NeuroFyzzy Methods

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Neuro-Fyzzy Methods for Modeling and
Identification Part 2 Examples
Presented by Ali Maleki
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Presentation Agenda

• Introduction
• Tools for Fuzzy Identification and Modelling
• MATLAB Fuzzy Logic Toolbox ANFIS
• Fuzzy Modeling and Identification Toolbox
• Examples
• Example 1 Hair Dryer
• Example 2 Static Function
• Example 3 Neutralization Process

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Introduction

• Control Systems
• Competion
• Environment requirements
• Energy and material costs
• Demand for robust, fault-tolerant systems
• Extra needs for Effective process modeling
  techniques
• Conventional modeling?
• Lack precise and formal knowledg about
  the system
• Strongly nonlinear behavior,
• High degree of uncertainty,
• Time varying characteristics

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Introduction (cont.)

• Solution Neuro-fuzzy modeling
• A powerful tool which can facilitate the
  effective development of models by combining
  information from different source
• Empirical models
• Heuristics
• Data
• Neuro-fuzzy models
• Describe systems by means of fuzzy if-then rules
• Represented in a network structure
• Apply algorithms from the area of Neural Networks

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Introduction (cont.)
Zero-order TS fuzzy model
Typical membership function Input-output
equation
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Introduction (cont.)

• System identification steps
• Structure identification
• Parameter estimation
• choice of the models structure determines the
  flexibility of the model in the approximation of
  (unknown) systems
• model with a rich structure can approximate more
  complicated functions, but, will have worse
  generalization properties
• Good generalization means that a model fitted to
  one data set will also perform well on another
  data set from the same process.

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Tools for Fuzzy Modeling Identification

• Fuzzy Modelling and Identification Toolbox
• Develped by R. Babuska
• http//Lcewww.et.tudelft.nl/Babuska
• Installation
• Version 3.03 , April 2001
• Fuzzy Logic Toolbox for MATLAB
• www.Mathworks.com/products/fuzzylogic
• Version 2.1.3 , June 2004

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Fuzzy Modeling and Identification Toolbox
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Fuzzy Modeling and Identification Toolbox (cont.)
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Fuzzy Modeling and Identification Toolbox (cont.)
FMSIM function Simulate a MIMO input-output
fuzzy model
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Fuzzy Modeling and Identification Toolbox (cont.)
Structure of FM (fmstruct function)
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Fuzzy Modeling and Identification Toolbox (cont.)
Structure of FM (fmstruct function)
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Fuzzy Modeling and Identification Toolbox (cont.)
plotmfs function Plot membership functions rms
function Root mean square between two
signals vaf function Percentile variance
accounted for (VAF) between two signals
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MATLAB - Fuzzy Toolbox
anfis function Training routine for Sugeno-type
FIS anfisedit function Open the ANFIS Editor
GUI genfis1 function Generate an FIS structure
from data without data clustering genfis2
function Generate an FIS structure from data
using subtractive clustering
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MATLAB - Fuzzy Toolbox (cont.)
ANFIS Editor GUI
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Example 1 Hair Dryer (Fuzzy Logic Toolbox)

• Nonlinear dynamical system identification
• With use of ANFIS function in the Fuzzy Logic
  Toolbox
• Data set was obtained from a laboratory device
  called Feedback's Process Trainer PT 326,
• L. Ljung, "System Identification, Theory for the
  User", Prentice-Hall, 1987 Chapter 17
• The device's function is like a hair dryer
• Input u(k) Voltage over the mesh of resistor
  wires
• Output y(k) Outlet air temperature

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Input u(k) Binary random signal shifting
  between 3.41 and 6.41 V
• Output y(k) Outlet air temperature
• Sampling Time 0.08 sec

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Linear ARX model
• y(k)a1y(k-1)...amy(k-m)b1u(k-d)...bnu(k-
  d-n1)
• ai and bj are linear parameters to be determined
  by least-squares methods
• This structure is exactly specified by three
  integers m, n, d
• Remind
• System Identification structure selection
  parameter estimation

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Remove the means from the data
• The data set was divided into a training set and
  a checking set
• Training data set (k 1 to 300) Checking
  data set (k 301 to 600)
• An exhaustive search was performed to find the
  best combination m, n, d
• each of the integer is allowed to changed from 1
  to 10 independently
• Run through all different models
• V arxstruc(ze, zv, struc(110,
  110, 110))
• Find the best model nn selstruc(V,
  0)
• The best ARX model m, n, d 5, 10, 2

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Training RMSE 0.1122 Checking RMSE 0.0749

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Advantage of ARX model
• Rapid model structure selection
• Rapid parameter identification
• The performance in the above plots appear to be
  satisfactory.
• If a better performance level is desired, we
  might want to resort to a nonlinear model.
• Neuro-fuzzy modeling approach, ANFIS

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Use ANFIS for system identification
• First step input selection
• To determine which variables should be the input
  arguments to an ANFIS model.
• For simplicity, we suppose that there are 10
  input candidates
• y(k-1), y(k-2), y(k-3), y(k-4), u(k-1), u(k-2),
  u(k-3), u(k-4), u(k-5), u(k-6)
• Two approaches for input selection
• Sequential search
• Exhaustive search

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Sequential search for input selection can be
  done by the function seqsrch
• 10 9 8
• 27
• Selected inputs y(k-1), u(k-3), and u(k-4)
• Training RMSE 0.0609 Checking RMSE
  0.0604.

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Exhaustive search on all possible combinations
  of the input candidates
• Can be done by function exhsrch
• We want to selects 3 inputs from 10 candidates,
  therefore, the total number of ANFIS models is
• Fortunately, for dynamical system identification,
  we do know that the inputs should not come from
  either of the following two sets of input
  candidates exclusively
• Y y(k-1), y(k-2), y(k-3), y(k-4)
• U u(k-1), u(k-2), u(k-3), u(k-4), u(k-5),
  u(k-6)
• A reasonable guess two inputs from Y and one
  from U

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Exhaustive search
• Selected inputs y(k-1), y(k-2) , u(k-3)
• Training RMSE 0.0474 Checking RMSE
  0.0485

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• ARX model

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• ANFIS model

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Example 1 Hair Dryer (Fuzzy Logic Toolbox)
(cont.)

• Comparision
• If fast modeling is the goal, then ARX is the
  right choice,
• If precision is the utmost concern, then we can
  go for ANFIS that is designed for nonlinear
  modeling and higher precision

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Example 2 - Static Function
ANFIS model with linear consequent
function Number of rules five rules Construction
of initial model Gustafson-Kessel
algorithm Fit of the function with initial
model local models - membership functions
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Example 2 - Static Function (cont.)
this initial model can easily be interpreted in
terms of the local behavior It is reasonably
accurate (RMS 0.0258) ANFIS method, 100
learning epochs anfis function of the MATLAB
Fuzzy Logic Toolbox Fit of the function with
fine-tuned model, local models, membership
functions
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Example 2 - Static Function (cont.)
RMS error is about 23 times better than the
initial model Initial model Fine-tuned
model RMS error 0.0258 RMS error 0.0011
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Example 2 - Static Function (cont.)
after learning, the local models are much further
from the true local description of the
function Initial model Fine-tuned
model Fine-tuned model are thus less
accurate in describing the system locally
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Example 3 pH Neutralization Process
Influent streams
Acid Buffer Base
Neutralization tank
Effluent stream
Acid flowrate cteBuffer flowrate cteBase
stream flowrate
Neutralization tank
pH in the tank
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Example 3 - pH Neutralization Process (cont.)

• Identification and validation data sets
• Simulating the model by Hall and Seborg for
  random change of the influent base stream flow
  rate
• N 499 samples with the sampling time of 15 s.
• The process is approximated as a firstorder
  discrete-time NARX model

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Example 3 - pH Neutralization Process (cont.)
Membership functions Befor training
After training
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Example 3 - pH Neutralization Process (cont.)
Rules Initial Rules Fine Tuned Rules
after 1000 epochs of hybrid learning using the
ANFIS function of the MATLAB Fuzzy Logic Toolbox
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Example 3 - pH Neutralization Process (cont.)

• Overtraining Problem
• Comparision of RMS ERROR befor and after training
• Prediction befor and after training

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References
1 Robert Babuska, Neuro-Fuzzy Methods for
Modeling and Identification, Recent Advances in
Intelligent Paradigms and Application,
Springer-Verilag, 2002 2 Robert Babuska,
Fuzzy Modeling and Identification Toolbox Users
Guide - For Use with MATLAB, 1998. 3
MathWorks Inc., Fuzzy Logic Toolbox Users
Guide Version 2, 2004. 4 L. Ljung, System
Identification, Theory for the User,
Prentice-Hall, 1987.
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THANK YOU VERY MUCH For your Attention
Presented by Ali Maleki
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Introduction - appendix

• Types of fuzzy models (depending on the
  structure of if-then rules)
• Mamdani Model
• IF D1 is low and D2 is high THEN D is medium
• Takagi-Sugeno Model
• IF D1 is low and D2 is high THEN Dk
  (zero-order)
• IF D1 is low and D2 is high THEN
  D0.7D10.2D20.1 (first-order)