Bayesian Updating of Aleatory Uncertainties in Heterogeneous Materials

2017 ◽  
Vol 1144 ◽  
pp. 136-141
Author(s):  
Eliška Janouchová ◽  
Anna Kučerová ◽  
Jan Sýkora
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Parameter Identification ◽  
Material Properties ◽  
Model Parameters ◽  
Experimental Measurements ◽  
Identification Procedure ◽  
Model Response ◽  
Probabilistic Description ◽  
Probabilistic Setting

Advances in meta-modelling and increasing computational capacity of modern computerspermitted many researches to focus on parameter identification in probabilistic setting. Increasinglypopular Bayesian inference allows to estimate model parameters together with corresponding epistemicuncertainties from indirect experimental measurements. However in case of a heterogeneousmaterial model, the identification procedure has to be able to quantify the aleatory uncertainties capturingthe variability of the material properties. Parameter identification of a heterogeneous materialmodel can be formulated as a search for probabilistic description of its parameters providing the distributionof the model response corresponding to the distribution of the observed data, i.e. a stochasticinversion problem. By prescribing a specific type of probability distribution to the model parameterswith corresponding uncertain moments, the task changes to the identification of these so-calledhyperparameters of the distribution which can be inferred in the Bayesian way.

scholarly journals BAYESIAN INFERENCE OF HETEROGENEOUS VISCOPLASTIC MATERIAL PARAMETERS

2018 ◽  
Vol 15 ◽  
pp. 41-45
Author(s):  
Eliška Janouchová ◽  
Anna Kučerová
Keyword(s):  
Experimental Data ◽  
Bayesian Inference ◽  
Material Model ◽  
Isotropic Hardening ◽  
Model Parameters ◽  
Viscoplastic Material ◽  
Loading Test ◽  
Model Response ◽  
Probabilistic Description ◽  
Probabilistic Setting

<p>Modelling of heterogeneous materials based on randomness of model input parameters involves parameter identification which is focused on solving a stochastic inversion problem. It can be formulated as a search for probabilistic description of model parameters providing the distribution of the model response corresponding to the distribution of the observed data</p><p>In this contribution, a numerical model of kinematic and isotropic hardening for viscoplastic material is calibrated on a basis of experimental data from a cyclic loading test at a high temperature. Five material model parameters are identified in probabilistic setting. The core of the identification method is the Bayesian inference of uncertain statistical moments of a prescribed joint lognormal distribution of the parameters. At first, synthetic experimental data are used to verify the identification procedure, then the real experimental data are processed to calibrate the material model of copper alloy.</p>

Machine-Tool Error Observer Design With Application to Thermal Error Tracking

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Hua-Wei Ko ◽  
Patrick Bazzoli ◽  
J. Adam Nisbett ◽  
Douglas Bristow ◽  
Yujie Chen ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parameter Identification ◽  
Thermal Error ◽  
Error Model ◽  
Optimal Designs ◽  
Model Parameters ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Five Axis ◽  
Large Machine

Abstract A parameter identification procedure for identifying the parameters of a volumetric error model of a large machine tool requires hundreds of random volumetric error components in its workspace and thus takes hours of measurement time. It causes thermal errors of a large machine difficult to be tracked and compensated periodically. This paper demonstrates the application of the optimal observation design theories to volumetric error model parameter identification of a large five-axis machine. Optimal designs maximize the amount of information carried in the observations. In this paper, K-optimal designs are applied for the construction of machine-tool error observers by determining locations in the workspace at which 80 components of volumetric errors to be measured so that the model parameters can be identified in 5% of an 8-h shift. Many of optimal designs tend to localize observations at the boundary of the workspace. This leaves large volumes of the workspace inadequately represented, making the identified model inadequate. Therefore, the constrained optimization algorithms that force the distribution of observation points in the machine’s workspace are developed. Optimal designs reduce the number of observations in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic measurements. The design, implementation, and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 400-min period of operation are also reported. About 70–80% of machine-tool error can be explained using the proposed thermal error modeling methodology.

Simulations of Bending Experiments of Concrete Beams by Stochastic Discrete Model

2014 ◽  
Vol 627 ◽  
pp. 457-460
Author(s):  
Jana Kaděrová ◽  
Jan Eliáš
Keyword(s):  
Experimental Data ◽  
Material Properties ◽  
Discrete Model ◽  
Concrete Beams ◽  
Particle Model ◽  
Model Parameters ◽  
Three Point Bending ◽  
Model Response ◽  
Different Types ◽  
Lattice Particle

The paper describes results of numerical simulations of experiments on concrete beams loaded in three-point bending. Stochastic lattice-particle model has been applied in which the material was represented by discrete particles of random size and location. Additional spatial variability of material properties was introduced by stationary autocorrelated random field. Three different types of geometrically similar beams were modeled: half-notched, fifth-notched and unnotched, each in four different sizes. The deterministic and stochastic model parameters were identified via automatic procedure based on comparison to a subset of experimental data, so that the adequacy of the model response could be validated by comparison with the remaining experimental data.

Machine-Tool Error Observer Design With Application to Thermal Error Tracking

2018 ◽  
Author(s):  
Hua-Wei Ko ◽  
Shiv G. Kapoor ◽  
Placid M. Ferreira ◽  
Patrick Bazzoli ◽  
J. Adam Nisbett ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parameter Identification ◽  
Thermal Error ◽  
Error Model ◽  
Observer Design ◽  
Optimal Designs ◽  
Model Parameters ◽  
Volumetric Error ◽  
Identification Procedure ◽  
Volumetric Errors

A parameter identification procedure for identifying the parameters of a volumetric error model of a large and complex machine tool usually requires a large number of observations of volumetric error components in its workspace. This paper demonstrates the possibility of applying optimal observation/experimental design theories to volumetric error model parameter identification of a large 5-axis machine with one redundant axis. Several designs such as A-, D- and K-optimal designs seek to maximize the amount of information carried in the observations made in an experiment. In this paper, we adapt these design approaches in the construction of machine-tool error observers by determining locations in the workspace at which components of volumetric errors must be measured so that the underlying error model parameters can be identified. Many of optimal designs tend to localize observations at either the center or the boundary of the workspace. This can leave large volumes of the workspace inadequately represented, making the identified model parameters particularly susceptible to model inadequacy issues. Therefore, we develop constrained optimization algorithms that force the distribution of observation points in the machine’s workspace. Optimal designs provide the possibility of efficiency (reduced number of observations and hence reduced measurement time) in the identification procedure. This opens up the possibility of tracking thermal variations of the volumetric error model with periodic quick measurements. We report on the design, implementation and performance of a constrained K-optimal in tracking the thermal variations of the volumetric error over a 5.5 hour period of operations with measurements being made each hour.

scholarly journals Comparison of Bayesian Methods on Parameter Identification for a Viscoplastic Model with Damage

Metals ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 876 ◽  
Author(s):  
Ehsan Adeli ◽  
Bojana Rosić ◽  
Hermann G. Matthies ◽  
Sven Reinstädler ◽  
Dieter Dinkler
Keyword(s):  
Experimental Data ◽  
Parameter Identification ◽  
Measurement Errors ◽  
Surface Displacement ◽  
Life Time ◽  
Material Model ◽  
Model Parameters ◽  
Bayesian Approaches ◽  
Model Response ◽  
The Difference

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss-Markov-Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately.

scholarly journals Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

2017 ◽  
Vol 14 (134) ◽  
pp. 20170340 ◽  
Author(s):  
Aidan C. Daly ◽  
Jonathan Cooper ◽  
David J. Gavaghan ◽  
Chris Holmes
Keyword(s):  
Bayesian Inference ◽  
Bayesian Methods ◽  
Sequential Monte Carlo ◽  
Model Parameters ◽  
Biological Models ◽  
Exact Inference ◽  
Modelling Studies ◽  
Approximate Bayesian ◽  
Approximate Bayesian Inference ◽  
Abc Methods

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara–Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

scholarly journals Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential

Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1516
Author(s):  
Daniel Gratz ◽  
Alexander J Winkle ◽  
Seth H Weinberg ◽  
Thomas J Hund
Keyword(s):  
Action Potential ◽  
Mathematical Models ◽  
Cardiac Myocyte ◽  
Population Level ◽  
Na Channel ◽  
Model Parameters ◽  
Healthy Population ◽  
Experimental Measurements ◽  
Voltage Gated ◽  
Experimental Variability

The voltage-gated Na+ channel Nav1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Nav1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Nav1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Nav1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

scholarly journals Parameter Identification and State-of-Charge Estimation for Lithium-Ion Batteries Using Separated Time Scales and Extended Kalman Filter

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1054
Author(s):  
Kuo Yang ◽  
Yugui Tang ◽  
Zhen Zhang
Keyword(s):  
Kalman Filter ◽  
Parameter Identification ◽  
Open Circuit Voltage ◽  
Lithium Ion ◽  
Open Circuit ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Soc Estimation ◽  
Battery Model

With the development of new energy vehicle technology, battery management systems used to monitor the state of the battery have been widely researched. The accuracy of the battery status assessment to a great extent depends on the accuracy of the battery model parameters. This paper proposes an improved method for parameter identification and state-of-charge (SOC) estimation for lithium-ion batteries. Using a two-order equivalent circuit model, the battery model is divided into two parts based on fast dynamics and slow dynamics. The recursive least squares method is used to identify parameters of the battery, and then the SOC and the open-circuit voltage of the model is estimated with the extended Kalman filter. The two-module voltages are calculated using estimated open circuit voltage and initial parameters, and model parameters are constantly updated during iteration. The proposed method can be used to estimate the parameters and the SOC in real time, which does not need to know the state of SOC and the value of open circuit voltage in advance. The method is tested using data from dynamic stress tests, the root means squared error of the accuracy of the prediction model is about 0.01 V, and the average SOC estimation error is 0.0139. Results indicate that the method has higher accuracy in offline parameter identification and online state estimation than traditional recursive least squares methods.

scholarly journals Developments in Modelling Bone Screwing

2020 ◽  
Vol 6 (3) ◽  
pp. 111-114
Author(s):  
Jack Wilkie ◽  
Paul D. Docherty ◽  
Knut Möller
Keyword(s):  
Material Properties ◽  
Frictional Coefficient ◽  
Viscous Friction ◽  
Model Parameters ◽  
General Shape ◽  
Bone Material ◽  
Bone Material Properties ◽  
Modelling Methodology ◽  
Recorded Data ◽  
Friction Models

AbstractINTRODUCTION: A torque-rotation model of the bone-screwing process has been proposed. Identification of model parameters using recorded data could potentially be used to determine the material properties of bone. These properties can then be used to recommend tightening torques to avoid over or under-tightening of bone screws. This paper improves an existing model to formulate it in terms of material properties and remove some assumptions. METHOD: The modelling methodology considers a critical torque, which is required to overcome friction and advance the screw into the bone. Below this torque the screw may rotate with elastic deformation of the bone tissue, and above this the screw moves relative to the bone, and the speed is governed by a speed-torque model of the operator’s hand. The model is formulated in terms of elastic modulus, ultimite tensile strength, and frictional coefficient of the bone and the geometry of the screw and hole. RESULTS: The model output shows the speed decreasing and torque increasing as the screw advances into the bone, due to increasing resistance. The general shape of the torque and speed follow the input effort. Compared with the existing model, this model removes the assumption of viscous friction, models the increase in friction as the screw advances into the bone, and is directly in terms of the bone material properties. CONCLUSION: The model presented makes significant improvements on the existing model. However it is intended for use in parameter identification, which was not evaluated here. Further simulation and experimental validation is required to establish the accuracy and fitness of this model for identifying bone material properties.

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