NETWORKS AND FUZZY LOGIC
QUESTION ONE[Perceptron Dichotomiser] [ 50 marks ]
Two perceptron dichotomisers are trained to recognise the following classification of six patternsxwith known class membershipd.
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1.1 The first dichotomiser is a discrete perceptron as shown in Figure 1.1.Assign
-1 to all augmented inputs.For the training task of this dichotomiser the fixed correction rule is used with an arbitrary selection of learning constant 0.05 and the initial weight vector
Assume that the above training set may need to be recycled if necessary calculate the final weight vector.Show that this weight vector provides the correct classification of the entire training set.Plot the pattern error curve and the cycle error curve for 10 cycles (60 steps).
[ 25 marks ]
1.2 The second dichotomiser is a continuous perceptron with a bipolar logistic
all augmented inputs.For the training task of this dichotomiser the delta training rule is used with an arbitrary selection of learning constant 0.5
with the same initial weight vectorw1in Question 1.1.1Assuming that the above training set may need to be recycled if necessary
calculate the weight vectorw7after one cycle and the weight vectorw301after 50 cycles.Obtain the cycle error at the end of each cycle and plot the
cycle error curve.How would the weight vectorsw7andw301classify the entire training set? Discuss your results.
[ 25 marks ]
Note:The following formulae may be used to calculate the pattern error curve andthe cycle error curve.There are 6 patterns in this question i.e.P=6.
Figure 1.1Discrete Perceptron Classifier Training
Figure 1.2Continuous Perceptron Classifier Training2QUESTION TWO[ 50 marks ]
2.1[Flight Simulation][ 15 marks ]
A new jet aircraft are subjected to intensive flight simulation studies before they are tested under actual flight conditions.In these studies an important relationship is that between the mach number (percent of the speed of sound) and the altitude of the aircraft.This relationship is important to the performance of the aircraft and has a definite impact in making flight plans over populated areas.If certain mach levels are reached breaking the sound barrier (sonic booms) can result in human discomfort and light damage to glass enclosures on the earths surface.
Current rules of thumb establish crisp breakpoints for the conditions which cause performance changes in aircrafts but in reality these breakpoints are fuzzy because other atmospheric conditions such as the humidity and temperature also affect breakpoints in performance.For this problem suppose the flight test data can be characterised as near or approximately or in the region of the crisp database breakpoints.
and define a universe of altitudes asY8350840084508500855086008650 m and a fuzzy setAfor the altitude approximately 8500 m where
2.1.2 For another aircraft speed sayM1for the speed in the region of mach 0.74 where
2.1.3 For the speed in the region of mach 0.74 where
determine the corresponding altitude fuzzy setA1bM1Rusing the sum-
[5 marks]32.2[Laser Beam Alignment][ 35 marks ]
Fuzzy logic is used to control a two-axis mirror gimball for aligning a laser beam using a quadrant detector.Electronics sense the error in the position of the beam relative to the centre of the detector and produces two signals representing the x and y direction errors.The controller processes the error information using fuzzy logic and provides appropriate control voltages to run the motors which reposition the beam.The fuzzy logic controller for this system is shown in Figure 2.1.
To represent the error input to the controller a set of linguistic variables is chosen to represent 5 degrees of error 3 degrees of change of error and 5 degrees of armature voltage.Membership functions are constructed to represent the input and output values grades of membership as shown in Figure 2.2.The rule set in the form of Fuzzy Associative Memories is shown in Figure 2.3.
The controller gains are assumed to beGE1GCE1GU1.
2.2.1 If the Mean of Maximum (MOM) defuzzification strategy (sum-product inference) is used with the fire strengthiof the i-th rule calculated from
calculate the defuzzified output voltages of this fuzzy controller at a particular instant.The error and the change of error at this instant aree3.20 andce0.47.
2.2.2 If the Centre of Area (COA) defuzzification strategy (max-min inference) is used with the fire strengthiof the i-th rule calculated from
calculate the corresponding defuzzified output voltage at a particular instant when the error and the change of error aree3.20 andce0.47.
Figure 2.1Fuzzy logic control system4.gif>
Figure 2.2Membership functions of a laser beam alignment system
Figure 2.3Fuzzy Associative Memories