstly, a novel MOC model is proposed, departing from the conventional normal distribution for the mobility of variables. Instead, alternative distribution functions such as the Pareto distribution, extreme value distribution, t-distribution, and generalized extreme value distribution are employed. Furthermore, the system's performance is enhanced by optimizing the distribution function and model parameters, such as the diffusion coefficient, using the optimization of optimization (OtoO) approach. In this approach, the Multi-Verse Optimization (MVO) algorithm serves as the primary algorithm, while the Grey Wolf Optimization (GWO) algorithm functions as the auxiliary algorithm. Essentially, the MVO algorithm optimizes the parameters of the MOC model, while simultaneously, the GWO algorithm optimizes the impact of the optimization processes of MVO on the parameters ``p'' and ``N'' as well as the constant parameter of the distribution function. By optimizing both the parameters of the MOC model and the distribution function, the number of received molecules is significantly increased. Therefore, this study not only improves the results of the MOC model structure based on different distribution functions but also optimizes all parameters of the proposed model using the MVO-GWO OtoO approach.

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

Review of Fourth-Order Predictive Modeling and Illustrative Application to a Nuclear Reactor Benchmark. I. Typical High-Order Sensitivity and Uncertainty Analysis

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to nuclear energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, while yielding best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC), as will be illustrated in this work by means of the above-mentioned OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation involving 21,976 imprecisely known parameters, the solution of which is representative of “large-scale computations”. The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

Bayesian peak identification method for low count rate gamma spectrum under short-time measurement based on physical priors

A Bayesian peak identification method based on physical model had been proposed in this study to perform qualitative analysis for the low count rate gamma spectrum under short-time measurement. Based on the prior knowledge about gamma detection, the distribution of energy deposited in the detector near the region of interest of a target peak through photoelectric effect, Compton scattering and multiple scattering had been analyzed and approximated using three elementary components, then, the distribution of each component after convolution had been studied, and at last, a probabilistic mixture model had been proposed to directly describe the distribution of measured energy within region of interest. When the data measurement has been completed, a Gibbs sampler was used to estimate the posterior distribution of model parameters to discriminate the existence of target peaks. The numerical and physical experiments were performed to verify the effectiveness of the parameter estimation algorithm and the performance of the proposed identification method. The numerical experiments showed the identification precision is proportional to counts and peak-to-total ratio, when the peak-to-total ratio is greater than 0.5, the proposed method could identify the peak with a probability greater than 50% given 50 observations. The physical experiment used a NaI(Tl) detector to measure 137Cs, 60Co and 152Eu sources in a laboratory environment at different equivalent distances, the peak identification precision had been tested for the proposed method, and the experiments proved that the probabilistic model is a good approximation to the physical process, and the proposed identification method outperformed the conventional method under short-time measurement conditions.

Applying Machine Learning Techniques: Uncertainty Quantification in Nonlinear Dynamics Characters Predictions via Gated Recurrent Unit-Based Reduced-Order Models

The development of reduced-order models has been a pivotal advancement in the computational analysis of fluid dynamics, substantially simplifying the complexity and boosting the efficiency of simulations. The accuracy and practicality of these models largely depend on the reduction techniques applied and the inherent characteristics of the fluid dynamics systems they represent. In this paper, we introduce an innovative machine-learning framework for assessing model uncertainty in computationally intensive reduced-order models. By combining subspace construction methods with advanced Bayesian inference techniques, our approach effectively captures the posterior distribution of model parameters, thereby providing an accurate representation of uncertainty in aerodynamic performance predictions. We employ the NACA0012 airfoil as a case study to validate our method’s ability to enhance the efficiency of reduced-order models and precisely measure the uncertainty inherent in predictions made by recurrent neural networks. It is important to note that our approach is influenced by specific constraints and variables that significantly impact the mean and variability of the predicted final lift coefficient distribution. Our findings indicate that setting the goodness of fit (R2) threshold above 0.985 markedly improves the correlation between Computational Fluid Dynamics (CFD) outcomes and model predictions, increasing from 72.2% to 97.9% as the interval amplification factor adjusts from 1.5 to 3. However, this adjustment causes a considerable expansion of the confidence interval, from 0.0737 to 0.1282, an increase of over 70%. Despite these challenges, our machine learning-based methodology provides essential insights into the further development of reduced-order modeling and uncertainty quantification in fluid dynamics. This highlights the need for ongoing research into the model parameters, especially in applications concerning aircraft control systems, to meet design specifications and ensure system reliability.

Bayesian Model Updating of Multiscale Simulations Informing Corrosion Prognostics Using Conditional Invertible Neural Networks

Abstract Physics-based multi-scale corrosion simulation plays a vital role in predicting the evolution of pitting corrosion on large civil infrastructure such as miter gates, contributing to a model-informed structural health monitoring (SHM) strategy for risk-based asset health management. The physics-based analysis, however, may not accurately reflect the underlying true physics due to various uncertainty sources and needs to be updated using Bayesian inference methods based on observations to make the prediction closer to field observations. However, traditional Bayesian inference requires the evaluation of a likelihood function, which is often unavailable due to the complex model architecture and various surrogate models used in the analysis. Therefore, likelihood-free inference approaches are required for the updating of the multi-scale corrosion simulation models. This paper meets this need by proposing a conditional invertible neural network (cINN)-based Bayesian model updating method for an existing corrosion simulation model. We first train an cINN model based on simulated observations generated from a high-fidelity forward corrosion analysis model. A convolutional neural network (CNN)-based feature extraction algorithm is then employed to extract key features from corrosion images. After that, the extracted corrosion features from CNN is used as inputs of the cINN model to directly obtain posterior distributions of uncertain corrosion model parameters without evaluating the likelihood function. The results show that the proposed cINN-based model updating approach can provide more accurate inference results with a reduced computational cost in comparison to the classical approximate Bayesian computation (ABC) approach.

Advancing estimation techniques and their applications in engineering and medical data analysis through novel continuous and discrete linear failure rate distribution extension

In this paper, we present a new heavy-tailed distribution called the heavy-tailed linear failure rate (HTLFR) distribution. Various statistical properties of the proposed distribution are derived, including the quantile function, the median, the ordinary moments, the moment generating function, the incomplete moments and the conditional moments. Some actuarial measures such as value at risk, expected shortfall, tail value at risk, tail variance and tail variance premium are calculated. Three different methods of estimation such as the maximum likelihood method, the maximum product spacing method and the Bayesian method as well as some simulation results for the model parameters of the HTLFR distribution under complete samples are examined. The results of the real data set show that the proposed distribution has greater flexibility and has been empirically evaluated under complete data. Discrimination analysis was employed to ensure fairness, equity, and accuracy in decision-making processes for selecting the best model, comparing the proposed distribution with known distributions. A discrete analog of the HTLFR distribution is proposed.

A hierarchical Bayesian model to monitor pelagic larvae in response to environmental changes

AbstractEuropean anchovies and round sardinella play a crucial role, both ecological and commercial, in the Mediterranean Sea. In this paper, we investigate the distribution of their larval stages by analyzing a dataset collected over time (1998–2016) and spaced along the area of the Strait of Sicily. Environmental factors are also integrated. We employ a hierarchical spatio-temporal Bayesian model and approximate the spatial field by a Gaussian Markov Random Field to reduce the computation effort using the Stochastic Partial Differential Equation method. Furthermore, the Integrated Nested Laplace Approximation is used for the posterior distributions of model parameters. Moreover, we propose an index that enables the temporal evaluation of species abundance by using an abundance aggregation within a spatially confined area. This index is derived through Monte Carlo sampling from the approximate posterior distribution of the fitted models. Model results suggest a strong relationship between sea currents’ directions and the distribution of larval European anchovies. For round sardinella, the analysis indicates increased sensitivity to warmer ocean conditions. The index suggests no clear overall trend over the years.

Effect of loading conditions on short fatigue crack propagation behaviours in cast Al[sbnd]Si alloys

The effect of loading conditions on short crack propagation behaviours in cast AlSi alloys was investigated by a combination of photo-microscopy monitoring and post mortem analysis. The findings suggest that the path of short cracks is minimally influenced by loading conditions, whereas loading conditions significantly affect the fatigue crack growth rate (FCGR) and its statistical characteristics. Crack closure effect is observed under zero and negative stress ratio conditions. Roughness-induced crack closure occurs due to the coarse grain microstructure of cast AlSi alloys and the Stage-I mode growth of cracks within grains in the microstructural short crack regime. The high level of plasticity around the crack tip under negative stress ratio conditions has a significant impact on FCGR, resulting in a negative crack opening stress. When the stress ratio exceeds approximately 0.3, short cracks exhibit no crack closure. The load-level effect is observed only at high load conditions with negative stress ratios. Finally, a probabilistic short crack growth model was established using a Bayesian linear regression model to analyse the effect of stress ratio on the uncertainty of FCGR. After considering the crack closure effect, the difference in distributions of FCGR model parameters decreases significantly among different stress ratio conditions.