Abstract: Two finite element (FEM) models are presented in
this paper to address the random nature of the response of glued
timber structures made of wood segments with variable elastic
moduli evaluated from 3600 indentation measurements. This total
database served to create the same number of ensembles as was the
number of segments in the tested beam. Statistics of these ensembles
were then assigned to given segments of beams and the Latin
Hypercube Sampling (LHS) method was called to perform 100
simulations resulting into the ensemble of 100 deflections subjected
to statistical evaluation. Here, a detailed geometrical arrangement of
individual segments in the laminated beam was considered in the
construction of two-dimensional FEM model subjected to in fourpoint
bending to comply with the laboratory tests. Since laboratory
measurements of local elastic moduli may in general suffer from a
significant experimental error, it appears advantageous to exploit the
full scale measurements of timber beams, i.e. deflections, to improve
their prior distributions with the help of the Bayesian statistical
method. This, however, requires an efficient computational model
when simulating the laboratory tests numerically. To this end, a
simplified model based on Mindlin’s beam theory was established.
The improved posterior distributions show that the most significant
change of the Young’s modulus distribution takes place in laminae in
the most strained zones, i.e. in the top and bottom layers within the
beam center region. Posterior distributions of moduli of elasticity
were subsequently utilized in the 2D FEM model and compared with
the original simulations.
Abstract: The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to
obtain the Bayes estimate of the failure rate under Topp Leone distribution.
Abstract: This paper presents an online method that learns the
corresponding points of an object from un-annotated grayscale images
containing instances of the object. In the first image being
processed, an ensemble of node points is automatically selected
which is matched in the subsequent images. A Bayesian posterior
distribution for the locations of the nodes in the images is formed.
The likelihood is formed from Gabor responses and the prior assumes
the mean shape of the node ensemble to be similar in a translation
and scale free space. An association model is applied for separating
the object nodes and background nodes. The posterior distribution is
sampled with Sequential Monte Carlo method. The matched object
nodes are inferred to be the corresponding points of the object
instances. The results show that our system matches the object nodes
as accurately as other methods that train the model with annotated
training images.