New Paradigms in Computational Modeling and Its Applications

By Snehashish Chakraverty

In general, every problem of science and engineering is governed by mathematical models. There is often a need to model, solve and interpret the problems one encounters in the world of practical problems. Models of practical application problems usually need to be handled by efficient computational models.

New Paradigms in Computational Modeling and Its Applications deals with recent developments in mathematical methods, including theoretical models as well as applied science and engineering. The book focuses on subjects that can benefit from mathematical methods with concepts of simulation, waves, dynamics, uncertainty, machine intelligence, and applied mathematics. The authors bring together leading-edge research on mathematics combining various fields of science and engineering. This perspective acknowledges the inherent characteristic of current research on mathematics operating in parallel over different subject fields.

New Paradigms in Computational Modeling and Its Applications meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of mathematics on the other. As such, the book contains 13 chapters covering various aspects of computational modeling from theoretical to application problems. The first six chapters address various problems of structural and fluid dynamics.

The next four chapters include solving problems where the governing parameters are uncertain regarding fuzzy, interval, and affine. The final three chapters will be devoted to the use of machine intelligence in artificial neural networks.

• Presents a self-contained and up to date review of modelling real life scientific and engineering application problems
• Introduces new concepts of various computing techniques to handle different engineering and science problems
• Demonstrates the efficiency and power of the various algorithms and models in a simple and easy to follow style, including numerous examples to illustrate concepts and algorithms

• Language: English
• Publisher: Academic Press
• Release date: Jan 9, 2021
• ISBN: 9780128221686

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Preface

Snehashish Chakraverty, Editor

In general, every problem of science and engineering is governed by mathematical models. There is often a need to model, solve, and interpret the problems one encounters in the world of practical problems. Models of practical application problems are usually need to be handled by efficient computational models.

New Paradigms in Computational Modeling and Its Applications contains 15 chapters covering various aspects of computational methods to handle diversified application problems. The first six chapters address various problems of structural and fluid dynamics. The next four chapters include solving problems where the governing parameters are uncertain, viz., fuzzy, interval, and affine. Finally, the last five chapters are devoted to the use of machine intelligence, viz., artificial neural network and data analysis. This book is an attempt to combine various science, engineering and technological problems to discuss the recent trends, usefulness and challenges of computational modeling in various application problems.

In general, dynamic problems of nanostructures follow differential equations that are often nonlinear, and solving them requires efficient and suitable methods. The objective of the first chapter (by Subrat Kumar Jena and Snehashish Chakraverty) is to solve dynamic problems of nanostructures that are encountered in civil, mechanical, and aerospace structures. The vibration characteristics of armchair-type single-walled carbon nanotubes (SWCNTs) have been studied by employing Navier’s approach for the HH boundary condition. The governing equation of motion of the SWCNTs is derived by employing the Euler-Bernoulli beam theory considering moisture concentration, and the size-dependent effect has been captured by the differential form of the strain gradient model.

The second chapter (by K.K. Pradhan and Snehashish Chakraverty) is on transverse vibration of closed circuit-based functionally graded piezoelectric material (FGPM) beams subject to different mechanical boundary conditions. Material properties of FG bimorphs are assumed to vary continuously along the thickness direction in a simple power-law form. This study involves three different piezoelectric components, and the electric field is assumed to vary across the thickness direction in half-cosine and linear variation. The numerical formulation is carried out using the orthogonal polynomials-based Rayleigh-Ritz method to obtain the generalized eigenvalue problem. New results for eigen frequencies are incorporated after checking the test of convergence and comparing with the available literature.

In the third chapter (by Subrat Kumar Jena, Rashmita Mundari, and Snehashish Chakraverty), the vibration problem of a microbeam placed in a thermal environment has been considered. Navier’s technique has been implemented to find nondimensional frequency parameters of the microbeam placed in both low and high thermal environments.

The fourth chapter (by P. Karunakar and Snehashish Chakraverty) deals with coupled shallow water wave equations (CSWWE) governing tsunami wave propagation. The homotopy perturbation transform method (HPTM) has been used to solve the targeted problem.

Natural convection of non-Newtonian nanofluid flow between two vertical parallel plates is studied in Chapter 5 (by U. Biswal, Snehashish Chakraverty, and B.K. Ojha). Galerkin’s method is applied to solve the considered problem. Legendre polynomials are used to approximate the series solution. Results obtained from the proposed method are compared and verified with the existing results in special cases.

In the sixth chapter (by Rajarama Mohan Jena and Snehashish Chakraverty), time-fractional porous medium equation (PME) is considered. A hybrid method, which is a mixture of the homotopy perturbation method (HPM) and integral transform, namely, the ZZ transform (ZZT) method, is applied to achieve the solution of time-fractional PME. Computed results are compared with the existing results for the special case of integer-order derivatives.

A new inverse iteration method is proposed in Chapter 7 (by T.D. Rao and Snehashish Chakraverty) to find approximate bounds of nonprobabilistic parameters involved in various diffusion models. For validation of the method, radon diffusion model is considered.

The eighth chapter (by S. Rout and Snehashish Chakraverty) proposes an affine approach for solving linear structural dynamic problems with nonprobabilistic model parameters. Several application problems from structural dynamics, viz., the spring-mass structural systems with multidegrees-of-freedom, multistoried shear building, and multistoried frame structure are investigated. In order to show the powerfulness and efficacy of the proposed procedure, comparisons of the results (obtained by utilizing the proposed procedure) with those of other methods have been included. Though affine arithmetic is more complex than the classical interval arithmetic, it yields better and tighter enclosures of the solutions.

Stochastic differential equations (SDEs) with impreciseness and vagueness turns into uncertain SDEs (USDEs). As such, in the ninth chapter (by Sukanta Nayak and Snehashish Chakraverty), two different approaches for solving USDEs are discussed. Uncertainties are considered in initial conditions as well as associated parameters in terms of triangular fuzzy numbers (TFNs). Limit method for fuzzy arithmetic has been used as a tool to handle fuzzy SDEs (FSDEs). In particular, a system of Itô SDEs has been analyzed with fuzzy parameters. Further, the fuzzy Euler Maruyama method (FEMM) and the fuzzy Milstein method (FMM) are demonstrated through an example problem with different cases.

The tenth chapter (by S.K. Jeswal and Snehashish Chakraverty) includes uncertain dynamic analysis of structures using artificial neural networks (ANNs). Dynamic analysis of structures usually leads to eigenvalue problems. Eigenvalue problems with uncertainty (viz., fuzzy) may transform these into fuzzy eigenvalue problems (FEPs). Accordingly, ANN-based approach is used in this chapter to handle the titled problem. The entries in the FEPs are considered to be triangular fuzzy numbers (TFNs). Further, the FEPs are converted to the interval form using a single-parametric form and two example problems, viz., a numerical and a two-story frame structure, are investigated.

In various applied problems (such as an electrical circuit), governing differential equations may be of fractional order. Fractional-order differential equations (FDEs) play an important role in explaining many physical phenomena. As such, in Chapter 11 (by Susmita Mall and Snehashish Chakraverty), FDEs are solved using a new approach based on a single-layer ANN named the functional link neural network (FLNN) model. Some application problems are solved and compared with other available traditional techniques to show the effectiveness of the proposed ANN method.

Chapter 12 (by Tanmoy Roy, Marwala Tshilidzi, and Snehashish Chakraverty) explores the deep neural network (DNN) approach in speech emotion recognition (SER). A novel model is built using the DL architecture to produce results that can show directions toward building more robust solutions for SER. The dataset used here is EmoDB, a popular dataset for SER research, and the data are augmented using the random displacement technique. The model has produced approximately 10% cross-validation accuracy improvement over models trained on nonaugmented data.

In Chapter 13 (by Jaya Prakash Sahoo, Samit Ari, and Sarat Kumar Patra), a user-independent static hand gesture recognition technique is analyzed using handcrafted features like the histogram of oriented gradients (HOG) and the deep convolutional neural network (CNN) feature. Extensive analysis is performed on three benchmark static hand gesture datasets with uniform and nonuniform backgrounds on both the cross validation (CV) test. The experimental result shows that the proposed technique is superior in terms of the individual deep CNN features and state-of-the-art techniques. A real-time application of the gesture recognition system is developed and tested using the proposed technique.

In this era of bigdata, recommender systems have played a vital role in suggesting customized recommendations to the users. Recommender systems generally deal with user preferences. As such, Chapter 14 (by Jitendra Kumar, Y.V. Ramanjaneyulu, Korra Sathya Babu, and Bidyut Kumar Patra) explores various group modeling strategies, their implementation methods, and modified variations. Various modeling techniques are explained with suitable examples.

Finally, in Chapter 15 (by Jagadeesh Thati, Samit Ari, and Kajal Agrawal), unsupervised classification techniques are developed to extract the region of glacial lakes in the Himalayan area. Due to the remote location of the Himalayas, a field survey of the glacial lakes is very difficult, and physically acquiring data of the glacial lakes in the Himalayas is time-consuming, complicated, expensive, and risky. Therefore, glacial lakes in the Himalayas region can be detected by processing high-resolution satellite images. A comparative analysis of the unsupervised iterative self-organizing data analysis (ISODATA) technique and K-means techniques is developed to extract the region around glacial lakes. Experiments are conducted using qualitative and quantitative performance analyses.

The audiences of this challenging book are academics and industry. In academics, this book will be useful for graduates and researchers of various science and engineering fields of most of the universities throughout the globe. The Editor believes the integrated and holistic computational approaches in the chapters will certainly benefit the readers for their future studies and research. I would like to thank all the chapter authors for their efforts and support in writing the content and submitting on time. Finally, I would also like to thank the Elsevier team for their help and support throughout this project.

Chapter 1: Nanostructural dynamics problems with complicating effects

Subrat Kumar Jena; Snehashish Chakraverty    Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

Abstract

In this chapter, vibration characteristics of single-walled carbon nanotubes (SWCNTs) have been investigated by exposing to the hygroscopic environment. The Euler-Bernoulli beam theory and the differential form of strain gradient theory (SGT) have been incorporated to derive the proposed model by using Hamilton’s principle. Frequency parameters for the hinged-hinged (HH) boundary condition have been calculated analytically by using Navier’s approach. Further, the effects of the length scale parameter and hygroscopic environment on the frequency parameters have been analyzed through graphical and tabular results.

Keywords

Hygroscopic environment; Strain gradient theory; Navier’s approach; Nanobeam; Vibration

Acknowledgment

The first two authors are thankful to Defence Research and Development Organization (DRDO), New Delhi, India (Sanction Code: DG/TM/ERIPR/GIA/17-18/0129/020) for the funding to carry out the present research work.

1.1: Introduction

With the advancement of nanotechnology, the growing requisite for advanced equipment has led the way to the development of microelectromechanical or nanoelectromechanical systems with advance features. Many advanced devices require small and precise nanoscale displacements; for example, industrial actuators have a fast and accurate response and are highly durable, and they can be a good solution to meet this need. Industrial actuators, commonly used in the form of nanobeams, are used in a variety of industries, such as the automotive industry and medical industry.

Various environmental conditions play significant roles in influencing the dynamical characteristics of various devices; these devices include thermal sensors and humidity sensors. Humidity sensors are now extensively used in the industrial processes and environmental control. For the designing and manufacturing of high-precision circuits in the semiconductor industry, the effects of humidity must be considered. There are many household applications such as intelligent control of the environmental features of buildings, baking control for microwave ovens, and intelligent control for washing machines. In the medical industry, humidity sensors are used in respiratory equipment, sterilizers, early childhood growth chambers, medicine manufacturing processes, and biological products. To this date, various researchers have proposed different structures for the construction of humidity sensors. But carbon nanotubes (CNTs), i.e., single-walled and multiwalled structures, are among the best types of structures that may be used for humidity sensors. In this regard, many studies have been conducted, but some of the important investigations are discussed below.

Zhao et al. [1] investigated vibration characteristics of a humidity sensor using multiwalled carbon nanotubes and based on alternative current. Han et al. [2] studied a humidity sensor on a cellulose paper by using single-walled carbon nanotubes and carboxylic acid. Quelennec et al. [3] designed a multifunctional sensor for both humidity and temperature using multiwalled carbon nanotubes. Jung et al. [4] analyzed the effectiveness of spin-capable multiwalled carbon nanotubes for the humidity sensor. Some other studies related to the dynamic analysis of nanostructures can be found in Refs. [5–16].

In Section 1.2, the governing equation of motion for the proposed model has been derived by incorporating the Euler-Bernoulli beam theory and differential form of strain gradient theory (SGT). Frequency parameters for the hinged-hinged (HH) boundary condition have been calculated analytically by using Navier’s approach. Further, the effects of the length scale parameter and hygroscopic environment on frequency parameters have been studied.

1.2: Proposed model

According to the Euler-Bernoulli beam theory, the displacement fields can be defined as [17, 18]

   (1.1)

Here, u(x, t) is the displacement of the neutral axis in the axial direction and w(x, t) is the displacement along the transverse direction. The strain-displacement relations of the Euler-Bernoulli beam theory by considering the axial strain due to the hygroscopic environment can be expressed