如何才能使残差平方和最小且稳定？

mason84

请问：我以应变为输入，应力为输出，求Z变换中系统函数的系数，系统函数为：
H(z)=(a0+a1*z^-1+a2*z^-2)/(1+b1*z^-1+b2*z^-2)。我给的程序为：
fun=inline('filter([c(1),c(2),c(3)],[1,c(4),c(5)],x)','c','x')
x=[0
0.04184
0.0723
0.09697
0.12765
0.14643
0.18806
0.21472
0.24872
0.274
0.31424
0.34338
0.38413
0.40982
0.43935
0.47852
0.51226
0.55601
0.58149
0.6067
0.65799
0.68482
0.71612
0.74669
0.78257
0.81653
0.84114
0.88515
0.90503
0.95437
0.99401
1.03018
1.07001
1.09692
1.13359
1.16586
1.20422
1.23284
1.27008
1.30559
1.33511
1.36488
1.39604
1.4368
1.48007
1.50529
1.54148
1.57062
1.60625
1.64458
1.67206
1.69548
1.72982
1.75103
1.78209
1.81385
1.84224
1.87819
1.91252
1.95262
1.99029
2.01074
2.04062
2.07771
2.11211
2.15843
2.18518
2.21771
2.25465
2.28911
2.32975
2.3703
2.40311
2.42575
2.45578
2.48918
2.52038
2.54504
2.5843
2.61687
2.66173
2.69973
2.72396
2.75938
2.79057
2.82948
2.86455
2.89998
2.93049
2.96599
2.99538
3.02256
3.0531
3.09923
3.13175
3.16963
3.2007
3.22395
3.26119
3.28289
3.32448
3.35429
3.39607
3.42836
3.45972
3.49106
3.5258
3.56124
3.59887
3.62621
3.66916
3.70183
3.73496
3.76974
3.81062
3.83572
3.87426
3.89934
3.93226
3.96968
3.99744
4.03502
4.05332
4.09946
4.12185
4.16443
4.19266
4.22326
4.25951
4.29977
4.33016
4.36806
4.39555
4.43072
4.46429
4.4971
4.52435
4.55015
4.59955
4.63352
4.65829
4.69313
4.73175
4.76842
4.79993
4.8396
4.86629
4.89499
4.92756
4.95622
5.00288
5.04173
5.06193
5.1007
5.13492
5.16483
5.19276
5.22734
5.26197
5.30333
5.32328
5.36434
5.39049
5.42528
5.46141
5.49911
5.53525
5.56081
5.60465
5.63623
5.66569
5.69759
5.73525
5.75805
5.8004
5.82936
5.8606
5.9011
5.93159
5.95796
6.00133
6.03144
6.06915
6.10134
6.13008
6.16008
6.19659
6.2324
6.25308
6.30428
6.34202
6.38009
6.41834
6.44187
6.47252
6.49623
6.52641
6.55032
6.58991
6.62817
6.6531
6.68856
6.71997
6.76109
6.79241
6.82325
6.86189
6.89738
6.93344
6.96427
6.99494
7.02926
7.05449
7.09268
7.12332
7.15789
7.19914
7.21253
7.26827
7.29794
7.32499
7.35409
7.40213
7.43511
7.46431
7.51619
7.5363
7.57552
7.60182
7.63537
7.66498
7.70605
7.75344
7.79759
7.77898
7.8112
7.86755
7.90392
7.95149
7.97473
8.00003
8.04018
8.07058
8.08401
8.11324
8.14079
8.18598
8.21957
8.24979
8.28848
8.32537
8.35594
8.37807
8.41175
8.4509
8.48628
8.51356
8.55325
8.58747
8.6266
8.65416
8.68671
8.72488
8.75856
8.7915
8.81836
8.85095
8.88708
8.92416
8.95412
8.99097
9.01534
9.06178
9.09297
9.12941
9.15899
9.19373
9.22771
9.26071
9.3033
9.32241
9.35759
9.38942
9.42511
9.45873
9.48631
9.51427
9.5482
9.58832
9.61305
9.65848
9.67824
9.71916
9.75012
9.78509
9.81962
9.85985
9.87647
9.92312
9.95367
9.98774
10.02001
10.07027
10.09096
10.12162
10.16387
10.19477
10.23955
10.2703
10.29964
10.33119
10.36366
10.39749
10.43043
10.47679
10.4959
10.53289
10.55996
10.59567
10.62817
10.65516
10.69677
10.73925
10.77326
10.8079
10.83291
10.86726
10.9055
10.92626
10.96635
10.99523
11.03516
11.05582
11.09097
11.12161
11.16252
11.19185
11.22945
11.26106
11.29351
11.32171
11.36404
11.39146
11.42015
11.46425
11.50176
11.52324
11.55944
11.59694
11.62553
11.66851
11.68641
11.72852
11.75839
11.79368
11.82127
11.85348
11.89686
11.93196
11.95951
11.98863
12.01626
12.05162
12.08499
12.1163
12.16077
12.19756
12.23491
12.26268
12.28921
12.33412
12.36348
12.39549
12.42417
12.45477
12.48644
12.52109
12.55274
12.59121
12.62855
12.66111
12.68516
12.72177
12.75438
12.78826
12.81615
12.85644
12.88826
12.92151
12.95549
12.98374
13.02855
13.04983
13.08479
13.11996
13.15135
13.19171
13.22577
13.25863
13.28199
13.32103
13.34626
13.38368
13.41747
13.45474
13.47819
13.52555
13.5597
13.58579
13.60962
13.66044
13.68161
13.72306
13.75718
13.7873
13.82453
13.85207
13.89734
13.92965
13.95742
13.99382
14.01911
14.0458
14.07771
14.12018
14.1457
14.18577
14.23065
14.25319
14.27291
14.31865
14.35981
14.38703
14.42774
14.45957
14.48846
14.51641
14.54583
14.57634
14.61505
14.65591
14.69607
14.74002
14.75981
14.79788
14.83308
14.85351
14.89163
14.92159
14.95932
14.98334
15.01615
15.05692
15.09074
15.11421
15.14863
15.18246
15.21118
15.24696
15.27932
15.32347
15.35065
15.40286
15.42742
15.4722
15.50232
15.5305
15.57094
15.59242
15.63842
15.66693
15.69814
15.72776
15.76166
15.79871
15.8215
15.85675
15.88175
15.91924
15.94533
15.98558
16.0217
16.05387
16.08423
16.11928
16.15197
16.18573
16.21901
16.26238
16.29427
16.32957
16.36651
16.39154
16.42808
16.46096
16.50346
16.53663
16.55904
16.59482
16.62626
16.67325
16.69964
]
y=[0
2.22706
3.43038
4.74759
6.12396
7.52601
8.85312
10.23552
11.75023
13.19102
14.478
15.76179
17.04159
18.30623
19.41019
20.67491
21.83206
22.87327
23.91457
24.89781
25.6566
26.66895
27.48176
28.39649
27.87783
28.66951
29.62519
30.39358
30.13339
31.47516
32.58952
33.36521
34.05291
34.83105
35.45816
36.08929
36.8247
37.30941
38.11074
38.72409
39.26332
39.71719
39.40274
39.76842
40.11729
40.73095
41.38138
41.96251
42.41055
42.97496
43.20802
43.34687
43.65675
44.04883
44.58999
45.12298
45.45707
45.93214
46.51006
46.99229
47.46624
47.86492
48.42063
48.76448
49.19703
49.65806
50.08144
50.4338
50.60946
50.14119
50.26582
50.64448
50.82981
51.09169
51.07878
51.64113
52.0424
52.33643
52.48674
52.75898
53.15988
53.02189
52.34407
52.61269
53.05369
53.27154
53.67513
53.94555
54.25561
54.5257
54.83912
53.75085
54.02481
54.20423
54.45853
54.66331
54.97543
55.21124
55.40853
55.72106
55.96817
56.28686
56.60777
55.95763
56.19494
56.47899
56.90151
57.15637
57.5872
57.89085
58.1802
58.40978
58.70672
58.93353
59.17317
58.7148
58.65042
58.65793
58.68906
58.92208
58.96577
59.20878
59.43533
59.6018
59.68907
59.84442
59.64005
59.76074
59.66439
59.67888
59.81611
58.79138
58.73958
58.81452
58.7731
58.76244
58.66726
57.87344
56.95613
56.94362
57.07987
57.09685
57.18062
57.41115
57.625
57.62626
57.88063
58.03192
58.18315
58.33429
57.11147
56.97453
57.04866
56.92496
56.87003
56.89703
57.06182
57.24099
57.34236
57.26749
57.46299
57.51161
57.73992
57.7455
57.80883
57.87843
57.89264
57.88245
58.03639
58.08778
58.19261
58.2986
58.4765
58.48622
58.61223
58.79484
58.72151
58.84081
58.81015
58.84315
58.73355
58.827
58.80639
58.86318
58.88495
58.81673
58.69553
58.53684
53.40177
53.23465
53.26344
53.30994
53.36812
53.34163
53.41563
53.43634
53.57613
53.70575
53.72633
53.94654
53.9556
53.99022
53.72787
53.76606
53.83164
53.96337
53.96169
54.15055
54.11472
54.20528
54.20714
54.25158
54.32478
54.4001
54.43499
54.02398
53.94456
53.77576
53.89794
53.53378
53.46417
53.19174
52.73403
52.4474
52.31394
51.97332
51.64801
51.27558
50.37632
49.41588
48.74969
48.22655
44.15822
27.45595
26.38314
26.60866
26.78083
26.97411
27.11933
27.0829
27.07852
27.10873
27.22207
27.30874
27.42201
27.6543
27.9021
28.10165
28.13552
28.3642
28.44604
28.58875
28.54836
28.77028
28.91048
29.19444
29.17721
29.27253
29.54689
29.67245
29.76925
29.88042
29.9764
29.9345
30.02562
30.05705
30.19808
30.24149
30.45228
30.40616
30.53858
30.67101
30.7043
30.77484
30.88836
30.927
30.88273
30.85456
30.94667
30.92765
30.96346
31.11109
31.23839
31.21446
31.34578
31.40582
31.41198
31.47261
31.44641
31.379
31.48253
31.52678
31.63714
31.69524
31.82301
31.76312
31.97689
32.04688
32.13117
32.13164
32.27206
32.20003
32.25127
32.32904
32.30411
32.45016
32.45372
32.5542
32.55813
32.7511
32.76915
32.73937
32.75256
32.76181
32.74043
32.87048
32.92553
32.87631
33.01062
32.98148
33.11365
33.15453
33.28092
33.0525
33.08495
33.07624
33.12697
33.03576
33.07903
33.18733
33.17118
33.23942
33.26119
33.28931
33.37205
33.37551
33.27902
33.27477
33.30728
33.20496
33.2423
33.24969
33.28801
33.21016
33.28226
33.12421
33.06346
32.99568
32.97368
32.84107
32.82412
32.73946
32.60654
32.46427
32.36982
32.4547
32.39445
32.39918
32.29957
32.36156
32.21407
32.19553
32.21593
32.23859
32.21168
28.64696
28.53008
28.60799
28.6123
28.72395
28.81287
28.78225
28.71411
28.73823
28.80343
28.76831
28.93862
28.9645
29.09116
29.21326
29.18794
29.27723
29.24472
29.28378
29.18674
29.28914
29.2728
29.3122
29.35178
29.29728
29.3098
29.25676
29.17133
29.17426
29.10458
29.20968
29.14834
29.03957
29.08676
29.02496
29.07269
29.15109
29.2266
29.1721
29.2794
29.19087
29.13896
29.26984
29.07595
28.95273
28.9379
28.92957
28.89023
28.94402
28.89263
29.07488
29.07778
29.09395
29.03612
29.03456
28.99224
28.91553
28.80358
28.95277
28.86224
28.8264
28.88143
28.9298
28.81363
28.7633
28.83732
28.82238
28.85548
28.83985
28.57578
28.25604
28.04689
27.9289
27.79863
27.87754
27.84235
27.8255
27.71943
27.62214
27.55033
27.58092
27.36102
27.24952
27.16757
27.04796
26.99109
27.00574
26.98379
26.9264
27.08502
26.96409
26.97118
26.86751
26.84509
26.76489
26.64142
26.66427
26.65488
26.6514
26.50383
26.51129
26.2845
26.16074
26.07768
26.02423
25.7713
25.78345
25.75336
25.7038
25.75763
25.69103
25.58768
25.48948
25.4694
25.36603
25.35237
25.05193
24.97365
24.93658
24.78399
24.66088
24.45947
24.28255
24.10683
24.0248
23.95669
23.553
23.24336
23.23101
23.07033
22.74799
22.53765
22.16505
21.93497
20.87579
18.21851
2.62556
]
c=lsqcurvefit(fun,[ 8.7624   , 0.1151  , -8.9131,   -1.1710   ,
0.1787],x,y)
norm(feval(fun,c,x)-y)^2
其中：[8.7624,0.1151,-8.9131,-1.1710]是我自己赋的初值，这样，可以求出一组系数，为使结果理想，我又将求得系数作为初始值带进去求出新的系数，发现这时残差平方和会变小，不知道该怎样改进这个程序，才能使残差平方和最小且稳定？谢谢诸位。

rocktzc

自己慢慢摸索了

LiuFengz

那你多迭代几次试试？不行你用最小二乘法试试。

lengyunfeng

像这种情况，建议在赋初值的时候不要定死，你完全可以采用蒙特-卡罗方法对初始值进行取值，然后再考虑取最大概率或者最小值。坛子里的caoer大侠对蒙特-卡罗方法有很多好的例子，你可以去搜一下。

shamohu

用1stOpt可以得到稳定唯一的结果；