def generate_mf_group(self, G, x):
mf_group = {}
for (k, v) in G.iteritems():
shp = v['shp']
mf = v['mf']
if mf == 'trap':
mf_group[k] = trapmf(x, shp)
if mf == 'tri':
mf_group[k] = trimf(x, shp)
if mf == 'gbell':
mf_group[k] = gbellmf(x, shp[0], shp[1], shp[2])
if mf == 'gauss':
mf_group[k] = gaussmf(x, shp[0], shp[1])
if mf == 'gauss2':
mf_group[k] = gauss2mf(x, shp[0], shp[1])
if mf == 'sig':
mf_group[k] = sigmf(x, shp[0], shp[1])
if mf == 'psig':
mf_group[k] = psigmf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'zmf':
mf_group[k] = zmf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'smf':
mf_group[k] = smf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'pimf':
mf_group[k] = pimf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'piecemf':
mf_group[k] = piecemf(x, shp[0], shp[1], shp[2], shp[3])
return mf_group
def test_interp_membership():
x = np.r_[0:4.1:0.1]
mfx = trapmf(x, [0, 1, 2, 4])
yy = interp_membership(x, mfx, 0)
assert yy == 0
yy = interp_membership(x, mfx, 0.535)
assert_allclose(np.r_[yy], np.r_[0.535])
yy = interp_membership(x, mfx, np.pi / 3.)
assert yy == 1
yy = interp_membership(x, mfx, 2.718)
assert_allclose(np.r_[yy], np.r_[0.641])
assert_allclose(interp_membership(x, mfx, [0.2, 2.73, 3.14]),
np.asarray([interp_membership(x, mfx, i)
for i in [0.2, 2.73, 3.14]]))
mfx[-1] = 0.7
mfx[0] = 0.2
assert_allclose([0, 0], interp_membership(x, mfx, [-11, 5]))
assert_allclose([0.2, 0.7], interp_membership(x, mfx, [-11, 5],
False))
def _plot_mf_for(x):
'''Given the x-values, plot a series of example membership functions'''
tests = OrderedDict([
# Gaussians:
('gauss', skmemb.gaussmf(x, 50, 10)),
('left gauss', leftgaussmf(x, 50, 10)),
('right gauss', rightgaussmf(x, 50, 10)),
# Triangles:
('triangular', skmemb.trimf(x, [25, 50, 75])),
('left linear', leftlinearmf(x, 25, 75)),
('right linear', rightlinearmf(x, 25, 75)),
# fuzzylite:
('cosine', cosinemf(x, 50, 50)),
('inc concave', concavemf(x, 50, 75)),
('dec concave', concavemf(x, 50, 25)),
('spike', spikemf(x, 50, 50)),
('inc ramp', rampmf(x, 25, 75)),
('dec ramp', rampmf(x, 75, 25)),
# Rectangle-ish
('trapezoid', skmemb.trapmf(x, [20, 40, 60, 80])),
('rectangle', rectanglemf(x, 25, 75)),
('singleton', singletonmf(x, 50)),
])
# Example point sets:
ps_tests = [[(40, 0.5), (60, 1)],
[(10, 0.5), (25, 0.25), (40, 0.75), (80, .5)],
[(0, 1), (40, 0.25), (50, .5), (99, 0)]]
# Now try some interpolation methods on these:
for method in ['linear', 'lagrange', 'spline', 'cubic']:
tests.update([('{} ex{}'.format(method, i), pointsetmf(x, ps, method))
for i, ps in enumerate(ps_tests)])
return tests
def generate_mf_group(self, G, x):
mf_group = {}
for (k, v) in G.iteritems():
shp = v['shp']
mf = v['mf']
if mf == 'trap':
mf_group[k] = trapmf(x, shp)
if mf == 'tri':
mf_group[k] = trimf(x, shp)
if mf == 'gbell':
mf_group[k] = gbellmf(x, shp[0], shp[1], shp[2])
if mf == 'gauss':
mf_group[k] = gaussmf(x, shp[0], shp[1])
if mf == 'gauss2':
mf_group[k] = gauss2mf(x, shp[0], shp[1])
if mf == 'sig':
mf_group[k] = sigmf(x, shp[0], shp[1])
if mf == 'psig':
mf_group[k] = psigmf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'zmf':
mf_group[k] = zmf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'smf':
mf_group[k] = smf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'pimf':
mf_group[k] = pimf(x, shp[0], shp[1], shp[2], shp[3])
if mf == 'piecemf':
mf_group[k] = piecemf(x, shp[0], shp[1], shp[2], shp[3])
return mf_group
def test_trapmf():
x = np.arange(-4, 3.1, 0.1)
abcd = (-4, -4, 2, np.pi)
expected = np.ones_like(x)
idx = np.logical_and(x > 2, x < np.pi)
expected[idx] = np.interp(x[idx], np.r_[2, np.pi], np.r_[1, 0])
expected[x > np.pi] = 0
test = trapmf(x, abcd)
assert_allclose(test, expected)
def test_trapmf():
x = np.arange(-4, 3.1, 0.1)
abcd = (-4, -4, 2, np.pi)
expected = np.ones_like(x)
idx = np.logical_and(x > 2, x < np.pi)
expected[idx] = np.interp(x[idx], np.r_[2, np.pi], np.r_[1, 0])
expected[x > np.pi] = 0
test = trapmf(x, abcd)
assert_allclose(test, expected)
def test_interp_membership():
x = np.r_[0:4.1:0.1]
mfx = trapmf(x, [0, 1, 2, 4])
yy = interp_membership(x, mfx, 0)
assert yy == 0
yy = interp_membership(x, mfx, 0.535)
assert_allclose(np.r_[yy], np.r_[0.535])
yy = interp_membership(x, mfx, np.pi / 3.)
assert yy == 1
yy = interp_membership(x, mfx, 2.718)
assert_allclose(np.r_[yy], np.r_[0.641])
def test_interp_membership():
x = np.r_[0:4.1:0.1]
mfx = trapmf(x, [0, 1, 2, 4])
yy = interp_membership(x, mfx, 0)
assert yy == 0
yy = interp_membership(x, mfx, 0.535)
assert_allclose(np.r_[yy], np.r_[0.535])
yy = interp_membership(x, mfx, np.pi / 3.)
assert yy == 1
yy = interp_membership(x, mfx, 2.718)
assert_allclose(np.r_[yy], np.r_[0.641])
def test_interp_universe():
x = np.r_[0:4.1:0.1]
mfx = trapmf(x, [0, 1, 2, 4])
xx = interp_universe(x, mfx, 0.5)
assert_allclose(xx, [0.5, 3])
xx = interp_universe(x, mfx, 0.0)
assert_allclose(xx, [0, 4])
xx = interp_universe(x, mfx, 1.5)
assert len(xx) == 0
xx = interp_universe(x, mfx, 0.3)
y = [interp_membership(x, mfx, value) for value in xx]
assert_allclose(y, 0.3)
ax[2].set_ylabel('Control u')
ax[2].set_title('Fuzzy logic control action u')
fig.suptitle('Simulation. Gain K = ' + str(K))
plt.show()
return xx1, xx2, uu, tt
if __name__ == '__main__':
"""
These functions represent an inverted pendulum.
"""
# Membership Matrices
x1 = np.arange(-10, 10.1, 0.1) # Angle range, 1d array, length N, Fuzzy state variable #1.
N1 = trapmf(x1, [-10, -10, -2, 0]) # Negative membership function
Z1 = trimf(x1, [-2, 0, 2]) # Zero membership function
P1 = trapmf(x1, [0, 2, 10, 10]) # Positive membership function
M1 = np.vstack((N1, Z1, P1)) # Input 1 membership matrix, 2d array, shape (Q1, N), Matrix with Q1 membership functions for x1.
x2 = np.arange(-10, 10.1, 0.1) # Angular velocity range, 1d array, length M, Fuzzy state variable #2.
N2 = trapmf(x2, [-10, -10, -2, 0]) # Negative membership function
Z2 = trimf(x2, [-2, 0, 2]) # Zero membership function
P2 = trapmf(x2, [0, 2, 10, 10]) # Positive membership function
M2 = np.vstack((N2, Z2, P2)) # Input 2 membership matrix, 2d array, shape (Q2, M), Matrix with Q2 membership functions for x2.
# Fuzzy control (u) and member functions
u = np.arange(-25, 25.25, 0.25) # Fuzzy control output variable, 1d array, length U, Feedback control action variable.
NBu = trapmf(u, [-25, -25, -16, -8]) # Big Negative` membership function
Nu = trimf(u, [-16, -8, 0]) # Negative` membership function
Zu = trimf(u, [-8, 0, 8]) # Zero` membership function
import numpy as np import skfuzzy as fuzz import skfuzzy.membership as mf import matplotlib.pyplot as plt x_tempTest = np.arange(0, 101, 1) x_firmTest = np.arange(0, 101, 1) y_quality = np.arange(0, 101, 1) temp_low = mf.trapmf(x_tempTest, [0, 0, 10, 40]) temp_med = mf.trimf(x_tempTest, [20, 50, 80]) temp_hig = mf.trapmf(x_tempTest, [60, 90, 100, 100]) firm_low = mf.trimf(x_firmTest, [0, 0, 40]) firm_med = mf.trimf(x_firmTest, [30, 50, 70]) firm_hig = mf.trimf(x_firmTest, [60, 100, 100]) #result_no = mf.trimf(y_quality, [0, 0, 100]) #result_ok = mf.trimf(y_quality, [0, 100, 100]) quality_verylow = mf.trimf(y_quality, [0, 0, 25]) quality_bitlow = mf.trimf(y_quality, [0, 25, 50]) quality_middle = mf.trimf(y_quality, [25, 50, 75]) quality_bithigh = mf.trimf(y_quality, [50, 75, 100]) quality_veryhig = mf.trimf(y_quality, [75, 100, 100]) fig, (ax0, ax1, ax2) = plt.subplots(nrows=3, figsize=(6, 10)) ax0.plot(x_tempTest, temp_low, 'r', linewidth=2, label='Düşük') ax0.plot(x_tempTest, temp_med, 'g', linewidth=2, label='Orta') ax0.plot(x_tempTest, temp_hig, 'b', linewidth=2, label='Yüksek')
def __init__(self):
# Create input and output variables
self.lsonar = ctrl.Antecedent(self.sonar_interval, 'lsonar')
self.rsonar = ctrl.Antecedent(self.sonar_interval, 'rsonar')
self.last_theta = ctrl.Antecedent(self.theta_interval, 'last_theta')
self.theta = ctrl.Consequent(self.theta_interval, 'theta')
self.v_x = ctrl.Consequent(self.v_interval, 'v_x')
# we need membership functions!
distance_levels = ['dangerous', 'unsafe', 'safe']
theta_directions = ['left', 'centre', 'right']
velocity_levels = ['slow', 'medium', 'fast']
self.lsonar.automf(names=distance_levels)
self.rsonar.automf(names=distance_levels)
self.last_theta.automf(names=theta_directions)
self.theta.automf(names=theta_directions)
self.v_x.automf(names=velocity_levels)
low_mshp = mshp.trimf(self.sonar_interval, [0.25, 0.25, 0.31])
mid_mshp = mshp.trimf(self.sonar_interval, [0.28, 0.35, 0.45])
high_mshp = mshp.trapmf(self.sonar_interval, [0.4, 0.6, 2.55, 2.55])
self.lsonar['dangerous'] = low_mshp
self.lsonar['unsafe'] = mid_mshp
self.lsonar['safe'] = high_mshp
self.rsonar['dangerous'] = low_mshp
self.rsonar['unsafe'] = mid_mshp
self.rsonar['safe'] = high_mshp
left_angle_mshp = mshp.gaussmf(self.theta_interval, 0.7, 0.2)
centre_angle_mshp = mshp.gaussmf(self.theta_interval, 0, 0.1)
right_angle_mshp = mshp.gaussmf(self.theta_interval, -0.7, 0.2)
self.theta['left'] = left_angle_mshp
self.theta['centre'] = centre_angle_mshp
self.theta['right'] = right_angle_mshp
self.last_theta['left'] = left_angle_mshp
self.last_theta['centre'] = centre_angle_mshp
self.last_theta['right'] = right_angle_mshp
self.v_x['slow'] = mshp.trimf(self.v_interval, [0, 0, 0.32])
self.v_x['medium'] = mshp.gaussmf(self.v_interval, 0.5, 0.36)
self.v_x['fast'] = mshp.trapmf(self.v_interval, [0.75, 0.95, 1.0, 1.0])
# Here the rules are defined!
# look at http://pythonhosted.org/scikit-fuzzy/auto_examples/plot_control_system_advanced.html#set-up-the-fuzzy-control-system
# and http://pythonhosted.org/scikit-fuzzy/auto_examples/plot_tipping_problem_newapi.html
# for good examples
rules = []
# Sonars are NOT dangerous, go fast and forward
rules.append(ctrl.Rule(label="FastAndForward",
antecedent=(~self.lsonar['dangerous'] & ~self.rsonar['dangerous']),
consequent=(self.theta['centre'], self.v_x['fast'])))
# Right sonar reads dangerous, left does not, steer left
rules.append(ctrl.Rule(label="SteerLeftCaution",
antecedent=(~self.lsonar['dangerous'] & self.rsonar['dangerous']),
consequent=(self.theta['left'], self.v_x['slow'])))
# Left sonar reads dangerous, right does not, steer left
rules.append(ctrl.Rule(label="SteerRightCaution",
antecedent=(self.lsonar['dangerous'] & ~self.rsonar['dangerous']),
consequent=(self.theta['right'], self.v_x['slow'])))
# Right sonar is NOT safe, left reads safe, turn left full speed
rules.append(ctrl.Rule(label="SteerLeftReckless",
antecedent=(self.lsonar['safe'] & ~self.rsonar['safe']),
consequent=(self.theta['left'], self.v_x['fast'])))
# Left sonar is NOT safe, right reads safe, turn right full speed
rules.append(ctrl.Rule(label="SteerRightReckless",
antecedent=(~self.lsonar['safe'] & self.rsonar['safe']),
consequent=(self.theta['right'], self.v_x['fast'])))
# Left sonar is NOT dangerous and right is NOT safe, turn left medium speed
rules.append(ctrl.Rule(label="SteerLeftWatchSpeed",
antecedent=(~self.lsonar['dangerous'] & ~self.rsonar['safe']),
consequent=(self.theta['left'], self.v_x['medium'])))
# Right sonar is NOT dangerous and left is NOT safe, turn right medium speed
rules.append(ctrl.Rule(label="SteerRightWatchSpeed",
antecedent=(~self.lsonar['safe'] & ~self.rsonar['dangerous']),
consequent=(self.theta['right'], self.v_x['medium'])))
# Last theta was right, right sonar is dangerous, turn left slow speed
rules.append(ctrl.Rule(label="SteerLeftMedSpeed",
antecedent=(self.rsonar['dangerous'] & self.last_theta['right']),
consequent=(self.theta['left'], self.v_x['medium'])))
# Last theta was left, left sonar is dangerous, turn right slow speed
rules.append(ctrl.Rule(label="SteerRightMedSpeed",
antecedent=(self.lsonar['dangerous'] & self.last_theta['left']),
consequent=(self.theta['right'], self.v_x['medium'])))
# Last theta was left, rsonar reads not dangerous, turn centre, full speed
rules.append(ctrl.Rule(label="OutOfDangerFromLeft",
antecedent=(~self.rsonar['dangerous'] & self.last_theta['left']),
consequent=(self.theta['centre'], self.v_x['fast'])))
# Last theta was right, lsonar reads not dangerous, turn centre, full speed
rules.append(ctrl.Rule(label="OutOfDangerFromRight",
antecedent=(~self.lsonar['dangerous'] & self.last_theta['right']),
consequent=(self.theta['centre'], self.v_x['fast'])))
# Create the control system
self.system = ctrl.ControlSystem(rules=rules)
# System is created, just create a simulation, input values and call compute()
self.sim = ctrl.ControlSystemSimulation(self.system)
import numpy as np from skfuzzy import control as ctrl from skfuzzy import membership as mf speed = ctrl.Antecedent(np.arange(0, 85, 0.1), 'speed') distance = ctrl.Antecedent(np.arange(0, 3000, 0.5), 'distance') brake = ctrl.Consequent(np.arange(0, 100, 0.5), 'brake') throttle = ctrl.Consequent(np.arange(0, 100, 0.5), 'throttle') speed['stopped'] = mf.trimf(speed.universe, [0, 0, 2]) speed['very slow'] = mf.trimf(speed.universe, [1, 2.5, 4]) speed['slow'] = mf.trimf(speed.universe, [2.5, 6.5, 10.5]) speed['medium fast'] = mf.trimf(speed.universe, [6.5, 26.5, 46.5]) speed['fast'] = mf.trapmf(speed.universe, [26.5, 70, 85, 85]) distance['at'] = mf.trimf(distance.universe, [0, 0, 2]) distance['very near'] = mf.trimf(distance.universe, [1, 3, 5]) distance['near'] = mf.trimf(distance.universe, [3, 101.5, 200]) distance['medium far'] = mf.trimf(distance.universe, [100, 1550, 3000]) distance['far'] = mf.trapmf(distance.universe, [1500, 2250, 3000, 3000]) brake['no'] = mf.trimf(brake.universe, [0, 0, 40]) brake['very slight'] = mf.trimf(brake.universe, [20, 50, 80]) brake['slight'] = mf.trimf(brake.universe, [70, 83.5, 97]) brake['medium'] = mf.trimf(brake.universe, [95, 97, 99]) brake['full'] = mf.trimf(brake.universe, [98, 100, 100]) throttle['no'] = mf.trimf(throttle.universe, [0, 0, 2]) throttle['very slight'] = mf.trimf(throttle.universe, [1, 3, 5]) throttle['slight'] = mf.trimf(throttle.universe, [3, 16.5, 30]) throttle['medium'] = mf.trimf(throttle.universe, [20, 50, 80])
import matplotlib.pyplot as plt
import skfuzzy.membership as skmemb
def visualise_all(x, y1, y2, all_norms=_all_norms):
'''Plot the norm and conorm for the given sample inputs'''
ncols = 3
fig, axes = plt.subplots(nrows=len(all_norms), ncols=ncols, figsize=(8, 9))
fig.tight_layout()
fig.subplots_adjust(bottom=-.25)
for row, name in enumerate(_all_norms.keys()):
for col in range(ncols): # so all have the same (0,1) y-axis
axes[row][col].set_ylim([-0.05, 1.05])
axes[row][0].set_title('Sample inputs')
axes[row][0].plot(x, y1)
axes[row][0].plot(x, y2)
axes[row][1].set_title(name + ' norm')
axes[row][1].plot(x, _all_norms[name].and_func(y1, y2))
axes[row][2].set_title(name + ' co-norm')
axes[row][2].plot(x, _all_norms[name].or_func(y1, y2))
if __name__ == '__main__':
for fam in _all_norms.values():
check_classic(fam)
check_duality(fam)
sample_x = np.arange(0, 100)
sample_y1 = skmemb.trapmf(sample_x, [15, 30, 55, 75])
sample_y2 = skmemb.trapmf(sample_x, [25, 45, 70, 85])
visualise_all(sample_x, sample_y1, sample_y2)
import matplotlib.pyplot as plt # In[45]: x_bodytemp = np.arange(20, 50 , 1) x_respiratory = np.arange(0, 50 , 1) x_pulse = np.arange(0, 150 , 1) y_areacolour = np.arange(0, 4, 1) # In[46]: bodytemp_verylow = mf.trapmf(x_bodytemp, [-100, 0, 30, 34.5]) bodytemp_low = mf.trapmf(x_bodytemp, [0, 34.5, 35 ,36 ]) bodytemp_normal = mf.trimf(x_bodytemp, [36, 36.5, 37]) bodytemp_high = mf.trapmf(x_bodytemp, [36, 38, 41, 42]) bodytemp_veryhigh = mf.trapmf(x_bodytemp, [41, 42,45, 100]) # In[47]: respiratory_low = mf.trimf(x_respiratory, [-100, 0, 12]) respiratory_normal = mf.trapmf(x_respiratory, [8, 12, 20, 24]) respiratory_high = mf.trimf(x_respiratory, [20, 50, 100]) # In[48]:
