Abstract: Airborne Laser Scanning (ALS) is one of the main technologies for generating high-resolution digital terrain models (DTMs). DTMs are crucial to several applications, such as topographic mapping, flood zone delineation, geographic information systems (GIS), hydrological modelling, spatial analysis, etc. Laser scanning system generates irregularly spaced three-dimensional cloud of points. Raw ALS data are mainly ground points (that represent the bare earth) and non-ground points (that represent buildings, trees, cars, etc.). Removing all the non-ground points from the raw data is referred to as filtering. Filtering heavily forested areas is considered a difficult and challenging task as the canopy stops laser pulses from reaching the terrain surface. This research presents an approach for removing non-ground points from raw ALS data in densely forested areas. Smoothing splines are exploited to interpolate and fit the noisy ALS data. The presented filter utilizes a weight function to allocate weights for each point of the data. Furthermore, unlike most of the methods, the presented filtering algorithm is designed to be automatic. Three different forested areas in the United Kingdom are used to assess the performance of the algorithm. The results show that the generated DTMs from the filtered data are accurate (when compared against reference terrain data) and the performance of the method is stable for all the heavily forested data samples. The average root mean square error (RMSE) value is 0.35 m.
Abstract: Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.
Abstract: The logistic regression (LR) and multivariate adaptive regression spline (MarSpline) are applied and verified for analysis of landslide susceptibility map in Oudka, Morocco, using geographical information system. From spatial database containing data such as landslide mapping, topography, soil, hydrology and lithology, the eight factors related to landslides such as elevation, slope, aspect, distance to streams, distance to road, distance to faults, lithology map and Normalized Difference Vegetation Index (NDVI) were calculated or extracted. Using these factors, landslide susceptibility indexes were calculated by the two mentioned methods. Before the calculation, this database was divided into two parts, the first for the formation of the model and the second for the validation. The results of the landslide susceptibility analysis were verified using success and prediction rates to evaluate the quality of these probabilistic models. The result of this verification was that the MarSpline model is the best model with a success rate (AUC = 0.963) and a prediction rate (AUC = 0.951) higher than the LR model (success rate AUC = 0.918, rate prediction AUC = 0.901).
Abstract: In contrast to existing methods which do not take into account
multiconnectivity in a broad sense of this term, we develop
mathematical models and highly effective combination (BIEM
and FDM) numerical methods of calculation of stationary and
quasi-stationary temperature field of a profile part of a blade
with convective cooling (from the point of view of realization
on PC). The theoretical substantiation of these methods is
proved by appropriate theorems. For it, converging quadrature
processes have been developed and the estimations of errors in
the terms of A.Ziqmound continuity modules have been
received. For visualization of profiles are used: the method of the least
squares with automatic conjecture, device spline, smooth
replenishment and neural nets. Boundary conditions of heat
exchange are determined from the solution of the
corresponding integral equations and empirical relationships.
The reliability of designed methods is proved by calculation
and experimental investigations heat and hydraulic
characteristics of the gas turbine first stage nozzle blade.
Abstract: The aim of this work is to modelize the occlusion of a
person with temporomandibular disorders as an evolutionary equation
and approach its solution by the construction and characterizing
of discrete variational splines. To formulate the problem, certain
boundary conditions have been considered. After showing the
existence and the uniqueness of the solution of such a problem, a
convergence result of a discrete variational evolutionary spline is
shown. A stress analysis of the occlusion of a human jaw with
temporomandibular disorders by finite elements is carried out in
FreeFem++ in order to prove the validity of the presented method.
Abstract: We develop a method based on polynomial quintic
spline for numerical solution of fourth-order non-homogeneous
parabolic partial differential equation with variable coefficient. By
using polynomial quintic spline in off-step points in space and
finite difference in time directions, we obtained two three level
implicit methods. Stability analysis of the presented method has been
carried out. We solve four test problems numerically to validate the
derived method. Numerical comparison with other methods shows
the superiority of presented scheme.
Abstract: This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole
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: Bringing forth a survey on recent higher order spline
techniques for solving boundary value problems in ordinary
differential equations. Here we have discussed the summary of the
articles since 2000 till date based on higher order splines like Septic,
Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree
splines. Comparisons of methods with own critical comments as
remarks have been included.
Abstract: Pulmonary Function Tests are important non-invasive
diagnostic tests to assess respiratory impairments and provides
quantifiable measures of lung function. Spirometry is the most
frequently used measure of lung function and plays an essential role
in the diagnosis and management of pulmonary diseases. However,
the test requires considerable patient effort and cooperation,
markedly related to the age of patients resulting in incomplete data
sets. This paper presents, a nonlinear model built using Multivariate
adaptive regression splines and Random forest regression model to
predict the missing spirometric features. Random forest based feature
selection is used to enhance both the generalization capability and the
model interpretability. In the present study, flow-volume data are
recorded for N= 198 subjects. The ranked order of feature importance
index calculated by the random forests model shows that the
spirometric features FVC, FEF25, PEF, FEF25-75, FEF50 and the
demographic parameter height are the important descriptors. A
comparison of performance assessment of both models prove that, the
prediction ability of MARS with the `top two ranked features namely
the FVC and FEF25 is higher, yielding a model fit of R2= 0.96 and
R2= 0.99 for normal and abnormal subjects. The Root Mean Square
Error analysis of the RF model and the MARS model also shows that
the latter is capable of predicting the missing values of FEV1 with a
notably lower error value of 0.0191 (normal subjects) and 0.0106
(abnormal subjects) with the aforementioned input features. It is
concluded that combining feature selection with a prediction model
provides a minimum subset of predominant features to train the
model, as well as yielding better prediction performance. This
analysis can assist clinicians with a intelligence support system in the
medical diagnosis and improvement of clinical care.
Abstract: This paper consider the solution of the matrix
differential models using quadratic, cubic, quartic, and quintic
splines. Also using the Taylor’s and Picard’s matrix methods, one
illustrative example is included.
Abstract: In this paper, numerical solution of system of
Fredholm and Volterra integral equations by means of the Spline
collocation method is considered. This approximation reduces the
system of integral equations to an explicit system of algebraic
equations. The solution is collocated by cubic B-spline and the
integrand is approximated by the Newton-Cotes formula. The error
analysis of proposed numerical method is studied theoretically. The
results are compared with the results obtained by other methods to
illustrate the accuracy and the implementation of our method.
Abstract: The generalized wave equation models various
problems in sciences and engineering. In this paper, a new three-time
level implicit approach based on cubic trigonometric B-spline for the
approximate solution of wave equation is developed. The usual finite
difference approach is used to discretize the time derivative while
cubic trigonometric B-spline is applied as an interpolating function in
the space dimension. Von Neumann stability analysis is used to
analyze the proposed method. Two problems are discussed to exhibit
the feasibility and capability of the method. The absolute errors and
maximum error are computed to assess the performance of the
proposed method. The results were found to be in good agreement
with known solutions and with existing schemes in literature.
Abstract: In this paper, a backward semi-Lagrangian scheme
combined with the second-order backward difference formula
is designed to calculate the numerical solutions of nonlinear
advection-diffusion equations. The primary aims of this paper are
to remove any iteration process and to get an efficient algorithm
with the convergence order of accuracy 2 in time. In order to achieve
these objects, we use the second-order central finite difference and the
B-spline approximations of degree 2 and 3 in order to approximate
the diffusion term and the spatial discretization, respectively. For the
temporal discretization, the second order backward difference formula
is applied. To calculate the numerical solution of the starting point
of the characteristic curves, we use the error correction methodology
developed by the authors recently. The proposed algorithm turns out
to be completely iteration free, which resolves the main weakness
of the conventional backward semi-Lagrangian method. Also, the
adaptability of the proposed method is indicated by numerical
simulations for Burgers’ equations. Throughout these numerical
simulations, it is shown that the numerical results is in good
agreement with the analytic solution and the present scheme offer
better accuracy in comparison with other existing numerical schemes.
Abstract: Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.
Abstract: In this paper, Semi-orthogonal B-spline scaling
functions and wavelets and their dual functions are presented
to approximate the solutions of integro-differential equations.The
B-spline scaling functions and wavelets, their properties and the
operational matrices of derivative for this function are presented to
reduce the solution of integro-differential equations to the solution of
algebraic equations. Here we compute B-spline scaling functions of
degree 4 and their dual, then we will show that by using them we have
better approximation results for the solution of integro-differential
equations in comparison with less degrees of scaling functions
Abstract: This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.
Abstract: Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.
Abstract: GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).