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Licensed Unlicensed Requires Authentication Published by De Gruyter April 13, 2016

Recursive Orthogonal Least Square Based Soft Sensor for Batch Distillation

Shubham Mehta, Harish Ramani, Nileshkumar N. Yelgatte and Imran Rahman

Abstract

A multiple-input and multiple-output (MIMO) model, namely Recursive Orthogonal Least Square (ROLS) based radial basis function (RBF) is developed to estimate product compositions in a batch distillation process from temperature measurements. The process data is generated by simulating the differential equations of the batch distillation process, changing the initial feed composition and boiluprate from batch to batch. Moreover, the reflux ratio is also randomly varied within each batch to represent the exact dynamics of the batch distillation. Temperature and distillate composition is correlated by the RBF trained by ROLS algorithm. A Single RBF network estimate the quality of products in real-time. The results show that ROLS based estimator give correct composition estimations for a batch distillation process. The robustness of the ROLS algorithm and low computational requirement makes the estimator attractive for on-line use.

Nomenclature

y

system output

u

system input

x

RBF network input vector

yˆ

RBF network output vector or estimated output vector

yˆi

estimate obtained from ROLS model for ith pattern

yi

desiredd value of ith input-ouput pattern

W

weight matrix

d

Euclidean distance

c

center vector

nh

number of nodes in hidden layer

J

error cost function

N

number of input-output patterns for test data

xF

feed composition vector

V

vapor boilup rate, kmol h−1

TB

temperature of the reboiler, K

Tk

temperature of k th tray, K

LR

liquid refluxed, kmol h−1

xBi

mole fraction of component i in the reboiler

xDi

mole fraction of component i in the distillate

Greek Symbols
Δ

increment

Φ

hidden layer output vector

ϕi

ith element of vector Φ

Appendix I

Table 4:

Training data.

S. No.TBT5T10T15T17xD1xD2xB3
1364.08359.67355.91354.15353.790.9900.0100.151
2364.47360.23356.21354.16353.760.9920.0080.156
3364.87360.95356.78354.30353.780.9900.0100.161
4365.30361.80357.64354.56353.840.9860.0140.166
5365.82362.69358.73354.98353.940.9790.0210.172
6366.32363.72360.43355.82354.150.9660.0340.178
7366.77364.54361.89356.93354.480.9430.0570.185
8367.24365.32363.30358.41355.040.9050.0940.192
9367.72365.31362.42357.16354.830.9170.0830.199
10368.14365.33361.14355.77354.230.9590.0410.204
11368.55365.66360.81355.34354.050.9720.0280.209
12368.95366.30361.47355.50354.050.9720.0280.215
13369.32367.19362.91356.22354.210.9610.0390.220
14369.72368.02364.91357.81354.650.9330.0670.227
15370.04368.60366.42359.84355.380.8820.1180.233
16370.37369.10367.70362.02356.550.8080.1920.239
17370.66369.30367.73361.77356.800.7870.2120.245
18370.91369.58367.88361.41356.410.8140.1850.250
19371.14369.87368.29361.79356.510.8090.1910.254
20371.34370.15368.79362.64356.970.7800.2200.259
21371.52370.40369.27363.71357.690.7330.2660.263
22371.71370.64369.72364.94358.700.6740.3240.268
23371.86370.83370.04365.95359.810.6100.3880.273
24372.02371.04370.36367.11361.070.5450.4510.278
25372.12371.09370.39367.10361.440.5070.4880.283
26372.22371.17370.45366.83361.100.5280.4680.286
27372.32371.28370.56366.93361.110.5290.4680.290
28372.41371.39370.70367.32361.400.5150.4810.293
29372.48371.47370.81367.64361.790.4910.5040.296
30372.54371.54370.91367.98362.250.4610.5330.299
31372.62371.63371.03368.44362.950.4270.5660.302
32372.68371.70371.13368.83363.620.3920.6000.306
33372.73371.89371.38369.88365.110.3050.6820.310
34372.82372.06371.58370.66367.690.1810.7910.318
35372.92372.17371.70371.02369.070.1210.8410.327
36373.02372.25371.77371.20369.710.0890.8660.337
37373.11372.32371.83371.30370.060.0710.8800.348
38373.20372.39371.88371.38370.330.0580.8880.360
39373.31372.46371.93371.45370.530.0490.8930.372
40373.43372.53371.99371.51370.710.0420.8970.386
41373.53372.47371.93371.47370.700.0410.9010.399
42373.64372.49371.91371.46370.700.0400.9070.410
43373.73372.52371.93371.47370.750.0370.9110.422
44373.86372.58371.96371.51370.850.0330.9140.435
45373.97372.63371.99371.54370.940.0290.9160.448
46374.07372.68372.01371.57371.020.0250.9180.462
47374.21372.74372.05371.60371.100.0220.9200.477
48374.35372.80372.08371.63371.180.0180.9210.493
49374.53373.01372.21371.72371.300.0140.9180.513
50374.76373.17372.33371.80371.430.0110.9120.537
51375.19373.34372.42371.87371.520.0080.9070.565
52375.54373.52372.51371.92371.580.0070.9030.596
53375.91373.69372.59371.96371.630.0050.8990.632
54376.39373.93372.69372.01371.670.0040.8940.673
55377.08374.27372.84372.07371.720.0040.8890.720
56377.90374.72373.02372.15371.780.0030.8810.774
57378.96375.49373.26372.24371.830.0020.8720.835
58380.47376.96373.76372.40371.920.0020.8590.901
59382.02380.20375.21372.75372.080.0010.8310.961
60367.67366.34362.43356.96355.270.8880.0950.217
61368.06365.84362.36356.49354.220.9630.0370.224
62368.44366.83365.10360.34355.700.8640.1350.232
63368.86367.43366.19362.61357.370.7630.2360.240
64369.24367.92366.92363.75358.400.6950.3040.248
65369.61368.38367.46364.63359.330.6450.3530.257
66369.99368.86367.99365.46360.160.5970.4000.267
67370.29369.23368.40366.08360.820.5500.4440.277
68370.70369.74368.95366.99361.760.5050.4870.288
69370.94369.72368.87366.15361.200.5230.4690.300
70371.24369.87368.98365.78360.310.5760.4200.309
71371.50370.15369.29366.18360.570.5640.4320.317
72371.74370.44369.63366.80361.240.5270.4680.326
73371.94370.68369.90367.46361.930.4820.5110.335
74372.17370.95370.20368.08362.810.4310.5590.345
75372.40371.22370.49368.66363.740.3870.6000.355
76372.60371.44370.72369.11364.530.3450.6380.366
77372.73371.37370.65368.72364.100.3590.6260.375
78372.89371.46370.73368.65363.720.3790.6100.383
79373.01371.58370.84368.80363.870.3710.6170.390
80373.15371.71370.98369.09364.320.3490.6380.398
81373.26371.83371.11369.37364.830.3210.6630.406
82373.37371.94371.22369.65365.400.2910.6900.414
83373.48372.03371.32369.89365.940.2620.7170.422
84373.59372.14371.42370.14366.530.2340.7420.431
85373.68372.07371.37369.99366.390.2370.7410.438
86373.76372.10371.39369.95366.200.2460.7340.444
87373.82372.14371.43369.99366.230.2440.7360.449
88373.90372.20371.48370.10366.440.2360.7440.454
89373.96372.25371.53370.20366.670.2240.7550.460
90374.02372.30371.57370.33367.070.2090.7680.466
91374.10372.35371.62370.47367.470.1930.7820.471
92374.15372.39371.66370.58367.770.1760.7970.477
93374.22372.67371.88371.01368.600.1370.8290.485
94374.37372.93372.12371.40369.940.0800.8630.499
95374.53373.08372.24371.58370.540.0540.8740.516
96374.72373.21372.33371.69370.850.0410.8790.534
97375.05373.34372.41371.76371.040.0340.8810.554
98375.25373.45372.47371.81371.150.0290.8810.575
99375.55373.61372.56371.87371.260.0250.8810.599
100375.78373.73372.62371.91371.330.0220.8790.625
101376.08373.61372.50371.84371.300.0220.8840.650
102376.38373.64372.45371.80371.260.0220.8920.673
103376.71373.75372.48371.81371.280.0200.8950.696
104377.01373.87372.53371.83371.320.0180.8960.721
105377.45374.07372.60371.87371.390.0160.8950.747
106377.85374.26372.68371.91371.450.0140.8930.775
107378.37374.54372.78371.96371.510.0120.8900.805
108379.00375.02372.92372.02371.580.0100.8870.837
109379.71376.07373.38372.21371.700.0080.8740.874
110380.78377.94374.20372.52371.910.0060.8450.917
111381.92380.98376.36373.10372.190.0040.8020.957
112382.86382.78381.38375.19372.910.0030.6930.983
113364.27361.89358.72355.91354.990.9090.0790.166
114364.63359.45355.53354.03353.760.9920.0080.171
115365.02359.94355.69354.00353.720.9940.0050.176
116365.53360.65356.12354.08353.730.9940.0060.182
117365.96361.57356.85354.25353.770.9910.0090.187
118366.37362.53357.82354.52353.820.9870.0130.193
119366.83363.63359.39355.07353.950.9790.0210.200
120367.31364.72361.25356.08354.200.9620.0380.207
121367.77365.59362.98357.54354.660.9310.0690.215
122368.23365.94363.22357.63354.850.9170.0830.222
123368.68366.56363.55357.55354.730.9260.0740.228
124369.08367.17364.50358.31354.950.9110.0890.235
125369.48367.80365.69359.81355.500.8750.1250.243
126369.87368.36366.76361.50356.390.8170.1830.250
127370.25368.88367.74363.21357.560.7410.2580.259
128370.61369.35368.41364.64358.790.6680.3300.267
129370.96369.79368.98365.86360.150.5970.4000.277
130371.20369.92369.04365.47360.020.5930.4040.285
131371.45370.17369.30365.58359.870.6030.3950.293
132371.68370.45369.63366.13360.320.5760.4210.300
133371.91370.72369.98366.89361.160.5310.4650.307
134372.09370.93370.23367.62361.960.4790.5150.315
135372.27371.14370.48368.24362.890.4260.5650.324
136372.46371.37370.73368.86363.940.3760.6130.332
137372.61371.53370.91369.28364.740.3300.6550.341
138372.74371.52370.89369.08364.680.3250.6600.350
139372.85371.57370.93368.94364.210.3500.6390.356
140372.94371.66371.01369.00364.190.3520.6380.361
141373.03371.75371.11369.17364.430.3390.6490.367
142373.13371.85371.21369.43364.900.3190.6680.372
143373.20371.91371.28369.62365.290.2940.6920.378
144373.28371.99371.37369.87365.840.2670.7160.384
145373.35372.05371.43370.08366.340.2400.7410.390
146373.44372.33371.70370.76367.950.1690.8010.399
147373.56372.49371.85371.12369.210.1110.8440.411
148373.71372.61371.96371.32369.940.0810.8640.425
149373.84372.70372.03371.43370.270.0640.8750.441
150373.99372.79372.10371.51370.520.0520.8810.458
151374.17372.90372.17371.58370.720.0440.8850.476
152374.36373.01372.23371.65370.880.0380.8870.496
153374.59373.13372.30371.71371.020.0320.8890.518
154374.90373.20372.34371.74371.110.0280.8900.542
155375.18373.31372.38371.77371.190.0250.8920.567
156375.53373.47372.45371.82371.280.0220.8920.594
157375.77373.58372.51371.86371.340.0190.8920.624
158376.26373.82372.61371.92371.430.0160.8900.657
159376.69374.03372.71371.97371.500.0130.8870.695
160377.27374.34372.84372.03371.570.0110.8830.737
161377.98374.74373.00372.11371.650.0090.8770.784
162378.91375.18373.06372.12371.680.0080.8740.834
163379.89375.82373.24372.17371.720.0070.8730.883
164381.13377.29373.69372.31371.800.0060.8630.931
165382.39380.67375.20372.66371.980.0040.8380.972
166365.88362.08358.64355.84354.930.9090.0800.256
167366.31360.84356.24354.19353.790.9900.0100.263
168366.80362.08357.27354.41353.800.9890.0110.271
169367.31363.32358.72354.91353.910.9810.0190.281
170367.87364.62360.86355.98354.180.9650.0350.291
171368.32365.53362.54357.34354.600.9360.0640.301
172368.87366.55364.21359.38355.390.8850.1150.313
173369.36367.29365.37361.06356.320.8220.1780.325
174369.87368.00366.33362.55357.340.7560.2420.338
175370.34368.00366.03361.24356.850.7860.2130.350
176370.76368.34366.08360.42356.030.8390.1600.360
177371.15368.88366.73360.89356.110.8350.1640.369
178371.50369.37367.62362.02356.690.7980.2010.379
179371.87369.90368.45363.61357.760.7390.2590.390
180372.16370.29369.02364.86358.810.6650.3320.401
181372.50370.73369.59366.19360.270.5950.4000.413
182372.73371.01369.93367.06361.210.5290.4630.425
183372.95370.97369.86366.36360.870.5420.4510.436
184373.14371.10369.98366.15360.360.5730.4220.444
185373.32371.29370.19366.40360.480.5670.4280.452
186373.51371.53370.47367.09361.070.5390.4550.460
187373.64371.67370.65367.56361.660.5010.4920.468
188373.78371.82370.83368.07362.360.4570.5330.477
189373.93371.98371.02368.62363.230.4130.5740.486
190374.18372.13371.18369.09364.070.3700.6140.495
191374.28372.10371.17369.03364.270.3500.6330.504
192374.38372.11371.18368.92363.950.3660.6200.510
193374.47372.17371.24368.97363.960.3670.6200.516
194374.55372.24371.31369.11364.150.3570.6280.522
195374.64372.33371.40369.33364.530.3410.6430.527
196374.70372.38371.45369.48364.830.3210.6610.533
197374.79372.44371.52369.71365.300.2990.6820.539
198374.88372.51371.59369.93365.810.2760.7030.546
199374.93372.69371.73370.37366.340.2440.7320.552
200375.11373.17372.15371.13368.750.1400.8090.567
201375.29373.36372.31371.42369.750.0930.8370.584
202375.54373.54372.44371.61370.350.0690.8490.604
203375.75373.67372.52371.69370.600.0570.8540.624
204376.06373.86372.63371.79370.820.0480.8570.647
205376.34374.03372.72371.85370.950.0420.8570.671
206376.68374.23372.82371.92371.080.0380.8560.697
207377.03374.08372.67371.84371.050.0370.8600.723
208377.42374.11372.61371.78370.980.0380.8700.746
209377.74374.23372.64371.79371.010.0360.8740.769
210378.14374.42372.71371.83371.080.0330.8750.793
211378.71374.75372.83371.90371.200.0290.8750.818
212379.12375.12372.93371.95371.270.0260.8730.844
213379.64375.52373.07372.02371.370.0230.8700.872
214380.30376.16373.29372.11371.480.0190.8650.900
215381.13378.48374.33372.48371.730.0140.8440.930
216381.97381.26376.83373.19372.130.0100.7900.960
217382.76382.69381.44375.39372.960.0060.6740.980
218365.61362.57358.78355.72354.830.9160.0730.197
219365.99361.27356.51354.20353.780.9900.0090.202
220366.45362.64358.04354.61353.840.9860.0140.209
221366.91363.81359.90355.37354.020.9740.0260.216
222367.38364.84361.78356.64354.370.9510.0490.224
223367.83365.64363.36358.21354.930.9140.0860.232
224368.29366.44364.61359.99355.720.8600.1390.240
225368.79367.13365.67361.64356.720.8000.2000.250
226369.25367.74366.48362.95357.680.7380.2610.260
227369.64367.84366.26361.72357.120.7680.2310.269
228370.06368.27366.49361.17356.430.8130.1870.277
229370.40368.72367.17361.76356.640.8020.1980.285
230370.73369.16367.84362.84357.280.7590.2400.293
231371.11369.66368.60364.37358.460.6990.2990.301
232371.40370.03369.11365.52359.660.6280.3700.310
233371.69370.40369.57366.57360.860.5610.4350.320
234371.93370.69369.91367.44361.860.4990.4950.330
235372.11370.73369.93367.13361.760.4880.5050.339
236372.30370.88370.07367.05361.390.5120.4830.347
237372.48371.08370.29367.37361.660.4980.4970.354
238372.64371.27370.51367.86362.260.4650.5280.361
239372.78371.43370.69368.32362.930.4240.5670.369
240372.94371.61370.90368.87363.840.3810.6070.377
241373.10371.77371.08369.34364.750.3390.6460.386
242373.19371.86371.17369.59365.260.3000.6820.394
243373.29371.83371.15369.46365.340.2910.6910.402
244373.37371.83371.14369.25364.760.3210.6660.407
245373.45371.89371.19369.21364.570.3310.6570.412
246373.52371.96371.25369.29364.630.3290.6590.416
247373.57372.01371.31369.41364.820.3180.6690.421
248373.64372.07371.37369.57365.130.3020.6830.425
249373.71372.13371.44369.79365.600.2830.7010.430
250373.76372.18371.49369.96365.980.2620.7210.435
251373.82372.43371.71370.58367.120.2080.7680.441
252373.94372.68371.96371.15369.100.1170.8370.454
253374.09372.82372.09371.42370.080.0760.8640.469
254374.24372.92372.16371.53370.490.0550.8760.485
255374.41373.03372.23371.62370.750.0440.8820.503
256374.64373.15372.31371.70370.950.0370.8840.522
257374.93373.26372.37371.75371.060.0310.8850.543
258375.14373.37372.43371.79371.160.0270.8860.566
259375.35373.07372.19371.64371.040.0300.8930.586
260375.51372.98372.07371.54370.860.0340.9040.600
261375.65372.99372.06371.51370.810.0350.9090.611
262375.77373.02372.06371.52370.820.0340.9110.623
263375.92373.07372.08371.53370.870.0320.9130.635
264376.06373.11372.10371.55370.930.0290.9150.648
265376.21373.17372.13371.58370.990.0270.9160.660
266376.38373.23372.15371.60371.060.0240.9170.674
267376.82374.97373.30372.24371.610.0100.8850.705
268377.69376.28374.42372.93372.160.0050.8090.762
269378.98377.97375.88373.61372.530.0030.7530.831
270380.42380.01378.30374.73373.000.0030.6760.905
271382.15382.04381.80378.92374.620.0020.4840.964
272366.72364.76360.94356.54355.190.8920.0920.217
273367.12363.92359.47355.09353.960.9780.0210.223
274367.53365.09362.10356.83354.390.9490.0510.230
275367.96365.89363.87358.93355.210.8950.1050.238
276368.39366.63365.01360.79356.180.8330.1660.246
277368.76367.13365.73361.95356.970.7790.2200.254
278369.22367.72366.47363.15357.890.7260.2730.264
279369.65368.27367.23364.18358.780.6750.3230.274
280369.96368.68367.68364.88359.530.6240.3720.284
281370.35368.83367.74364.23359.330.6310.3660.295
282370.69369.03367.83363.53358.150.7010.2980.303
283371.01369.41368.25363.91358.250.7010.2980.311
284371.24369.71368.63364.55358.720.6680.3310.319
285371.51370.05369.07365.44359.620.6190.3780.328
286371.80370.41369.53366.43360.690.5610.4350.337
287372.03370.70369.86367.28361.630.5060.4870.346
288372.26370.96370.16367.92362.530.4550.5360.356
289372.43370.93370.11367.34361.980.4740.5190.365
290372.60371.07370.23367.26361.630.4970.4970.372
291372.73371.21370.38367.46361.770.4890.5040.378
292372.89371.40370.59367.91362.310.4650.5280.385
293372.99371.51370.73368.25362.800.4310.5600.392
294373.12371.66370.89368.69363.490.3940.5950.399
295373.23371.77371.02369.05364.150.3570.6300.407
296373.36371.90371.16369.42364.880.3210.6630.414
297373.45371.89371.16369.38365.070.3060.6770.422
298373.53371.90371.17369.27364.720.3230.6630.427
299373.60371.96371.22369.29364.690.3250.6610.432
300373.67372.02371.28369.40364.830.3180.6680.436
301373.73372.08371.34369.53365.080.3050.6800.441
302373.80372.13371.40369.69365.400.2880.6960.446
303373.87372.20371.47369.91365.870.2680.7130.451
304373.93372.24371.51370.05366.220.2480.7320.456
305374.00372.57371.79370.75367.610.1840.7870.464
306374.13372.83372.05371.25369.380.1070.8390.477
307374.29372.98372.19371.48370.170.0730.8590.492
308374.45373.09372.27371.59370.530.0560.8670.509
309374.63373.21372.35371.67370.750.0470.8700.527
310374.96373.35372.43371.75370.930.0400.8720.547
311375.17373.47372.50371.80371.040.0350.8720.568
312375.47373.64372.60371.87371.170.0310.8720.592
313375.67373.54372.50371.82371.170.0290.8730.616
314375.91373.45372.38371.73371.060.0310.8850.636
315376.16373.50372.37371.71371.050.0300.8900.656
316376.43373.60372.40371.73371.090.0280.8930.677
317376.76373.74372.46371.77371.170.0250.8940.699
318377.09373.88372.52371.80371.240.0230.8940.722
319377.49374.07372.59371.85371.320.0200.8930.747
320377.84374.24372.66371.89371.380.0170.8920.773
321378.30374.75372.90372.00371.480.0140.8870.802
322379.05375.67373.31372.20371.670.0110.8690.841
323380.07376.87373.81372.41371.830.0080.8520.883
324381.00378.55374.54372.64371.970.0070.8300.926
325382.05381.35376.91373.25372.240.0050.7880.962
326382.93382.86381.76375.59373.050.0030.6700.985
327368.13366.46362.62357.18355.410.8750.1050.266
328368.51365.90362.03356.26354.190.9620.0370.274
329368.90366.96364.86359.79355.420.8800.1200.283
330369.30367.56366.01362.03356.890.7850.2140.292
331369.72368.13366.88363.44358.070.7150.2840.302
332370.13368.67367.51364.46358.990.6630.3340.312
333370.42369.05367.94365.12359.720.6140.3810.323
334370.87369.65368.59366.10360.730.5670.4250.334
335371.14369.99368.96366.73361.320.5220.4670.347
336371.44369.93368.86365.82360.680.5550.4370.359
337371.75370.05368.96365.52359.970.5970.3980.369
338372.00370.33369.26365.93360.230.5840.4120.379
339372.27370.64369.63366.60360.920.5480.4470.389
340372.49370.92369.94367.33361.680.5030.4890.399
341372.74371.21370.26367.98362.580.4540.5350.410
342372.91371.41370.48368.41363.230.4100.5750.421
343373.13371.65370.73368.89364.020.3690.6120.433
344373.29371.56370.65368.50363.670.3840.5990.444
345373.45371.61370.69368.35363.180.4100.5780.452
346373.59371.73370.80368.47363.250.4060.5820.460
347373.72371.87370.95368.74363.620.3880.5990.468
348373.84371.98371.07369.02364.070.3610.6230.477
349373.98372.11371.21369.34364.670.3320.6500.485
350374.12372.24371.34369.68365.360.3030.6760.494
351374.34372.34371.44369.91365.890.2740.7020.503
352374.42372.32371.43369.89366.070.2570.7170.512
353374.52372.28371.40369.77365.730.2720.7070.519
354374.59372.32371.43369.78365.680.2750.7050.525
355374.67372.38371.48369.86365.790.2690.7100.531
356374.75372.44371.54369.97366.020.2580.7200.536
357374.82372.49371.59370.09366.300.2440.7320.543
358374.92372.56371.65370.27366.730.2290.7460.549
359375.00372.61371.70370.41367.180.2120.7610.555
360375.08373.03372.02370.98368.320.1560.8050.565
361375.24373.29372.25371.36369.590.0980.8380.580
362375.44373.46372.39371.56370.230.0710.8510.597
363375.66373.61372.49371.68370.580.0570.8570.616
364375.92373.77372.58371.77370.810.0480.8590.636
365376.21373.94372.68371.84370.960.0420.8600.658
366376.48374.10372.76371.89371.070.0370.8600.682
367376.82374.31372.86371.96371.170.0330.8580.707
368377.16374.20372.74371.90371.160.0330.8610.732
369377.51374.21372.67371.84371.100.0330.8700.755
370377.89374.35372.71371.85371.120.0320.8740.778
371378.31374.57372.78371.88371.190.0290.8750.801
372378.78374.94372.88371.94371.270.0260.8740.826
373379.40375.38373.04372.01371.370.0230.8710.851
374379.82375.75373.17372.07371.440.0200.8680.878
375380.49376.50373.43372.17371.550.0170.8620.906
376381.20378.59374.37372.49371.750.0130.8420.934
377382.01381.34376.93373.22372.150.0090.7890.961
378382.76382.69381.40375.34372.950.0060.6770.980
379365.14360.67357.54355.34354.660.9210.0700.236
380365.54359.43355.40353.99353.740.9930.0070.242
381366.03360.43355.93354.06353.730.9940.0060.251
382366.55361.59356.81354.27353.770.9910.0090.260
383367.08362.89358.16354.68353.860.9850.0150.269
384367.60364.13360.01355.45354.040.9720.0270.279
385368.17365.33362.16356.94354.460.9450.0550.290
386368.74366.41364.01358.94355.230.8940.1060.302
387369.32367.28365.41361.07356.310.8260.1730.315
388369.81367.30364.97359.76355.950.8430.1560.327
389370.27367.73364.90358.72355.250.8910.1090.336
390370.69368.32365.63359.13355.290.8880.1110.346
391371.11368.97366.89360.65355.870.8530.1460.356
392371.47369.49367.86362.34356.820.7910.2080.366
393371.83370.00368.68364.12358.130.7090.2890.378
394372.15370.42369.27365.51359.530.6290.3680.389
395372.45370.80369.75366.63360.800.5540.4400.402
396372.69370.79369.70365.97360.390.5690.4260.412
397372.90370.98369.87365.88360.040.5930.4030.421
398373.09371.19370.12366.25360.290.5790.4170.429
399373.27371.42370.40366.97360.940.5440.4510.437
400373.45371.62370.65367.67361.800.4980.4940.446
401373.60371.79370.86368.26362.660.4490.5410.455
402373.78371.97371.07368.87363.700.4010.5870.464
403373.86372.05371.16369.14364.190.3550.6290.474
404373.99372.02371.14369.02364.230.3510.6330.483
405374.10372.08371.19369.01364.090.3590.6270.489
406374.17372.14371.25369.11364.200.3530.6330.495
407374.26372.22371.34369.29364.500.3380.6470.502
408374.36372.30371.42369.52364.950.3170.6660.508
409374.44372.37371.50369.75365.430.2940.6880.515
410374.61372.42371.55369.93365.840.2690.7100.521
411374.69372.48371.61370.12366.300.2440.7320.528
412374.82372.95372.00370.95368.210.1640.7970.539
413375.00373.18372.21371.34369.560.1010.8370.557
414375.21373.35372.34371.54370.220.0720.8530.576
415375.46373.51372.44371.66370.580.0560.8600.597
416375.75373.68372.54371.75370.820.0470.8630.620
417376.07373.86372.64371.83370.980.0410.8630.646
418376.47374.09372.76371.91371.130.0350.8630.673
419376.77374.27372.84371.96371.210.0310.8610.703
420377.20374.14372.69371.88371.170.0310.8660.733
421377.58374.22372.67371.85371.150.0300.8740.759
422378.05374.42372.73371.87371.190.0280.8770.787
423378.60374.71372.83371.92371.280.0250.8770.816
424379.18375.19372.97371.99371.370.0220.8740.846
425379.82375.71373.15372.07371.460.0190.8700.879
426380.69376.71373.49372.20371.590.0160.8630.911
427381.48378.18374.00372.36371.720.0130.8500.943
428382.33381.68376.87373.10372.080.0080.8050.971
429383.03382.99382.14375.99373.140.0050.6520.988
430363.90359.79357.64355.68354.910.9070.0850.265
431364.31357.41354.79353.94353.750.9920.0070.271
432364.88357.27354.47353.79353.680.9970.0030.280
433365.37357.59354.50353.78353.670.9980.0020.289
434365.88358.19354.67353.80353.670.9980.0020.300
435366.41359.12354.96353.85353.680.9970.0030.310
436367.00360.32355.50353.95353.700.9960.0040.322
437367.63361.86356.45354.15353.740.9930.0070.334
438368.27363.63358.11354.60353.830.9870.0130.348
439368.88362.62356.97354.28353.820.9880.0120.360
440369.40361.69355.59353.91353.710.9950.0050.370
441369.91362.13355.47353.85353.680.9970.0030.379
442370.38363.50356.05353.91353.690.9960.0030.389
443370.83365.28357.37354.10353.720.9940.0060.400
444371.31367.30360.10354.67353.820.9870.0120.412
445371.75368.70363.60356.15354.130.9680.0320.423
446372.13369.59366.46358.85354.910.9150.0850.436
447372.48369.71366.63359.14355.330.8850.1150.446
448372.76370.04367.04359.10355.220.8930.1060.455
449373.13370.44367.82360.01355.480.8770.1220.463
450373.34370.78368.61361.28356.030.8400.1600.471
451373.56371.10369.34362.89356.950.7820.2160.480
452373.78371.40369.93364.57358.190.7120.2850.489
453373.97371.64370.34365.92359.560.6370.3590.498
454374.14371.83370.64367.05360.760.5630.4300.508
455374.26371.80370.62366.95361.050.5330.4590.516
456374.39371.87370.69366.76360.800.5470.4470.523
457374.49371.96370.79367.00360.900.5420.4520.529
458374.59372.07370.92367.31361.210.5240.4690.534
459374.69372.18371.06367.73361.730.4980.4930.540
460374.78372.26371.17368.09362.230.4670.5230.547
461374.86372.35371.28368.48362.830.4330.5550.553
462374.98372.45371.41368.98363.690.3980.5880.559
463375.07372.93371.84370.22365.660.2870.6860.569
464375.26373.24372.13370.94368.030.1760.7720.585
465375.48373.44372.30371.27369.190.1230.8090.603
466375.73373.61372.42371.46369.790.0960.8260.623
467375.99373.79372.53371.58370.160.0800.8340.645
468376.27373.96372.63371.68370.400.0690.8390.667
469376.59374.16372.74371.77370.600.0600.8410.692
470376.98374.41372.87371.86370.780.0540.8410.719
471377.34374.28372.73371.78370.760.0530.8440.745
472377.74374.30372.66371.73370.690.0530.8540.769
473378.13374.46372.71371.75370.740.0500.8580.792
474378.55374.69372.79371.80370.840.0460.8600.816
475379.03375.10372.90371.86370.970.0410.8610.841
476379.58375.52373.06371.95371.100.0360.8600.868
477380.22376.14373.28372.05371.250.0310.8560.895
478381.02377.30373.69372.21371.430.0260.8500.922
479381.65379.77375.04372.61371.710.0200.8290.949
480382.36382.09378.79373.73372.290.0130.7560.971
481382.98382.94382.39376.97373.540.0080.5940.986

Table 5:

Test data.

S.No.TBT5T10T15T17xD1xD2xB3
1364.27361.89358.72355.91354.990.8990.0880.166
2364.61359.64355.73354.10353.780.9900.0100.171
3364.99359.99355.77354.02353.730.9940.0060.176
4365.48360.60356.10354.08353.730.9930.0070.181
5365.90361.46356.76354.23353.760.9920.0080.187
6366.29362.34357.63354.46353.810.9880.0120.192
7366.73363.39358.94354.92353.910.9810.0190.198
8367.17364.41360.69355.73354.110.9680.0320.205
9367.64365.36362.51357.09354.500.9420.0580.212
10368.09365.66362.60357.03354.620.9320.0680.219
11368.50366.11362.82356.90354.510.9400.0590.225
12368.90366.85363.75357.50354.650.9310.0690.232
13369.31367.51365.04358.79355.100.9030.0970.239
14369.68368.09366.23360.55355.840.8540.1450.246
15370.06368.64367.33362.36356.920.7850.2150.254
16370.44369.14368.12364.01358.210.7120.2870.262
17370.72369.50368.61365.08359.320.6410.3570.270
18371.00369.68368.73364.82359.400.6310.3670.278
19371.26369.94368.99364.85359.060.6460.3520.285
20371.49370.22369.33365.38359.530.6240.3740.291
21371.73370.52369.72366.22360.350.5820.4150.298
22371.92370.76370.02367.06361.210.5310.4650.306
23372.10370.97370.28367.73362.110.4770.5170.313
24372.25371.14370.49368.26362.910.4250.5670.321
25372.43371.34370.71368.82363.870.3760.6130.329
26372.55371.32370.67368.44363.540.3880.6030.336
27372.67371.41370.74368.30363.100.4110.5810.341
28372.77371.51370.84368.39363.120.4120.5800.346
29372.85371.60370.94368.58363.360.3990.5930.351
30372.94371.70371.05368.86363.790.3760.6140.356
31373.01371.77371.14369.12364.240.3490.6400.361
32373.10371.86371.23369.43364.840.3190.6680.366
33373.16371.92371.31369.68365.370.2900.6950.371
34373.25372.19371.58370.49367.100.2120.7640.379
35373.35372.34371.74370.91368.550.1400.8210.390
36373.47372.45371.84371.14369.380.1020.8490.402
37373.60372.54371.92371.29369.860.0810.8640.415
38373.74372.64371.99371.39370.200.0670.8730.429
39373.88372.73372.06371.47370.430.0570.8790.445
40374.04372.83372.12371.54370.630.0490.8830.461
41374.20372.92372.18371.60370.770.0420.8860.479
42374.37372.97372.20371.63370.880.0370.8890.498
43374.58373.06372.24371.67370.970.0330.8920.518
44374.92373.17372.30371.72371.080.0290.8930.540
45375.20373.31372.37371.77371.190.0250.8940.563
46375.48373.44372.44371.81371.270.0220.8940.589
47375.81373.60372.52371.86371.360.0190.8930.617
48376.24373.81372.61371.92371.440.0160.8910.649
49376.66374.02372.70371.97371.510.0140.8880.684
50377.02374.11372.73371.98371.540.0120.8850.722
51377.63374.27372.74371.97371.550.0110.8880.760
52378.28374.57372.83372.01371.590.0090.8880.800
53379.22375.23373.02372.08371.650.0080.8840.843
54380.21376.05373.29372.17371.720.0070.8770.889
55381.25377.46373.73372.32371.810.0050.8640.935
56382.52380.75375.24372.67371.990.0040.8370.973
57365.44362.10358.71355.87354.950.9090.0800.226
58365.85360.47356.02354.13353.770.9910.0090.232
59366.30361.63356.96354.32353.780.9900.0100.240
60366.78362.80358.26354.74353.870.9840.0160.248
61367.29364.00360.12355.55354.070.9710.0290.257
62367.78365.01361.93356.82354.430.9480.0520.266
63368.27365.87363.53358.48355.040.9060.0940.276
64368.81366.78364.89360.45355.970.8490.1510.286
65369.29367.46365.86361.94356.920.7860.2140.298
66369.75367.47365.43360.46356.380.8140.1850.309
67370.15367.83365.36359.48355.570.8690.1310.317
68370.56368.39366.00359.80355.560.8720.1280.325
69370.91368.90366.95360.86356.010.8430.1570.334
70371.22369.36367.78362.26356.800.7900.2090.343
71371.57369.83368.56363.89357.970.7170.2810.353
72371.85370.21369.10365.16359.110.6440.3530.363
73372.13370.57369.57366.29360.420.5740.4210.373
74372.37370.66369.64366.09360.610.5570.4380.383
75372.58370.81369.77365.86360.090.5890.4070.391
76372.76371.02370.01366.15360.240.5830.4140.398
77372.93371.23370.26366.69360.760.5540.4420.406
78373.11371.44370.52367.46361.570.5130.4810.413
79373.24371.59370.71368.00362.320.4670.5240.421
80373.40371.76370.91368.59363.250.4210.5680.430
81373.50371.86371.03368.93363.850.3760.6100.438
82373.61371.82371.00368.71363.760.3760.6110.445
83373.71371.88371.05368.64363.490.3910.5980.451
84373.78371.95371.11368.71363.530.3890.6000.456
85373.86372.02371.19368.87363.750.3780.6110.461
86373.93372.09371.27369.08364.080.3590.6280.466
87374.00372.16371.34369.30364.500.3370.6490.472
88374.07372.22371.41369.53364.950.3120.6710.477
89374.14372.28371.48369.75365.450.2870.6950.483
90374.23372.60371.76370.52366.770.2210.7530.490
91374.38372.88372.03371.12368.910.1320.8180.504
92374.54373.03372.16371.37369.790.0910.8450.520
93374.82373.15372.25371.51370.260.0700.8580.537
94375.00373.26372.32371.60370.510.0570.8640.556
95375.21373.39372.40371.67370.710.0490.8670.576
96375.45373.52372.48371.74370.860.0430.8690.597
97375.78373.70372.57371.81371.020.0370.8690.621
98376.02373.63372.49371.77371.030.0350.8710.645
99376.27373.60372.42371.72370.970.0360.8800.666
100376.58373.70372.44371.72370.990.0340.8840.688
101376.90373.82372.49371.75371.060.0310.8860.710
102377.19373.96372.55371.79371.130.0280.8870.734
103377.59374.15372.62371.84371.220.0250.8860.759
104378.14374.44372.74371.90371.320.0220.8850.786
105378.51374.64372.81371.94371.380.0190.8830.814
106379.15375.62373.23372.13371.550.0150.8730.848
107380.05376.81373.76372.36371.750.0110.8520.888
108381.06378.73374.63372.66371.940.0090.8270.929
109382.12381.59377.44373.40372.280.0070.7810.963
110382.92382.86381.90375.83373.140.0040.6560.984
111366.17362.27358.72355.84354.920.9110.0790.266
112366.59360.88356.10354.14353.770.9910.0090.273
113367.11362.46357.49354.45353.810.9890.0110.282
114367.62363.80359.32355.10353.950.9790.0210.292
115368.12364.97361.31356.24354.250.9580.0420.302
116368.63366.05363.19357.95354.820.9210.0780.313
117369.16366.90364.71360.01355.700.8630.1360.325
118369.66367.64365.80361.67356.700.7970.2020.337
119370.19368.39366.85363.16357.790.7310.2670.351
120370.64368.37366.50361.92357.290.7560.2420.364
121371.06368.70366.64361.21356.460.8100.1890.374
122371.46369.23367.41361.85356.660.8030.1960.384
123371.76369.64368.03362.83357.230.7620.2370.395
124372.08370.09368.69364.14358.200.7020.2960.406
125372.43370.55369.32365.54359.580.6290.3670.418
126372.74370.94369.80366.63360.790.5620.4320.430
127373.04371.31370.22367.65361.980.4990.4910.443
128373.20371.17370.06366.78361.300.5160.4760.454
129373.41371.33370.22366.74360.980.5370.4570.463
130373.58371.52370.43367.17361.260.5240.4690.472
131373.82371.67370.61367.58361.730.4940.4980.481
132374.01371.88370.85368.20362.580.4540.5350.490
133374.16372.03371.02368.66363.310.4120.5750.500
134374.29372.16371.16369.03363.980.3710.6130.509
135374.44372.29371.30369.42364.740.3310.6490.520
136374.55372.20371.24369.21364.600.3320.6490.528
137374.65372.24371.27369.15364.360.3440.6400.535
138374.74372.31371.33369.23364.430.3420.6420.541
139374.83372.37371.40369.36364.640.3310.6520.548
140374.92372.45371.47369.56364.990.3150.6670.554
141374.99372.50371.53369.72365.340.2940.6850.561
142375.08372.57371.60369.93365.790.2730.7050.567
143375.18372.63371.66370.12366.260.2510.7250.574
144375.26373.00371.93370.72367.370.1970.7700.583
145375.47373.40372.28371.30369.280.1170.8220.600
146375.71373.61372.45371.56370.140.0800.8410.619
147375.94373.77372.56371.68370.490.0620.8490.640
148376.22373.95372.66371.78370.740.0520.8520.663
149376.60374.19372.79371.87370.940.0450.8530.688
150376.95374.40372.90371.95371.070.0400.8520.714
151377.41374.71373.04372.03371.200.0350.8490.743
152377.77374.62372.94371.98371.200.0340.8500.773
153378.27374.63372.83371.90371.110.0350.8610.799
154378.70374.92372.88371.91371.140.0330.8650.825
155379.20375.24372.98371.95371.210.0300.8660.851
156379.91375.82373.18372.04371.330.0260.8630.879
157380.47376.45373.40372.13371.430.0230.8580.907
158381.27377.80373.87372.30371.590.0190.8490.935
159381.96379.80374.73372.55371.780.0150.8310.959
160382.71382.50379.15373.74372.300.0100.7670.978
161383.12383.10382.78377.56373.750.0050.5710.990
162366.04363.03359.37355.98354.970.9010.0850.226
163366.44361.50356.70354.27353.810.9880.0120.232
164366.86362.49357.58354.45353.810.9880.0120.239
165367.31363.58358.90354.89353.910.9820.0180.247
166367.76364.65360.72355.72354.110.9680.0320.255
167368.18365.56362.47357.00354.470.9440.0560.262
168368.63366.45364.05358.71355.110.9000.0990.271
169369.07367.13365.29360.59356.000.8420.1570.280
170369.56367.81366.31362.27357.080.7790.2200.291
171369.93368.02366.41361.92357.080.7700.2290.300
172370.32368.45366.96362.16357.020.7760.2230.309
173370.66368.91367.57363.01357.520.7450.2540.318
174371.00369.36368.18364.11358.350.6930.3050.328
175371.38369.85368.81365.36359.600.6340.3630.338
176371.66370.20369.23366.21360.520.5700.4250.349
177371.96370.57369.65367.16361.560.5130.4800.360
178372.24370.92370.03367.88362.540.4590.5300.372
179372.43370.96370.07367.68362.540.4460.5420.384
180372.65371.09370.20367.68362.270.4620.5290.394
181372.86371.30370.42368.03362.640.4430.5470.404
182373.05371.50370.64368.48363.260.4100.5780.414
183373.25371.71370.87368.96364.070.3720.6130.424
184373.38371.85371.01369.27364.630.3330.6480.435
185373.54372.01371.18369.62365.340.2970.6800.447
186373.71372.17371.33369.92365.990.2630.7090.459
187373.85372.07371.25369.70365.800.2700.7060.469
188373.96372.08371.25369.57365.380.2900.6910.477
189374.07372.16371.32369.62365.360.2920.6900.485
190374.16372.23371.39369.73365.540.2830.6980.492
191374.27372.31371.47369.91365.890.2670.7120.499
192374.36372.38371.54370.09366.290.2480.7290.507
193374.44372.44371.60370.23366.650.2270.7470.515
194374.63372.51371.66370.40367.170.2070.7650.523
195374.75372.90371.96370.97368.430.1480.8110.534
196374.95373.14372.18371.33369.620.0990.8390.551
197375.16373.30372.30371.51370.180.0750.8520.570
198375.37373.43372.39371.61370.470.0610.8580.590
199375.65373.60372.49371.71370.710.0510.8620.612
200375.91373.75372.57371.77370.860.0440.8630.636
201376.25373.94372.67371.85371.010.0390.8630.662
202376.71374.21372.81371.93371.160.0340.8620.691
203377.06374.31372.82371.94371.200.0310.8620.721
204377.46374.51372.90371.98371.270.0280.8630.752
205378.18375.06373.09372.07371.390.0250.8600.786
206378.82375.54373.28372.16371.480.0220.8560.823
207379.46376.13373.51372.25371.570.0190.8490.863
208380.48377.48374.04372.45371.720.0160.8370.903
209381.44379.59375.17372.76371.910.0130.8140.942
210382.38382.06378.54373.68372.340.0100.7590.972
211383.06383.01382.04375.86373.190.0060.6410.988
212365.67361.07358.06355.68354.870.9100.0810.285
213366.10359.51355.44354.03353.760.9920.0080.292
214366.62360.40355.76354.03353.720.9940.0060.302
215367.18361.59356.51354.19353.750.9920.0080.313
216367.74363.02357.81354.54353.830.9870.0130.324
217368.25364.34359.64355.21353.980.9770.0230.335
218368.84365.78361.99356.66354.360.9510.0490.348
219369.44366.89364.11358.83355.150.9010.0990.362
220369.99367.76365.53360.95356.190.8300.1690.376
221370.52367.71365.13359.82355.990.8410.1590.390
222370.98368.06365.02358.75355.260.8900.1100.401
223371.44368.72365.83359.30355.310.8890.1110.411
224371.79369.27366.91360.48355.780.8560.1430.422
225372.20369.89368.04362.40356.820.7980.2010.434
226372.54370.36368.80364.04358.010.7180.2800.447
227373.00370.84369.47365.61359.560.6390.3560.460
228373.29371.22369.92366.67360.750.5650.4270.473
229373.51371.12369.81366.02360.440.5680.4250.485
230373.72371.24369.92365.79359.920.6000.3950.495
231373.91371.45370.16366.07360.060.5930.4020.504
232374.09371.66370.41366.60360.550.5640.4300.512
233374.27371.86370.66367.35361.300.5230.4690.522
234374.43372.03370.87367.94362.090.4770.5130.531
235374.57372.18371.05368.45362.880.4300.5560.541
236374.74372.34371.23368.97363.780.3850.5980.551
237374.86372.28371.20368.88363.940.3690.6130.561
238374.97372.29371.21368.79363.660.3840.6020.568
239375.08372.37371.28368.87363.700.3830.6030.574
240375.16372.43371.35369.00363.880.3720.6130.581
241375.25372.51371.43369.20364.220.3540.6290.587
242375.36372.59371.52369.46364.710.3330.6490.594
243375.46372.67371.60369.71365.240.3100.6700.601
244375.55372.73371.66369.91365.670.2860.6920.608
245375.67373.32372.11370.85367.630.1950.7640.619
246375.89373.64372.39371.33369.240.1210.8110.637
247376.15373.86372.55371.56370.010.0870.8300.657
248376.42374.05372.67371.70370.400.0690.8370.679
249376.74374.26372.79371.80370.650.0580.8400.703
250377.13374.52372.93371.90370.850.0510.8410.728
251377.52374.89373.06371.98370.990.0460.8390.756
252378.00375.25373.23372.08371.130.0410.8360.785
253378.49375.08373.03371.97371.080.0410.8410.814
254378.96375.18372.99371.92371.020.0410.8500.839
255379.57375.56373.09371.96371.090.0380.8540.864
256380.19376.13373.28372.04371.200.0340.8530.890
257380.70376.79373.51372.13371.320.0300.8490.916
258381.45378.29374.06372.33371.510.0250.8400.940
259382.09380.37375.20372.63371.740.0200.8210.962
260382.71382.19377.70373.28372.100.0140.7790.979
261383.10383.07382.51376.44373.230.0090.6360.989
262365.77362.54358.82355.78354.870.9100.0780.216
263366.17361.22356.47354.21353.780.9900.0100.222
264366.61362.45357.71354.51353.820.9870.0130.230
265367.08363.65359.45355.14353.970.9780.0220.237
266367.54364.70361.28356.21354.250.9590.0410.245
267368.01365.59363.01357.76354.750.9260.0730.254
268368.52366.51364.51359.76355.580.8760.1240.263
269368.94367.12365.48361.23356.430.8150.1840.273
270369.45367.80366.41362.73357.490.7530.2460.283
271369.83367.85366.15361.49356.960.7770.2220.293
272370.23368.24366.31360.89356.280.8230.1770.301
273370.57368.70366.99361.39356.420.8140.1850.309
274370.95369.22367.79362.64357.130.7760.2240.318
275371.28369.66368.47363.98358.110.7180.2810.327
276371.54370.00368.95365.06359.080.6470.3500.337
277371.85370.40369.47366.25360.440.5810.4150.346
278372.07370.67369.79367.08361.340.5180.4750.357
279372.29370.74369.85366.72361.350.5140.4800.366
280372.50370.91370.00366.65360.990.5360.4590.374
281372.66371.09370.20367.04361.210.5220.4720.382
282372.85371.31370.46367.62361.880.4910.5030.389
283373.01371.50370.68368.18362.670.4500.5410.397
284373.14371.64370.84368.61363.350.4070.5820.405
285373.29371.79371.01369.07364.180.3640.6220.414
286373.42371.92371.16369.44364.920.3240.6590.423
287373.51371.88371.12369.29364.990.3110.6710.431
288373.60371.87371.10369.03364.340.3440.6430.437
289373.68371.94371.15368.98364.090.3570.6310.441
290373.75372.00371.22369.05364.130.3570.6310.446
291373.82372.07371.28369.18364.340.3480.6400.450
292373.87372.11371.34369.32364.570.3330.6540.455
293373.93372.17371.40369.52364.960.3140.6710.460
294374.00372.23371.46369.73365.420.2920.6910.465
295374.07372.56371.76370.55366.830.2200.7540.472
296374.21372.81372.01371.13368.970.1290.8230.485
297374.35372.93372.12371.37369.820.0860.8510.500
298374.55373.07372.22371.53370.370.0650.8640.517
299374.80373.16372.28371.60370.600.0520.8710.535
300375.00373.27372.35371.67370.780.0440.8740.554
301375.25373.41372.43371.74370.950.0380.8760.575
302375.50373.55372.50371.80371.060.0340.8760.598
303375.72373.26372.28371.66370.980.0350.8810.620
304375.88373.12372.13371.54370.760.0400.8930.633
305376.02373.12372.10371.49370.670.0420.8990.645
306376.17373.15372.10371.49370.660.0420.9010.657
307376.32373.19372.12371.51370.700.0400.9030.669
308376.48373.25372.14371.53370.770.0380.9050.681
309376.67373.32372.17371.56370.850.0350.9070.693
310376.85373.38372.20371.59370.930.0310.9080.706
311377.12374.69372.98372.01371.320.0190.8980.728
312377.90376.41374.40372.86372.050.0070.8160.778
313378.95377.97375.87373.57372.480.0050.7500.838
314380.39380.04378.50374.99373.060.0040.6700.901
315381.87381.76381.49378.47374.470.0030.5030.954
316382.98382.93382.87381.83377.320.0010.2570.986
317365.71362.67359.37356.16355.110.8990.0880.236
318366.11361.12356.60354.30353.820.9870.0120.242
319366.58362.21357.59354.52353.830.9870.0130.250
320367.05363.32358.95355.03353.950.9790.0210.258
321367.54364.41360.79355.97354.180.9630.0370.267
322368.00365.31362.44357.29354.590.9360.0640.276
323368.51366.26363.99359.07355.310.8900.1090.286
324368.98366.96365.11360.76356.160.8330.1660.297
325369.50367.68366.10362.30357.170.7720.2270.309
326369.91367.67365.75360.99356.720.7930.2060.320
327370.34368.02365.71359.96355.810.8520.1480.328
328370.68368.48366.22360.22355.790.8560.1440.336
329371.02368.97367.10361.19356.210.8280.1710.345
330371.39369.50368.00362.74357.130.7780.2210.354
331371.72369.96368.71364.26358.290.7090.2890.364
332371.94370.25369.12365.21359.160.6410.3560.374
333372.25370.63369.61366.37360.520.5740.4210.384
334372.45370.64369.57365.82360.300.5750.4210.394
335372.65370.80369.70365.61359.810.6060.3910.401
336372.84371.02369.95365.89359.950.6010.3960.408
337373.00371.21370.19366.41360.420.5740.4220.415
338373.16371.41370.44367.14361.130.5350.4590.423
339373.33371.60370.69367.84362.070.4910.5020.430
340373.45371.74370.85368.34362.820.4450.5450.438
341373.54371.83370.96368.67363.360.4000.5870.446
342373.65371.80370.94368.48363.360.4000.5890.453
343373.76371.86370.99368.39363.070.4150.5760.459
344373.84371.93371.06368.47363.110.4140.5760.464
345373.92372.02371.15368.65363.340.4030.5870.469
346373.98372.08371.22368.84363.640.3850.6030.474
347374.06372.15371.31369.11364.100.3630.6240.479
348374.15372.23371.40369.42364.700.3380.6470.484
349374.18372.26371.43369.54364.940.3130.6700.489
350374.28372.65371.78370.50366.680.2320.7410.497
351374.41372.88372.01371.03368.580.1430.8080.511
352374.70373.05372.16371.33369.650.1000.8370.526
353374.87373.17372.25371.47370.110.0780.8500.542
354375.03373.28372.32371.56370.360.0650.8570.560
355375.25373.40372.39371.64370.580.0560.8610.579
356375.47373.53372.47371.71370.740.0490.8630.599
357375.74373.68372.55371.77370.890.0430.8640.621
358375.99373.56372.43371.70370.860.0430.8680.643
359376.22373.55372.38371.66370.800.0430.8760.662
360376.47373.63372.40371.67370.830.0410.8800.681
361376.79373.76372.45371.70370.920.0380.8830.701
362377.05373.88372.50371.74370.990.0340.8840.722
363377.48374.08372.58371.80371.110.0310.8840.745
364377.78374.23372.64371.83371.180.0270.8840.768
365378.16374.43372.72371.88371.260.0240.8830.794
366378.67375.23373.07372.05371.430.0190.8760.822
367379.46376.16373.52372.27371.650.0150.8580.858
368380.33377.39374.05372.48371.810.0120.8400.897
369381.22379.32375.11372.78371.990.0100.8160.935
370382.21381.85378.30373.67372.380.0070.7640.965
371382.93382.88382.13376.32373.320.0050.6310.984

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Received: 2015-12-20
Revised: 2016-3-18
Accepted: 2016-3-18
Published Online: 2016-4-13
Published in Print: 2016-9-1

©2016 by De Gruyter