7.1 INTRODUCTION [LO1]

The problems of stresses and deformations in disks rotating at high speeds are important in the design of both gas and steam turbines, generators and many such rotating machinery in industry. As discussed in earlier chapters, this is another example of axisymmetric problems in polar coordinates. Although the theoretical treatment of a flat disk is simpler, in many industrial applications, disks are tapered. They are usually thicker near the hub, and their theoretical analysis is slightly more involved. We shall first take up the analysis for flat disks.

In the case of rotating disks with centrifugal force as body force, the equation of equilibrium reduces to as in equation (6.1.3).

Combining this with displacement equations, we have, as in equation (6.1.5), a general equation for determining the stress distribution in axisymmetric problems. This is given as

This is a nonhomogeneous differential equation. The associated homogeneous equation (complementary equation) is

The solution of this equation is Lame's equation as discussed in Chapter 6, equation (6.2.3), and taking into consideration the particular solution, the solution to equation (7.1.2) turns out to be

We may also determine the radial displacement from equation (6.2.11), and this is given as

We may therefore write the stresses and displacement for the rotating disk under one bracket as

With these introductory basic equations, we shall now set out to discuss the stress distribution and displacement in rotating disks.

14.1 Introduction to Association Rule Mining

Association rule mining is a rule-based technique to discover the relation between the attributes of a dataset. It is used to find the relation between the sales of item X and item Y. It is often called a “market basket” analysis, as shown in Figure 14.1. Here, the market analyst examines the items that consumers often purchase together to find the relation between the sale of item X and item Y.

In other words, when customers visit a store, they may buy a certain type of items together during a shopping trip. For example, as shown in Figure 14.1, a database of customer’s transactions (e.g., shopping baskets) is shown where each transaction consists of a set of items (e.g., products) purchased during a visit, machine learning (ML) engineers can use association mining for finding out a group of items which are frequently purchased together (customers purchasing behavior). This is also referred to as an analysis of customer purchasing behavior. For example, “IF one buys bread, THEN there is a high probability of buying butter with it”, as it is common that people who buy bread often buy butter with it. The store manager can use this information and arrange the items accordingly to increase sales and the overall efficiency of the store.

Let us consider a situation where the store manager feels that there is a lot of rush and customers always complain about the slow working of his store. He is exploring different ways to improve the efficiency of his store. He performed an association analysis and prepared a list of associated items like bread and butter. He may decide to put all these associated items together on the same shelf or near each other so that customers can find them quickly, reducing their shopping time. It will also improve the overall efficiency of the store and the sale of the products. To further improve the shopping experience of his customers, he can create different combos and put sales over these combos.

22.1 Intuition of Genetic Algorithm

Genetic algorithm (GA) is inspired by nature, and it plays a vital role in the field of machine learning (ML). It selects the best-optimized solution from all available possible solutions or candidates. As nature selects the best possible candidates using the theory of evolution, in the same way, the GA selects the best possible solution from the available solutions.

One of the applications of GAs in ML is to select the global minima from all possible (local) minima by using natural selection. In earlier chapters, we learned that during the training of an artificial neural network, the main goal is to obtain the weights with a minimum cost function value. The gradient descent algorithm is commonly used to find the local minima of the cost function. But, we must find the global minima to reach the optimal weights. A GA can be used to find the global minima out of all available local minima or possible solutions. In this case, the set of possible local minima becomes the population containing possible candidates.

In this chapter, we will discuss inspiration from nature which is the main driving concept in working of GAs and their implementation. To get a good idea about the GA, we will discuss the basics of natural selection by revisiting the theory of evolution in the next section.

22.2 The Inspiration behind Genetic Algorithm

The concepts discussed in this chapter are also available in the form of the free online Udemy Course, Genetic Algorithm for Machine Learning by Parteek Bhatia,

https://www.udemy.com/course/genetic-algorithm-for-machine-learning/

The GA is one of the first and most well-regarded evolutionary algorithms in computer science literature. John Holland, a researcher at the University of Michigan, gave this algorithm in the 1970s, but it became popular in the ‘90s.

3.1 Need for Data Pre-processing

We live in an age where data is considered oil because we need data to train machine learning (ML) algorithms. The most important job for a data analyst is to collect, clean, and analyze the data and build ML models on the cleaned dataset. But often, the raw data that we obtain is noisy. It consists of many discrepancies, inconsistencies, and often missing values. To understand this situation, let us consider an example.

Suppose we have to predict the house price, and for this, we have collected data from a few previous transactions, as shown in Figure 3.1.

In a perfect situation, the captured data should be of this format, as shown in Figure 3.1. Here, we have the size of the house and the number of bedrooms as input features, while the price is the output attribute. We can predict the price of an unknown instance through regression.

But practically, in most situations, the captured data is not of good quality, and usually, we have a dataset, as shown in Figure 3.2.

You can see that this data is messy. There are a lot of unknown or missing values, and if we trained the model on this data, its prediction would be very poor. Also, you can identify the noise and incorrect labels like the second record price is incorrect and will result in poor model training.

We can also consider some more examples like if someone entered –1 in the “salary credited” column in the case of employee dataset. It does not make any sense and will be considered noise. Sometimes, we may have an unrealistic and impossible combination of data; for example, let us consider a record where we have Gender–Male and Pregnant–Yes.

6.1 INTRODUCTION [LO1]

In earlier chapters, we have discussed axisymmetric problems in two-dimensional (2D) polar coordinate systems. Thick cylinders fall into this class of problems. Cylindrical pressure vessels, hydraulic cylinders, gun-barrels, and pipes carrying fluids at high pressure develop radial and tangential stresses (circumferential). Longitudinal stresses can also be developed if the ends are closed. Therefore, ideally, this is a triaxial stress system as shown in Figure 6.1.

• (a) Circumferential or hoop stress (σθ)

• (b) Longitudinal stress (σz)

• (c) Radial stress (σr)

If the wall thickness of a hollow cylinder is less than about 10% of its radius, it may be treated as a thin cylinder. Cylinders with higher wall thickness are considered to be thick cylinders. Before analyzing the stress in a thick cylinder, we should briefly consider the stress state in thin cylinders, where radial stress is small compared to the other stresses, and this can be neglected. Stress variation across the thin wall is also negligible. Analysis of thin-walled pressure vessels may therefore be carried out on the basis of biaxial stress system. Since the presence of shear stress at the cut section would lead to incompatible distortion, the longitudinal and circumferential stresses in this case are both principal stresses. We now take another section of the cut section as shown in Figure 6.2 (a) to consider the equilibrium of the section, and this is shown in Figure 6.2 (b).

The section is acted upon by internal pressure p and the circumferential stress developed at the cut section is σθ. Force on an infinitesimal small area subtended by angle dθ at θ inclination from the horizontal axis is pridθ.

Today, Python is known to be one of the most in-demand programming languages. As per the stats of GitHub (a provider of Internet hosting for software development), Python is the second most popular programming language, following JavaScript, as shown in Figure 2.1, and soon it may be on the top of the chart. Python surpassed Java, PHP, and other prominent languages in 2019.

Python is easy and versatile. So it is acclaimed as the major programming language to work on many new-age technologies like machine learning (ML), artificial intelligence, data science, and natural language processing. The creator of Python, Guido van Rossum, in 1991, stated that Python is a high-level programming language, and its core design philosophy is about code readability and syntax, which allows programmers to express concepts in a few lines of code. Interestingly, the name Python is inspired by Guido's favorite television show Monty Python's Flying Circus.

In this chapter, we will discuss various programming constructs of Python so that you can easily implement ML algorithms by using it. Before writing the actual code in Python, let us focus on the features of Python that make it so popular and unique.

2.1 Features of Python

Features offered by Python can be visualized in Figure 2.2. Talking about them profoundly, the main features of Python are as follows:

• • Beginner's Language: Python is not only just easy to code and learn, but also fast to grasp, and hence it is a suitable choice for any novice user who wants to learn to program. This is why nowadays this language is introduced to students in schools.

• • Interpreted: Unlike other programming languages such as C or C++, Python does not require you to compile programs before executing them. It is an interpreted language, i.e., the code written in Python gets processed in real-time line by line.

• • Interactive: The interactive feature of Python enables real-time feedback, allowing programmers to experiment, debug, and make adjustments on the go.

5.1 Introduction to Simple Linear Regression

As discussed in earlier chapters, regression predicts a continuous value or real-valued output. This chapter will discuss how regression works (from a mathematical aspect) to predict the continuous value for the given dataset. Our first learning algorithm is simple linear regression. In this section, we will discuss the fundamental concepts and mathematical modeling of simple linear regression.

We usually have a dependent variable having a continuous value whose value we wish to predict based on one or more independent variables. If we have only one independent or input variable, this situation is known as simple linear regression (also called univariate regression). If we have multiple independent or input variables, it is known as multiple linear regression or multivariate regression.

Linear regression could be used for studying patterns in different real-life scenarios. Consider a research lab where a researcher wants to understand how the stipend is effected by the years of experience, or, in simple words, we wish to predict the stipend based on the years of experience of the researcher. Machine learning (ML) is about learning from past experiences or data. Thus, to predict the researcher's stipend, we have to collect some data about past researchers, specifically their stipend and experience.

In the supervised learning models, we need a dataset called a training set. We will use the dataset as given in Table 5.1 for training the model, and our job will be to build the ML model that learns from this data and hence predicts the stipend of a researcher based on his experience. Here, the stipend will be considered the dependent or output variable because it depends on the researcher's years of experience. Thus, years of experience will be considered an independent or input variable. So, we will use simple linear regression to build the ML model. For proceeding with this problem, we will use a dataset of researchers’ stipends with their corresponding years of experience, as shown in Table 5.1.

5.1 INTRODUCTION [LO1]

In any three-dimensional (3D) elasticity problem, there are 15 unknown parameters: 6 stress components, 6 strain components, and 3 displacements. There are 15 related equations: 3 equations of equilibrium, 6 compatibility equations, and 6 constitutive equations. Solutions to a particular elasticity problem require evaluation of these 15 unknown parameters using 15 equations, satisfying all the boundary conditions. As discussed in the earlier chapters, there may be displacement or stress, or mixed boundary conditions. In many cases, solutions to 3D problems are not easy analytically. Even numerical solutions may be difficult.

There are mainly three methods of simplification of solution techniques:

• (a) If the boundary conditions are in terms of stresses, stress function approach may be made as discussed in the earlier chapter. This makes the solution simpler.

• (b) Assumptions of plane stress and plane strain reduce 3D problems to two-dimensional (2D) ones and this also makes the solution simpler.

• (c) Use of St. Venant's principle and superposition principle also makes the solution of elasticity problems simpler.

An introduction to stress function approach has been discussed in Chapter 4. We therefore start our discussion on plane stress and plane strain approaches.

5.2 PLANE STRESS AND PLANE STRAIN PROBLEMS [LO2]

The idealizations of both plane stress and plane strain states are suitable for certain classes of problems that are made to reduce the complexity of solutions. We shall consider the plane stress state first.

Chapter Objectives

• To understand the process of implementation of the artificial neural network (ANN).

• To understand the role of keras and its different modules in building the ANN.

• To understand the syntax for adding input layer, hidden layers, and output layer to ANN.

• To perform a compilation of the ANN model.

• To fit the ANN model on the training dataset.

• To make predictions with a trained ANN model.

• To evaluate the performance of the ANN classifier by using confusion matrix, precision, and recall.

17.1 Building Artificial Neural Network for Cancer Detection

Machine learning (ML) can play a crucial role in cancer detection. In this chapter, we will build a neural network for cancer detection by using a breast cancer dataset.

You can download this dataset by using the following link.

https://www.kaggle.com/datasets/uciml/breast-cancer-wisconsin-data

The acquired data contains the records of cancer patients in the United States. These records were created by Dr William H. Wolberg and others at the University of Wisconsin, USA. The whole data has 32 columns along with 569 rows. The prominent attributes are the radius, texture, perimeter, smoothness, concavity, symmetry, area, compactness, concave points, and the fractal dimension of the tumor. A snapshot of the dataset is depicted in Figure 17.1.

The dataset has a diagnosis column used as an output variable, while the remaining variables will be used as input data. The class attribute diagnosis has two classes, i.e., malignant identified as M and benign identified as B. Thus, it will be a binary classifier.

The code and dataset used in this chapter are also available at the following link.

https://github.com/bhatiaparteek/ml_with_python/tree/main/Chapter_17_ANN

To build ANN over this dataset, the whole procedure can be divided into three sub-parts below.

• i. Loading the dataset and performing pre-processing of data

• ii. Building the artificial neural network (ANN)

• iii. Making predictions and performing the validations

Let us perform all these operations by following a step-by-step approach.

17.2 Loading the Dataset and Pre-processing

In this step, we will perform tasks of loading the dataset and pre-processing.

17.2.1 Step 1: Importing the Libraries

To perform this task, we need to import two libraries, i.e., Pandas and NumPy, as shown in code snippet 1. NumPy facilitates mathematical operations, while Pandas specializes in loading and extracting datasets.

15.1 Building Association Mining Model

In this chapter, we will implement the Apriori algorithm in Python to solve a business problem. Association rule mining is one of the most popular machine learning applications, which is often used by supermarket chains and retail outlets to find the relation between the sales of item X and item Y. It is often called a “market basket” analysis. Discovering associations among attributes can lead to fact-based marketing strategies for store floor plans, special discounts, coupon offerings, product clustering, and catalog design to identify items that need to be put in combo packs.

Let us solve the problem of one such retail store by implementing the Apriori algorithm in Python.

Problem statement: Consider a supermarket store selling 16 products. To better understand the association between the sales of different items, the store manager decides to perform a market-basket analysis through the Apriori algorithm. The goal is to find association mining rules to improve the store's sales. The list of 16 items in-store is shown in Table 15.1, and the manager is analyzing 25 transactions of the sale of these items as given in Table 15.2. The number of items and transactions in a real application will be larger. In Table 15.2, each row in the table represents one transaction, i.e., the items bought by one customer.

In this dataset, the manager is interested in finding association rules that should have a minimum of 25% support and 70% confidence.

The implementation of association mining can be broken down into multiple steps. These steps are described below:

• Step 1: Importing libraries and loading the dataset—We must import the required libraries for model building into the environment, and then we must load the required dataset.

• Step 2: Making transactions—Apriori takes an input as a set of transactions in the desired structure; thus, we need to prepare a set of transactions containing the combination of items.

• Step 3: Building the model—An Apriori model will be trained on the lists of transactions, and rules will be generated based on some key parameters (support and confidence).

10.1 INTRODUCTION [LO1]

There are many applications where structures or machine parts are subjected to significant changes in temperature, for example, turbine blades, high-speed rotating machinery, and boilers in thermal power plants. Large thermal stresses may be developed in such applications, and sometimes such stresses may exceed the yield limit. It is therefore necessary to make provisions in the design of components to avoid failure due to thermal stresses. If the ends of a rod or any other machine parts are rigidly fixed such that the expansion or compression is prevented and the temperature is changed, tensile or compressive stress would be set up, and in simple terms, these stresses are called thermal stresses. In a long steam pipe, expansion joints are sometimes inserted, and in bridges, one end may be rigidly fastened to the main structure while the other end rests on rollers to avoid thermal stresses. In simple terms, this may be demonstrated considering a rod of length l and cross-sectional area A fixed at both ends (Figure 10.1) and temperature is raised by ΔT. This would produce a thermal strain ∈t in the rod such that

where a is the coefficient of thermal expansion. Since the rod is not free to expand, a compressive stress σc would be developed in the rod, and this is given by

If the rise in temperature is significant, the rod may buckle, which is of serious consideration in the design of machine parts or structures. To avoid this, we need to find the critical force Pcr for buckling. Using the basic buckling criterion, this can be given for a column pin ended at both ends, by

where I is the least moment of inertia of the constant cross-section column (rod) and A is the cross-sectional area of the column.

Machine learning (ML) algorithms work on cleaned data. Usually, the data we collect for building ML models suffers from noise, missing values, inconsistent data types, and different data scales. This makes pre-processing of data a very important phase in preparing the data for building ML models. Pre-processing is when we apply transformations over the data before feeding it to the ML algorithm. In short, data pre-processing symbolizes a set of procedures applied to the data to make it fit for ML algorithms. It generally involves the following steps:

• Step 1—Importing libraries: It involves importing the necessary libraries that are required to carry out the subsequent data manipulation and cleaning tasks.

• Step 2—Loading the dataset: The dataset that needs to be pre-processed must be loaded.

• Step 3—Handling the missing values: Dataset often contains missing or null values; these values need to be handled appropriately.

• Step 4—Handling the categorical data: In the data pre-processing phase, it is crucial to address categorical attributes that often contain multiple categories. Handling categorical data becomes an important step to ensure proper treatment and transformation of these attributes.

• Step 5—Splitting the dataset into training and testing datasets: Training and testing is the most important part of ML; thus, we need to split the dataset into training and testing subsets before building the ML models.

• Step 6—Feature scaling: In datasets, the range of data often varies, or data is often of different scales. Thus, feature scaling needs to be done to ensure uniformity in results.

It is important to note that it is not necessary to apply all of these steps to pre-process the data. However, based on the nature of the dataset, some of these steps may be skipped for building the model. In the coming sections, we will discuss the importance or need of these steps and discuss how to perform these steps in Python.

20.1 Neural Networks and Human Brain

The inspiration to build artificial neural networks (ANNs) has come from the deep desire to simulate the working of the human brain. As our understanding of the human brain is getting enriched and improved daily due to the ongoing research on this topic, researchers are also improving the ANNs accordingly. One such recent addition is the recurrent neural networks (RNNs) and the long short-term memory (LSTM). In this chapter, we will discuss these developments in a simplified manner so that our readers can understand this amazing technology and use it for their development projects.

Sections 20.1 and 20.2 draw their inspiration from the blog titled “The Ultimate Guide to Recurrent Neural Networks (RNN)” published by SuperDataScience Team. Most of the figures used in these sections are adapted from this blog.

For detailed information on the blog, please refer to the “Additional Resources” section of this chapter.

Research on the human brain gives us the idea that the human brain has three main parts: cerebrum, cerebellum, and brainstem, as shown in Figure 20.1. Let us briefly discuss the main functions of these parts and their components to understand the association between neural networks and the human brain.

Cerebrum

From Figure 20.1, we can understand that the cerebrum has four lobes. These are as follows.

Welcome to the World of Machine Learning!

In this ever-evolving era of technology, the field of machine learning (ML) stands at the forefront of innovation, promising unprecedented insights and solutions to complex problems. This textbook provides a comprehensive understanding of the theoretical foundations of ML algorithms, coupled with practical implementation using Python, designed to be a companion for both beginners venturing into the field and seasoned practitioners seeking to deepen their understanding.

Why Machine Learning?

ML is not just a technical endeavor; it is a transformational force shaping the future of how we interact with data. From enhancing search engines and revolutionizing social media to powering self-driving cars and advancing artificial intelligence (AI), the applications of ML are boundless. ML has paved the way for developing sophisticated chatbots, generative AI models, and AI copilots. This book aims to demystify the intricate concepts of ML, making them accessible to learners of all backgrounds.

What This Book Offers

• - Foundations: We begin with the fundamentals, laying a solid groundwork to help you grasp the core concepts of ML.

• - “Learning by Doing” Approach: This book adopts a “learning by doing” approach, offering step-by-step coding instructions for various ML techniques. The aim is to empower you with the knowledge and skills to implement these principles effectively.

• - Real-World Applications: Understanding theory is essential, but applying it to real-world scenarios is where the true power of ML unfolds. This book bridges theory and application, ensuring a holistic learning experience.

For Whom This Book Is Intended

Whether you are a student exploring the realms of ML for the first time, a data professional aiming to expand your skill set, or a business leader seeking insights into how ML can elevate your organization, this book is crafted with you in mind.

How to Use This Book

Feel free to navigate the chapters based on your familiarity with the subject. If you’re a beginner, start from the beginning, and if you’re seeking advanced knowledge, dive into specific sections of interest. Explore GitHub resources that provide access to datasets, sample code, and examples used in this book for hands-on learning. For enhanced visual understanding, this book is complemented by an online video course available at learncompscience.com, allowing you to reinforce your knowledge through engaging video sessions.

19.1 Building Image Classifier with CNN

The convolutional neural network (CNN) is the perfect choice for building an image classifier system. In this chapter, we will implement various CNN classifiers in Python by considering various case studies.

19.2 Dog–Cat Classifier

Consider an image classification problem that involves identifying photos as either containing a cat or dog. Our task is to develop a CNN model that can identify the object in the image as a dog or cat. The CNN model will be trained on a dataset of images containing a dog or cat, and then this trained model will be used for classification. Once the model is built, it can be used as a template to build other models for predicting the class of any image on the trained dataset. It means we can use the same model to classify the tumors by training them on medical images.

Preparing the Dataset

To build a dog–cat classifier, we will use 11000 manually annotated photos of dogs and cats, where 5500 photos are of dogs, and the remaining ones are of cats. This is the partial dataset that has been created from the dogs-vs-cats dataset available at Kaggle. The link for this dataset is given below.

https://www.kaggle.com/competitions/dogs-vs-cats/data

This full dataset contains 37500 images (24000 in the train and 13500 in the test folders), which must be manually segregated into dog and cat folders. Since the dataset is huge and segregation is time-consuming, we took 10000 images (5000 images of dogs and 5000 images of cats) in the train folder and 1000 images in the test folder (500 images of dogs and 500 images of cats).

12.1 Introduction to Clustering

In machine learning (ML), labeling the data is one of the crucial tasks. But sometimes, we do not have the labeled data. Even though the data is not labeled, we can still analyze it using clustering techniques. As you know, algorithms in ML are broadly classified as supervised and unsupervised techniques. In the case of supervised learning, the input data points/examples are labeled, while in unsupervised learning, the input data points/examples are not labeled. Cluster analysis, also called clustering, comes under unsupervised learning. Here, the input data points are not labeled. Clustering is the most popular technique in unsupervised learning.

Clustering is defined as grouping the input data points into various clusters/groups based on their similarity.

A cluster contains objects that are more similar to each other. In other words, during cluster analysis, the data is grouped into classes or clusters, so that records within a cluster (intra-cluster) have high similarity with one another but have high dissimilarities in comparison to objects in other clusters (inter-cluster).

The clustering algorithm aims to minimize the intra-cluster distance and maximize the inter-cluster distance, as shown in Figure 12.1.

An example of clustering is shown in Figure 12.2. Here, records in the input have different shapes. Here, we only have the input data without any label of shape. After applying the clustering algorithm, they were classified into three types of clusters. Here, the clustering algorithm considers the dimensions of the object and its color as the input features. Records whose features are highly similar are gathered to form a single cluster. In this case, we get three clusters representing three types of records, i.e., it clusters rhombus, circle, and triangle separately, as shown in Figure 12.2.