18.1 Image Recognition

Using a convolutional neural network (CNN), technological development in image recognition has revolutionized far beyond our imagination. Let us consider the comic scene shown in Figure 18.1, as it provides interesting insights into the development of image recognition and depicts a decade-back possible scenario. Here, a manager asks his computer programmer to “Develop an app which can check whether the user is in a national park or not, when he clicks some photo!” Being an easy and feasible task, the computer programmer responds that the task is merely of few hours. But, the manager's curiosity goes up, and he asks the programmer further to check whether the image is of a bird or not? Surprisingly, the programmer responds, “I need a research team and five years for this task.”

This surprised the manager as he expected it to be an easy task. But the programmer who has a knack in the field knows that it is one of the complex problems to be addressed in computer science.

In the last decade, we have provided solutions to many complex problems in the field of computers. But, for the last 50 years, we have been struggling to solve the problems in image recognition. However, thanks to the efforts of researchers and computer scientists across the globe, we can solve these problems now. Even a three-year-old child can identify a bird's photo, but identifying a way by which computers can do the same task was not a cake-walk; hence, it took almost 50 years!

We have finally found a promising approach for object recognition using deep CNN in recent years. In this chapter, we will discuss the working principle and concepts of CNN, a deep neural network approach to solving the problem of image recognition.

12.1 INTRODUCTION [LO1]

There are in general two approaches to solving equilibrium problems in solid mechanics: Eulerian and Lagrangian. The first approach deals with vectors such as force and moments, and considers the static equilibrium and compatibility equations to solve the problems. In the second approach, scalars such as work and energy are used, and here solutions to problems are based on the principle of conservation of energy. There are many situations where the second approach is more advantageous, and here some powerful methods, such as the method of virtual work, based on this approach, are used.

Eulerian and Lagrangian approaches to solving solid mechanics problems are much more involved. However, here we have chosen to describe these in a simplified manner, which is suitable as a prologue to the present discussion on energy methods.

In mechanics, energy is defined as the capacity to do work, and this may exist in different forms. We are concerned here with elastic strain energy, which is a form of potential energy stored in a body on which some work is done by externally applied forces. Here it is assumed that the material remains elastic when work has been done so that all the energy is recoverable and no permanent deformation occurs. This means that strain energy U = work done. If the load is applied gradually in straining, the material load–extension graph is as shown in Figure 12.1, and we may write U = ½ Pδ.

The hatched portion of the load–extension graph represents the strain energy and the unhatched portion ABD represents the complementary energy that is utilized in some advanced energy methods of solution.

7.1 Introduction to Multiple Linear Regression

In simple linear regression, we have one dependent variable and only one independent variable. As we discussed in the previous chapter, the stipend of a research scholar is dependent on his years of research experience.

But most of the time, the dependent variable is influenced by more than one independent variable. When the dependent variable depends on more than one independent variable, it is known as multiple linear regression.

Figure 7.1 indicates the difference between simple and multiple regressions mathematically.

In Figure 7.1(b), b0 is the constant while x1, x2, and xn are independent variables on which the dependent variable y depends. You can point out that mathematically multiple linear regression is derived similarly to simple linear regression. The major difference is that in multiple linear regression, we have multiple independent variables, as it is from x1 to xn instead of only one independent variable, x1, in the case of simple linear regression. It is also important to note that we have b1 to bn as the coefficients of these independent variables, respectively.

The price prediction of a house can be viewed as a multiple linear regression problem, where factors such as plot size, number of bedrooms, and location play a significant role in determining the price. Unlike simple linear regression, which relies solely on plot size, multiple linear regression considers various features to accurately estimate the house price.

Let us understand this concept further with a real-life example. Consider a case where a venture capitalist has hired a data scientist to analyze different companies’ data to predict their profit. Identifying the company having maximum profit will help the venture capitalist to select the company he could invest in the near future to earn maximum profit.

21.1 Introduction

In recent years, a recurrent neural network (RNN) has become one of the most prominent neural networks for predicting values based on time series data. The time series is a collection of data points ordered over even intervals in time. Hence, time series analysis is useful when we want to study some parameter changes over time. In RNNs, the output from the previous steps is fed into the input of the current state. Thus, RNN could predict the next letter of any word, the next word of the sentence, and the diesel prices, stock prices, or weather. In all these tasks, there is a need to remember the previous values, and consequently, the output at t+1 will be dependent on the output at the time t interval. In this chapter, we will implement an RNN to predict the trend of diesel prices.

We will implement an RNN through long short-term memory (LSTM) units. We will use stacked layers of LSTM, as RNNs suffer from the issue of vanishing gradient and exploding gradient. Whereas LSTM encompasses gates through which they can regulate the flow of information. Because of this added advantage, LSTMs are commonly used for implementing RNNs.

21.2 Implementation of RNN in Python

Problem Statement: In this experiment, our primary objective is to predict the trend of diesel prices in Delhi, i.e., we wish to predict that the diesel prices in Delhi will witness an upward or downward trend for the near future. It is difficult to predict the exact future price of diesel on a particular day, as our dataset for this problem is quite small. Hence, using an RNN model (implemented through stacked layers of LSTM), we will predict an approximate value of future diesel prices in Delhi, which helps to predict the trend accurately (upward or downward).

11.1 Introduction to Classification Algorithms and Steps for Its Implementation

In this chapter, we will implement several classification algorithms of machine learning (ML) in Python. For the same, we will consider the Purchase Alexa Dataset, which contains multiple users’ information and their decision to buy Alexa in terms of “YES” or “NO”. The dataset features several independent columns and a labeled class attribute. Our main objective is to predict whether a user will buy Alexa or not (class attribute). The class predictions are based on the input attributes composed of several independent columns.

To better understand, we will use the same dataset, i.e., Purchase Alexa Dataset, to implement all the classification algorithms such as decision tree, random forest, naive Bayes, k-NN, logistic regression, and support vector machine (SVM). This will allow us to compare the results and the working of different classification algorithms. We will start by creating a pre-processing data template for our dataset, which shall remain common for all the classification models. Later, we will implement a classification model for each algorithm mentioned above. Then the performance of the model under study would be analyzed using the confusion matrix and the performance metrics. Finally, the training and testing results would be visualized graphically to better understand the working of classifiers.

A stepwise approach to implementing a classification model in Python is as follows:

• Step 1: Importing libraries—Importing of libraries is required to perform various functions and steps related to data pre-processing and building the classifiers.

• Step 2: Loading dataset—Download and load the desired dataset to Spyder.

• Step 3: Splitting the dataset into training and testing datasets—Splitting the loaded dataset into training and testing subsets.

In this chapter, we are going to implement the simple linear regression in Python. To implement this concept, we will analyze how the stipend of a researcher is related to their years of research experience. Our aim is to predict the stipend of the researcher based on his/her research experience.

Problem Statement and Dataset

To perform this task, we will consider a dataset consisting of two attributes: ResearchExperience and Stipend. There are 30 observations in this dataset to draw the correlation between the research experience and their corresponding stipend. A research institute aims to find this correlation between research experience and the stipend. This will assist the management in providing an appropriate stipend to new research scholars based on their years of research experience, rather than deciding randomly. The obvious thing is that the stipend is directly proportional to the research experience. The higher the experience, the more will be the stipend. We will use a simple linear regression model to solve this problem.

Let us quickly refresh our concepts of a simple linear regression model. We know that simple linear regression can best fit the straight line to generate a relationship between the research experience and the stipend. Though the dataset is quite simple, it has a great business value to it, as the model created will help the institute predict the stipend of the researcher based on their experience. Therefore, using this model, the stipend of the new researchers can be easily predicted, and this would also acknowledge the transparency in the management. Here, ResearchExperience (independent variable) will be our X and act as horizontal axis. In contrast, the Stipend (variable to be predicted is the dependent variable) will be Y and act as vertical axis, as shown in Figure 6.1.

In the ever-evolving landscape of technology, machine learning (ML) has emerged as a transformative force, reshaping industries and empowering innovations across the globe. Its profound impact on diverse fields, from healthcare and finance to autonomous vehicles and natural language processing, makes it an indispensable skill for the modern-day learner and practitioner.

Machine Learning with Python: Principles and Practical Techniques is a comprehensive and timely written book that navigates through the intricacies of this fascinating field. Written by Dr Parteek Bhatia, an expert in the domain, this book aims to provide a solid foundation for understanding the principles of ML and equipping readers with the practical techniques to tackle real-world challenges.

As we embark on this enlightening journey, the author starts by laying a solid groundwork, demystifying the fundamental concepts of ML. He skilfully explains the various learning paradigms, such as supervised, unsupervised, and reinforcement learning, and elucidates the key algorithms underpinning each. From linear regression and decision trees to support vector machines and deep neural networks, the book offers a comprehensive exposition that caters to readers with varying levels of expertise.

A distinguishing feature of this book is its strong emphasis on Python, a versatile, opensource, and widely used programming language in the realm of ML. By utilizing Python, readers are empowered with a practical and accessible toolset, facilitating the implementation and experimentation of various algorithms discussed in the text. The authors provide hands-on examples and code snippets, fostering a learning-by-doing approach that ensures readers can confidently harness the power of ML in their projects.

Whether you are a seasoned data scientist seeking to enhance your skillset or a curious beginner eager to dive into the world of ML, this book offers something for everyone. Its clear and concise presentation, enriched with illustrative examples and practical exercises, makes it an invaluable resource for self-study or classroom instruction.

Machine Learning with Python: Principles and Practical Techniques is a must-have addition to the library of any aspiring or seasoned ML practitioner. Its comprehensive coverage of key concepts, coupled with the practical implementation guidance using Python, makes it a timeless reference in the fast-paced landscape of ML.

8.1 Introduction to Multiple Linear Regression

In the previous chapter, we covered the concepts of multiple linear regression and polynomial linear regression. There, we defined regression as the prediction of continuous values; and in the case of multiple linear regression, there are multiple independent variables and a single dependent variable. If Y is a dependent variable whose value depends on X1, X2, X3,…, Xn independent variables, then mathematically, multiple linear regression is represented by Equation (8.1).

where b0 is the constant and b1, b2, …, bn are the coefficients. Each of the coefficients represents the change in the dependent variable due to the per unit change in the independent variable value. Let us move ahead and implement a multiple linear regression model in Python.

8.1.1 Understanding Dataset and Problem Statement

Let us consider the dataset of 50 advertisement agencies in India. A few instances of this dataset are shown in Table 8.1. The goal is to predict the agency's profit based on different parameters – Print Media Expenses, Social Media Expenses, Outdoor AD Expenses, and City or Location. All the figures mentioned in this dataset is in INR (Indian rupees).

The dataset used in this chapter is derived from the SuperDataScience dataset by Kirill Eremenko and his team. A big thanks to SuperDataScience for granting us permission to use and reference the dataset in this book. You can find it at https://www.superdatascience.com/pages/machine-learning.

Machine learning (ML) is one of the most upcoming knowledge areas transforming the world. It is a dynamic and transformative field that has the potential to reshape the way we interact with technology and the world around us. In the book, Machine Learning with Python: Principles and Practical Techniques, author Parteek Bhatia offers an insightful and hands-on approach to demystifying this complex subject.

In a world where ML plays an increasingly central role in our lives, understanding its principles and practical applications is essential. In this book, numerous algorithms are explained in detail, assuming no previous knowledge of readers. All these algorithms are widely used in the practicing world and research areas. This book is an invaluable resource for beginners and those looking to deepen their knowledge in the field.

Parteek Bhatia takes the reader on an engaging journey, starting from the basics and gradually building up to more advanced concepts. What sets this book apart is its focus on practicality. The book covers various ML techniques, from data pre-processing and regression to classification, clustering, and association mining. Each concept is illuminated with detailed Python implementations, allowing you to see firsthand how these algorithms work and how they can be applied to real-world problems. It also delves into more advanced topics like artificial neural networks, deep learning, convolutional neural networks, recurrent neural networks, and genetic algorithms. This comprehensive approach equips you with the tools and knowledge to tackle complex ML challenges.

Parteek Bhatia's passion for the subject and dedication to making it accessible shines through every chapter. This book is not just a collection of information; it is a learning adventure. It takes the reader from a beginner to a confident practitioner, ready to take on the exciting and everevolving world of ML.

Whether you are a student, a professional, or simply someone eager to explore the possibilities of ML, this book will be your trusted guide. Machine Learning with Python is your gateway to unlocking the potential of this fascinating field.

I commend Parteek Bhatia for his commitment to creating this educational masterpiece. As you embark on your journey through the captivating realm of ML, I encourage you to embrace the concepts, put them into practice, and let your curiosity and creativity flourish.

9.1 Introduction to Classification

We rely on machine learning (ML) to make critical decisions or predictions in the modern world. It is very important to understand how computers by using ML make these predictions. Usually, the predictions made by ML models are classified into two types, i.e., classification and regression. The ML models use various techniques to predict the outcome of an event by analyzing already available data. As machines learn from data, the type of training or input data plays a crucial role in deciding the machine's capability to make accurate decisions and predictions. Usually, this data is available in two forms, i.e., labeled and unlabeled. In label data, we know the value of the output attribute for the sample input attributes, while in unlabeled data, we do not have the output attribute value.

For analyzing labeled data, supervised learning is used. Classification and regression are the two types of supervised learning techniques used to predict the outcome of an unknown instance by analyzing the available labeled input instances. Classification is applied when the outcome is finite or discrete, while the regression model is applied when the outcome is infinite or continuous. For example, a classification model is used to predict whether a customer will buy a product or not. Here the outcome is finite, i.e., buying the product or not buying. In this case, the regression model predicts the number of products that the customer may buy. Here the outcome is infinite, i.e., all possible numbers, since the term quantity refers to a set of continuous numbers.

8.1 INTRODUCTION [LO1]

In simple words, the application of a torque on a prismatic member causes twisting or torsion. This causes shear stress if a torque alone is applied. However, this is rarely true in practical cases. A circular bar, used to transmit torque between a prime mover and a machine, is a typical example of a torsion member. However, in many applications, a torque along with a bending moment and axial loading are applied, and there we need to combine these effects and find the principal stresses. A typical example of such combined stresses is a propeller shaft. Torsional problems are important in many applications both in industry and in our daily life. Therefore, we consider torsion alone in this chapter in some detail.

Torsional problems for circular members are generally solved assuming that plane sections normal to the axis of the bar remain plane even after twisting. This assumption was first made by Coulomb intuitively in 1784, and he came up with a correct usable equation for members with circular sections. However, this assumption does not apply to bars with a noncircular cross-section. Navier attempted to solve torsional problems with noncircular sections using Coulomb's assumption and came up with an erroneous solution. The correct solution was provided by St. Venant in 1853 using a warping function. Much later, in 1903, Prandtl came up with a membrane analogy method that could solve problems with any complicated cross-section. First, we shall consider torsional problems with circular cross-sections.

8.2 TORSION OF MEMBERS WITH CIRCULAR CROSS-SECTION [LO2]

The torsion analysis of members with a circular cross-section starts with simplified assumptions made by Coulomb. In order to establish a relation between the applied torque and shear stress developed and the angle of twist in such cases, the following assumptions are made:

• 1. Material is homogeneous and isotropic.

• 2. Plane sections perpendicular to the axis of a circular member remain plane after twisting. No warping or distortion of the parallel planes occurs.

11.1 INTRODUCTION [LO1]

Stresses developed at the contact between two loaded elastic bodies are generally localized and most machine parts or structures are designed based on the stresses in the main body. However, there are many important machine members where the localized stresses developed at the contact between curved surfaces with initially limited contact area play an important role in their design. Ball or roller bearings, gears, cams, and valve tappets of internal combustion engines are some of the examples of machine parts where contact stresses must be taken into account in order to predict their failure probability.

The localized contact stresses that develop between two curved bodies as they are loaded with small deformations are often referred to as Hertzian stresses, following the work of H. Hertz (1881), who first solved these contact problems elegantly more than a century ago. Since then the topic has received a good deal of attention by the researchers due to its importance in engineering practice and science. Much work has been done on the stress distribution at the Hertzian contact surfaces and sub-surfaces. Ball bearings and gear teeth often fail by pitting. Hertzian stress analysis can precisely locate the depth at which maximum shear stress occurs where cracks may initiate and propagate leading to failure. Thus, a remedy to such failures may be prescribed in terms of limiting stresses. In many rolling contact problems, failure occurs with the initiation of a tiny crack that eventually grows due to repeated contacts. Analysis of crack initiation and growth is often based on Hertzian stress analysis. In this chapter, we shall consider the basics and application of contact stress analysis, beginning with some basic elasticity theory necessary for such analyses.

2.1 MATHEMATICAL PRELIMINARIES [LO1]

In any scientific or engineering field of study, knowledge of some mathematical techniques and methods are essential. Solid mechanics is no exception. To develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background. In this chapter, we shall discuss Cartesian tensors, which have a special significance in the discussion of stress, strain, and displacement fields, and their manipulation. Other mathematical details will be discussed as and when they are required in solving different problems.

Tensors may be defined in a number of ways. One simple definition is that a tensor is a physical quantity that is governed by certain transformation laws when the coordinate system is changed. A tensor is invariant under any change of coordinate system, but its components along the coordinate axes change with the changed coordinate system. Tensors of order zero are called scalars. Common examples of scalars are temperature, density, Young's modulus, or Poisson's ratio. They have a single magnitude at each point in space, and they are invariant with coordinate transformations. A typical example of scalars is often taken as temperature T at a point in space with coordinates (x, y, z) represented as T(x, y, z). Temperature at the same point does not change if we choose a different coordinate system (x′, y′, z′) represented as T′(x′, y′, z′) and we may say

T=T′. (2.1.1)

Tensors of first order are vectors, and we know that a vector has a magnitude and a direction. A typical example of a vector is a velocity vector V. It is sometimes taken as a convention to represent a vector by a bold letter. Consider the velocity vector V in (x, y, z) coordinate system.

Solid mechanics, compared to mechanics of materials or strength of materials, is generally considered to be a higher level course. It is usually offered in higher semester to senior students. There are many textbooks available on solid mechanics, but they generally include a large part of theory of elasticity with in depth mathematical formulations. The usual prerequisites are one or two semester course on elementary strength of materials and a thorough mathematical background, including scalar, vector, and tensor field theory and cartesian and curvilinear index notation. The difference in levels between these books and elementary texts on strength of materials is generally formidable. However, in our experience of teaching this course for many years at premier institutes like IIT Kharagpur and Jadavpur University, despite its complexity, senior students generally cope well with the course using the readily available textbooks.

However, there is a vast student population pursuing mechanical, civil, or allied engineering disciplines across the country in colleges where AICTE curriculum is followed. Through several years of interaction with this group of students, we have found that there is no suitable textbook that suits their requirements. The book is primarily aimed at this group of students, attempting to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner for better understanding. Index notations have been avoided, and the mathematical derivations are restricted to second-order differential equations, their solution methodologies, and only a few special functions, such as stress function and Laplacian operators.

The text follows more or less the AICTE guidelines and consists of twelve chapters. The first five chapters introduce the engineering aspects of solid mechanics and establish the basic theorems of elasticity, governing equations, and their solution methodologies. The next four chapters discuss thick cylinders, rotating disks, torsion of members with both circular and noncircular cross-sections, and stress concentration in some depth using the elasticity approaches. Thermoelasticity is an important issue in the design of high-speed machinery and many other engineering applications. This is dealt with in some detail in the tenth chapter. Problems on contact between curved bodies in two-dimensional and three-dimensional situations can be challenging, and they have wide applications in mechanical engineering such as in bearing and gear technology.