Parameter Estimation of RIG Roll Experiments

Setup and descriptions

Without ACM model
Turn on wind tunnel
Only 1DoF for RIG roll movement
Use small-amplitude aileron command of CMP as inputs (in degrees) $$U = \delta_{a,cmp}(t)$$
Consider RIG roll angle and its derivative as States (in radians) $$X = \begin{pmatrix} \phi_{rig} \\ \dot{\phi}_{rig} \end{pmatrix}$$
Observe RIG roll angle and its derivative as Outputs (in degrees) $$Z = \begin{pmatrix} \phi_{rig} \\ \dot{\phi}_{rig} \end{pmatrix}$$
Use output error method based on most-likehood(ML) to estimate $$ \theta = \begin{pmatrix} C_{l,\delta_a,cmp} \\ C_{lp,cmp} \end{pmatrix} $$

Startup computation engines



In [1]:

    
%run matt_startup
%run -i matt_utils

button_qtconsole()

#import other needed modules in all used engines
#with dview.sync_imports():
#   import os









    



importing numpy on engine(s)
importing scipy on engine(s)
importing matplotlib on engine(s)
importing scipy.integrate on engine(s)
importing scipy.interpolate on engine(s)
importing math on engine(s)
importing time on engine(s)
importing itertools on engine(s)
importing random on engine(s)






    



:0: FutureWarning: IPython widgets are experimental and may change in the future.

Data preparation

Load raw data



In [2]:

    
filename = 'FIWT_Exp052_20150616144645.dat.npz'

def loadData():
    # Read and parse raw data
    global exp_data
    exp_data = np.load(filename)

    # Select colums
    global T_cmp, da1_cmp, da2_cmp, da3_cmp , da4_cmp
    T_cmp = exp_data['data33'][:,0]
    da1_cmp = exp_data['data33'][:,3]
    da2_cmp = exp_data['data33'][:,5]
    da3_cmp = exp_data['data33'][:,7]
    da4_cmp = exp_data['data33'][:,9]

    global T_rig, phi_rig
    T_rig = exp_data['data44'][:,0]
    phi_rig = exp_data['data44'][:,2]

loadData()



In [3]:

    
text_loadData()



In [4]:

    
V = exp_data['data44'][:,13]
%matplotlib inline
plt.plot(T_rig, V*1.05)
plt.ylim((28,32))









    Out[4]:





(28, 32)

Check time sequence and inputs/outputs

Click 'Check data' button to show the raw data.

Click on curves to select time point and push into queue; click 'T/s' text to pop up last point in the queue; and click 'Output' text to print time sequence table.



In [5]:

    
def checkInputOutputData():

    #check inputs/outputs
    fig, ax = plt.subplots(2,1,True)
    ax[0].plot(T_cmp,da1_cmp,'r', T_cmp,da2_cmp,'g',
               T_cmp,da3_cmp,'b', T_cmp,da4_cmp,'m',
               picker=1)
    ax[1].plot(T_rig,phi_rig, 'b', picker=2)
    ax[0].set_ylabel('$\delta \/ / \/ ^o$')
    ax[1].set_ylabel('$\phi \/ / \/ ^o/s$')
    ax[1].set_xlabel('$T \/ / \/ s$', picker=True)
    ax[0].set_title('Output', picker=True)
    

    fig.canvas.mpl_connect('pick_event', onPickTime)
    fig.show()
    display(fig)

button_CheckData()

Input $\delta_T$ and focused time ranges



In [6]:

    
# Pick up focused time ranges
time_marks = [
[18.8573202878,137.312699085,"ramp cmp4 u"],
[141.408935166,260.27090166,"ramp cmp4 d"],
[265.592177186,384.456691192,"ramp cmp3 u"],
[391.487466737,509.969548357,"ramp cmp3 d"],
[518.478950349,638.264844453,"ramp cmp2 u"],
[644.71182051,763.983487372,"ramp cmp2 d"],
[770.300044567,889.812031944,"ramp cmp1 u"],
[895.995020394,1014.85848293,"ramp cmp1 d"],
[1022.19234822,1141.45367229,"ramp cmp4 d"],
[1145.14958662,1265.23165475,"ramp cmp4 u"],
[1279.28149733,1397.62176653,"ramp cmp3 u"],
[1411.53843282,1530.01180295,"ramp cmp2 d"],
[1536.98628003,1657.06650374,"ramp cmp2 u"],
[1671.68321255,1792.31335791,"ramp cmp1 d"],
[1798.33449076,1918.9341565,"ramp cmp1 u"],
]

# Decide DT,U,Z and their processing method
DT=0.2
process_set = {
            'U':[(T_cmp, da1_cmp,0),
                (T_cmp, da2_cmp,0),
                (T_cmp, da3_cmp,0),
                (T_cmp, da4_cmp,0),],
            'Z':[(T_rig, phi_rig,1),],
            'cutoff_freq': 1 #Hz
           }

U_names = ['$\delta_{a1,cmp} \, / \, ^o$',
          '$\delta_{a2,cmp} \, / \, ^o$',
          '$\delta_{a3,cmp} \, / \, ^o$',
          '$\delta_{a4,cmp} \, / \, ^o$']
Y_names = Z_names = ['$\phi_{a,rig} \, / \, ^o$']

display_data_prepare()









    





$$\delta_T=200.0(ms)$$






    




Time ranges






    




Idx Start(s) Spam(s) Description
0 18.86 118.46 ramp cmp4 u
1 141.41 118.86 ramp cmp4 d
2 265.59 118.86 ramp cmp3 u
3 391.49 118.48 ramp cmp3 d
4 518.48 119.79 ramp cmp2 u
5 644.71 119.27 ramp cmp2 d
6 770.30 119.51 ramp cmp1 u
7 896.00 118.86 ramp cmp1 d
8 1022.19 119.26 ramp cmp4 d
9 1145.15 120.08 ramp cmp4 u
10 1279.28 118.34 ramp cmp3 u
11 1411.54 118.47 ramp cmp2 d
12 1536.99 120.08 ramp cmp2 u
13 1671.68 120.63 ramp cmp1 d
14 1798.33 120.60 ramp cmp1 u






    




$U$
$\delta_{a1,cmp} \, / \, ^o$
$\delta_{a2,cmp} \, / \, ^o$
$\delta_{a3,cmp} \, / \, ^o$
$\delta_{a4,cmp} \, / \, ^o$






    




$Z$
$\phi_{a,rig} \, / \, ^o$

Resample and filter data in sections

For each section,

Select time range and shift it to start from zero;
Resample Time, Inputs, Outputs in unique $\delta_T$;
Smooth Input/Observe data if flag bit0 is set;
Take derivatives of observe data if flag bit1 is set.



In [7]:

    
resample(True);

Define dynamic model to be estimated

$$\left\{\begin{matrix}\begin{align} M_{x,rig} &= M_{x,a} + M_{x,f} + M_{x,cg} = 0 \\ M_{x,a} &= \frac{1}{2} \rho V^2S_cb_c C_{la,cmp}\delta_{a,cmp} \\ M_{x,f} &= -F_c \, sign(\dot{\phi}_{rig}) \\ M_{x,cg} &= -m_T g l_{zT} \sin \left ( \phi - \phi_0 \right ) \end{align}\end{matrix}\right.$$



In [19]:

    
%%px --local
#update common const parameters in all engines

angles = range(-40,41,5)
angles[0] -= 1
angles[-1] += 1
del angles[angles.index(0)]
angles_num = len(angles)

#problem size
Nx = 0
Nu = 4
Ny = 1
Npar = 4*angles_num+1

#reference
S_c = 0.1254   #S_c(m2) 
b_c = 0.7      #b_c(m)
g = 9.81       #g(m/s2)

#static measurement
m_T = 9.585   #m_T(kg)
l_z_T = 0.0416 #l_z_T(m)
V = 30         #V(m/s)

#previous estimations
F_c = 0.06 #F_c(N*m)
Clda_cmp = -0.2966 #Clda_cmp(1/rad)

#for short
qbarSb = 0.5*1.225*V*V*S_c*b_c
_m_T_l_z_T_g = -(m_T*l_z_T)*g


def obs(Z,T,U,params):
    s = T.size
    
    k1 = np.array(params[0:angles_num])
    k2 = np.array(params[angles_num:angles_num*2])
    k3 = np.array(params[angles_num*2:angles_num*3])
    k4 = np.array(params[angles_num*3:angles_num*4])
    phi0 = params[-1]

    Clda1 = scipy.interpolate.interp1d(angles, Clda_cmp*0.00436332313*k1*angles,assume_sorted=True)
    Clda2 = scipy.interpolate.interp1d(angles, Clda_cmp*0.00436332313*k2*angles,assume_sorted=True)
    Clda3 = scipy.interpolate.interp1d(angles, Clda_cmp*0.00436332313*k3*angles,assume_sorted=True)
    Clda4 = scipy.interpolate.interp1d(angles, Clda_cmp*0.00436332313*k4*angles,assume_sorted=True)
    
    moments_a = qbarSb*(Clda1(U[:s,0])+Clda2(U[:s,1])
                       +Clda3(U[:s,2])+Clda4(U[:s,3]))

    phi = phi0+np.arcsin(np.clip(-moments_a/_m_T_l_z_T_g, -1, 1))
    
    return (phi*57.3).reshape((-1,1))



In [20]:

    
display(HTML('<b>Constant Parameters</b>'))
table = ListTable()
table.append(['Name','Value','unit'])
table.append(['$S_c$',S_c,'$m^2$'])
table.append(['$b_c$',b_c,'$m$'])
table.append(['$g$',g,'$m/s^2$'])
table.append(['$m_T$',m_T,'$kg$'])
table.append(['$l_{zT}$',l_z_T,'$m$'])
table.append(['$V$',V,'$m/s$'])
table.append(['$F_c$',F_c,'$Nm$'])
table.append(['$C_{l \delta a,cmp}$',Clda_cmp,'$rad^{-1}$'])
display(table)









    




Constant Parameters






    




Name Value unit
$S_c$ 0.1254 $m^2$
$b_c$ 0.7 $m$
$g$ 9.81 $m/s^2$
$m_T$ 9.585 $kg$
$l_{zT}$ 0.0416 $m$
$V$ 30 $m/s$
$F_c$ 0.06 $Nm$
$C_{l \delta a,cmp}$ -0.2966 $rad^{-1}$

Initial guess

Input default values and ranges for parameters
Select sections for trainning
Adjust parameters based on simulation results
Decide start values of parameters for optimization



In [21]:

    
#initial guess
param0 = [1]*(4*angles_num)+[0]

param_name = ['k_{}_{}'.format(i/angles_num+1, angles[i%angles_num]) for i in range(4*angles_num)] + ['$phi_0$']
param_unit = ['1']*(4*angles_num) + ['$rad$']

NparID = Npar
opt_idx = range(Npar)
opt_param0 = [param0[i] for i in opt_idx]
par_del = [0.001]*(4*angles_num) + [0.0001]
bounds =  [(0,1.5)]*(4*angles_num) +[(-0.1, 0.1)]
display_default_params()

#select sections for training
section_idx = range(14)
display_data_for_train()

#push parameters to engines
push_opt_param()









    




Default Parameters for optimization






    




Idx Description $x_0$ unit opt $\delta_{par}$ min max
0 k_1_-41 1 1 * 0.001 0 1.5
1 k_1_-35 1 1 * 0.001 0 1.5
2 k_1_-30 1 1 * 0.001 0 1.5
3 k_1_-25 1 1 * 0.001 0 1.5
4 k_1_-20 1 1 * 0.001 0 1.5
5 k_1_-15 1 1 * 0.001 0 1.5
6 k_1_-10 1 1 * 0.001 0 1.5
7 k_1_-5 1 1 * 0.001 0 1.5
8 k_1_5 1 1 * 0.001 0 1.5
9 k_1_10 1 1 * 0.001 0 1.5
10 k_1_15 1 1 * 0.001 0 1.5
11 k_1_20 1 1 * 0.001 0 1.5
12 k_1_25 1 1 * 0.001 0 1.5
13 k_1_30 1 1 * 0.001 0 1.5
14 k_1_35 1 1 * 0.001 0 1.5
15 k_1_41 1 1 * 0.001 0 1.5
16 k_2_-41 1 1 * 0.001 0 1.5
17 k_2_-35 1 1 * 0.001 0 1.5
18 k_2_-30 1 1 * 0.001 0 1.5
19 k_2_-25 1 1 * 0.001 0 1.5
20 k_2_-20 1 1 * 0.001 0 1.5
21 k_2_-15 1 1 * 0.001 0 1.5
22 k_2_-10 1 1 * 0.001 0 1.5
23 k_2_-5 1 1 * 0.001 0 1.5
24 k_2_5 1 1 * 0.001 0 1.5
25 k_2_10 1 1 * 0.001 0 1.5
26 k_2_15 1 1 * 0.001 0 1.5
27 k_2_20 1 1 * 0.001 0 1.5
28 k_2_25 1 1 * 0.001 0 1.5
29 k_2_30 1 1 * 0.001 0 1.5
30 k_2_35 1 1 * 0.001 0 1.5
31 k_2_41 1 1 * 0.001 0 1.5
32 k_3_-41 1 1 * 0.001 0 1.5
33 k_3_-35 1 1 * 0.001 0 1.5
34 k_3_-30 1 1 * 0.001 0 1.5
35 k_3_-25 1 1 * 0.001 0 1.5
36 k_3_-20 1 1 * 0.001 0 1.5
37 k_3_-15 1 1 * 0.001 0 1.5
38 k_3_-10 1 1 * 0.001 0 1.5
39 k_3_-5 1 1 * 0.001 0 1.5
40 k_3_5 1 1 * 0.001 0 1.5
41 k_3_10 1 1 * 0.001 0 1.5
42 k_3_15 1 1 * 0.001 0 1.5
43 k_3_20 1 1 * 0.001 0 1.5
44 k_3_25 1 1 * 0.001 0 1.5
45 k_3_30 1 1 * 0.001 0 1.5
46 k_3_35 1 1 * 0.001 0 1.5
47 k_3_41 1 1 * 0.001 0 1.5
48 k_4_-41 1 1 * 0.001 0 1.5
49 k_4_-35 1 1 * 0.001 0 1.5
50 k_4_-30 1 1 * 0.001 0 1.5
51 k_4_-25 1 1 * 0.001 0 1.5
52 k_4_-20 1 1 * 0.001 0 1.5
53 k_4_-15 1 1 * 0.001 0 1.5
54 k_4_-10 1 1 * 0.001 0 1.5
55 k_4_-5 1 1 * 0.001 0 1.5
56 k_4_5 1 1 * 0.001 0 1.5
57 k_4_10 1 1 * 0.001 0 1.5
58 k_4_15 1 1 * 0.001 0 1.5
59 k_4_20 1 1 * 0.001 0 1.5
60 k_4_25 1 1 * 0.001 0 1.5
61 k_4_30 1 1 * 0.001 0 1.5
62 k_4_35 1 1 * 0.001 0 1.5
63 k_4_41 1 1 * 0.001 0 1.5
64 $phi_0$ 0 $rad$ * 0.0001 -0.1 0.1






    




Training Data






    




Idx Start(s) Spam(s) Description
0 18.86 118.46 ramp cmp4 u
1 141.41 118.86 ramp cmp4 d
2 265.59 118.86 ramp cmp3 u
3 391.49 118.48 ramp cmp3 d
4 518.48 119.79 ramp cmp2 u
5 644.71 119.27 ramp cmp2 d
6 770.30 119.51 ramp cmp1 u
7 896.00 118.86 ramp cmp1 d
8 1022.19 119.26 ramp cmp4 d
9 1145.15 120.08 ramp cmp4 u
10 1279.28 118.34 ramp cmp3 u
11 1411.54 118.47 ramp cmp2 d
12 1536.99 120.08 ramp cmp2 u
13 1671.68 120.63 ramp cmp1 d



In [22]:

    
# select 4 section from training data
#idx = random.sample(section_idx, 4)
idx = section_idx[:]

interact_guess();

Optimize using ML



In [23]:

    
display_preopt_params()

if False:
    InfoMat = None
    method = 'trust-ncg'
    def hessian(opt_params, index):
        global InfoMat
        return InfoMat
    dview['enable_infomat']=True
    options={'gtol':1}
    opt_bounds = None
else:
    method = 'L-BFGS-B'
    hessian = None
    dview['enable_infomat']=False
    options={'ftol':1e-6,'maxfun':400}
    opt_bounds = bounds

cnt = 0
tmp_rslt = None
T0 = time.time()
print('#cnt,     Time,      |R|')

%time res =  sp.optimize.minimize(fun=costfunc, x0=opt_param0, \
        args=(opt_idx,), method=method, jac=True, hess=hessian, \
        bounds=opt_bounds, options=options)









    




Parameters for optimization






    




Idx Description $x_0$ unit opt $\delta_{par}$ min max
0 k_1_-41 1.0 1 * 0.001 0 1.5
1 k_1_-35 1.0 1 * 0.001 0 1.5
2 k_1_-30 1.0 1 * 0.001 0 1.5
3 k_1_-25 1.0 1 * 0.001 0 1.5
4 k_1_-20 1.0 1 * 0.001 0 1.5
5 k_1_-15 1.0 1 * 0.001 0 1.5
6 k_1_-10 1.0 1 * 0.001 0 1.5
7 k_1_-5 1.0 1 * 0.001 0 1.5
8 k_1_5 1.0 1 * 0.001 0 1.5
9 k_1_10 1.0 1 * 0.001 0 1.5
10 k_1_15 1.0 1 * 0.001 0 1.5
11 k_1_20 1.0 1 * 0.001 0 1.5
12 k_1_25 1.0 1 * 0.001 0 1.5
13 k_1_30 1.0 1 * 0.001 0 1.5
14 k_1_35 1.0 1 * 0.001 0 1.5
15 k_1_41 1.0 1 * 0.001 0 1.5
16 k_2_-41 1.0 1 * 0.001 0 1.5
17 k_2_-35 1.0 1 * 0.001 0 1.5
18 k_2_-30 1.0 1 * 0.001 0 1.5
19 k_2_-25 1.0 1 * 0.001 0 1.5
20 k_2_-20 1.0 1 * 0.001 0 1.5
21 k_2_-15 1.0 1 * 0.001 0 1.5
22 k_2_-10 1.0 1 * 0.001 0 1.5
23 k_2_-5 1.0 1 * 0.001 0 1.5
24 k_2_5 1.0 1 * 0.001 0 1.5
25 k_2_10 1.0 1 * 0.001 0 1.5
26 k_2_15 1.0 1 * 0.001 0 1.5
27 k_2_20 1.0 1 * 0.001 0 1.5
28 k_2_25 1.0 1 * 0.001 0 1.5
29 k_2_30 1.0 1 * 0.001 0 1.5
30 k_2_35 1.0 1 * 0.001 0 1.5
31 k_2_41 1.0 1 * 0.001 0 1.5
32 k_3_-41 1.0 1 * 0.001 0 1.5
33 k_3_-35 1.0 1 * 0.001 0 1.5
34 k_3_-30 1.0 1 * 0.001 0 1.5
35 k_3_-25 1.0 1 * 0.001 0 1.5
36 k_3_-20 1.0 1 * 0.001 0 1.5
37 k_3_-15 1.0 1 * 0.001 0 1.5
38 k_3_-10 1.0 1 * 0.001 0 1.5
39 k_3_-5 1.0 1 * 0.001 0 1.5
40 k_3_5 1.0 1 * 0.001 0 1.5
41 k_3_10 1.0 1 * 0.001 0 1.5
42 k_3_15 1.0 1 * 0.001 0 1.5
43 k_3_20 1.0 1 * 0.001 0 1.5
44 k_3_25 1.0 1 * 0.001 0 1.5
45 k_3_30 1.0 1 * 0.001 0 1.5
46 k_3_35 1.0 1 * 0.001 0 1.5
47 k_3_41 1.0 1 * 0.001 0 1.5
48 k_4_-41 1.0 1 * 0.001 0 1.5
49 k_4_-35 1.0 1 * 0.001 0 1.5
50 k_4_-30 1.0 1 * 0.001 0 1.5
51 k_4_-25 1.0 1 * 0.001 0 1.5
52 k_4_-20 1.0 1 * 0.001 0 1.5
53 k_4_-15 1.0 1 * 0.001 0 1.5
54 k_4_-10 1.0 1 * 0.001 0 1.5
55 k_4_-5 1.0 1 * 0.001 0 1.5
56 k_4_5 1.0 1 * 0.001 0 1.5
57 k_4_10 1.0 1 * 0.001 0 1.5
58 k_4_15 1.0 1 * 0.001 0 1.5
59 k_4_20 1.0 1 * 0.001 0 1.5
60 k_4_25 1.0 1 * 0.001 0 1.5
61 k_4_30 1.0 1 * 0.001 0 1.5
62 k_4_35 1.0 1 * 0.001 0 1.5
63 k_4_41 1.0 1 * 0.001 0 1.5
64 $phi_0$ 0.0 $rad$ * 0.0001 -0.1 0.1






    



#cnt,     Time,      |R|
0001,    0.197,       36.6
0002,    0.350,      686.4
0003,    0.495,       17.3
0004,    0.645,        8.6
0005,    0.781,      101.5
0006,    0.940,       14.5
0007,    1.105,        6.9
0008,    1.270,        7.6
0009,    1.435,        6.3
0010,    1.587,       11.6
0011,    1.725,        7.6
0012,    1.880,        6.6
0013,    2.036,        6.3
0014,    2.187,        6.3
0015,    2.330,        6.6
0016,    2.469,        6.2
0017,    2.610,        6.2
0018,    2.764,        6.0
0019,    2.927,        5.4
0020,    3.102,        5.4
0021,    3.267,        4.8
0022,    3.447,        4.4
0023,    3.619,        4.4
0024,    3.792,        4.4
0025,    3.977,        4.4
0026,    4.157,        4.4
0027,    4.324,        4.4
0028,    4.486,        4.4
0029,    4.629,        4.4
0030,    4.773,        4.4
0031,    4.918,        4.4
0032,    5.056,        4.4
0033,    5.192,        4.4
0034,    5.336,        4.4
0035,    5.470,        4.4
0036,    5.611,        4.4
0037,    5.754,        4.4
0038,    5.915,        4.4
0039,    6.067,        4.4
0040,    6.207,        4.4
0041,    6.350,        4.4
0042,    6.493,        4.4
0043,    6.630,      363.2
0044,    6.767,       26.1
0045,    6.907,        5.0
0046,    7.049,        3.5
0047,    7.188,        3.0
0048,    7.320,        3.1
0049,    7.462,        2.9
0050,    7.594,        2.9
0051,    7.737,        2.9
0052,    7.871,        2.9
0053,    8.017,        2.9
0054,    8.177,       46.4
0055,    8.355,       10.1
0056,    8.506,        4.8
0057,    8.674,        3.5
0058,    8.835,        3.0
0059,    8.979,        2.9
0060,    9.127,        2.9
0061,    9.264,        2.9
0062,    9.410,        2.9
0063,    9.553,        2.9
0064,    9.697,        2.9
0065,    9.835,        2.9
0066,    9.970,        2.9
0067,   10.109,        2.9
0068,   10.256,        2.9
0069,   10.404,        2.9
0070,   10.544,        2.9
0071,   10.696,        2.9
0072,   10.838,        2.9
0073,   10.975,        2.9
0074,   11.124,      820.8
0075,   11.265,       45.0
0076,   11.407,        6.2
0077,   11.549,        2.6
0078,   11.692,        2.1
0079,   11.837,        2.1
0080,   11.971,        2.0
0081,   12.126,        2.0
0082,   12.273,        1.9
0083,   12.414,        1.8
0084,   12.562,        1.7
0085,   12.703,        1.6
0086,   12.842,        1.6
0087,   12.987,        1.6
0088,   13.130,        1.6
0089,   13.268,        1.6
0090,   13.409,        1.6
0091,   13.554,        1.6
0092,   13.719,        1.6
0093,   13.884,        1.6
0094,   14.052,        1.6
0095,   14.203,        1.6
0096,   14.348,        1.6
0097,   14.489,        1.6
0098,   14.630,        1.6
0099,   14.770,        1.6
0100,   14.904,        1.6
0101,   15.056,        1.6
0102,   15.209,        1.6
0103,   15.347,        1.6
0104,   15.499,        1.6
0105,   15.644,        1.6
0106,   15.782,      508.0
0107,   15.926,       33.6
0108,   16.066,        5.6
0109,   16.200,        2.1
0110,   16.342,        1.5
0111,   16.476,        1.5
0112,   16.636,        1.4
0113,   16.776,        1.4
0114,   16.932,        1.4
0115,   17.095,        1.4
0116,   17.226,        1.4
0117,   17.370,        1.4
0118,   17.516,        1.4
0119,   17.665,        1.4
0120,   17.808,        1.4
0121,   17.959,        1.4
0122,   18.120,        1.4
0123,   18.268,        1.4
0124,   18.414,        1.4
0125,   18.563,        1.4
0126,   18.709,        1.4
0127,   18.849,        1.4
0128,   18.993,        1.4
0129,   19.142,        1.4
0130,   19.280,        1.4
0131,   19.416,        1.4
0132,   19.565,        1.4
0133,   19.704,        1.4
0134,   19.842,      492.2
0135,   19.990,       27.4
0136,   20.133,        5.8
0137,   20.275,        2.3
0138,   20.427,        1.5
0139,   20.584,        1.4
0140,   20.763,        1.4
0141,   20.931,        1.3
0142,   21.100,        1.3
0143,   21.247,        1.3
0144,   21.386,        1.3
0145,   21.524,        1.3
0146,   21.662,        1.3
0147,   21.805,        1.3
0148,   21.939,        1.3
0149,   22.074,        1.3
0150,   22.212,        1.3
0151,   22.353,        1.3
0152,   22.491,        1.3
0153,   22.636,        1.3
0154,   22.772,        1.3
0155,   22.912,        1.3
0156,   23.050,        1.3
0157,   23.192,        1.3
0158,   23.336,        1.3
0159,   23.485,        1.3
0160,   23.628,        1.3
0161,   23.772,        1.3
0162,   23.916,      281.7
0163,   24.063,       24.0
0164,   24.206,        5.6
0165,   24.344,        2.2
0166,   24.492,        1.4
0167,   24.637,        1.3
0168,   24.779,        1.3
0169,   24.921,        1.3
0170,   25.061,        1.3
0171,   25.210,        1.3
0172,   25.346,        1.3
0173,   25.489,        1.3
0174,   25.640,        1.3
0175,   25.779,        1.3
0176,   25.916,        1.3
0177,   26.050,        1.3
0178,   26.182,        1.3
0179,   26.326,        1.3
0180,   26.472,        1.3
0181,   26.617,        1.3
0182,   26.762,        1.3
0183,   26.896,        1.3
0184,   27.034,        1.3
0185,   27.184,        1.3
0186,   27.321,        1.3
0187,   27.464,        1.3
0188,   27.606,        1.3
0189,   27.744,        1.3
0190,   27.878,        1.3
0191,   28.019,        1.3
0192,   28.157,      482.8
0193,   28.297,       29.6
0194,   28.442,        6.2
0195,   28.583,        2.4
0196,   28.722,        1.5
0197,   28.859,        1.2
0198,   28.994,        1.2
0199,   29.132,        1.2
0200,   29.274,        1.2
0201,   29.413,        1.2
0202,   29.556,        1.2
0203,   29.707,        1.2
0204,   29.853,        1.2
0205,   29.989,        1.1
0206,   30.142,        1.1
0207,   30.287,        1.0
0208,   30.419,        1.0
0209,   30.561,        0.9
0210,   30.695,        0.9
0211,   30.840,        0.8
0212,   30.983,        0.8
0213,   31.119,        0.8
0214,   31.256,        0.8
0215,   31.407,        0.8
0216,   31.550,        0.8
0217,   31.690,        0.8
0218,   31.844,        0.8
0219,   31.990,        0.8
0220,   32.132,        0.8
0221,   32.287,        0.8
0222,   32.444,        0.8
0223,   32.593,        0.8
0224,   32.746,        0.8
0225,   32.880,        0.8
0226,   33.018,        0.8
0227,   33.166,        0.8
0228,   33.307,        0.8
0229,   33.453,        0.8
0230,   33.589,        0.8
0231,   33.734,        0.8
0232,   33.870,        0.8
0233,   34.009,      745.3
0234,   34.149,       34.8
0235,   34.289,        8.5
0236,   34.439,        3.0
0237,   34.582,        1.5
0238,   34.725,        1.0
0239,   34.876,        0.9
0240,   35.024,        0.8
0241,   35.201,        0.8
0242,   35.356,        0.8
0243,   35.499,        0.8
0244,   35.650,        0.8
0245,   35.815,        0.8
0246,   35.992,        0.8
0247,   36.192,        0.8
0248,   36.393,        0.8
0249,   36.568,        0.8
0250,   36.731,        0.8
0251,   36.891,        0.8
0252,   37.080,        0.8
CPU times: user 10.1 s, sys: 712 ms, total: 10.9 s
Wall time: 37.1 s

Show and test results



In [24]:

    
display_opt_params()

# show result
idx = [0,1, 8,9,
       2,3,10,
       4,5,11,12,
       6,7,13,14,]
display_data_for_test();

update_guess();









    




Parameters from optimization






    




Idx Description $x$
0 k_1_-41 1.14629833042
1 k_1_-35 1.16285127459
2 k_1_-30 1.17710541985
3 k_1_-25 1.1848702943
4 k_1_-20 1.20462684676
5 k_1_-15 1.26263485422
6 k_1_-10 1.2516653674
7 k_1_-5 0.980486789023
8 k_1_5 0.921488273382
9 k_1_10 1.18096915384
10 k_1_15 1.18680742601
11 k_1_20 0.976157836667
12 k_1_25 0.981902151188
13 k_1_30 0.981624526926
14 k_1_35 1.03185651775
15 k_1_41 1.00522359098
16 k_2_-41 0.902541621017
17 k_2_-35 0.884894492126
18 k_2_-30 0.85779634002
19 k_2_-25 0.850118219298
20 k_2_-20 0.857266999961
21 k_2_-15 0.954364989351
22 k_2_-10 0.985177949469
23 k_2_-5 0.920009656205
24 k_2_5 0.882755514768
25 k_2_10 0.8702506961
26 k_2_15 0.904451603012
27 k_2_20 0.822128063143
28 k_2_25 0.807405493692
29 k_2_30 0.833238377866
30 k_2_35 0.867097942574
31 k_2_41 0.901428442592
32 k_3_-41 0.783253295092
33 k_3_-35 0.80961579614
34 k_3_-30 0.808739907178
35 k_3_-25 0.796131138216
36 k_3_-20 0.801968396797
37 k_3_-15 0.823087064097
38 k_3_-10 0.971335363651
39 k_3_-5 1.04014757757
40 k_3_5 0.766494037217
41 k_3_10 0.784015882181
42 k_3_15 0.814137346191
43 k_3_20 0.833601120864
44 k_3_25 0.803644778053
45 k_3_30 0.801404908323
46 k_3_35 0.781241093956
47 k_3_41 0.751036228465
48 k_4_-41 0.67726168876
49 k_4_-35 0.709191222946
50 k_4_-30 0.730766942093
51 k_4_-25 0.757722730251
52 k_4_-20 0.77644120936
53 k_4_-15 0.842963957098
54 k_4_-10 0.832071019129
55 k_4_-5 0.890877419764
56 k_4_5 0.712761573116
57 k_4_10 0.75747752219
58 k_4_15 0.693799985731
59 k_4_20 0.615338433167
60 k_4_25 0.624007620236
61 k_4_30 0.642944325071
62 k_4_35 0.67409581342
63 k_4_41 0.69184419717
64 $phi_0$ 0.0102403971686






    




Test Data






    




Idx Start(s) Spam(s) Description
0 18.86 118.46 ramp cmp4 u
1 141.41 118.86 ramp cmp4 d
8 1022.19 119.26 ramp cmp4 d
9 1145.15 120.08 ramp cmp4 u
2 265.59 118.86 ramp cmp3 u
3 391.49 118.48 ramp cmp3 d
10 1279.28 118.34 ramp cmp3 u
4 518.48 119.79 ramp cmp2 u
5 644.71 119.27 ramp cmp2 d
11 1411.54 118.47 ramp cmp2 d
12 1536.99 120.08 ramp cmp2 u
6 770.30 119.51 ramp cmp1 u
7 896.00 118.86 ramp cmp1 d
13 1671.68 120.63 ramp cmp1 d
14 1798.33 120.60 ramp cmp1 u



In [25]:

    
res_params = res['x']
params = param0[:]
for i,j in enumerate(opt_idx):
    params[j] = res_params[i]

k1 = np.array(params[0:angles_num])
k2 = np.array(params[angles_num:angles_num*2])
k3 = np.array(params[angles_num*2:angles_num*3])
k4 = np.array(params[angles_num*3:angles_num*4])

Clda_cmp1 = Clda_cmp*0.00436332313*k1*angles
Clda_cmp2 = Clda_cmp*0.00436332313*k2*angles
Clda_cmp3 = Clda_cmp*0.00436332313*k3*angles
Clda_cmp4 = Clda_cmp*0.00436332313*k4*angles

print('angeles = ')
print(angles)
print('Clda_cmpx = ')
print(np.vstack((Clda_cmp1,Clda_cmp2,Clda_cmp3,Clda_cmp4)))

%matplotlib inline
plt.figure(figsize=(12,8),dpi=300)
plt.plot(angles,  Clda_cmp1, 'r')
plt.plot(angles,  Clda_cmp2, 'g')
plt.plot(angles,  Clda_cmp3, 'b')
plt.plot(angles,  Clda_cmp4, 'm')
plt.xlabel('$\delta_{a,cmp}$')
plt.ylabel('$C_{l \delta a,cmp}$')
plt.show()









    



angeles = 
[-41, -35, -30, -25, -20, -15, -10, -5, 5, 10, 15, 20, 25, 30, 35, 41]
Clda_cmpx = 
[[ 0.06082331  0.05267211  0.04570094  0.03833534  0.03117964  0.0245108
   0.01619857  0.00634454 -0.00596277 -0.01528365 -0.02303881 -0.02526612
  -0.0317685  -0.03811142 -0.04673862 -0.05333779]
 [ 0.04788942  0.04008188  0.03330381  0.02750476  0.02218884  0.01852654
   0.0127498   0.00595321 -0.00571214 -0.01126245 -0.0175576  -0.02127933
  -0.02612283 -0.03235035 -0.03927577 -0.04783036]
 [ 0.04155991  0.03667208  0.0313992   0.02575806  0.02075753  0.01597812
   0.01257065  0.0067306  -0.00495984 -0.01014643 -0.01580438 -0.02157629
  -0.02600116 -0.03111442 -0.03538683 -0.03985045]
 [ 0.03593593  0.03212328  0.02837192  0.02451539  0.02009681  0.01636397
   0.01076834  0.0057647  -0.00461214 -0.00980298 -0.01346834 -0.01592695
  -0.02018917 -0.02496222 -0.03053361 -0.03670969]]



In [ ]:



In [ ]:

    
toggle_inputs()
button_qtconsole()

Idx	Start(s)	Spam(s)	Description
0	18.86	118.46	ramp cmp4 u
1	141.41	118.86	ramp cmp4 d
2	265.59	118.86	ramp cmp3 u
3	391.49	118.48	ramp cmp3 d
4	518.48	119.79	ramp cmp2 u
5	644.71	119.27	ramp cmp2 d
6	770.30	119.51	ramp cmp1 u
7	896.00	118.86	ramp cmp1 d
8	1022.19	119.26	ramp cmp4 d
9	1145.15	120.08	ramp cmp4 u
10	1279.28	118.34	ramp cmp3 u
11	1411.54	118.47	ramp cmp2 d
12	1536.99	120.08	ramp cmp2 u
13	1671.68	120.63	ramp cmp1 d
14	1798.33	120.60	ramp cmp1 u

Name	Value	unit
$S_c$	0.1254	$m^2$
$b_c$	0.7	$m$
$g$	9.81	$m/s^2$
$m_T$	9.585	$kg$
$l_{zT}$	0.0416	$m$
$V$	30	$m/s$
$F_c$	0.06	$Nm$
$C_{l \delta a,cmp}$	-0.2966	$rad^{-1}$

Idx	Description	$x_0$	unit	opt	$\delta_{par}$	min	max
0	k_1_-41	1	1	*	0.001	0	1.5
1	k_1_-35	1	1	*	0.001	0	1.5
2	k_1_-30	1	1	*	0.001	0	1.5
3	k_1_-25	1	1	*	0.001	0	1.5
4	k_1_-20	1	1	*	0.001	0	1.5
5	k_1_-15	1	1	*	0.001	0	1.5
6	k_1_-10	1	1	*	0.001	0	1.5
7	k_1_-5	1	1	*	0.001	0	1.5
8	k_1_5	1	1	*	0.001	0	1.5
9	k_1_10	1	1	*	0.001	0	1.5
10	k_1_15	1	1	*	0.001	0	1.5
11	k_1_20	1	1	*	0.001	0	1.5
12	k_1_25	1	1	*	0.001	0	1.5
13	k_1_30	1	1	*	0.001	0	1.5
14	k_1_35	1	1	*	0.001	0	1.5
15	k_1_41	1	1	*	0.001	0	1.5
16	k_2_-41	1	1	*	0.001	0	1.5
17	k_2_-35	1	1	*	0.001	0	1.5
18	k_2_-30	1	1	*	0.001	0	1.5
19	k_2_-25	1	1	*	0.001	0	1.5
20	k_2_-20	1	1	*	0.001	0	1.5
21	k_2_-15	1	1	*	0.001	0	1.5
22	k_2_-10	1	1	*	0.001	0	1.5
23	k_2_-5	1	1	*	0.001	0	1.5
24	k_2_5	1	1	*	0.001	0	1.5
25	k_2_10	1	1	*	0.001	0	1.5
26	k_2_15	1	1	*	0.001	0	1.5
27	k_2_20	1	1	*	0.001	0	1.5
28	k_2_25	1	1	*	0.001	0	1.5
29	k_2_30	1	1	*	0.001	0	1.5
30	k_2_35	1	1	*	0.001	0	1.5
31	k_2_41	1	1	*	0.001	0	1.5
32	k_3_-41	1	1	*	0.001	0	1.5
33	k_3_-35	1	1	*	0.001	0	1.5
34	k_3_-30	1	1	*	0.001	0	1.5
35	k_3_-25	1	1	*	0.001	0	1.5
36	k_3_-20	1	1	*	0.001	0	1.5
37	k_3_-15	1	1	*	0.001	0	1.5
38	k_3_-10	1	1	*	0.001	0	1.5
39	k_3_-5	1	1	*	0.001	0	1.5
40	k_3_5	1	1	*	0.001	0	1.5
41	k_3_10	1	1	*	0.001	0	1.5
42	k_3_15	1	1	*	0.001	0	1.5
43	k_3_20	1	1	*	0.001	0	1.5
44	k_3_25	1	1	*	0.001	0	1.5
45	k_3_30	1	1	*	0.001	0	1.5
46	k_3_35	1	1	*	0.001	0	1.5
47	k_3_41	1	1	*	0.001	0	1.5
48	k_4_-41	1	1	*	0.001	0	1.5
49	k_4_-35	1	1	*	0.001	0	1.5
50	k_4_-30	1	1	*	0.001	0	1.5
51	k_4_-25	1	1	*	0.001	0	1.5
52	k_4_-20	1	1	*	0.001	0	1.5
53	k_4_-15	1	1	*	0.001	0	1.5
54	k_4_-10	1	1	*	0.001	0	1.5
55	k_4_-5	1	1	*	0.001	0	1.5
56	k_4_5	1	1	*	0.001	0	1.5
57	k_4_10	1	1	*	0.001	0	1.5
58	k_4_15	1	1	*	0.001	0	1.5
59	k_4_20	1	1	*	0.001	0	1.5
60	k_4_25	1	1	*	0.001	0	1.5
61	k_4_30	1	1	*	0.001	0	1.5
62	k_4_35	1	1	*	0.001	0	1.5
63	k_4_41	1	1	*	0.001	0	1.5
64	$phi_0$	0	$rad$	*	0.0001	-0.1	0.1

Idx	Description	$x$
0	k_1_-41	1.14629833042
1	k_1_-35	1.16285127459
2	k_1_-30	1.17710541985
3	k_1_-25	1.1848702943
4	k_1_-20	1.20462684676
5	k_1_-15	1.26263485422
6	k_1_-10	1.2516653674
7	k_1_-5	0.980486789023
8	k_1_5	0.921488273382
9	k_1_10	1.18096915384
10	k_1_15	1.18680742601
11	k_1_20	0.976157836667
12	k_1_25	0.981902151188
13	k_1_30	0.981624526926
14	k_1_35	1.03185651775
15	k_1_41	1.00522359098
16	k_2_-41	0.902541621017
17	k_2_-35	0.884894492126
18	k_2_-30	0.85779634002
19	k_2_-25	0.850118219298
20	k_2_-20	0.857266999961
21	k_2_-15	0.954364989351
22	k_2_-10	0.985177949469
23	k_2_-5	0.920009656205
24	k_2_5	0.882755514768
25	k_2_10	0.8702506961
26	k_2_15	0.904451603012
27	k_2_20	0.822128063143
28	k_2_25	0.807405493692
29	k_2_30	0.833238377866
30	k_2_35	0.867097942574
31	k_2_41	0.901428442592
32	k_3_-41	0.783253295092
33	k_3_-35	0.80961579614
34	k_3_-30	0.808739907178
35	k_3_-25	0.796131138216
36	k_3_-20	0.801968396797
37	k_3_-15	0.823087064097
38	k_3_-10	0.971335363651
39	k_3_-5	1.04014757757
40	k_3_5	0.766494037217
41	k_3_10	0.784015882181
42	k_3_15	0.814137346191
43	k_3_20	0.833601120864
44	k_3_25	0.803644778053
45	k_3_30	0.801404908323
46	k_3_35	0.781241093956
47	k_3_41	0.751036228465
48	k_4_-41	0.67726168876
49	k_4_-35	0.709191222946
50	k_4_-30	0.730766942093
51	k_4_-25	0.757722730251
52	k_4_-20	0.77644120936
53	k_4_-15	0.842963957098
54	k_4_-10	0.832071019129
55	k_4_-5	0.890877419764
56	k_4_5	0.712761573116
57	k_4_10	0.75747752219
58	k_4_15	0.693799985731
59	k_4_20	0.615338433167
60	k_4_25	0.624007620236
61	k_4_30	0.642944325071
62	k_4_35	0.67409581342
63	k_4_41	0.69184419717
64	$phi_0$	0.0102403971686