def cost_m1_only(theta):
M = np.eye(3)
M[0, 0] = theta[0]
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return np.linalg.norm(sol - measured)
def optiminum_plot(theta):
M = np.eye(3)
M[0, 0] = theta[0]
X0 = np.array([theta[1:4]]).T
Xd0 = np.array([theta[4:]]).T
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return sol
def cost_m1_init_cond_meas1_state(theta):
M = np.eye(3)
M[0, 0] = theta[0]
X0 = np.array([theta[1:4]]).T
Xd0 = np.array([theta[4:]]).T
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return np.linalg.norm(sol[:, -3] - measured[:, -3])
def cost_m1_init_cond_meas1_state(theta):
def K(t):
freq = 10
return Km + np.array([[1, -1, 0], [-1, 0, 0], [
0, 0, 1
]]) * theta[0] * 0.5 * (1 + sig.square(t * 2 * np.pi * freq))
X0 = np.array([theta[1:4]]).T
Xd0 = np.array([theta[4:]]).T
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return np.linalg.norm(sol[:, -3] - measured[:, -3])
def optiminum_plot(theta):
M = np.eye(3)
M[0, 0] = 1.5
X0 = np.array([theta[1:4]]).T
Xd0 = np.array([theta[4:]]).T
f = np.zeros((3, 1))
f[0, 0] = 100
def K(t):
freq = 10
return Km + np.array([[1, -1, 0], [-1, 0, 0], [
0, 0, 1
]]) * theta[0] * 0.5 * (1 + sig.square(t * 2 * np.pi * freq))
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return sol
C = np.array([[0.55, -0.2, 0], [-0.2, 0.55, -0.2], [0, -0.2, 0.35]])
M = np.eye(3)
M[0, 0] = 1.5
f = np.zeros((3, 1))
f[0, 0] = 100
X0 = np.zeros((3, 1))
Xd0 = np.ones((3, 1)) * 0.8
t = np.linspace(0, 10, 10000)
# Generate actual and measured response
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
true = lmm.solve_de("RK")
measured = np.random.normal(true, 0.16)
def cost_m1_init_cond_meas1_state(theta):
def K(t):
freq = 10
return Km + np.array([[1, -1, 0], [-1, 0, 0], [
0, 0, 1
]]) * theta[0] * 0.5 * (1 + sig.square(t * 2 * np.pi * freq))
X0 = np.array([theta[1:4]]).T
Xd0 = np.array([theta[4:]]).T
-------
freq: Frequency range
magnitude:
phase:
"""
d = data
length = len(d)
Y = np.fft.fft(d) / length
magnitude = np.abs(Y)[0:int(length / 2)]
phase = np.angle(Y)[0:int(length / 2)]
freq = np.fft.fftfreq(length, 1 / fs)[0:int(length / 2)]
return freq, magnitude, phase
solver = s.LMM_sys(PG.M, PG.C, PG.K, PG.T, X0, Xd0, timerange, solver_options={"beta_1": 0.55, "beta_2": 0.4})
#tnm = time.time()
#sol_nm = solver.solve_de("Newmark")
#print("Newmark time: ", time.time() - tnm)
trk = time.time()
sol = solver.solve_de("RK")
print("Runge Kutta time: ", time.time() - trk)
# t_stiff = time.time()
# sol = solver.solve_de("Radau")
# print("Radau time: ", time.time() - t_stiff)
# t_stiff = time.time()
# sol_bdf = solver.solve_de("BDF")
def sys_model_deterministic(m1):
M = np.eye(dim)
M[0, 0] = m1
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return sol[:, -1]
def make_measurements(m1):
M = np.eye(dim)
M[0, 0] = m1
lmm = s.LMM_sys(M, C, K, f, X0, Xd0, t)
sol = lmm.solve_de("RK")
return sol[:, -1]