Soft Modeling of Complex Systems

1. Soft Modeling of Complex Systems P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi A Soft and virtual Power Plant ……

2. Modeling of Analytically Complex Systems • Learn input and output relations of a complex system under special conditions. • Identify the important input parameters and expected output parameters. • Look for soft modeling techniques. • Neural networks are trainable systems that can "learn" to solve complex problems • from a set of exemplars and • generalize the "acquired knowledge" to solve unforeseen problems. • They are self-adaptive systems containing the cognizance • The psychological result of perception and learning and reasoning is called cognition.

3. Neural Networks • Traditionally, the term neural network has been used to refer to a network of biological neurons. • In modern usage, the term is often used to refer to artificial neural networks, which are composed of artificial neurons or nodes. • Thus the term 'Neural Network' has two distinct connotations: • Biological neural networks are made up of real biological neurons that are connected or functionally • related in the peripheral nervous system or the central nervous system. • In the field of neuroscience, they are often identified as groups of neurons that perform a specific physiological function in laboratory analysis. • Artificial neural networks are made up of interconnecting artificial neurons (usually simplified neurons) designed to model (or mimic) some properties of biological neural networks.

4. View of Artificial Neural Networks Hidden Layer Input Output

5. Interactions of Artificial Neural Networks

6. Artifical Neural NETWORK ARCHITECTURE

7. ANN Models • These are essentially simple mathematical models defining a function. • Each type of ANN model corresponds to a class of such functions. • The network in artificial neural network • Arises because the function f(x) is defined as a composition of other functions gi(x), which can further be defined as a composition of other functions. • This can be conveniently represented as a network structure, with arrows depicting the dependencies between variables.

8. This figure depicts such a decomposition of f, with dependencies between variables indicated by arrows. • These can be interpreted in two ways. • The first view is the functional view: • the input x is transformed into a 3-dimensional vector h, which is then transformed into a 2-dimensional vector g, which is finally transformed into f. • This view is most commonly encountered in the context of optimization.

9. Radial Basis Function : ANN Model • RBF Networks have their origin in the solution of the multivariate interpolation or curve fitting problem. • These networks have traditionally only one hidden layer. • Properly trained, they can approximate an arbitrary function • where {wi; i = 1, . . . ,m} denotes the weights coefficients, w0 is the bias and • zj(x)represents the activation function (also known as radial basis function), which is given by:

10. Structure of Radial Function • f(·)is a non-linear function that monotonically decreases (or increases) as xmoves away from cj. • A common example of a radial basis function is the Gaussian function : Others are:

11. A Radial Basis Function Network

12. Example

13. Development, TRAINING AND TESTING • Combinations of data sets • Type of neural networks • Number of neurons : Hidden Variables • Learning parameters : Slope, momentum, spread • Number of iterations

14. A N N 1 FEGT Target value ANN Training for FEGT INPUTS #1 FG, coal, air, water and steam parameters Analytical Model

15. A N N 1 ANN TESTING FOR EFFICIENCY FEGT INPUTS #1 A N N 2 SG EFFICIENCY INPUTS #2

17. INPUTS FOR ANN1 : (Parameters for FEGT) • Feed Water flow • Mill combinations, • Burner tilt • Sec Air flow, • Wind Box to Furnace Differential Pressure • Oxygen in Flue Gas • Low NOx operations (Overfire damper control) • Coal quality (Coal flow/plant load) • Primary Air to Coal flow ratio • Air Differential Temperature across Air Heater

18. INPUTS FOR ANN2 : (Parameters for SG Efficiency) • Air Flow • Coal Flow, • Main Steam Press • Main Steam Temp, • FEGT • Feed Water Flow, • Feed Water Temp at Economizer Inlet • Oxygen in Flue Gas • Flue Gas Temp Air Heater Outlet • Air Ingress through Furnace (By Analytical Model)

19. SELECTION OF NETWORK ARCHITETURE

20. COMPARISON OF NW PERFORMANCE

21. ANN TRAINING PERFORMANCE FOR TRAINING ,TEST AND VALIDATION DATA

22. ANN SENSITIVITY OF O2 VS BOILER EFFICIENCY

25. ANN SENSITIVITY OF MW Vs EFFICIENCY

28. VARIATION IN ANN PREDICT VALUE WITH ACTUAL VALUE (

29. OPTIMIZATION AT 210 MW

30. OPTIMIZATION AT 150 MW