Foundations of Mathematical Modelling for Engineering Problem Solving

178 Pages·2023·6.433 MB·English

by  Parikshit Narendra Mahalle, Nancy Ambritta P., Sachin R. Sakhare, Atul P. Kulkarni

Studies in Autonomic,
Data-driven and Industrial Computing
Parikshit Narendra Mahalle
Nancy Ambritta P.
Sachin R. Sakhare
Atul P. Kulkarni
Foundations
of Mathematical
Modelling
for Engineering
Problem Solving
Studies in Autonomic, Data-driven and
Industrial Computing
Series Editors
Swagatam Das, Indian Statistical Institute, Kolkata, West Bengal, India
Jagdish Chand Bansal, South Asian University, Chanakyapuri, India
The book series Studies in Autonomic, Data-driven and Industrial Computing
(SADIC) aims at bringing together valuable and novel scientific contributions
that address new theories and their real world applications related to autonomic,
data-driven, and industrial computing. The area of research covered in the series
includes theory and applications of parallel computing, cyber trust and security, grid
computing, optical computing, distributed sensor networks, bioinformatics, fuzzy
computing and uncertainty quantification, neurocomputing and deep learning, smart
grids, data-driven power engineering, smart home informatics, machine learning,
mobile computing, internet of things, privacy preserving computation, big data
analytics, cloud computing, blockchain and edge computing, data-driven green
computing, symbolic computing, swarm intelligence and evolutionary computing,
intelligent systems for industry 4.0, as well as other pertinent methods for autonomic,
data-driven, and industrial computing.
The series will publish monographs, edited volumes, textbooks and proceedings of
important conferences, symposia and meetings in the field of autonomic, data-driven
and industrial computing.

· ·
Parikshit Narendra Mahalle Nancy Ambritta P.
·
Sachin R. Sakhare Atul P. Kulkarni
Foundations of Mathematical
Modelling for Engineering
Problem Solving
Parikshit Narendra Mahalle Nancy Ambritta P.
Department of Artificial Intelligence Glareal Software Solutions PTE. Ltd.
and Data Science Singapore, Singapore
Vishwakarma Institute of Information
Technology Atul P. Kulkarni
Pune, India Department of Mechanical Engineering
Vishwakarma Institute of Information
Sachin R. Sakhare Technology
Department of Computer Engineering Pune, India
Vishwakarma Institute of Information
Technology
Pune, India
ISSN 2730-6437 ISSN 2730-6445 (electronic)
Studies in Autonomic, Data-driven and Industrial Computing
ISBN 978-981-19-8827-1 ISBN 978-981-19-8828-8 (eBook)
https://doi.org/10.1007/978-981-19-8828-8
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Singapore Pte Ltd. 2023
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse
of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmission or information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.
The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,
Singapore
Preface
Scientists investigate that which already is ... Engineers
create that which has never been.
—Albert Einstein
Due to the transformation to Industry 4.0 and emergence of Society 5.0, there is
a need of reliable problem solving and mathematical modeling. This will enable
the support to advance architectures and technologies resulting into the optimal and
efficient solutions. This book aims at introducing fundamentals of problem solving,
need of mathematical modeling and the importance of mathematical modeling for
different categories of the problems to undergraduate and postgraduate students and
researchers in science and engineering. The text is divided into three parts: concepts,
mathematical theories and case studies in different domains of engineering problem
solving.
Research and development plays a major role in the economic growth and the
GDP of a nation. Hence, every nation takes steps toward the improvement of the
Gross Enrollment Ration (GER) under the advisory of the National Knowledge
Commission, thereby increasing the funding in support of admissions to postgrad-
uation (PG) and Ph.D. programs. In these PG and Ph.D. programs, mathematical
modeling becomes an integral part of research. However, there is a scarcity of good
literature for engineering problem solving. This book aims at providing an insight into
mathematical modeling for engineering problem solving irrespective of the branch
of study, thereby making it worthwhile for the researchers.
This book fundamentally aims at improving the mathematical modeling skills
among the users by enhancing the ability to understand, connect, apply and use
the mathematical concepts to the problem at hand. This book provides the readers
with an in-depth knowledge of the various categories/classes of research problems
that professionals, researchers and students might encounter following which the
application of appropriate mathematical models is explained with the help of case
studies. This book is majorly concerned in developing the expertise of identifying the
category or class into which the problem at hand falls, which eventually makes the
v
vi Preface
modelling aspect easier. This book is targeted at academicians, researchers, students
and professionals who belong to all engineering disciplines.
This book is aimed at providing timely and useful content to the mass readers, espe-
cially to researchers and Ph.D. scholars to whom mathematical modeling becomes
inevitable, irrespective of the branch of study.
The main characteristics of this book are:
•
Provides a strong foundation for the readers regarding the basics of mathematical
modeling, its relevance and need.
•
Provides illustrations and pseudo-code for better understanding and applicability.
•
Elaborates on the problem solving and mathematical modeling process.
•
Equips the readers with the ability to identify and categorize the problem at hand
(specifically regarding computer engineering), thereby making it an effortless task
for the users to arrive at an appropriate mathematical model for representing the
problem.
•
Provides an in-depth understanding on the various categories/classes of problems
(dedicated chapter for each category of problem).
•
Provides numerous case studies for providing a clear understanding of concepts
in real time and serves as a guide to aspiring students/professionals by presenting
various research openings in the field.
This book is specifically designed for beginners who want to get acquainted
with the concept of mathematical modelling and the various categories. Focus on
identification of the category of problem and the application of appropriate model is
a key highlight in this book. The book is useful for undergraduates, postgraduates,
industry, researchers, teachers and research scholars in engineering, and we are sure
that this book will be well received by all stakeholders.
Pune, India Parikshit Narendra Mahalle
Singapore Nancy Ambritta P.
Pune, India Sachin R. Sakhare
Pune, India Atul P. Kulkarni
Contents
1 Introduction ................................................... 1
1.1 Modeling .................................................. 1
1.2 Mathematical Modeling ..................................... 2
1.3 General Steps .............................................. 7
1.4 Trends in Teaching and Learning ............................. 9
1.5 Summary .................................................. 9
References ..................................................... 10
2 Problem Solving and Mathematical Modeling ..................... 11
2.1 Problem Evolution .......................................... 11
2.2 Problem Solving ........................................... 13
2.3 Problem Classification ...................................... 17
2.4 Modeling Process and Teaching Approaches ................... 19
2.5 Summary .................................................. 22
References ..................................................... 22
3 Decision Problems .............................................. 23
3.1 Introduction ............................................... 23
3.1.1 Control Theory ...................................... 23
3.1.2 Game Theory ........................................ 25
3.1.3 Probability and Statistics .............................. 28
3.1.4 Multicriteria Decision Analysis ........................ 32
3.2 Motivation ................................................ 33
3.3 Case Studies ............................................... 34
3.4 Summary .................................................. 37
References ..................................................... 38
4 Optimization Problems ......................................... 39
4.1 Introduction ............................................... 39
4.1.1 Mathematical Modeling ............................... 39
4.1.2 History Development of Optimization ................... 40
4.1.3 Optimization ........................................ 41
vii
viii Contents
4.2 Motivation ................................................ 43
4.3 Case Study ................................................ 43
4.4 Summary .................................................. 55
References ..................................................... 55
5 Delay Problems ................................................ 57
5.1 Introduction ............................................... 57
5.1.1 Queuing Theory ..................................... 58
5.1.2 Delay Differential Equations ........................... 66
5.2 Motivation ................................................ 82
5.3 Case Studies ............................................... 82
5.4 Summary .................................................. 86
References ..................................................... 86
6 Data Science Problems .......................................... 87
6.1 Introduction ............................................... 87
6.1.1 Data Analytics and Learning Methodologies ............. 101
6.1.2 Data Visualization Tools and Data Modeling ............. 104
6.2 Motivation ................................................ 136
6.3 Case Studies ............................................... 138
6.4 Summary .................................................. 140
References ..................................................... 140
7 Pandemic Problems ............................................ 143
7.1 Introduction ............................................... 143
7.1.1 Impacts of Pandemics ................................ 145
7.2 Motivation ................................................ 145
7.2.1 Types of Epidemic Models ............................ 147
7.3 Case Studies ............................................... 150
7.3.1 Compartmental Models ............................... 150
7.3.2 COVID-19 Pandemic Problem ......................... 151
7.4 Summary .................................................. 153
References ..................................................... 154
8 Interdisciplinary Engineering Problems .......................... 157
8.1 Introduction ............................................... 157
8.2 Motivation ................................................ 158
8.3 Case Studies ............................................... 159
8.4 Summary .................................................. 165
References ..................................................... 166
9 Conclusion .................................................... 167
9.1 Summary .................................................. 167
9.2 Research Openings and Future Outlook ........................ 168