Advances in Intelligent Systems and Computing 1048

Kedar Nath DasJagdish Chand BansalKusum DeepAtulya K. NagarPonnambalam PathipooranamRani Chinnappa Naidu Editors

Soft Computing for Problem SolvingSocProS 2018, Volume 1

Advances in Intelligent Systems and Computing

Volume 1048

Series Editor

Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,Warsaw, Poland

Advisory Editors

Nikhil R. Pal, Indian Statistical Institute, Kolkata, IndiaRafael Bello Perez, Faculty of Mathematics, Physics and Computing,Universidad Central de Las Villas, Santa Clara, CubaEmilio S. Corchado, University of Salamanca, Salamanca, SpainHani Hagras, School of Computer Science and Electronic Engineering,University of Essex, Colchester, UKLászló T. Kóczy, Department of Automation, Széchenyi István University,Gyor, HungaryVladik Kreinovich, Department of Computer Science, University of Texasat El Paso, El Paso, TX, USAChin-Teng Lin, Department of Electrical Engineering, National ChiaoTung University, Hsinchu, TaiwanJie Lu, Faculty of Engineering and Information Technology,University of Technology Sydney, Sydney, NSW, AustraliaPatricia Melin, Graduate Program of Computer Science, Tijuana Instituteof Technology, Tijuana, MexicoNadia Nedjah, Department of Electronics Engineering, University of Rio de Janeiro,Rio de Janeiro, BrazilNgoc Thanh Nguyen , Faculty of Computer Science and Management,Wrocław University of Technology, Wrocław, PolandJun Wang, Department of Mechanical and Automation Engineering,The Chinese University of Hong Kong, Shatin, Hong Kong

The series “Advances in Intelligent Systems and Computing” contains publicationson theory, applications, and design methods of Intelligent Systems and IntelligentComputing. Virtually all disciplines such as engineering, natural sciences, computerand information science, ICT, economics, business, e-commerce, environment,healthcare, life science are covered. The list of topics spans all the areas of modernintelligent systems and computing such as: computational intelligence, soft comput-ing including neural networks, fuzzy systems, evolutionary computing and the fusionof these paradigms, social intelligence, ambient intelligence, computational neuro-science, artificial life, virtual worlds and society, cognitive science and systems,Perception and Vision, DNA and immune based systems, self-organizing andadaptive systems, e-Learning and teaching, human-centered and human-centriccomputing, recommender systems, intelligent control, robotics and mechatronicsincluding human-machine teaming, knowledge-based paradigms, learning para-digms, machine ethics, intelligent data analysis, knowledge management, intelligentagents, intelligent decision making and support, intelligent network security, trustmanagement, interactive entertainment, Web intelligence and multimedia.

The publications within “Advances in Intelligent Systems and Computing” areprimarily proceedings of important conferences, symposia and congresses. Theycover significant recent developments in the field, both of a foundational andapplicable character. An important characteristic feature of the series is the shortpublication time and world-wide distribution. This permits a rapid and broaddissemination of research results.

** Indexing: The books of this series are submitted to ISI Proceedings,EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink **

More information about this series at http://www.springer.com/series/11156

Kedar Nath Das • Jagdish Chand Bansal •

Kusum Deep • Atulya K. Nagar •

Ponnambalam Pathipooranam •

Rani Chinnappa NaiduEditors

Soft Computing for ProblemSolvingSocProS 2018, Volume 1

123

EditorsKedar Nath DasDepartment of MathematicsNational Institute of Technology SilcharSilchar, Assam, India

Jagdish Chand BansalDepartment of MathematicsSouth Asian UniversityNew Delhi, Delhi, India

Kusum DeepDepartment of MathematicsIndian Institute of Technology RoorkeeRoorkee, Uttarakhand, India

Atulya K. NagarDepartment of MathematicsFaculty of ScienceLiverpool Hope UniversityLiverpool, UK

Ponnambalam PathipooranamSchool of Electrical EngineeringVIT UniversityVellore, Tamil Nadu, India

Rani Chinnappa NaiduSchool of Electrical EngineeringVIT UniversityVellore, Tamil Nadu, India

ISSN 2194-5357 ISSN 2194-5365 (electronic)Advances in Intelligent Systems and ComputingISBN 978-981-15-0034-3 ISBN 978-981-15-0035-0 (eBook)https://doi.org/10.1007/978-981-15-0035-0

© Springer Nature Singapore Pte Ltd. 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof 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 transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe 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 thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto 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

SocProS stands for Soft Computing for Problem Solving. It is an Eight years oldseries of International Conferences held annually under the joint collaborationamong a group of faculty members from the institutes of repute like NIT Silchar,IIT Roorkee, South Asian University Delhi, Liverpool Hope University, UK andVIT Vellore.

For the first time, SocProS was held at IE(I), RLC, Roorkee, India during Dec20-22, 2011, with General Chairs as Prof Kusum Deep, Indian Institute ofTechnology Roorkee and Prof Atulya K. Nagar, Liverpool Hope University, UK.The second SocProS was held at JKLU, Jaipur, India during Dec 28–20, 2012.Similarly, the third SocProS was held at the Greater Noida Extension Centre of IITRoorkee during December 26–28, 2013, fourth SocProS was held at NIT Silchar,Assam during December 27–29, 2014, Fifth SocProS was held at SaharanpurCampus of IIT Roorkee, during December 18–20, 2015, Sixth SocProS was held atThapar University, Patiala, Punjab, during December 23–24, 2016, SeventhSocProS was held at IIT Bhubaneswar, Odisha, During December 23–24, 2017,Now the name ‘SocProS’ became a brand name which has already established itsbenchmark in last eight years through its successful milestones every time inattracting many participants from all over the world like UK, US, Korea, France,Dubai, South Africa etc.

This time, the Eighth SocProS has been held at VIT Vellore, India during Dec17–19, 2018. Like earlier SocProS conferences, the focus of SocProS 2018 lies inSoft Computing and its applications to solve real life problems occurring in dif-ferent domains in the field of medical and health care, supply chain management,signal processing and multimedia, industrial optimization, image processing,cryptanalysis etc. SocProS 2018 attracted a wide spectrum of thought-provokingresearch papers on various aspects of Soft Computing with umpteen applications,theories and techniques. A total 176 quality research papers are selected for pub-lication in the form of proceedings in its Volume 1 and Volume 2.

We are sure that the research findings in the novel papers contained in thisproceeding will be much fruitful and may inspire more and more researchers to workin the field of soft computing. The topics that are presented in this proceedings

v

are Fuzzy logic & Fuzzy controller, Artificial Neural Network, Face Recognition &Classification, Feature Extraction, Machine learning, Reinforcement learning, Deeplearning, Supervised learning, Different optimization techniques like Spider-MonkeyOptimization, Particle Swarm Optimization, Meta heuristic Optimization, ArtificialBee Colony Optimization, Walk Grey Wolf Optimization, Algorithms like FlowerPollination Algorithm, Parallel Random Forest Algorithm, C-mode ClusteringAlgorithm, Crow Search Algorithm, Genetic Algorithm, Artificial Bee ColonyAlgorithm,AdaptiveMulti-SwarmBatAlgorithm etc. Therefore this proceedingmustprovide an excellent platform to explore the assorted soft computing techniques to thereaders.

The editors would like to express their sincere gratitude to its Patron, PlenarySpeakers, Invited Speakers, Reviewers, Programme Committee Members,International Advisory Committee, and Local Organizing Committee; withoutwhose support the quality and standards of the Conference could not be maintained.Special thanks to Springer and its team for this valuable publication.

Over and above, we would like to express our deepest sense of gratitude to ‘VITVellore’ for hosting this conference. Also, sincere thanks to all sponsors ofSocProS’ 2018.

Silchar, India Kedar Nath DasNew Delhi, India Jagdish Chand BansalRoorkee, India Kusum DeepLiverpool, UK Atulya K. NagarVellore, India Ponnambalam PathipooranamVellore, India Rani Chinnappa Naidu

vi Preface

About This Book

The proceedings of SocProS 2018 will serve as an academic bonanza for scientistsand researchers working in the field of Soft Computing. This book contains theo-retical as well as practical aspects using fuzzy logic, neural networks, evolutionaryalgorithms, swarm intelligence algorithms, etc. with many applications under theumbrella of ‘Soft Computing’. This book is beneficial for the young as well asexperienced researchers dealing across complex and intricate real world problemsfor which finding a solution by traditional methods is a difficult task.

The different application areas covered in the proceedings are: Image Processing,Cryptanalysis, Industrial Optimization, Supply Chain Management, NewlyProposed Nature Inspired Algorithms, Signal Processing, Problems related toMedical and Health Care, Networking Optimization Problems etc. This will surelyhelpfully for the researchers/scientists working in similar fields of optimization.

vii

Contents

Analysis of Fractional-Order Deterministic HIV/AIDS Model DuringDrug Therapy Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Ajoy Dutta, Asish Adak and Praveen Kumar Gupta

Load Bearing Capacity for a Ferrofluid Squeeze Film in DoubleLayered Porous Rough Conical Plates . . . . . . . . . . . . . . . . . . . . . . . . . 9Yogini D. Vashi, Rakesh M. Patel and Gunamani B. Deheri

Effect of Slip Velocity on a Ferrofluid-Based Longitudinally RoughPorous Plane Slider Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Mohmmadraiyan M. Munshi, A. R. Patel and G. M. Deheri

Intelligent Controller Based Solar Photovoltaic with Battery StorageSystem for Conditioning the Electrical Power . . . . . . . . . . . . . . . . . . . 43Ravi Dharavath and I. Jacob Raglend

Autonomous Vehicle for Obstacle Detection and AvoidanceUsing Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55C. S. Arvind and J. Senthilnath

Evaluation of Deep Learning Model with Optimizing and SatisficingMetrics for Lung Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Usma Niyaz, Abhishek Singh Sambyal and Devanand Padha

Improved Flower Pollination Algorithm for Linear AntennaDesign Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Rohit Salgotra, Urvinder Singh, Sriparna Saha and Atulya K. Nagar

Texture-Based Fuzzy Connectedness Algorithm for Fetal UltrasoundImage Segmentation for Biometric Measurements . . . . . . . . . . . . . . . . 91S. Jayanthi Sree and C. Vasanthanayaki

THD Analysis of Flying-Capacitor Multilevel ConverterUsing Fuzzy Logic Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105M. Priya, Ponnambalam Pathipooranam and K. Muralikumar

ix

Adaptive Neuro-Fuzzy Inference System for Predicting Strengthof High-Performance Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119L. V. Prasad Meesaraganda, Nilarghya Sarkar and Nilanjan Tarafder

Optimization of Target Oriented Network Intelligence Collectionfor the Social Web by Using k-Beam Search . . . . . . . . . . . . . . . . . . . . 135Aditya Shaha and B. K. Tripathy

Compressed Air Energy Storage Driven by Wind Power Plantfor Water Desalination Through Reverse Osmosis Process . . . . . . . . . . 145M. B. Hemanth Kumar and B. Saravanan

Fully Fuzzy Semi-linear Dynamical System Solved by Fuzzy LaplaceTransform Under Modified Hukuhara Derivative . . . . . . . . . . . . . . . . 155Purnima Pandit and Payal Singh

Comparison of Performance of Four-Element Microstrip ArrayAntenna Using Electromagnetic Bandgap Structures . . . . . . . . . . . . . . 181K. Prahlada Rao, R. M. Vani and P. V. Hunagund

Model Development for Strength Properties of Laterized ConcreteUsing Artificial Neural Network Principles . . . . . . . . . . . . . . . . . . . . . . 197P. O. Awoyera, J. O. Akinmusuru, A. Shiva Krishna, R. Gobinath,B. Arunkumar and G. Sangeetha

Wind Power Forecasting Using Parallel RandomForest Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209V. Anantha Natarajan and N. Sandhya Kumari

Leukemia Cell Segmentation from Microscopic Blood Smear ImageUsing C-Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Neha Singh and B. K. Tripathy

Implementation of Exploration in TONIC Using Non-stationaryVolatile Multi-arm Bandits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Aditya Shaha, Dhruv Arya and B. K. Tripathy

Fuzzy Logic-Based Model for Predicting Surface Roughnessof Friction Drilled Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251N. Narayana Moorthy and T. C. Kanish

Face Recognition and Classification Using GoogleNETArchitecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261R. Anand, T. Shanthi, M. S. Nithish and S. Lakshman

Enhancing Public Health Surveillance by Measurement of SimilarityUsing Rough Sets and GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Priyansh Jain, Harshal Varday, K. Sharmila Banu and B. K. Tripathy

x Contents

Data Analytics Implemented over E-commerce Data to EvaluatePerformance of Supervised Learning Approaches in Relationto Customer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285Kailash Hambarde, Gökhan Silahtaroğlu, Santosh Khamitkar,Parag Bhalchandra, Husen Shaikh, Govind Kulkarni, Pritam Tamsekarand Pranita Samale

Optimal Renewable Energy Resource Based Distributed GenerationAllocation in a Radial Distribution System . . . . . . . . . . . . . . . . . . . . . . 295Kola Sampangi Sambaiah and T. Jayabarathi

PV Module Temperature Estimation by Using ANFIS . . . . . . . . . . . . . 311Challa Babu and Ponnambalam Pathipooranam

Modified Artificial Potential Field Approaches for Mobile RobotNavigation in Unknown Environments . . . . . . . . . . . . . . . . . . . . . . . . . 319Ngangbam Herojit Singh, Salam Shuleenda Deviand Khelchandra Thongam

Analysis of BASNs Battery Performance at Different TemperatureConditions Using Artificial Neural Networks (ANN) . . . . . . . . . . . . . . . 329B. Banuselvasaraswathy, R. Vimalathithan and T. Chinnadurai

ASIC Implementation of Fixed-Point Iterative, Parallel, and PipelineCORDIC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Grande Naga Jyothi, Kundu Debanjan and Gorantla Anusha

Elephant Herding Optimization Based Neural Network to PredictElastic Modulus of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353B. S. Adarsha, Narayana Harish, Prashanth Janardhanand Sukomal Mandal

Adaptive Sensor Ranking Based on Utility Using LogisticRegression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365S. Sundar, Cyril Joe Baby, Anirudh Itagi and Siddharth Soni

Detection of Dementia from Brain Tissues Variation in MR ImagesUsing Minimum Cross-Entropy Based Crow Search Algorithmand Structure Tensor Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377N. Ahana Priyanka and G. Kavitha

A Hybrid Approach for Intrusion Detection System . . . . . . . . . . . . . . . 391Neelam Hariyale, Manjari Singh Rathore, Ritu Prasadand Praneet Saurabh

Inspection of Crop-Weed Image Database Using Kapur’s Entropyand Spider Monkey Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405V. Rajinikanth, Nilanjan Dey, Suresh Chandra Satapathyand K. Kamalanand

Contents xi

Implementation of Fuzzy-Based Multicarrier and Phase ShiftedPWM Symmetrical Cascaded H-Bridge Multilevel Inverter . . . . . . . . . 415K. Muralikumar, Ponnambalam Pathipooranam and M. Priya

Derived Shape Features for Brain Hemorrhage Classification . . . . . . . 431Soumi Ray and Vinod Kumar

Prediction of Crime Rate Using Data Clustering Technique . . . . . . . . . 443A. Anitha

Identification of Astrocytoma Grade Using Intensity, Texture,and Shape Based Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455Arkajyoti Mitra, Prasun Chandra Tripathi and Soumen Bag

Early Prenatal Diagnosis of Down’s Syndrome-A MachineLearning Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467Esther Hannah, Lilly Raamesh and Sumathi

Recent Research Advances in Black and White Visual CryptographySchemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479T. E. Jisha and Thomas Monoth

An N-Puzzle Solver Using Tissue P System with EvolutionalSymport/Antiport Rules and Cell Division . . . . . . . . . . . . . . . . . . . . . . 493Resmi RamachandranPillai and Michael Arock

Renewable Energy Management and Implementation in IndianEngineering Institutions—A Case Study . . . . . . . . . . . . . . . . . . . . . . . . 505Shekhar Nair, Senthil Prabu Ramalingam,Prabhakar Karthikeyan Shanmugam and C. Rani

Inverse Kinematics Analysis of Serial Manipulators Using GeneticAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519Satyendra Jaladi, T. E. Rao and A. Srinath

Deep Learning for People Counting Model . . . . . . . . . . . . . . . . . . . . . 531T. Revathi and T. M. Rajalaxmi

Hybrid Variable Length Partial Pulse Modulation for VisibleLight Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539Jyothi and Ponnambalam Pathipooranam

An Efficient Dynamic Background Subtraction Algorithmfor Vehicle Detection Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . 551Rashmita Khilar, Sarat Kumar Sahoo, C. Raniand Prabhakar Karthikeyan Shanmugam

PV-Based High-Gain Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . 563Ritanjali Behera, Sarat Kumar Sahoo, M. Balamurugan,Prabhakar Karthikeyan Shanmugam and C. Rani

xii Contents

Indoor Object Classification Using Higher Dimensional MPEGFeatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573Dibyendu Roy Chaudhuri, Dhairya Chandra and Ankush Mittal

Lung Nodule Segmentation Using 3-Dimensional ConvolutionalNeural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585Subham Kumar and Sundaresan Raman

Improved Performance and Execution Time of Face RecognitionUsing MRSRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597Jitendra Madarkar, Poonam Sharma and Rimjhim Singh

Motion Detection Using a Hybrid Texture-Based Approach . . . . . . . . . 609Rimjhim Padam Singh, Poonam Sharma and Jitendra Madarkar

Selection of Television Channels for Product Promotion:A Fuzzy-TOPSIS Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621Arshia Kaul, Sugandha Aggarwal and P. C. Jha

Implementation of ACO Tuned Modified PI-like Position and SpeedControl of DC Motor: An Application to Electric Vehicle . . . . . . . . . . 629Geetha Mani

A Bidirectional Converter for Integrating DVR-UCap to ImproveVoltage Profile Using Fuzzy Logic Controller . . . . . . . . . . . . . . . . . . . . 647T. Y. Saravanan and Ponnambalam Pathipooranam

Comparative Study on Histogram Equalization Techniquesfor Medical Image Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657Sakshi Patel, K. P. Bharath, S. Balaji and Rajesh Kumar Muthu

A Fuzzy Multi-criteria Decision Model for Analysisof Socio-ecological Performance Key Factors of Supply Chain . . . . . . . 671Rahul Solanki, Jyoti Dhingra Darbari, Vernika Agarwal and P. C. Jha

A Fuzzy MCDM Model for Facility Location Evaluation Basedon Quality of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687Aditi, Arshia Kaul, Jyoti Dhingra Darbari and P. C. Jha

Analytical Structural Model for Implementing Innovation Practicesin Sustainable Food Value Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699Rashi Sharma, Jyoti Dhingra Darbari, Venkata S. S. Yadavalli,Vernika Agarwal and P. C. Jha

Mathematical Design and Analysis of Photovoltaic Cell UsingMATLAB/Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711CH Hussaian Basha, C. Rani, R. M. Brisilla and S. Odofin

Contents xiii

Development of Cuckoo Search MPPT Algorithm for PartiallyShaded Solar PV SEPIC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . 727CH Hussaian Basha, Viraj Bansal, C. Rani, R. M. Brisilla and S. Odofin

An Improved Fuzzy Clustering Segmentation Algorithm Basedon Animal Behavior Global Optimization . . . . . . . . . . . . . . . . . . . . . . . 737A. Absara, S. N. Kumar, A. Lenin Fred, H. Ajay Kumar and V. Suresh

Fitness-Based Controlled Movements in Artificial Bee ColonyAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749Harish Sharma, Kritika Sharma, Nirmala Sharma, Assif Assadand Jagdish Chand Bansal

Herbal Plant Classification and Leaf Disease IdentificationUsing MPEG-7 Feature Descriptor and Logistic Regression . . . . . . . . . 761Ajay Rana and Ankush Mittal

Simulation of Metaheuristic Intelligence MPPT Techniques for SolarPV Under Partial Shading Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 773CH Hussaian Basha, C. Rani, R. M. Brisilla and S. Odofin

Closed Loop Control of Diode Clamped Multilevel InverterUsing Fuzzy Logic Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787K. Muralikumar and Ponnambalam Pathipooranam

Prediction of California Bearing Ratio Using Particle SwarmOptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795T. Vamsi Nagaraju, Ch. Durga Prasad and M. Jagapathi Raju

Adaptive Multi-swarm Bat Algorithm (AMBA) . . . . . . . . . . . . . . . . . . 805Reshu Chaudhary and Hema Banati

Fuzzy-Based-Cascaded-Multilevel Inverter Topologywith Galvanic Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823K. Muralikumar, C. Sivakumar, Ankit Rautelaand Ponnambalam Pathipooranam

Modeling the Efficacy of Geopolymer Mosquito Repellent StripsLeachate Distribution Using Meta-heuristic Optimization . . . . . . . . . . 839D. K. D. B. Rupini and T. Vamsi Nagaraju

Optimization of Drilling Rig Hydraulics in Drilling OperationsUsing Soft Computing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849G. Sangeetha, B. Arun kumar, A. Srinivas, A. Siva Krishna, R. Gobinathand P. O. Awoyera

Renewable Energy Harnessing by Implementing a Three-PhaseMultilevel Inverter with Fuzzy Controller . . . . . . . . . . . . . . . . . . . . . . 863K. Muralikumar and Ponnambalam Pathipooranam

xiv Contents

Design of SVPWM-Based Two-Leg VSI for Solar PVGrid-Connected Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879CH Hussaian Basha, V. Govinda Chowdary, C. Rani, R. M. Brisillaand S. Odofin

Performance Analysis and Optimization of Process Parametersin WEDM for Inconel 625 Using TLBO Couple with FIS . . . . . . . . . . 893Anshuman Kumar, Chinmaya P. Mohanty, R. K. Bhuyanand Abdul Munaf Shaik

Application of WDO for Decision-Making in Combined Economicand Emission Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907V. Udhay Sankar, Bhanutej, C. H. Hussaian Basha, Derick Mathew,C. Rani and K. Busawon

Application of Wind-Driven Optimization for Decision-Makingin Economic Dispatch Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925V. Udhay Sankar, Bhanutej, C. H. Hussaian Basha, Derick Mathew,C. Rani and K. Busawon

Reliability–Redundancy Allocation Using Random Walk GrayWolf Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 941Shubham Gupta, Kusum Deep and Assif Assad

Optimal Control of Roll Axis of Aircraft Using PID Controller . . . . . . 961V. Bagyaveereswaran, Subhashini, Abhilash Sahu and R. Anitha

Adaptive Noise Cancellation Using Improved LMS Algorithm . . . . . . . 971Sai Saranya Thunga and Rajesh Kumar Muthu

Variant Roth-Erev Reinforcement Learning Algorithm-Based SmartGenerator Bidding as Agents in Electricity Market . . . . . . . . . . . . . . . 981P. Kiran and K. R. M. Vijaya Chandrakala

Standalone Solar Photovoltaic Fed Automatic Voltage Regulatorfor Voltage Control of Synchronous Generator . . . . . . . . . . . . . . . . . . 991Garapati Vinayramsatish, K. R. M. Vijaya Chandrakalaand S. Sampath Kumar

Optimizing Vertical Air Gap Location Inside the Wall for EnergyEfficient Building Enclosure Design Based on Unsteady HeatTransfer Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003Saboor Shaik, Sunnam Nagaraju, Shaik Mohammed Rizvanand Kiran Kumar Gorantla

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011

Contents xv

About the Editors

Dr. Kedar Nath Das is an Assistant Professor at the Department of Mathematics,National Institute of Technology, Silchar, Assam, India. Over the past 10 years, hehas made substantial contributions to research on soft computing, and has publishedseveral research papers in prominent national and international journals. His chiefarea of interest is in evolutionary and bio-inspired algorithms for optimization.

Dr. Jagdish Chand Bansal is an Associate Professor at the South AsianUniversity, New Delhi, India and visiting research fellow at Liverpool HopeUniversity, Liverpool, UK. He has an excellent academic record and is a leadingresearcher in the field of swarm intelligence. Further, he has published numerousresearch papers in respected international and national journals.

Prof. Kusum Deep is a Professor at the Department of Mathematics, IndianInstitute of Technology Roorkee, India. Over the past 25 years, her research hasmade her a central international figure in the areas of nature-inspired optimizationtechniques, genetic algorithms and particle swarm optimization.

Prof. Atulya K. Nagar holds the Foundation Chair as Professor of MathematicalSciences and is Dean of the Faculty of Science at Liverpool Hope University, UK.Prof. Nagar is an internationally respected scholar working at the cutting edgeof theoretical computer science, applied mathematical analysis, operations research,and systems engineering. He received a prestigious Commonwealth Fellowship forpursuing his doctorate (DPhil) in Applied Non-Linear Mathematics, which heearned from the University of York (UK) in 1996; and he holds BSc (Hons.), MSc,and MPhil (with Distinction) from the MDS University of Ajmer, India.

Prof. Ponnambalam Pathipooranam is an Associate Professor at the School ofElectrical Engineering, VIT University, India. His areas of research interests areMultilevel Converters, Fuzzy controller for multilevel converters, MPC controllers,Thermoelectric Generators for Solar Photo voltaic cells areas in which he is activelypublishing. He is having 15 years of teaching experience.

xvii

Prof. Rani Chinnappa Naidu received the B.Eng. and M.Tech. degrees from VITUniversity, Vellore, India, and Ph.D. degree from Northumbria University,Newcastle upon Tyne, UK., all in Electrical Engineering. After that, she joined as aPostdoctoral Researcher in Northumbria Photovoltaic Applications Centre,Northumbria University, UK. She is currently an Associate Professor at VITUniversity. She is an Senior member in IEEE. She leads an appreciable number ofresearch groups and projects in the areas such as solar photovoltaic, wind energy,power generation dispatch, power system optimization, and artificial intelligencetechniques.

xviii About the Editors

Analysis of Fractional-OrderDeterministic HIV/AIDS Model DuringDrug Therapy Treatment

Ajoy Dutta, Asish Adak and Praveen Kumar Gupta

Abstract In this study, we discussed the Caputo sense fractional-order HIV/AIDSmodel including the drug therapy, and mathematically examined the dynamicbehaviour of the model. We have discussed qualitative analysis of the proposedmathematical model and defined the existence and uniqueness conditions. Local sta-bility is also checked for HIV-free equilibrium point.We have given some facts aboutthe growth rate of HIV/AIDS, the source of HIV virus, as well as death rate of CD4+

T cells, which play a vital role in HIV dynamics. The numerical simulations aredemonstrated to reveal the analytical results.

Keywords Mathematical modelling · Caputo derivative · HIV/AIDS model ·Stability analysis

1 Introduction

At present, more than 50 million citizens worldwide are living with Human Immun-odeficiency Virus, and most of the citizens have become resistant to the existingantiretroviral therapies. In the current scenario, there has been a lot of progress inthe HIV treatment due to tremendous use of cART (combined antiretroviral therapy)and HAART (highly active antiretroviral therapy). These treatments have yieldedconsiderable improvements in diagnosis and have moderated the rate of infections incitizens who follow their drug treatment. Therefore, scientists need to build up newantiretroviral drugs to fight HIV while it is located in the vital fact that replicationof this virus is a very unproductive process [1, 2]. The impact of the traditional drughas to conquer the drug deficiency in lymphoid cells and tissues (CD4 T lympho-cytes, host HIV infection). Ho et al. [3] constructed a ‘Systems Approach’ for HIVtreatment through multi-drug-involved nanoparticles. Otunuga [4] has defined and

A. Dutta · A. Adak · P. K. Gupta (B)Department of Mathematics, National Institute of Technology Silchar, Silchar 788010, Assam,Indiae-mail: pkguptaitbhu@gmail.com

© Springer Nature Singapore Pte Ltd. 2020K. N. Das et al. (eds.), Soft Computing for Problem Solving,Advances in Intelligent Systems and Computing 1048,https://doi.org/10.1007/978-981-15-0035-0_1

1

2 A. Dutta et al.

examined a 2n + 1-dimensional differential equation model with the introducingnoise in the transmission rate and treatment of HIV disease.

In the current scenario, fractional calculus is in this phasewhere numerousmodelsare going to be proposed, described, and applied to real-world problems in the area ofphysical, biological, engineering sciences and many more branches [5, 6]. However,the researchers have previously accounted for many outstanding results. But, in realsituation, many non-local phenomena are unexplored and it will be discovered inthe near future. Recently, Pinto and Carvalho [7] analysed the effect of screeningand pre-exposure prophylaxis on HIV dynamics in infected citizens, and the saidmodel reported that the fractional derivative order has an influential role during theHIV epidemics. Recently, Pinto and Carvalho [8] studied a mathematical modelfor HIV infection with fractional-order derivatives where latent T helper cells areincorporated. With these motivations of application of fractional derivatives, weanalysed a fractional-order HIV/AIDS dynamical model with the impact of drugtherapy.

2 Fractional HIV/AIDS Model

In this part of the study, we constructed a mathematical model which has four com-partments: uninfected, HIV-infected CD4+ T cells, virus cells, and drugs concen-tration as T, I, V, C , respectively. More precisely, we constructed an HIV/AIDSdynamic model that describes the relationship between all the said compartments,and it is formulated by the following fractional-order non-linear systemof differentialequations in the Caputo sense

C Dαt T = s − βV T + γI − d1T − f1CT, (1)

C Dαt I = βV T − γI − d2 I − f2(1 − η)C I, (2)

C Dαt V = bd2 I − d3V − f3(1 − η)CV, (3)

C Dαt C = ν − δC, (4)

with

T (0) = T0, I (0) = I0, V (0) = V0, C(0) = C0. (5)

Here, the inflow rate and the die rate are s , d1T of uninfected CD4+ T cells. Theuninfected CD4+ T cells converted into infected CD4+ T cells by a virus as βV T ,recovered or cured infected CD4+ T cells as a rate γI, obliterated at a rate f1CT dueto injecting of drugs. Infected cells might be killed because of virion in their nucleus.

Analysis of Fractional-Order Deterministic HIV/AIDS Model … 3

The loss rate of an HIV infected cell is considered as (γ + d2)I , where d2 I is theelimination rate of HIV-infected cells, γI is the cure rate of infected cells into theuninfected compartment, and infected cells are destroyed at a rate f2(1−η)CV dueto injecting of drugs. Virions are generated by infected cells at a rate b d2 I , decayedat a rate d3V , and destroyed at a rate f3(1 − η)CV due to injecting of drugs.

3 Analysis of the Model

Before starting the study of stability analysis of the fractional-order system (1)–(5),we begin with some basic results: definition of Caputo fractional-order differentia-tion, theorems, and lemmas. Let us consider x(t) = [T (t), I (t), V (t), C(t)]T and�4+ = {x ∈ �4 : x ≥ 0}.Definition 1 (see [9]). Consider that α > 0, t > a where α, a, t ∈ R. Therefore,Caputo fractional operator formula is

C Dαt f (t) =

⎧⎨

⎩

1�(n−α)

t∫

a

f (n)(τ )

(t−τ)α+1−n dτ, (n − 1) < α ≤ n

dn f (t)dtn , α = n

of order α, where �(·) is the Euler Gamma function.

3.1 Positivity and Boundedness

Assume that f : Rn → Rn for n = 4. Consider the fractional-order system

C Dαt x(t) = F(x), 0 < α ≤ 1, and x(0) = x0, (6)

where F(x) = [ f1, f2, f3, f4]T and x0 ∈ Rn . For the global existence of the solutionfor the system (1)–(4) with initial conditions (5), we have to define the subsequentlemmas.

Lemma 2 (see [10]). If F(x) and ∂ F∂x (x) are continuous and ‖F(x)‖ ≤ λ + μ‖x‖

for all x ∈ Rn , where λ and μ are two positive constants. Then, the system (1)–(4)has the one and only solution on [0, +∞).

Theorem 3 (see [10]). Consider that f (t) ∈ C[a, b] and Caputo derivativeC Dα

t f (t) ∈ C[a, b] for 0 < α ≤ 1, so we define

f (t) = f (a) + 1

�(α)

(C Dα

t f)(ξ)(t − a)α, (7)

for a < ξ < t , ∀ t ∈ (a, b].

4 A. Dutta et al.

Lemma 4 (see [10]). Consider that f (t) ∈ C[a, b] and Caputo derivativeC Dα

t f (t) ∈ C[a, b] for 0 < α ≤ 1. If C Dαt f (t) ≥ 0, ∀ t ∈ [a, b], then f (t)

is increasing, moreover C Dαt f (t) ≤ 0, ∀ t ∈ [a, b], then f (t) is decreasing,

∀ t ∈ [a, b].Theorem 5 (see [11]). Let x∗ = [T ∗, I ∗, V ∗, C∗]T is one of the equilibriumpoints of the fractional-order system C Dα

t x(t) = F(x), 0 < α ≤ 1 and x(0) = x0.Then x∗ is asymptotically stable locally if the spectrum of the Jacobian matrix J (x∗)for the system (1)–(5) satisfies the following:

∣∣arg

(Eigenvalues J (x∗)

)∣∣ >

απ

2,

where J (x∗) = [bi j]x=x∗ , i, j = 1, 2, 3, 4, and bi j = ∂ fi

∂x j.

3.2 Equilibrium Points and Reproduction Number

Equilibrium Points. In this subsection, we define all the equilibria for the system(1)–(4) after solving the following non-linear algebraic equations:

C Dαt T = C Dα

t I = C Dαt V = C Dα

t C = 0. (8)

Then, we get two equilibrium points:

(i) the first one, infection-free equilibrium point, i.e.

E0 =[

sδ

d1δ + f1ν, 0, 0,

ν

δ

]T

. (9)

(ii) the second one, endemic equilibrium point, i.e.

E1 = [T1, I1, V1, C1]T , (10)

where

T1 =[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν]

d2bβ δ2,

I1 = sd2bβδ3 − (d1δ + f1ν)[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν]

d2bβδ2[d2δ + f2(1 − η)ν],

V1 = sd2bβδ3 − (d1δ + f1ν)[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν]

βδ[d2δ + f2(1 − η)ν][d3δ + f3(1 − η)ν],

and C1 = νδ.

Analysis of Fractional-Order Deterministic HIV/AIDS Model … 5

Reproduction Number. Afterwards, we calculate the basic reproduction number(�0) of system (1)–(4). Biologically, let �0 be a symbol of the average number ofnew infections developed by single infected cell during infection.

�0 = sd2bβδ3

(d1δ + f1ν)[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν]

. (11)

3.3 Local Stability

In this subsection, we define the local stability of system (1)–(4) with the help of theJacobian matrix,

J (x)|E0 =

⎛

⎜⎜⎜⎝

−βV − d1 − f1C γ −βT − f1T

βV −d2 − γ − f2(1 − η) C βT − f2(1 − η)I

0 bd2 −d3 − f3(1 − η) C − f3(1 − η)V

0 0 0 −δ

⎞

⎟⎟⎟⎠

Hence, the associated transcendental equation for the above matrix is

∣∣ J (x)|E0

− λI∣∣ = 0, (12)

where I is the 4 × 4 identity matrix.Now, we defined the stability behaviour of the infection-free equilibrium point,

i.e. E0 =[

s δd1δ+ f1ν

, 0, 0, νδ

]Tin the following theorem:

Theorem 6 The infection-free equilibrium point E0 of fractional-order system(1)–(4) is locally asymptotically stable for �0 < 1 if all eigenvalues λi of the Jaco-bian matrix J (E0) satisfy the condition |arg(λi )| > α π

2 .

Proof The Jacobian matrix J (E0) for the systems (1)–(4) calculated at the infection-free equilibrium point E0 is

J (E0) =

⎛

⎜⎜⎜⎜⎝

−d1 − f1(νδ

)γ −β

(s δ

d1δ+ f1ν

)− f1

(sδ

d1δ+ f1ν

)

0 −d2 − γ − f2(1 − η)(νδ

)β

(s δ

d1δ+ f1ν

)0

0 bd2 −d3 − f3(1 − η)(νδ

)0

0 0 0 −δ

⎞

⎟⎟⎟⎟⎠

.

The characteristic equation of the Jacobian matrix J (E0) is

(λ + δ)(λ + d1 + f1

ν

δ

)(λ2 + a1λ + a2) = 0 (13)

6 A. Dutta et al.

Fig. 1 Stability region ofthe fractional-order system(1)–(4) is enlarged when 0 <α≤1, where λ is the root ofthe characteristic equation

where

a1 =(

d2 + d3 + γ + ( f2 + f3)(1 − η)ν

δ

)> 0

and

a2 = 1

δ2

[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν] −

(sd2bβδ

d1δ + f1ν

)

,

or

a2 = 1

δ2

[(d2 + γ )δ + f2(1 − η)ν

][d3δ + f3(1 − η)ν] (1 − �0) (14)

The literature suggests the Routh–Hurwitz stability criterion for fractional-ordersystems [7, 10], and describes the necessary and sufficient condition |arg(λi )| >

α π2 for various models. According to this criterion, it is clear that all roots of the

characteristic Eq. (13) have negative real parts if and only if a1 > 0 and a2 > 0.Equation (14) implies that if �0 < 1, then all roots will be negative and for �0 < 1the necessary and sufficient condition will satisfy (Fig. 1).

Hence, the system (1)–(4) is asymptotically stable at E0 if �0 < 1; otherwise,if �0 > 1, the characteristic Eq. (13) has given at least one positive eigenvalues,therefore, E0 is unstable.

4 Numerical Solution and Discussion

In this paper, we presented a numerical solution of the fractional-order HIV/AIDSmodel (1)–(5). Here, we solve this system using Mathematica 8.0. Consider thats = 3mm−3day−1, β = 0.000024mm3day−1, γ = 0.2 day−1, b = 1940, d1 =0.01 day−1, d2 = 0.5 day−1, d3 = 3.4 day−1 (since removal rate of infected cells willbe higher than uninfected cells), α = 1, f1 = 0.009 day−1, f2 = 2 × 10−10 day−1

and f3 = 10−4 day−1 [10, 11].

Analysis of Fractional-Order Deterministic HIV/AIDS Model … 7

In view of the reality that the recovery rate (γ) will also depend on drugs whichare given to the patient, we are defining the variation of γ with initial conditionsT (0) = 1000, I (0) = 0, V (0) = 0.001 and C(0) = 0.5 in Fig. 2.

Fig. 2 Plot of a uninfectedCD4 + T cells b infectedCD4 + T cells c virus versustime for various values of γ

(a)

0 10 20 30 40 500

200

400

600

800

1000

Time in days

Time in days

Time in days

Uni

nfec

tedC

D4+

Tcel

ls γ=0.1γ=0.2 γ=0.3 γ=0.4

(b)

(c)

0 10 20 30 40 500

50

100

150

200

Infe

cted

CD

4+Tc

ells

γ=0.1γ=0.2 γ=0.3 γ=0.4

0 10 20 30 40 500

5000

10000

15000

20000

Viru

s

γ=0.1γ= 0.2 γ= 0.3 γ= 0.4

8 A. Dutta et al.

5 Conclusion

In this paper, we presented a Caputo sense fractional-order HIV/AIDS dynamicsmodel with drug therapy. The authors have defined the equilibrium points and repro-duction number by Jacobian-based spectral radius method for the proposed model.The recent appearance of fractional differential equations as models makes it neces-sary to investigate analysis of solution for such equations. So, the authors describethe stability analysis on a proposed fractional order model, and obtained a sufficientcondition on the parameters for asymptotically stable infection-free steady state. Thenumerical solutions have demonstrated the impact of drugs in the patients and it isdepicted through Fig. 2 for various values of γ.

Acknowledgements The authors are very thankful to the respected reviewers for their positivecomments towards the improvement of the manuscript. This research work is financially supportedby TEQIP-III, National Institute of Technology Silchar, Assam-788010 under MHRD, India.

References

1. Perelson, A.S., Kirschner, D.E., Boer, R.: Dynamics of HIV infection of CD4 + T cells. Math.Biosci. 114, 81–125 (1993)

2. Duncan, S., Dorrell, L.: Promising new drugs and drug targets for HIV treatment. Future Prescr.14, 1–4 (2013)

3. Ho, R.J.Y., Yu, J., Li, B., Kraft, J.C., Freeling, J.P., Koehn, J., Shao, J.: Systems approach totargeted and long-acting HIV/AIDS therapy. Drug Deliv. Trans. Res. 5(6), 531–539 (2015)

4. Otunuga, O.M.: Global stability for a 2n + 1 dimensional HIV/AIDS epidemic model withtreatments. Math. Biosci. 299, 138–152 (2018)

5. Sun, H.G., Zhang, Y., Baleanu, D., Chen, W., Chen, Y.Q.: A new collection of real worldapplications of fractional calculus in science and engineering. Commun. Nonlinear Sci. Numer.Simul. 64, 213–231 (2018)

6. Gupta, P.K., Dhar, B.: Dynamical behaviour of fractional order tumor-immune model withtargeted chemotherapy treatment. Int. J. Eng. Tech. 7, 6–9 (2018)

7. Pinto, C.M.A., Carvalho, A.R.M.: The impact of pre-exposure prophylaxis (PrEP) and screen-ing on the dynamics of HIV. J. Comput. Appl. Math. 339, 231–244 (2018)

8. Pinto, C.M.A., Carvalho, A.R.M.: A latency fractional order model for HIV dynamics. J.Comput. Appl. Math. 312, 240–256 (2017)

9. Caputo,M.: Linearmodel of dissipationwhoseQ is almost frequency independent-II. Geophys.J. R. Astron. Soc. 13, 529–539 (1967)

10. Dutta, A., Gupta, P.K.: A mathematical model for transmission dynamics of HIV/AIDS witheffect of weak CD4 + T cells. Chin. J Phys. 56(3), 1045–1056 (2018)

11. Gupta, P.K.: Local and global stability of fractional order HIV/AIDS dynamics model. In:Ghosh, D., Giri, D., Mohapatra, R., Savas, E., Sakurai, K., Singh, L. (eds.) Mathematics andComputing. ICMC 2018. CCIS, vol. 834, pp. 141–148. Springer, Singapore (2018)

Load Bearing Capacity for a FerrofluidSqueeze Film in Double Layered PorousRough Conical Plates

Yogini D. Vashi, Rakesh M. Patel and Gunamani B. Deheri

Abstract This article goals to determine the enactment of double layeredporous rough conical plates with ferrofluid based squeeze film lubrication. TheNeuringer–Roseinweig model has been employed for magnetic fluid flow. Forthe characterization of roughness two different forms of polynomial distributionfunction have been used and comparison is made between both roughness structure.The stochastic model of Christensen and Tonder regarding transverse roughness hasbeen invoked to develop the associated Reynolds’ equation from which the pressurecirculation is found. This provides growth to the calculation of load-bearing capac-ity. From the graphical appearance it is established that from the design point ofview roughness pattern G1 is more suitable compared to G2. The results presentedhere confirm that the introduction of double layered plates results in improved loadcarrying capacity. This is further enhanced by the ferrofluid lubrication. Further, theroughness affects the bearing system significantly, however, the situation enhancedin the case of negatively skewed roughness. A noticeable fact is that the porosity ofthe outer layer influences more as compared to the inner layer even in the presenceof mild magnetic strength.

Keywords Squeeze film · Conical plates · Roughness · Ferrofluid · Load carryingcapacity

Y. D. Vashi (B)Department of Applied Sciences and Humanity, Alpha College of Engineeringand Technology, Khatraj, Kalol 382721, Gujarat, Indiae-mail: yogini.vashi@gmail.com

R. M. PatelDepartment of Mathematics, Gujarat Arts and Science College, Ahmedabad 380006, Gujarat,Indiae-mail: rmpatel12711@gmail.com

G. B. DeheriDepartment of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, Indiae-mail: gm.deheri@rediffmail.com

© Springer Nature Singapore Pte Ltd. 2020K. N. Das et al. (eds.), Soft Computing for Problem Solving,Advances in Intelligent Systems and Computing 1048,https://doi.org/10.1007/978-981-15-0035-0_2

9

10 Y. D. Vashi et al.

Nomenclature

a Dimension of bearing (mm)h Uniform fluid film thickness(mm)h Mean film thicknesshs Deviation from the mean film thickness•h0 Normal velocity of bearing surfaceH1 The thickness of the inner layer of the porous plate (mm)H2 The thickness of the outer layer of the porous plate (mm)H Magnetic field vectorp Pressure distribution(N/m2)p Non dimensional Pressure distributionW Load carrying capacity (N)W Non dimensional Load bearing capacityη Dynamic viscosity of fluid (NS/m2)μ0 Permeability of free space (N/A2)μ Magnetic susceptibility of magnetic fieldσ Standard deviation (mm)α Variance (mm)ε Skewness (mm)φ1 The permeability of the inner layer (m2)φ2 The permeability of the outer layer (m2)ψ1 Porosity of inner layerψ2 Porosity of outer layerα∗ Non dimensional varianceε∗ Non dimensional skewnessσ ∗ Non dimensional standard deviationρ Density of fluidq Velocity of fluidη Fluid viscosityM Magnetization vector

1 Introduction

Porous bearing is used very widely inmany devices such as Vacuum cleaners, extrac-tor fans, motorcar starters, hair dryer, etc. They are also used in business machines,farm and construction equipment, and aircraft automotive accessories. In addition,porous bearing can work hydrodynamically longer without maintenance and morestable than the equivalent conventional bearing. Also, in these bearings friction is less

Load Bearing Capacity for a Ferrofluid Squeeze Film … 11

as compared to the non-porous bearings. so many researchers have studied the effectof double layered porous bearings of various shapes. Uma Srinivasan [1] workedto study double layered slider bearing with a porous surface. The double layeredsurface enhanced the bearing’s load carrying capacity as well as the friction drag.However, it reduced the friction coefficient. Verma [2] investigated the influence ofdouble-layered porous slider bearing. The study of Rao et al. [3] focused on therelation between Brinkman model and a double layered porous journal bearing’sperformance. The results suggested that in a double layered bearing, the low perme-ability layer stuck to the high permeability one, leading to increased bearing capacityand as a result, a decreased friction coefficient. Uma Srinivasan [4] intended to studythe impact of time-height of squeeze films on a bearing’s load capacity. Various geo-metrical aspects like circular, elliptical, rectangular, etc. were used for the purpose.It was a comparative study focusing on two-layered porous bearing and conventionalbearings. The results suggested that double layered plates enhance a bearing’s loadcarrying capacity. Cusano [5] analyzed an infinitely long two-layered porous bearing.

Conical bearings have been developed for use in agricultural and constructionmachinery, for the suspension of jolts and insulation of engine vibrations from cabins.Lin et al. [6] studied the behavior of non-Newtonian micropolar fluid squeeze filmbetween conical plates. The non-Newtonian effects of micropolar fluid were foundto be better in comparison with the Newtonian case also its effect lengthened theapproaching time of squeeze film conical plates. Dinesh Kumar et al. [7] studied theeffect of ferrofluid squeeze film for spherical and conical bearings using perturbationanalysis. Prakash and Vij [8] analyzed the effect of the shape of the plate and porosityon the performance of squeeze films between porous plates of various shapes.

Practically, a perfectly smooth surface does not exist as all surfaces are roughto some extent. In applied settings, a smooth surface bearing does not provide anoptimum idea of performance and bearing life span. Thus, in the recent year studieshave focused on correlating surface roughness with the bearing capacity. Christensenand Tonder [9–11] worked on the stochastic surface roughness theory with hydrody-namic lubrication.Many authors have used this technique to understand the impact ofsurface roughness on performance. Patel and Deheri [12] made a comparative studyof different porous configurations and their impact on double layered slider bearingwith roughness and magnetic fluid base. The results suggested that Kozeny carmanmodel is more effective than Irmay’s model. Deheri et al. [13] made a theoreticalstudy of the influence of squeeze film with a magnetic base on porous rough conicalplates. The results showed that an appropriate semi-vertical angle can revert the neg-ative impacts of porosity and standard deviations for negatively skewed roughness.Patel and Deheri [14] deliberated the impact of slip velocity on a squeeze film withferrofluid in conical plates with longitudinal roughness. It was found that standarddeviation and magnetization can substantially neutralize the negative impact createdby slip velocity and surface roughness on bearing performance, provided that thenegatively skewed roughness was appropriate. Vashi et al. [21] studied the impact offerrofluid based rough porous parallel plates with couple stress effect.

12 Y. D. Vashi et al.

Various good research articles are available in the literature for the studyof squeezefilm lubrication of conical bearings and truncated conical bearings. For examplesShimpi and Deheri [15] in porous truncated conical plates, Patel and Deheri [16] inporous conical plates, Vadher et al. [17] in porous rough conical plates, Patel et al.[20] in rough conical bearing with deformation effect.

At present no work has been made to study the influence of surface roughnesswith two different patterns on ferrofluid based squeeze film in double layered porousconical plates. So in this current study the investigation of Patel and Deheri [13] isextended to the double layered porous conical plates with two different forms of thetransverse surface roughness patterns.

2 Analysis

All the traditions of hydrodynamic lubrication are reserved here. The lubricant is anincompressible ferrofluid lubrication, considered for the analysis. Both the porousfacings are supposed to be homogeneous and isotropic and porosity is directed by ageneralized form of Darcy’s law.

Figure 1 displays the geometrical structure of squeeze film lubrication of porousrough conical plates bearing.

Fig. 1 Physical structure of the bearing system

Load Bearing Capacity for a Ferrofluid Squeeze Film … 13

In the sought of the discussion of Uma Srinivasan [1] the modified Reynoldsequation comes out to be

1

x

d

dx

(dp

dx

)= 12η

•h0 sinω

h3 sin3 ω + 12φ1H1 + 12φ2H2(1)

The bearing faces are deliberated to be transversely rough in the context of Chris-tensen and Tonder’s [9–11] discussion the lubricant film thickness is taken as

h = h + hs

where h is mean film thickness and hs is the part due to the surface roughness asmeasured from nominal film thickness. According to Christensen and Tonder [9–11]Stochastic part hs is defined by the polynomial probability distribution functionf (hs)1 for the domain −c ≤ hs ≤ c,where c represents the maximum deviationfrom the mean film thickness.

f (hs)1 ={

3532c7

(c2 − h2s

)3, −c ≤ hs ≤ c

0, elsewhere(2)

Further, a different form of this type of polynomial distribution from Prajapati[18] is

f (hs)2 ={

1516c5

(c2 − h2s

)2, −c ≤ hs ≤ c

0, elsewhere(3)

The measure of the symmetry of the random variable hs are mean α the standarddeviation σ and the parameter ε defined by the relations

α = E(hs) σ 2 = E[(hs − α)2

]ε = E

[(hs − α)3

]

where E(•) is the expectancy operator given by the formula

E(•) =∞∫

−∞(•) f (hs)dhs (4)

The detailed study regarding the roughness model can be observed in Christensenand Tonder [9–11].

Neuringer and Rosensweig [19] established a model to designate the stable flowof magnetic fluid. This model involves the following equations.

Equation of motion:

ρ(q.∇)q = −∇ p + η∇2q + μ0(M .∇)

H (5)