Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology (Systems Innovation Book Series)

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
Authors
Chapter 1: Artificial Intelligence within Industrial and Systems Engineering Framework
	1.1 Introduction
	1.2 Quantum Potential for AI
	1.3 Old and New AI Achievements
	1.4 Industrial Engineering Linkage
	1.5 Historical Background of AI
	1.6 Origin of Artificial Intelligence
	1.7 Human Intelligence versus Machine Intelligence
	1.8 Natural Language Dichotomies
	1.9 The First Conference on Artificial Intelligence
	1.10 Evolution of Smart Programs
	1.11 Branches of Artificial Intelligence
	1.12 Neural Networks
	1.13 Emergence of Expert Systems
	References
Chapter 2: Mathematics of Cantor Set for AI Searches
	2.1 Introduction
	2.2 Intelligent Searches
	2.3 Backdrop for AI Searches
	2.4 Mathematics of Cantor Set
		2.4.1 Set Sectioning Technique of Cantor Set
		2.4.2 Search of Asymmetrically Distributed Data
		2.4.3 Derivation of the Mode Estimating Formula in Terms of Inclusive Graphic Skewness
		2.4.4 Graphical Verification of the mod%–IGS Relationship
	2.5 Results of Preliminary Research
	2.6 Cantor and Binary Search Comparison of 1500 Data Point Files
	2.7 Cantor and Binary Search Comparison of 150 Data Point Files
	2.8 Comparison of the Binary Search and the Cantor Search for the various Database Sizes
	2.9 Intelligent 1/n Sectioning of the Search Space
	References
Chapter 3: Set-theoretic Systems for AI Applications
	3.1 Set Systems in Problem Domains
	3.2 Sets and Systems in Innovation
	3.3 Ordered Pairs on Sets
	3.4 Set Relations in Innovation Systems
	3.5 Functions on Sets
	3.6 Cardinality of Sets
	3.7 Relationships of Set-to-System and Subset-to-Subsystem
	3.8 Integration Mapping of Subsets
	3.9 Model Reduction Approach
	3.10 Singular Value Decomposition in Innovation Systems
	3.11 Subsystem Surface Projection Integrals
	3.12 Set Projection and System Overlap
	3.13 Time-Variant Systems Integration
	3.14 Modal Canonical Representation
	3.15 Canonical Estimation Procedure
	3.16 Hypothetical Example
	3.17 Conclusion
	References
Chapter 4: AI Mathematical Modeling for Product Design
	4.1 Introduction
	4.2 Product Design Background
	4.3 Memetic Algorithm and Its Application to Collaborative Design
	4.4 A Framework for Collaborative Design
	4.5 The Pseudo Code
	4.6 Case Example of Forearm Crutch Design
	4.7 Design Problem Formulation
	4.8 Design Agent for Strength Decision
	4.9 System Implementation
	4.10 System Results and Analysis
	4.11 Conclusion
	References
Chapter 5: Mathematical Formulation of the Pursuit Problem for AI Gaming
	5.1 Introduction to the Pursuit Problem
	5.2 Introduction
	5.3 The Classical Approach
	5.4 The Intercept Approach
	5.5 Example
	5.6 Conclusion
	References
Chapter 6: AI Framework for the Financial Sector
	6.1 Introduction
	6.2 Methodology
	6.3 Discussion
	6.4 Conclusion
	References
Chapter 7: AI Neuro-Fuzzy Model for Healthcare Prediction
	7.1 Introduction
	7.2 Coupled Insulin and Meal Effect Neuro-Fuzzy Network Model
		7.2.1 Model Assumptions
		7.2.2 Model Formulation
		7.2.3 Blood Glucose Level (BGL), x ( k)
		7.2.4 Insulin Injection, u 1
		7.2.5 Meal Intake, u 2
	7.3 Fuzzification of State and Input Variables
		7.3.1 Formulation of the T-S Model Rule Bases
	7.4 Parameter Identification
	7.5 Prediction of Blood Glucose Level
	7.6 Choice of Training Scenario
	7.7 Results, Observations and Discussions
	7.8 Conclusion
	7.9 Contributions to Knowledge
	References
Chapter 8: Stochasticity in AI Mathematical Modeling
	8.1 Introduction
	8.2 The Material/Iconic Models
	8.3 AI Mathematical Models
	8.4 Systems Filtering and Estimation
		8.4.1 Identification
	8.5 Correlation Techniques
		8.5.1 System Estimation
		8.5.2 Problem Formulation
		8.5.3 Maximum Likelihood
		8.5.4 Bayes Estimators
		8.5.5 Minimum Variance
		8.5.6 For Linear Minimum Variance Unbiased (Gauss-Markov)
		8.5.7 Partitioned Data Sets
		8.5.8 Kalman Form
			8.5.8.1 Discrete Dynamic Linear System Estimation
		8.5.9 Prediction
		8.5.10 Filtering
		8.5.11 Smoothing
			8.5.11.1 Continuous Dynamic Linear System
	8.6 Continuous Nonlinear Estimation
	8.7 Extended Kalman Filter
		8.7.1 Partitional Estimation
	8.8 Invariant Imbedding
	8.9 Stochastic Approximations/Innovations Concept
	8.10 Model Control – Model Reduction, Model Analysis
		8.10.1 Introduction
	8.11 Modal Approach for Estimation in Distributed Parameter Systems
	8.12 The Modal Canonical Representation
	References
Chapter 9: Mathematical Utility Modeling for AI Application
	9.1 Introduction to Utility Modeling
	9.2 Innovation Investment Challenge
	9.3 Utility Models
		9.3.1 Additive Utility Model
		9.3.2 Multiplicative Utility Model
		9.3.3 Fitting a Utility Function
		9.3.4 Investment Value Model
	9.4 Capability
	9.5 Suitability
	9.6 Performance
	9.7 Productivity
	9.8 Polar Plots
	9.9 Technical Innovation Benchmarking
	References
Chapter 10: Artificial Intelligence and Human Factors Integration in Additive Manufacturing
	10.1 Introduction
	10.2 Background of Additive Manufacturing
	10.3 Cognitive Ergonomics
	10.4 Computational Methods
	10.5 Human Considerations in Additive Manufacturing
	10.6 Artificial Intelligence Case Studies
	10.7 Cognitive Ergonomics in Additive Manufacturing
	10.8 Human–Machine Integration
		10.8.1 Implementation Strategy for DEJI Model in Human Factors for Additive Manufacturing
	10.9 Conclusion
	References
Chapter 11: AI Systems Optimization Techniques
	11.1 Introduction
	11.2 Basic Structure of Local Methods
	11.3 Descent Directions
	11.4 Steepest Descent (SD)
	11.5 Conjugate Gradient (CG)
	11.6 Newton Methods
		11.6.1 Algorithm: Modified Newton
	11.7 The Stochastic Central Problems
		11.7.1 Stochastic Approximation
		11.7.2 General Stochastic Control Problem
	11.8 The Intelligent Heuristic Models
		11.8.1 Heuristics
		11.8.2 Intelligent Systems
		11.8.3 The General Search Paradigm
			11.8.3.1 General Search
		11.8.4 Integrated Heuristics
		11.8.5 Tabu Search
			11.8.5.1 Tabu Search
		11.8.6 Simulated Annealing (SA)
			11.8.6.1 Simulated Annealing
		11.8.7 Genetic Algorithms (GA)
			11.8.7.1 Genetic Algorithm (11.7)
			11.8.7.2 Procedure GA
		11.8.8 Genetic Algorithm Operators
			11.8.8.1 Examples
			11.8.8.2 Applications of Heuristics to Intelligent Systems
			11.8.8.3 High-Performance Optimization Programming
	References
Chapter 12: Mathematical Modeling and Control of Resource Constraints
	12.1 Introduction
	12.2 The Nature of Resource Constraints
	12.3 Literature Background
	12.4 Methodology
	12.5 Mathematical Notations
	12.6 Representation of Resource Interdependencies and Multifunctionality
	12.7 Modeling of Resource Characteristics
	12.8 Resource Mapper
	12.9 Activity Scheduler
	12.10 Model Implementation and Graphical Illustrations
	References
Appendix A: Mathematical Expressions and Collections (Series, Patterns, and Formulae)
	Greek Alphabet
	Number Sequence and Patterns
	Closed Form Mathematical Expressions
	Derivation of the Quadratic Formula
	Mathematical Signs and Symbols
		Overall Mean
		Definition of Set and Notation
			Set Terms and Symbols
			Operations on Sets
		Probability Terminology
			Basic Probability Principles
			Random Variable
			Mean Value x or Expected Value μ
			Series Expansions
		Algebra
			Laws of Algebraic Operations
			Special Products and Factors
			Powers and Roots
			Proportion
			Arithmetic Mean of n Quantities A
			Geometric Mean of n Quantities G
			Harmonic Mean of n Quantities H
			Generalized Mean
			Solution of Quadratic Equations
			Solution of Cubic Equations
			Trigonometric Solution of the Cubic Equation
			Partial Fractions
			Non-Repeated Linear Factors
			Repeated Linear Factors
			General Terms
			Repeated Linear Factors
			Factors of Higher Degree
		Geometry
			Triangles
			Right Triangle
			Equilateral Triangle
			General Triangle
			Quadrilaterals
			Rectangle
			Parallelogram
			Rhombus
			Trapezoid
			General Quadrilateral
			Cyclic Quadrilateral
		Planar Areas by Approximation
		Solids Bounded by Planes
			Cube
			Prism
			Pyramid
			Prismatoid
		Regular Polyhedra
		Spherical Triangle and Polygon
			Oblate Spheroid
			Prolate Spheroid
			Circular Torus
		Equation of Line Joining Two Points
			Equation of Line in Terms of x Intercept a ≠ 0 and y intercept b ≠ 0
			Normal Form for Equation of Line
			General Equation of Line
			Area of Triangle with Vertices
			Transformation of Coordinates Involving Pure Translation
			Transformation of Coordinates Involving Pure Rotation
			Transformation of Coordinates Involving Translation and Rotation
			Polar Coordinates ( r, θ)
			Plane Curves
			Catenary, Hyperbolic Cosine
			Cardioid
			Circle
			Cassinian Curves
			Cotangent Curve
			Cubical Parabola
			Cosecant Curve
			Cosine Curve
			Ellipse
			Gamma Function
			Hyperbolic Functions
			Inverse Cosine Curve
			Inverse Sine Curve
			Inverse Tangent Curve
			Logarithmic Curve
			Parabola
			Cubical Parabola
			Tangent Curve
			Ellipsoid
			Elliptic Cone
			Elliptic Cylinder
			Hyperboloid of One Sheet
			Elliptic Paraboloid
			Hyperboloid of Two Sheets
			Hyperbolic Paraboloid
			Sphere
		Logarithmic Identities
			Series Expansions
			Limiting Values
			Inequalities
			Continued Fractions
			Polynomial Approximations
			Exponential Function Series Expansion
			Fundamental Properties
			Definition of General Powers
			Slopes
		Trigonometric ratios
			Sine Law
			Cosine Law
			Expansions
			Factoring
			Roots of Quadratic
			Law of exponents
			Logarithms
	Six Simple Machines for Materials Handling
		Machine 1: The Lever
		Machine 2: Wheel and Axie
		Machine 3: The Pulley
		Machine 4: The Inclined Plane
		Machine 5: The Wedge
		Machine 6: The Screw
	Mechanics: Kinematics
		Scalars and Vectors
		Distance and Displacement
		Acceleration
			Speed and Velocity
			Frequency
			Period
			Angular Displacement
			Angular Velocity
			Angular Acceleration
			Rotational Speed
			Uniform Linear Motion
			Uniform Accelerated Linear Motion
		Rotational Motion
			Uniform Rotation and a Fixed Axis
			Uniform Accelerated Rotation about a Fixed Axis
		Simple Harmonic Motion
			Pendulum
			Free Fall
			Vertical Project
			Angled Projections
			Horizontal Projection: ( α = 0)
			Sliding Motion on an Inclined Plane
				Rolling Motion on an Inclined Plane
		Mechanics: Dynamics
			Newton’s First Law of Motion
			Newton’s Second Law
			Newton’s Third Law
			Momentum of Force
			Impulse of Force
			Law of Conservation of Momentum
			Friction
			General Law of Gravity
			Gravitational Force
			Centrifugal Force
			Centripetal Force
			Torque
			Work
			Energy
		Conservation of Energy
			Power
			Common Statistical Distributions
		Discrete Distributions
			Bernoulli Distribution
			Beta Binomial Distribution
			Beta Pascal Distribution
			Binomial Distribution
			Discrete Weibull Distribution
			Geometric Distribution
			Hypergeometric Distribution
			Negative Binomial Distribution
			Poisson Distribution
			Rectangular (Discrete Uniform) Distribution
		Continuous Distributions
			Arcsine Distribution
			Beta Distribution
			Cauchy Distribution
			Chi Distribution
			Chi-Square Distribution
			Erlang Distribution
			Exponential Distribution
			Extreme-Value Distribution
			F Distribution
			Gamma Distribution
			Half-Normal Distribution
			LaPlace (Double Exponential) Distribution
			Logistic Distribution
			Lognormal Distribution
			Noncentral Chi-Square Distribution
			Noncentral F Distribution
			Noncentral t Distribution
			Normal Distribution
			Pareto Distribution
			Rayleigh Distribution
			Triangular Distribution
			Uniform Distribution
			Weibull Distribution
		Distribution Parameters
			Average
			Variance
			Standard Deviation
			Standard Error
		Skewness
			Standardized Skewness
		Kurtosis
			Standardized Kurtosis
			Weighted Average
			Estimation and Testing
		Distribution Functions−Parameter Estimation
			Bernoulli
			Binomial
			Discrete Uniform
			Geometric
			Negative Binomial
			Poisson
			Beta
			Chi-Square
			Erlang
			Exponential
			F
			Gamma
			Log Normal
			Normal
			Student’s t
			Triangular
			Uniform
			Weibull
			Chi-square Test for Distribution Fitting
			Kolmogorov − Smirnov Test
		ANOVA
			Notations
			Standard Error (internal)
			Standard Error (pooled)
			Interval Estimates
			Tukey Interval
			Scheffe Interval
			Cochran C-Test
			Bartlett Test
			Hartley’s Test
			Kruskal-Wallis Test
			Freidman test
		Regression
			Notation
			Regression Statistics
			Predictions
			Nonlinear Regression
			Ridge Regression
		Quality Control
			Subgroup Statistics
			X Bar Charts
			Capability Ratios
			R Charts
			S Charts
			C Charts
			U Charts
			P Charts
			NP Charts
			CuSum Chart for the Mean
			Multivariate Control Charts
		Time Series Analysis
			Notation
			Autocorrelation at lag k
			Partial autocorrelation at lag k
			Cross Correlation at lag k
			Box-Cox
			Periodogram (computed using Fast Fourier Transform)
		Categorical Analysis
			Notation
			Totals
			Chi-Square
			Fisher’s Exact Test
			Lambda
			Uncertainty Coefficient
			Somer’s D
			Eta
			Contingency Coefficient
			Cramer’s V
			Conditional Gamma
			Pearson’s r
			Kendall’s Tau b
			Tau C
		Probability Terminology
			Basic Probability Principles
			Random Variable
			Mean Value or Expected Value μ
		Discrete Distribution Formulas
			Bernoulli Distribution
			Beta Binomial Distribution
			Beta Pascal Distribution
			Binomial Distribution
			Discrete Weibull Distribution
			Geometric Distribution
			Hypergeometric Distribution
			Negative Binomial Distribution
			Poisson Distribution
			Rectangular (Discrete Uniform) Distribution
		Continuous Distribution Formulas
			Arcsin Distribution
			Beta Distribution
			Cauchy Distribution
			Chi Distribution
			Chi-Square Distribution
			Erlang Distribution
			Exponential Distribution
			Extreme-Value Distribution
			F Distribution
			Gamma Distribution
			Half-Normal Distribution
			LaPlace (Double Exponential) Distribution
			Logistic Distribution
			Lognormal Distribution
			Noncentral Chi-Square Distribution
			Noncentral F Distribution
			Noncentral t Distribution
			Normal Distribution
			Pareto Distribution
			Rayleigh Distribution
			t -Distribution
			Triangular Distribution
			Uniform Distribution
			Weibull Distribution
	Variate Generation Techniques
	Generation Algorithms
	Formulas for Generating Event Times from a Renewal or Nonhomogeneous Poisson Process
		Example
Appendix B: Cantor Set Sectioning
	Application of the Cantor Set Approach
	Comments on the Search Procedure
	Modified Search Procedure
	Alternate Search Preference
Index