Probabilistic first ply failure prediction of composite laminates using a multi-scale M-SaF and Bayesian inference approach

2017 ◽  
Vol 52 (2) ◽  
pp. 169-195 ◽  
Author(s):  
Ghulam Mustafa ◽  
Afzal Suleman ◽  
Curran Crawford
Keyword(s):  
Bayesian Inference ◽  
Composite Laminates ◽  
Failure Criteria ◽  
Calibration Procedure ◽  
Strength Properties ◽  
Model Parameters ◽  
Successful Implementation ◽  
Damage State ◽  
Multi Scale ◽  
Unit Cells

This paper presents a probabilistic first ply failure analysis of composite laminates using a high-fidelity multi-scale approach called M-SaF (Micromechanics-based approach for Static Failure). To this end, square and hexagonal representative unit cells of composites are developed to calculate constituent stresses with the help of a bridging matrix between macro and micro stresses referred to as the stress amplification factor matrix. Separate failure criteria are applied to each of the constituents (fiber, matrix, and interface) in order to calculate the damage state. The successful implementation of M-SaF requires strength properties of the constituents which are the most difficult and expensive to characterize experimentally, limiting the use of M-SaF in the early design stages of a structure. This obstacle is overcome by integrating a Bayesian inference approach with M-SaF. An academic sample problem of a cantilever beam is used to first demonstrate the calibration procedure. Bayesian inference calibrates the M-SaF first ply failure model parameters as posterior distributions from the prior probability density functions drawn from lamina test data. The posterior statistics were then used to calculate probabilistic first ply failure for a range of different laminates.

A New Approach to Fatigue Damage Modeling of Composite Laminates

2011 ◽  
Vol 338 ◽  
pp. 315-318 ◽  
Author(s):  
Peng Gang Mu ◽  
Xiao Peng Wan ◽  
Mei Ying Zhao
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Composite Laminates ◽  
Fatigue Behavior ◽  
Failure Criteria ◽  
Damage State ◽  
Damage Indices ◽  
Model Combining ◽  
Proposed Model ◽  
Fatigue Damage Accumulation

Fatigue damage of composites can be described by the residual stiffness and residual strength, and the same damage state can be described by the two mechanical parameters equivalently. Based on this assumption, a new pair of fatigue damage accumulation models are established to simulate fatigue behavior and predict the fatigue life of composites. Each of two equations contains three parameters and has the similar form, and the power function relationships between the two damage indices are constructed. The proposed model, combining with constant life diagrams and failure criteria are used to estimate the fatigue life of composites, and good agreement is observed between the present model and experimental results.

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 A parametric prediction of the Young’s modulus of polymers enhanced with ΜWCNTs

2018 ◽  
Vol 233 ◽  
pp. 00025
Author(s):  
P.V. Polydoropoulou ◽  
K.I. Tserpes ◽  
Sp.G. Pantelakis ◽  
Ch.V. Katsiropoulos
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Experimental Results ◽  
Scale Model ◽  
Fe Model ◽  
Multi Scale ◽  
Unit Cells ◽  
Random Dispersion

In this work a multi-scale model simulating the effect of the dispersion, the waviness as well as the agglomerations of MWCNTs on the Young’s modulus of a polymer enhanced with 0.4% MWCNTs (v/v) has been developed. Representative Unit Cells (RUCs) have been employed for the determination of the homogenized elastic properties of the MWCNT/polymer. The elastic properties computed by the RUCs were assigned to the Finite Element (FE) model of a tension specimen which was used to predict the Young’s modulus of the enhanced material. Furthermore, a comparison with experimental results obtained by tensile testing according to ASTM 638 has been made. The results show a remarkable decrease of the Young’s modulus for the polymer enhanced with aligned MWCNTs due to the increase of the CNT agglomerations. On the other hand, slight differences on the Young’s modulus have been observed for the material enhanced with randomly-oriented MWCNTs by the increase of the MWCNTs agglomerations, which might be attributed to the low concentration of the MWCNTs into the polymer. Moreover, the increase of the MWCNTs waviness led to a significant decrease of the Young’s modulus of the polymer enhanced with aligned MWCNTs. The experimental results in terms of the Young’s modulus are predicted well by assuming a random dispersion of MWCNTs into the polymer.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

THE EFFECT OF LAMINATION SCHEME AND ANGLE VARIATIONS TO THE DISPLACEMENTS AND FAILURE BEHAVIOUR OF COMPOSITE LAMINATE

2015 ◽  
Vol 76 (11) ◽  
Author(s):  
Azizul Hakim Samsudin ◽  
Jamaluddin Mahmud
Keyword(s):  
Fiber Orientation ◽  
Composite Laminates ◽  
Finite Element Modelling ◽  
Composite Laminate ◽  
Maximum Stress ◽  
Failure Load ◽  
Failure Criteria ◽  
Stress Theory ◽  
Failure Behaviour ◽  
Failure Index

This paper aims to investigate the effect of lamination scheme and angle variations to the displacements and failure behaviour of composite laminate. Finite element modelling and analysis of symmetric, anti-symmetric and angle-ply Graphite/ Epoxy laminate with various angles of fiber orientation subjected to uniaxial tension are performed. Maximum Stress Theory and Tsai-Wu Failure Criteria are employed to determine the failure load (failure index = 1). Prior to that, convergence analysis and numerical validation are carried out. Displacements and failure behaviour of the composite laminates (symmetric, anti-symmetric and angle ply) are analysed. The failure curves (FPF and LPF) for both theories (Maximum Stress Theory and Tsai-Wu) are plotted and found to be very close to each other. Therefore, it can be concluded that the current study is useful and significant to the displacements and failure behaviour of composite laminate.

Device Modeling of a-Si:H Alloy Solar Cells: Calibration Procedure for Determination of Model Input Parameters

1998 ◽  
Vol 507 ◽  
Author(s):  
M. Zeman ◽  
R.A.C.M.M. Van Swaaij ◽  
E. Schroten ◽  
L.L.A. Vosteen ◽  
J.W. Metselaar
Keyword(s):  
Solar Cell ◽  
Material Properties ◽  
Calibration Procedure ◽  
Model Parameters ◽  
Model Input ◽  
A Value ◽  
Input Parameters ◽  
Simulated Material ◽  
Good Agreement

ABSTRACTA calibration procedure for determining the model input parameters of standard a-Si:H layers, which comprise a single junction a-Si:H solar cell, is presented. The calibration procedure consists of: i) deposition of the separate layers, ii) measurement of the material properties, iii) fitting the model parameters to match the measured properties, iv) simulation of test devices and comparison with experimental results. The inverse modeling procedure was used to extract values of the most influential model parameters by fitting the simulated material properties to the measured ones. In case of doped layers the extracted values of the characteristic energies of exponentially decaying tail states are much higher than the values reported in literature. Using the extracted values of model parameters a good agreement between the measured and calculated characteristics of a reference solar cell was reached. The presented procedure could not solve directly an important issue concerning a value of the mobility gap in a-Si:H alloys.

scholarly journals Estimation and optimal control of the multi-scale dynamics of the Covid-19

2021 ◽  
Author(s):  
David Jaurès Fotsa-Mbogne ◽  
Stéphane Yanick Tchoumi ◽  
Yannick Kouakep-Tchaptchie ◽  
Vivient Corneille Kamla ◽  
Jean-Claude Kamgang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Virus Transmission ◽  
Scale Model ◽  
Model Parameters ◽  
Optimal Control Strategy ◽  
Or Efficiency ◽  
Human Virus ◽  
Multi Scale ◽  
Human Density

AbstractThis work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). We first propose a multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism. We consider 10 compartments in the human population in order to take into accounts the effects of different specific mitigation policies: susceptible, infected, infectious, quarantined, hospitalized, treated, recovered, non-infectious dead, infectious dead, buried. The population of viruses is also partitioned into 10 compartments corresponding respectively to each of the first nine human population compartments and the free viruses available in the environment. Indeed, we have human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self infection by susceptible individuals. We show the global stability of the disease free equilibrium if a given threshold 𝒯0 is less or equal to 1 and we provide how to compute the basic reproduction number ℛ0. A convergence index 𝒯1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. We evaluate the sensitivity of ℛ0, 𝒯0 and 𝒯1 to control parameters such as the maximal human density allowed per unit of surface, the rate of disinfection both for people and environment, the mobility probability, the wearing mask probability or efficiency, and the human to human contact rate which results from the previous one. Except the maximal human density allowed per unit of surface, all those parameters have significant effects on the qualitative dynamics of the disease. The most significant is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into consideration economic impacts of SARS-CoV-2, we determine and discuss optimal fighting strategies. The study is applied to real available data from Cameroon and an estimation of model parameters is done. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy.

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