Abstract: In this article, a method is presented to effectively
estimate the deformed shape of a thick plate due to line heating. The
method uses a fifth order spline interpolation, with up to C3
continuity at specific points to compute the shape of the deformed
geometry. First and second order derivatives over a surface are the
resulting parameters of a given heating line on a plate. These
parameters are determined through experiments and/or finite element
simulations. Very accurate kriging models are fitted to real or virtual
surfaces to build-up a database of maps. Maps of first and second
order derivatives are then applied on numerical plate models to
evaluate their evolving shapes through a sequence of heating lines.
Adding an optimization process to this approach would allow
determining the trajectories of heating lines needed to shape complex
geometries, such as Francis turbine blades.
Abstract: This study suggests the estimation method of stress
distribution for the beam structures based on TLS (Terrestrial Laser
Scanning). The main components of method are the creation of the
lattices of raw data from TLS to satisfy the suitable condition and
application of CSSI (Cubic Smoothing Spline Interpolation) for
estimating stress distribution. Estimation of stress distribution for the
structural member or the whole structure is one of the important
factors for safety evaluation of the structure. Existing sensors which
include ESG (Electric strain gauge) and LVDT (Linear Variable
Differential Transformer) can be categorized as contact type sensor
which should be installed on the structural members and also there are
various limitations such as the need of separate space where the
network cables are installed and the difficulty of access for sensor
installation in real buildings. To overcome these problems inherent in
the contact type sensors, TLS system of LiDAR (light detection and
ranging), which can measure the displacement of a target in a long
range without the influence of surrounding environment and also get
the whole shape of the structure, has been applied to the field of
structural health monitoring. The important characteristic of TLS
measuring is a formation of point clouds which has many points
including the local coordinate. Point clouds are not linear distribution
but dispersed shape. Thus, to analyze point clouds, the interpolation is
needed vitally. Through formation of averaged lattices and CSSI for
the raw data, the method which can estimate the displacement of
simple beam was developed. Also, the developed method can be
extended to calculate the strain and finally applicable to estimate a
stress distribution of a structural member. To verify the validity of the
method, the loading test on a simple beam was conducted and TLS
measured it. Through a comparison of the estimated stress and
reference stress, the validity of the method is confirmed.
Abstract: Linear two-point boundary value problems of order
two are solved using cubic trigonometric B-spline interpolation
method (CTBIM). Cubic trigonometric B-spline is a piecewise
function consisting of trigonometric equations. This method is tested
on some problems and the results are compared with cubic B-spline
interpolation method (CBIM) from the literature. CTBIM is found to
approximate the solution slightly more accurately than CBIM if the
problems are trigonometric.
Abstract: A higher order spline interpolated contour obtained
with up-sampling of homogenously distributed coordinates for
segmentation of kidney region in different classes of ultrasound
kidney images has been developed and presented in this paper. The
performance of the proposed method is measured and compared with
modified snake model contour, Markov random field contour and
expert outlined contour. The validation of the method is made in
correspondence with expert outlined contour using maximum coordinate
distance, Hausdorff distance and mean radial distance
metrics. The results obtained reveal that proposed scheme provides
optimum contour that agrees well with expert outlined contour.
Moreover this technique helps to preserve the pixels-of-interest
which in specific defines the functional characteristic of kidney. This
explores various possibilities in implementing computer-aided
diagnosis system exclusively for US kidney images.
Abstract: Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.
Abstract: This paper discusses on the use of Spline Interpolation
and Mean Square Error (MSE) as tools to process data acquired from
the developed simulator that shall replicate sea bed logging environment.
Sea bed logging (SBL) is a new technique that uses marine
controlled source electromagnetic (CSEM) sounding technique and is
proven to be very successful in detecting and characterizing hydrocarbon
reservoirs in deep water area by using resistivity contrasts. It uses
very low frequency of 0.1Hz to 10 Hz to obtain greater wavelength.
In this work the in house built simulator was used and was provided
with predefined parameters and the transmitted frequency was varied
for sediment thickness of 1000m to 4000m for environment with and
without hydrocarbon. From series of simulations, synthetics data were
generated. These data were interpolated using Spline interpolation
technique (degree of three) and mean square error (MSE) were
calculated between original data and interpolated data. Comparisons
were made by studying the trends and relationship between frequency
and sediment thickness based on the MSE calculated. It was found
that the MSE was on increasing trends in the set up that has the
presence of hydrocarbon in the setting than the one without. The MSE
was also on decreasing trends as sediment thickness was increased
and with higher transmitted frequency.
Abstract: We present a new quadrature rule based on the spline
interpolation along with the error analysis. Moreover, some error
estimates for the reminder when the integrand is either a Lipschitzian
function, a function of bounded variation or a function whose
derivative belongs to Lp are given. We also give some examples
to show that, practically, the spline rule is better than the trapezoidal
rule.
Abstract: The study of the Andaman Sea can be studied by
using the oceanic model; therefore the grid covering the study area
should be generated. This research aims to generate grid covering
the Andaman Sea, situated between longitudes 90◦E to 101◦E and
latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear
with 87 × 217 grid points. The methods used in this study are
cubic spline and bilinear interpolations. The boundary grid points
are generated by spline interpolation while the interior grid points
have to be specified by bilinear interpolation method. A vertical grid
is sigma coordinate with 15 layers of water column.
Abstract: High precision in motion is required to manipulate the
micro objects in precision industries for micro assembly, cell
manipulation etc. Precision manipulation is achieved based on the
appropriate mechanism design of micro devices such as
microgrippers. Design of a compliant based mechanism is the better
option to achieve a highly precised and controlled motion. This
research article highlights the method of designing a compliant based
three fingered microgripper suitable for holding asymmetric objects.
Topological optimization technique, a systematic method is
implemented in this research work to arrive a topologically optimized
design of the mechanism needed to perform the required micro
motion of the gripper. Optimization technique has a drawback of
generating senseless regions such as node to node connectivity and
staircase effect at the boundaries. Hence, it is required to have post
processing of the design to make it manufacturable. To reduce the
effect of post processing stage and to preserve the edges of the image,
a cubic spline interpolation technique is introduced in the MATLAB
program. Structural performance of the topologically developed
mechanism design is tested using finite element method (FEM)
software. Further the microgripper structure is examined to find its
fatigue life and vibration characteristics.
Abstract: The RR interval series is non-stationary and unevenly
spaced in time. For estimating its power spectral density (PSD) using
traditional techniques like FFT, require resampling at uniform
intervals. The researchers have used different interpolation
techniques as resampling methods. All these resampling methods
introduce the low pass filtering effect in the power spectrum. The
lomb transform is a means of obtaining PSD estimates directly from
irregularly sampled RR interval series, thus avoiding resampling. In
this work, the superiority of Lomb transform method has been
established over FFT based approach, after applying linear and
cubicspline interpolation as resampling methods, in terms of
reproduction of exact frequency locations as well as the relative
magnitudes of each spectral component.
Abstract: A method for solving linear and non-linear Goursat
problem is given by using the two-dimensional differential transform
method. The approximate solution of this problem is calculated in
the form of a series with easily computable terms and also the exact
solutions can be achieved by the known forms of the series solutions.
The method can easily be applied to many linear and non-linear
problems and is capable of reducing the size of computational work.
Several examples are given to demonstrate the reliability and the
performance of the presented method.
Abstract: We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.