arXiv subjects

Zaid Sawlan

Publications and source records attributed to Zaid Sawlan.

7 recordsLinked to original sources

arXiv2024

Optimized Task Assignment and Predictive Maintenance for Industrial Machines using Markov Decision Process

This paper considers a distributed decision-making approach for manufacturing task assignment and condition-based machine health maintenance. Our approach considers information sharing between the task assignment and health management decision-making agents. We propose the design of the decision-making agents based on Markov decision processes. The key advantage of using a Markov decision process-based approach is the incorporation of uncertainty involved in the decision-making process. The paper provides detailed mathematical models along with the associated practical execution strategy. In order to demonstrate the effectiveness and practical applicability of our proposed approach, we have included a detailed numerical case study that is based on open source milling machine tool degradation data. Our case study indicates that the proposed approach offers flexibility in terms of the selection of cost parameters and it allows for offline computation and analysis of the decision-making policy. These features create and opportunity for the future work on learning of the cost parameters associated with our proposed model using artificial intelligence.

cs.AI↗

arXiv2023

Modeling metallic fatigue data using the Birnbaum--Saunders distribution

This work employs the Birnbaum--Saunders distribution to model the fatigue life of metallic materials under cyclic loading and compares it with the normal distribution. Fatigue-limit models are fitted to three datasets of unnotched specimens of 75S-T6 aluminum alloys and carbon laminate with different loading types. A new equivalent stress definition that accounts for the effect of the experiment type is proposed. The results show that the Birnbaum--Saunders distribution consistently outperforms the normal distribution in fitting the fatigue data and provides more accurate predictions of fatigue life and survival probability.

stat.CO↗

arXiv2018

Spatial Poisson processes for fatigue crack initiation

In this work we propose a stochastic model for estimating the occurrence of crack initiations on the surface of metallic specimens in fatigue problems that can be applied to a general class of geometries. The stochastic model is based on spatial Poisson processes with intensity function that combines stress-life (S-N) curves with averaged effective stress, $σ_{\mathrm{eff}}^Δ (\mathbf{x})$, which is computed after solving numerically the linear elasticity equations on the specimen domains using finite element methods. Here, $Δ$ is a parameter that characterizes the size of the neighbors covering the domain boundary. The averaged effective stress, parameterized by $Δ$, maps the stress tensor to a scalar field upon the specimen domain. Data from fatigue experiments on notched and unnotched sheet specimens of 75S-T6 aluminum alloys are used to calibrate the model parameters for the individual data sets and for their combination. Bayesian and classical approaches are applied to estimate the survival-probability function for any specimen tested under a prescribed fatigue experimental setup. Our proposed model can predict the initiation of cracks in specimens made from the same material with new geometries.

stat.ME↗

arXiv2018

Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls

In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using $50\%$ or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.

stat.CO↗

arXiv2017

Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements

The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of temperature and heat flux over extended time periods. The one-dimensional heat equation with unknown Dirichlet boundary conditions is used to model the heat transfer process through the wall. In [F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, Bayesian Analysis 12 (2) (2017) 407--433], it was assessed the uncertainty about the thermal diffusivity parameter using different synthetic data sets. In this work, we adapt this methodology to an experimental study conducted in an environmental chamber, with measurements recorded every minute from temperature probes and heat flux sensors placed on both sides of a solid brick wall over a five-day period. The observed time series are locally averaged, according to a smoothing procedure determined by the solution of a criterion function optimization problem, to fit the required set of noise model assumptions. Therefore, after preprocessing, we can reasonably assume that the temperature and the heat flux measurements have stationary Gaussian noise and we can avoid working with full covariance matrices. The results show that our technique reduces the bias error of the estimated parameters when compared to other approaches. Finally, we compute the information gain under two experimental setups to recommend how the user can efficiently determine the duration of the measurement campaign and the range of the external temperature oscillation.

stat.AP↗

arXiv2015

Bayesian inference and model comparison for metallic fatigue data

In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.

stat.CO↗

arXiv2015

A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions

In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.

stat.ME↗