Table Of ContentAdvanced Mathematical
Techniques in Engineering
Sciences
Science, Technology, and Management Series
Series Editor
J. Paulo Davim
Advanced Mathematical Techniques in Engineering Sciences
Mangey Ram and J. Paulo Davim
Optimizing Engineering Problems through Heuristic Techniques
Kaushik Kumar, Nadeem Faisal, and J. Paulo Davim
Advanced Mathematical
Techniques in Engineering
Sciences
Edited by
Mangey Ram and J. Paulo Davim
CRC Press
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Contents
Preface ............................................................................................................................................vii
Acknowledgments .........................................................................................................................xi
Editors ...........................................................................................................................................xiii
Contributors ...................................................................................................................................xv
Chapter 1 Application of the Laplace transform in problems of studying
the dynamic properties of a material system and in engineering
technologies .....................................................................................................1
Lubov Mironova and Leonid Kondratenko
Chapter 2 Fourier series and its applications in engineering ..........................................35
Smita Sonker and Alka Munjal
Chapter 3 Soft computing techniques and applications ...................................................57
Pankaj Kumar Srivastava, Dinesh Bisht, and Mangey Ram
Chapter 4 New approach for solving multi-objective transportation problem ...........71
Gurupada Maity and Sankar Kumar Roy
Chapter 5 An application of dual-response surface optimization methodology
to improve the yield of pulp cooking process .................................................91
Boby John and K.K. Chowdhury
Chapter 6 Time-dependent conflicting bifuzzy set and its applications in
reliability evaluation ...........................................................................................111
Shshank Chaube, S.B. Singh, Sangeeta Pant, and Anuj Kumar
Chapter 7 Recent progress on failure time data analysis of repairable system .........129
Yasuhiro Saito and Tadashi Dohi
Chapter 8 View-count based modeling for YouTube videos and weighted
criteria–based ranking ........................................................................................149
N. Aggrawal, A. Arora, A. Anand, and M.S. Irshad
Chapter 9 Market segmentation-based modeling: An approach to understand
multiple modes in diffusion curves .................................................................165
A. Anand, R. Aggarwal, and O. Singh
v
vi Contents
Chapter 10 Kernel estimators for data analysis ..................................................................177
Piotr Kulczycki
Chapter 11 A new technique for constructing exact tolerance limits on future
outcomes under parametric uncertainty .........................................................203
N.A. Nechval, K.N. Nechval, and G. Berzins
Chapter 12 Design of neural network–based PID controller for biped robot
while ascending and descending the staircase ..............................................227
Ravi Kumar Mandava and Pandu R. Vundavilli
Chapter 13 Modeling fertility in Murrah bulls with intelligent algorithms ...............247
Adesh Kumar Sharma, Ravinder Malhotra, and Atish Kumar Chakravarty
Chapter 14 Computational study of the Coanda flow for V/STOL .................................265
Maharshi Subhash and Michele Trancossi
Chapter 15 Introduction to collocation method with application of B-spline
basis functions to solve differential equations .............................................285
Geeta Arora
Chapter 16 Rayleigh’s approximation method on reflection/refraction
phenomena of plane SH-wave in a corrugated anisotropic structure ......297
Neelima Bhengra
Index .............................................................................................................................................327
Preface
Mathematical techniques are the strength of engineering sciences and form the common
foundation of all novel disciplines as engineering sciences. The book Advanced Mathematical
Techniques in Engineering Sciences involved an ample range of mathematical tools and tech-
niques applied in various fields of engineering sciences. Through this book, engineers
have the opportunity to gain a greater knowledge and it may help them in the applications
of mathematics in engineering sciences.
Chapter 1 presents the rules and methods for applying the Laplace transform. Three
sections of the mathematical investigation of applied questions are distinguished: the rules
for performing operations in the Laplace transform; Laplace transform in research tasks
of the vibrations of a rod; and application of the Laplace transform in engineering technol-
ogy. Specific examples of solving differential equations are presented, applied to prob-
lems of mechanics and the theory of oscillations. The essence of Kondratenko’s method is
described, on the basis of which mathematical modeling of some technological operations
of mechanical engineering was carried out and features of dynamic phenomena during
the work of equipment and interaction of the tool with detail were revealed.
Chapter 2 investigates the history, nature, and importance of the Fourier series. This
chapter describes the periodic function, orthogonal function, Fourier series, Fourier
approximation, Dirichlet’s theorem, Riemann–Lebesgue lemma for Fourier series, dif-
ferentiation of Fourier series, convergence of the Fourier series of the functions, Fourier
transform, Fourier analysis with Fourier transform, and Gibbs phenomenon. Also, some
of the summability methods (Cesàro, Nörlund, Riesz, weighted mean, etc.), absolute sum-
mability methods, strong summability methods, necessary and sufficient conditions for
regularity of matrix of summability methods, uses of summability, norm, modulus of con-
tinuity, Lipschitz condition, various Lipschitz classes in trigonometric Fourier approxima-
tion, and importance of degree of approximation have been explained. The applications of
summability methods in approximation of the signals, the behavior of the Fourier series
of a piecewise smooth function (Gibbs phenomenon), Fourier series of signals of bounded
bandwidth, filtering by Fourier transforms, and applications of summability technique
and Fourier series have been described.
Chapter 3 describes the basics of soft computing and their applications. The key goal
of soft computing is to develop intelligent machines to provide solutions to real-world
problems, which are difficult to model mathematically.
Chapter 4 describes the study on solving transportation problems under a multi-objec-
tive environment. The main focus of this chapter is to introduce a new approach for solv-
ing multi-objective transportation problems in addition to the existing approaches such
as goal programming, fuzzy programming, and revised multi-choice goal programming.
In the proposed approach a procedure to obtain a Pareto-optimal solution of a multi-
objective transportation problem using the Vogel approximation method is incorporated.
vii
viii Preface
The merits and demerits of the approaches goal programming, fuzzy programming, and
revised multi-choice goal programming compared to our new approach to solving a multi-
objective transportation problem are presented.
Chapter 5 provides the study of simultaneous optimization of yield and viscosity of
the pulp cooking process using the dual-response surface methodology. The pulp cook-
ing process is an important step in the manufacturing of rayon grade pulp. The pulp is
the cellulose component of the wood. The cellulose is separated from other components
and impurities of wood by cooking the wood chips in a highly pressurized chamber fol-
lowed by multiple stages of washing and chemical treatments. The study is undertaken
to increase the pulp yield as far as possible without increasing the viscosity beyond the
specified upper limit.
Chapter 6 gives the concept of a time-dependent conflicting bifuzzy set (CBFS), and a
new procedure to construct the membership and nonmembership functions of the fuzzy
reliability function is proposed with the help of time-dependent CBFS. The concept of
triangular CBFS has been developed, and triangular CBFS is used to represent the failure
rate function of the system.
Chapter 7 focuses on the failure time data analysis based on the nonhomogeneous
Poisson process (NHPP) and discusses several statistical estimation methods for a periodic
replacement problem with minimal repair as the simplest application of life data analysis
with NHPP. Not only the parametric maximum likelihood estimation of the power law
process is applied, but also constrained nonparametric maximum likelihood estimation
(CNPMLE) and kernel-based estimation methods for estimating the cost-optimal periodic
replacement problem with the minimal repair, where single or multiple minimal repair
data are assumed.
Chapter 8 extends the available literature and discusses the important attribute “view-
count” of content dynamically. With the Internet emerging as a rapidly growing new mar-
ket, the netizens are also growing at a fast pace. Making use of this ideology, a modeling
framework whose utility has been highlighted through three models is proposed that
describes the growing Internet market size and repeat viewers. The models have been
validated on a YouTube entertainment video data set.
Chapter 9 analyzes dual-market modeling. Dual-market modeling is an increasingly
important concept in marketing, and in order to inculcate heterogeneity and the require-
ment of some specific characteristics for some technologies to be adopted differently in
different geographical locations, the authors intend to study this behavior through a math-
ematical framework that exhibits the dual-market phenomenon.
Chapter 10 presents a uniform methodology for three fundamental problems in data
analysis: identification/detection of atypical elements (outliers), clustering, and classifica-
tion. Such a unification facilitates understanding of the material and adapting it to the
individual needs and preferences of particular users. The investigated material is ready
to use, is practically parameter free, and does not require laborious exploration from the
researcher. This has been illustrated with a number of applications in the fields of engi-
neering, management, medicine and biology, as well as supplemented by a thematic bibli-
ography extending the issues presented.
Chapter 11 analyzes the statistical tolerance limits used today in both production and
research. It is often desirable to have statistical tolerance limits available for the distribu-
tions used to describe time-to-failure data in reliability problems. For example, one might
wish to know if at least a certain proportion of a manufactured product will operate for
at least, say, the warranty period. This question cannot usually be answered exactly, but
it may be possible to determine a lower tolerance limit, based on a preliminary random
Preface ix
sample, such that one can say with a certain confidence that at least a specified proportion
or more of the product will operate longer than the lower tolerance limit. Then reliability
statements can be made based on the lower tolerance limit, or, decisions can be reached by
comparing the tolerance limit to the warranty period.
Chapter 11 analyzes the lower tolerance limit, based on a preliminary random sam-
ple, such that one can say with a certain confidence that at least a specified proportion or
more of the product will operate longer than the lower tolerance limit, which presents a
new technique for constructing exact lower and upper tolerance limits on outcomes (for
example, on order statistics) in future samples. The technique used here emphasizes piv-
otal quantities relevant for obtaining tolerance factors and is applicable whenever the sta-
tistical problem is invariant under a group of transformations that acts transitively on the
parameter space. The proposed technique is based on a probability transformation and
pivotal quantity averaging. It is conceptually simple and easy to use. The discussion is
restricted to one-sided tolerance limits.
Chapter 12 deals with the design of torque-based PID controller and tuning its gains
with the help of two algorithms, namely, modified chaotic invasive weed optimization
(MCIWO) and modified chaotic invasive weed optimization-neural network (MCIWO-NN)
algorithms for the biped robot while walking on a staircase. An analytical method has
been developed to generate the gaits and design the torque-based PID controller. The
dynamics of the biped robot utilized in the said controller have been derived after utiliz-
ing the Lagrange–Euler formulation. Alongside, the authors utilized the MCIWO algo-
rithm to optimize the gains of the PID controller. Further, in the MCIWO-NN algorithm,
the MCIWO algorithm is used to evolve the architecture of the NN, which helped in pre-
dicting the gains of the PID controller in an adaptive manner. The developed algorithms
are tested in computer simulations and on a real biped robot.
In Chapter 13, intelligent predictive models for modeling fertility of Murrah bulls
using the various emerging machine learning (ML) algorithms, namely, neural networks
(NNs), support vector regression (SVR), decision trees (DTs), and random forests (RFs), and
a conventional linear model (LM) for regression have been described. These intelligent
ML models would provide decision support to organized dairy farms for selecting good
bulls. Hence, the ML models can be employed as a plausible alternative to linear regres-
sion models to assess more accurately the conception rate in Murrah breeding bulls at the
organized farms.
In Chapter 14, the computational study has been performed on the two-jet vectoring
through the Coanda surface, realizing the future concept of the vertical and short takeoff
and landing (V/STOL) of an aircraft for civil aviation purposes. The set of computations
has been performed from the incompressible flow regime to the incipient of the compress-
ible flow regime. This computational study aims to identify the design parameters through
the flow characteristics using the computational fluid dynamics technique.
Chapter 15 deals with the discussion on the collocation method which is a very well-
known numerical technique. Along with the description of the methodology adopted,
details are given for the used B-spline basis function in the collocation method. The prop-
erties of B-spline basis functions are discussed in this chapter with a description of the
types and degrees of B-spline basis functions.
In Chapter 16, utilizing Rayleigh’s approximation method, an attempt has been
made to study the reflection and refraction patterns in a corrugated interface sand-
wiched between an initially stressed fluid-saturated poroelastic half-space and a highly
anisotropic half-space. The highly anisotropic half-space is considered as triclinic.
Various two-dimensional plots have been drawn to show the effects of some affecting
