Design and Optimization of Energy Systems

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Module 1: Introduction
Introduction to design and specifically system design.
Morphology of design with a flow chart.
Very brief discussion on market analysis, profit, time value of money, an example of discounted cash flow technique.
Concept of workable design, practical example on workable system and optimal design.
Module 2 : System Simulation
Successive substitution method – examples.
Newton Raphson method – one unknown – examples.
Newton Raphson method – multiple unknowns – examples.
Gauss Seidel method – examples.
Rudiments of finite difference method for partial differential equations, with an example.
Module 3: Regression and Curve Fitting
Need for regression in simulation and optimization.
Concept of best fit and exact fit.
Exact fit – Lagrange interpolation, Newton’s divided difference – examples.
Least square regression – theory, examples from linear regression with one and more unknowns – examples.
Power law forms – examples.
Gauss Newton method for non-linear least squares regression – examples.
Module 4: Optimization
Formulation of optimization problems – examples.
Calculus techniques – Lagrange multiplier method – proof, examples.
Search methods – Concept of interval of uncertainty, reduction ratio, reduction ratios of simple search techniques like exhaustive search, dichotomous search, Fibonacci search and Golden section search – numerical examples.
Method of steepest ascent/ steepest descent, conjugate gradient method – examples.
Geometric programming – examples.
Dynamic programming – examples.
Linear programming – two variable problem –graphical solution.
New generation optimization techniques – Genetic algorithm and simulated annealing – examples.
Introduction to Bayesian framework for optimization- examples.

Course Curriculum

Mod-01 Lec-01 Introduction to Optimization Details 50:13
Mod-01 Lec-02 System Design and Analysis Details 38:36
Mod-01 Lec-03 Workable system Details 40:51
Mod-01 Lec-04 System simulation Details 52:21
Mod-01 Lec-05 Information flow diagrams Details 36:32
Mod-01 Lec-06 Successive substitution method Details 49:57
Mod-01 Lec-07 Successive substitution method contd… Details 45:57
Mod-01 Lec-08 Successive substitution method and Newton-Raphson method Details 41:23
Mod-01 Lec-09 Newton-Raphson method contd… Details 40:4
Mod-01 Lec-10 Convergence characteristics of Newton-Raphson method Details 43:51
Mod-01 Lec-11 Newton-Raphson method for multiple variables Details 46:55
Mod-01 Lec-12 Solution of system of linear equations Details 48:10
Mod-01 Lec-13 Introduction to Curve fitting Details 0:46
Mod-01 Lec-14 Example for Lagrange interpolation Details 44:56
Mod-01 Lec-15 Lagrange interpolation contd… Details 45:43
Mod-01 Lec-16 Best fit Details 48:39
Mod-01 Lec-17 Least Square Regression Details 47:40
Mod-01 Lec-18 Least Square Regression contd….. Details 48:16
Mod-01 Lec-19 Least Square Regression contd….. Details 45:2
Mod-01 Lec-20 Non-linear Regression (Gauss – Newton Algorithm) Details 54:59
Mod-01 Lec-21 Optimization- Basic ideas Details 49:24
Mod-01 Lec-22 Properties of objective function and cardinal ideas in optimization Details 45:16
Mod-01 Lec-23 Unconstrained optimization Details 29:57
Mod-01 Lec-24 Constrained optimization problems Details 44:30
Mod-01 Lec-25 Mathematical proof of the Lagrange multiplier method Details 45:32
Mod-01 Lec-26 Test for Maxima/ Minima Details 49:11
Mod-01 Lec-27 Handling in-equality constraints Details 39:44
Mod-01 Lec-28 Kuhn-Tucker conditions contd… Details 51:30
Mod-01 Lec-29 Uni-modal function and search methods Details 51:10
Mod-01 Lec-30 Dichotomous search Details 49:18
Mod-01 Lec-31 Fibonacci search method Details 54:29
Mod-01 Lec-32 Reduction ratio of Fibonacci search method Details 50:6
Mod-01 Lec-33 Introduction to multi-variable optimization Details 50:42
Mod-01 Lec-34 The Conjugate gradient method Details 42:15
Mod-01 Lec-35 The Conjugate gradient method contd… Details 43:21
Mod-01 Lec-36 Linear programming Details 52:38
Mod-01 Lec-37 Dynamic programming Details 51:41
Mod-01 Lec-38 Genetic Algorithms Details 54:52
Mod-01 Lec-39 Genetic Algorithms contd… Details 58:16
Mod-01 Lec-40 Simulated Annealing and Summary Details 1:19:51

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