构造图片对网络进行对抗攻击n+m=7

本文通过构造一个满足n+m=7的图片，改变对角线的数值用来模拟0或者1，观察网络的分类能力的变化。

假设一组图片对神经网络有三个属性分别是频率和质量和对称关系。频率与点的分布有关，质量与点的数值大小有关，这两个属性可以通过迭代次数曲线携带。而和对称关系有关的信息只能有网络本身来携带。本文通过改变x的值也就是改变图片的质量信息来观察这一组斜线的频率和质量有哪些数值上的变化。

 

实验过程

制作一个带一个3*3卷积核的神经网络，测试集是mnist的0和1图片集，将28*28的图片缩小成9*9，隐藏层30个节点所以网络的结构是

 

这个网络分成两个部分左边的是让mnist 0向1,0收敛，右边的是让mnist 1向 0,1收敛。让左右两边的权重实现同步更新，实现权重共享。前面大量实验表明这种效果相当于将两个弹性系数是k1和k2的弹簧并联得到弹性系数为k的弹簧，并且使得k1=k2=k/2的过程。

将上图简写成

d2（mnist0,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

这个网络的收敛标准是

if (Math.abs(f2[0]-y[0])< δ  &&  Math.abs(f2[1]-y[1])< δ   )

每个神经网络对应每个收敛标准δ都有一个特征的迭代次数n，因此可以用迭代次数曲线n(δ)来评价网络性能。

本文尝试了δ从0.1到1e-6在内的22个值，训练集是mnist0和1的前4999张图片，

具体进样顺序
进样顺序	迭代次数
mnist 0-1	1		判断是否达到收敛
mnist 1-1	2		判断是否达到收敛
梯度下降
mnist 0-2	3		判断是否达到收敛
mnist 1-2	4		判断是否达到收敛
梯度下降
……
mnist 0-4999	9997		判断是否达到收敛
mnist 1-4999	9998		判断是否达到收敛
梯度下降
……
如果4999图片内没有达到收敛标准再次从头循环
mnist 0-1	9999		判断是否达到收敛
mnist 1-1	10000		判断是否达到收敛
……
达到收敛标准测量准确率

 

测试集中有980个0和1135个1.将整个过程重复299次，取平均值，用这种方式得到的迭代次数n，用n12表示。

再用同样的办法做两个网络

d2（mnist x,0）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

意思是用同样的网络分类mnist的0和一张x图片，让0向1，0收敛，让x向0，1收敛，得到的迭代次数用nx0表示

d2（mnist x,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

用同样的网络分类mnist的1和一张x图片，让x向1，0收敛，让1向0，1收敛，得到的迭代次数用nx1表示

这张图片x就是一个9*9的二维数组

double [][]conx=new double[9][9];

for(int n=0 ;n<9;n++){

for(int m=0 ;m<9 ;m++){

if(n+m==7){

conx[n][m]=d;

} } }

本文分别让d=0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9，1也就是计算了10组.

现在有了3个网络

A:d2（mnist0,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

B:d2（mnistx,0）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

C:d2（mnistx,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

根据前面的大量实验n01，nx0，nx1可以用两个方程组去计算

让n01=ω01，nx0=ωx0，nx1=ωx1

频率方程组

 

质量方程组

因为测量了10组d因此可以得到10组ωx，ω0, ω1,mx,m0,m1,mx0,mx1,m01,k的数据

首先观察网络

B:d2（mnistx,0）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

的平均准确率

xx0	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
δ	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave
0.5	0.498706	0.499213	0.504503	0.500836	0.505807	0.506046	0.504988	0.501772	0.506249	0.50471
0.4	0.4666	0.468664	0.477484	0.477423	0.48315	0.493614	0.508802	0.526803	0.539458	0.532645
0.3	0.49431	0.492826	0.518069	0.544055	0.583293	0.60028	0.644016	0.655474	0.705722	0.726319
0.2	0.511094	0.534946	0.561874	0.601448	0.63066	0.680133	0.722354	0.787563	0.775308	0.811971
0.1	0.525424	0.570268	0.602876	0.655267	0.671529	0.722025	0.765648	0.801602	0.825894	0.832611
0.01	0.543204	0.568431	0.587539	0.665459	0.674029	0.695129	0.753161	0.759597	0.782408	0.784562
0.001	0.517389	0.524611	0.546694	0.57323	0.587055	0.610766	0.626408	0.666346	0.66324	0.676947
1E-04	0.490685	0.5001	0.528967	0.532328	0.559164	0.570866	0.571498	0.619642	0.63906	0.649003
9E-05	0.491966	0.498147	0.515346	0.53507	0.532003	0.591032	0.57301	0.60679	0.622635	0.64129
8E-05	0.476931	0.489224	0.506832	0.523792	0.536561	0.581704	0.602418	0.627479	0.660269	0.642104
7E-05	0.478427	0.492192	0.514549	0.522212	0.542663	0.566335	0.584377	0.621798	0.651276	0.62258
6E-05	0.490364	0.491013	0.503995	0.529299	0.558198	0.578502	0.602592	0.63419	0.649405	0.630092
5E-05	0.477676	0.498612	0.508412	0.521889	0.541656	0.560372	0.571514	0.631925	0.651099	0.645733
0.00004	0.490685	0.492599	0.515136	0.52604	0.538095	0.569476	0.588583	0.607208	0.648507	0.64628
3E-05	0.479962	0.490092	0.503435	0.509492	0.550125	0.577229	0.589544	0.639081	0.623565	0.642012
0.00002	0.47927	0.486188	0.500995	0.498968	0.535541	0.558155	0.578527	0.605054	0.630935	0.609407
0.00001	0.474972	0.48936	0.498857	0.515575	0.530656	0.553634	0.57719	0.604407	0.593691	0.642088
9E-06	0.478291	0.488456	0.492077	0.50455	0.535202	0.537927	0.575072	0.591447	0.616387	0.626062
8E-06	0.485962	0.486028	0.493834	0.50995	0.534209	0.546713	0.562279	0.595313	0.598566	0.632986
0.000007	0.488913	0.489188	0.494839	0.502933	0.534461	0.532751	0.572289	0.581178	0.604355	0.606963
0.000006	0.479872	0.488414	0.497374	0.511315	0.511304	0.522647	0.566475	0.587639	0.608022	0.622347
5E-06	0.479719	0.481849	0.5016	0.512341	0.525885	0.541808	0.575278	0.580814	0.604377	0.619477
4E-06	0.475334	0.488003	0.49773	0.514388	0.521825	0.54689	0.556318	0.588086	0.590934	0.608762
0.000003	0.478849	0.483772	0.484613	0.498956	0.52953	0.538084	0.555222	0.565181	0.596711	0.602965
2E-06	0.470291	0.478972	0.491085	0.50987	0.520256	0.538264	0.559382	0.561792	0.595593	0.620489
1E-06	0.46933	0.478326	0.486939	0.497866	0.505244	0.508899	0.533264	0.565651	0.588494	0.6285

 

很明显x越大分类能力越差，表明x=0.1更接近图片1的特征。

B:d2（mnistx,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

的分类能力

xx1	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
δ	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave
0.5	0.517047	0.519064	0.514826	0.507428	0.5224	0.518248	0.515276	0.50745	0.5131	0.516005
0.4	0.668509	0.693649	0.719944	0.742948	0.76452	0.778184	0.798044	0.819023	0.791304	0.804304
0.3	0.67957	0.71175	0.73271	0.770251	0.783379	0.804319	0.815193	0.818663	0.828359	0.813089
0.2	0.684324	0.71947	0.746194	0.748514	0.787142	0.824234	0.833567	0.833541	0.829786	0.822206
0.1	0.684505	0.703919	0.737228	0.760908	0.791776	0.802843	0.81751	0.836372	0.833132	0.834519
0.01	0.647651	0.669799	0.692034	0.724171	0.740879	0.764107	0.802521	0.80231	0.829748	0.837161
0.001	0.634259	0.662228	0.680298	0.705844	0.727225	0.748514	0.793036	0.815682	0.81506	0.815011
1E-04	0.597403	0.615793	0.633858	0.670506	0.696233	0.720561	0.765833	0.802677	0.815529	0.818697
9E-05	0.587901	0.608507	0.630638	0.669458	0.692429	0.732263	0.751582	0.792286	0.821006	0.799902
8E-05	0.595534	0.601268	0.636581	0.665806	0.695508	0.730416	0.762156	0.790776	0.807712	0.813848
7E-05	0.58849	0.613125	0.638755	0.672056	0.697925	0.722778	0.756919	0.794725	0.811578	0.810456
6E-05	0.596671	0.61685	0.637632	0.675618	0.673512	0.718722	0.757113	0.804073	0.818886	0.82365
5E-05	0.598395	0.605992	0.641168	0.653279	0.675769	0.739436	0.764623	0.80102	0.815957	0.823478
0.00004	0.592419	0.614899	0.639935	0.669907	0.681473	0.716502	0.766815	0.786981	0.821824	0.801678
3E-05	0.595968	0.602298	0.64703	0.667592	0.703652	0.729323	0.756032	0.794597	0.810963	0.808389
0.00002	0.58512	0.604568	0.63816	0.656103	0.685296	0.72576	0.760655	0.783856	0.814134	0.810007
0.00001	0.580442	0.595283	0.629201	0.664325	0.688533	0.712703	0.737418	0.781374	0.804689	0.815176
9E-06	0.565855	0.590786	0.614131	0.653045	0.672557	0.730292	0.736955	0.783779	0.809206	0.811156
8E-06	0.572515	0.591957	0.616109	0.6494	0.681654	0.724759	0.747184	0.7909	0.799677	0.803969
0.000007	0.591456	0.604545	0.621906	0.641639	0.672255	0.71157	0.748348	0.785161	0.794707	0.803852
0.000006	0.580959	0.599331	0.614915	0.648006	0.674266	0.715393	0.745713	0.776143	0.801923	0.805176
5E-06	0.572189	0.599146	0.62153	0.664839	0.672016	0.722236	0.735598	0.790275	0.799145	0.81228
4E-06	0.57409	0.605011	0.622529	0.644267	0.674273	0.718192	0.736991	0.770338	0.799719	0.804167
0.000003	0.578369	0.597081	0.600419	0.645082	0.682097	0.725201	0.74936	0.786051	0.800217	0.802536
2E-06	0.576525	0.594209	0.622428	0.651095	0.679894	0.706997	0.763952	0.78947	0.796164	0.808305
1E-06	0.57134	0.592852	0.603998	0.655058	0.662615	0.712373	0.748209	0.781075	0.787916	0.797799

 

 

这个规律是同样的x越大分类能力越差，但是这个网络的平均性能要好于第一个网络，表明x=0.1是的特征更加接近0.

迭代次数综合

	x0
	迭代次数n
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	15.35452	18.94983	18.31104	17.69565	16.79599	16.83278	19.46154	16.26756	19.30769	16.67893
0.4	1117.99	1187.555	1197.535	1278.94	1357.803	1370.231	1421.395	1500.177	1462.839	1432.171
0.3	1378.371	1435.201	1520.753	1530.819	1637.542	1706.666	1754.612	1781.488	1685.408	1757.468
0.2	1522.672	1589.321	1682.732	1753.656	1803.742	1890.746	1950.117	1994.09	2100.505	1923.823
0.1	1773.977	1819.542	1963.361	2086.659	2082.431	2200.351	2250.518	2190.358	2302.98	2324.097
0.01	2553.468	2670.438	2806.231	2881.12	2973.214	2979.896	3068.03	3113.401	3191.147	3094.839
0.001	4228.445	4295.957	4218.144	4175.709	4204.88	4061.575	4170.385	4133.863	4244.017	4026.786
1.00E-04	8060.124	7499.415	7139.114	6891.462	6639.722	6176.211	6086.151	5947.14	5797.836	5812.579
9.00E-05	8283.04	7837.589	7530.839	6954.445	6802.833	6401.729	6208.906	6157.91	5787.227	5819.689
8.00E-05	8670.351	8223.756	7772.773	7223.201	6885.809	6568.358	6340.298	6148.251	5990.465	5969.468
7.00E-05	8966.037	8528.579	7851.02	7535.916	7169.147	6699.716	6450.946	6379.957	6187.936	6186.786
6.00E-05	9573.194	8989.475	8404.204	7887.582	7343.849	6958.98	6697.662	6525.368	6287.589	6416.866
5.00E-05	10486.42	9576.572	8879.983	8294.592	7708.411	7193.508	6791.047	6685.261	6478.786	6516.559
4.00E-05	10796.31	10328.2	9505.227	9020.278	8034.452	7545.167	7139.227	6966.732	6862.813	6701.776
3.00E-05	12615.76	11390.36	10206.77	9632.967	8653.843	8229.803	7763.602	7323.803	7081.261	7026.01
2.00E-05	14290.22	12712.02	11895.89	11004.82	9575.776	8871.783	8368.98	7958.324	7636.064	7654.806
1.00E-05	19590.14	16685.96	14971.21	13450.55	12115.49	10916.28	10131.43	9302.425	8972.926	8709.896
9.00E-06	19369.42	17926.62	15458.92	13700.68	12032.81	11171.62	10173.31	9456.13	9218.592	9183.783
8.00E-06	20898.02	17822.38	16138.6	14483.19	12438.18	11684.68	10413.79	9790.057	9631.656	9276.505
7.00E-06	21530.06	19599.07	17075.43	15177.07	13051.3	11766	10722.55	10215.11	9639.957	9697.167
6.00E-06	22983.2	20647.8	18229.57	15343.79	14013.39	12130.34	11103.27	10168.81	9737.134	10145.89
5.00E-06	25112.67	21185.3	19040.36	16908.94	15078.32	13247.34	11265.88	10872.95	10656.88	10276.24
4.00E-06	27894.48	25069.92	20645.43	17625.26	15866.23	14007.23	12300.8	11611.66	10945.6	10944.16
3.00E-06	32092.47	27664.89	23149.66	19667.91	17548.92	14726	12992.57	12128.02	11840.05	11454.33
2.00E-06	37375.13	30547.89	27850.06	23064.1	19158.65	15905.17	14769.62	13519.72	12690.2	12701.23
1.00E-06	51550.46	40985.27	34607.76	29823.74	24326.77	20274.39	17986.22	16094.89	15180.33	15012.21

 

	x1
	迭代次数n
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	17.15719	17.53846	18.57191	18.82943	18.17726	18.6388	18.77592	17.81271	20.61873	20.99331
0.4	1106.234	1143.639	1306.381	1322.341	1432.415	1523.01	1712.977	1767.264	1800.903	1978.649
0.3	1244.074	1399.692	1523.532	1601.137	1695.09	1832.408	1917.592	2039.98	2157.458	2331.157
0.2	1474.789	1596.094	1716.763	1766.361	1874.669	2003.344	2219.967	2308.054	2431.759	2497.405
0.1	1726.943	1826.207	1923.344	2057.913	2168.134	2340.181	2429.652	2632.562	2707.338	2801.452
0.01	2614.963	2825.211	2916.094	2968.02	2993.217	3136.615	3308.421	3500.783	3683.732	3690.662
0.001	4851.833	4871.699	4906.936	4831.833	4740.241	4720.482	4809.813	4778.435	4954.254	4990.328
1.00E-04	11627.7	10530.17	9840.08	8766.488	8058.054	7058.475	6852.783	6559.605	6530.134	6551.258
9.00E-05	11914.98	11208.97	9821.278	9220.274	8317.672	7569.873	7132.395	6686.635	6651.371	6651.137
8.00E-05	12895.67	12067	10495.94	9792.02	8357.03	7787.197	7132.522	6724.14	6635.853	6880.421
7.00E-05	13385.04	12058.49	10861.02	9882.615	9309.746	7879.13	7391.833	7031.418	6890.562	6950.662
6.00E-05	13818.58	12810.59	11776.17	10383.82	9067.545	8343.525	7327.632	7196.074	6921.94	7051.572
5.00E-05	16082.01	14173.44	12579.15	10779.86	9680.401	8610.95	7760.622	7312.341	7145.565	7242.776
4.00E-05	16973.04	16033.73	13479.8	11665.71	10494.13	9140.468	7962.482	7536.368	7409.117	7460.368
3.00E-05	20943.67	17167.83	15182.3	14249.18	11338.78	9946.602	8562.107	8129.679	7769.826	7918.736
2.00E-05	23995.46	21386.47	17906.29	15266.68	12616.27	10834.17	9379.639	8669.953	8285.05	8570.689
1.00E-05	33037.41	28373.46	24371.43	19940.94	16168.89	13458.85	11004.92	9840.1	9346.769	9550.836
9.00E-06	34781.26	29889.26	25603.51	19236.82	16701.53	13978.84	11406.21	9997.264	9488.207	9305.98
8.00E-06	38124.84	31047.18	25547.65	21355.55	17459.02	14283.77	12130.39	10238.3	9644.729	10029.36
7.00E-06	40778.25	33907.32	26963.9	22943.16	18022.86	15247.41	11984.52	10638.9	10025.21	9980.87
6.00E-06	44399.53	35151.1	30160.43	24085.9	19863.44	15602.85	12506.18	10952.92	10431.91	10619.42
5.00E-06	47481.75	39056.92	31852.49	25780.82	21343.05	16205.67	13408.98	11666.93	10749.43	10500.95
4.00E-06	51666.84	44700.93	35495.18	29009.14	21984.74	18251.19	14559.57	11822.75	11068.94	11001.82
3.00E-06	64737.61	52535.19	40708.62	32223.9	25491.04	20613.97	15032.35	13101.28	11883.68	11853.48
2.00E-06	78519.32	56693.77	49340.35	37336.09	29391.59	22241.87	17472.01	13730.76	12803.19	12470.37
1.00E-06	115929.9	92079.88	68424.07	51575.29	38724.45	28858.88	20547.67	16472.6	14605.4	14873.51

 

 

第一组数据计算ωx

计算ωx
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	1539.038	1641.757	1829.238	2063.258	2169.605	2513.723	2712.117	2864.885	3260.068	3499.26	减
0.01	2380.17	2649.823	2869.018	3002.942	3136.616	3311.985	3663.611	4026.954	4526.925	4274.625	减
0.001	5019.207	5156.789	5062.45	4910.674	4859.483	4623.414	4879.032	4789.238	5160.779	4816.197	增
1.00E-04	#NUM!	#NUM!	30140.3	13839.9	10405.27	7572.426	7171.466	6642.097	6408.155	6448.223	增
9.00E-05	#NUM!	#NUM!	72350.87	14695.48	11007.06	8438.51	7497.669	6912.429	6368.939	6412.073	减增
8.00E-05	#NUM!	#NUM!	#NUM!	17350.29	10462.58	8640.17	7400.499	6696.865	6414.751	6606.378	减增
7.00E-05	#NUM!	#NUM!	#NUM!	24228.82	14358.97	9037.877	7859.744	7322.583	6895.166	6953.754	减增
6.00E-05	#NUM!	#NUM!	#NUM!	26195.25	12114.66	9481.479	7663.888	7272.871	6700.216	6983.283	减增
5.00E-05	#NUM!	#NUM!	#NUM!	35939.95	13955.59	9784.514	7925.274	7310.599	6893.611	7028.09	减增
4.00E-05	#NUM!	#NUM!	#NUM!	86402.07	14047.89	9984.888	7933.484	7311.605	7080.917	6945.85	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	15223.37	11141.32	8633.63	7679.173	7126.365	7181.696	减增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	15600.06	11080.14	8921.115	7902.372	7324.669	7537.716	减增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	49685.45	16485.38	11347.07	9264.434	8564.156	8478.29	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	50700.31	18174.58	11747.74	9497.459	8848.366	8670.744	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	34488.15	17350.15	11856.66	9504.557	8899.501	8888.09	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	53708.59	18499.11	11903.55	10093.49	9087.892	9102.185	减增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	17616.44	12105.66	9841.334	9107.885	9578.021	减增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	20865.25	12667.73	10785.6	9877.095	9395.07	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	23977.86	14189.23	11035.46	9926.249	9876.698	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	24334.14	14039.53	11665.25	10577.13	10279.76	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	27607.32	17684.26	12790.35	11434.94	11203.53	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	41715.35	20408.98	14929.03	12944	13020.3	减增

 

当δ<0.001随着d的增大ωx有多个拐点

第二组数据计算ω0

计算ω0
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	2165.011	2071.282	2132.1	2110.875	2004.986	1980.942	1965.215	1841.054	1879.768	1861.435	增
0.01	2771.125	2691.542	2747.394	2773.016	2832.949	2731.111	2692.181	2629.189	2602.89	2547.542	增
0.001	3722.544	3759.142	3691.414	3695.269	3759.054	3664.772	3701.505	3690.125	3688.742	3530.436	增
1.00E-04	#NUM!	#NUM!	5120.446	5206.4	5260.99	5345.883	5379.925	5432.797	5334.152	5334.132	增减
9.00E-05	#NUM!	#NUM!	5339.59	5218.375	5348.074	5363.764	5416.007	5606.461	5340.423	5366.022	增减
8.00E-05	#NUM!	#NUM!	#NUM!	5344.392	5500.985	5508.014	5634.99	5715.58	5640.575	5487.158	增减
7.00E-05	#NUM!	#NUM!	#NUM!	5462.445	5418.252	5562.882	5601.358	5727.324	5661.499	5628.013	增减
6.00E-05	#NUM!	#NUM!	#NUM!	5708.249	5747.693	5756.711	6023.781	5969.279	5942.869	5969.134	增减
5.00E-05	#NUM!	#NUM!	#NUM!	5944.858	5920.959	5954.428	6036.192	6197.073	6130.835	6102.593	增减
4.00E-05	#NUM!	#NUM!	#NUM!	6395.75	6211.868	6311.837	6543.953	6666.467	6663.696	6481.747	增减
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	6682.842	6824.225	7112.733	7013.603	7037.003	6880.029	增减
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	7515.989	7610.593	7908.115	8015.482	7990.88	7777.528	增减
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	8697.208	8735.773	9237.971	9340.887	9446.436	8961.583	增减
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	8630.884	8771.393	9099.005	9415.337	9639.551	9800.19	减
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	9095.869	9396.133	9395.234	10102.93	10580.45	9720.741	增减
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	9367.995	9315.054	9835.187	10341.23	10306.64	10426.5	减
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	9820.101	10314.69	10531.31	10517.88	10828.44	减
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	10483.1	10245.61	10962.46	11656.3	11463.26	增减
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	10875.84	11008.93	12288.7	12361.25	12454.55	减
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	11520.93	12149.58	12650.63	13699.67	13152.67	增减
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	12314.86	12941.54	14390.02	14476.87	15023.24	减
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	15265.98	16261.79	17584.89	19207.74	18331.79	增减

当δ<0.001随着x的增大ω0有多个拐点

第三组数据计算ω1

计算ω1
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	2006.3	2091.121	2033.65	2052.61	2166.666	2198.24	2220.318	2448.91	2365.1	2403.051	减
0.01	2936.534	3040.777	2965.566	2934.289	2867.844	2986.445	3039.855	3138.419	3184.84	3295.024	减
0.001	4700.158	4629.202	4764.927	4756.671	4629.366	4823.932	4743.458	4767.704	4770.691	5184.823	减
1.00E-04	#NUM!	#NUM!	7151.15	6933.167	6809.636	6636.719	6573.127	6480.113	6659.354	6659.394	减增
9.00E-05	#NUM!	#NUM!	6976.907	7274.866	6958.101	6923.952	6815.783	6481.615	6975.05	6919.103	减增
8.00E-05	#NUM!	#NUM!	#NUM!	7551.373	7160.853	7145.428	6891.695	6751.752	6881.516	7191.667	减增
7.00E-05	#NUM!	#NUM!	#NUM!	7298.208	7407.298	7075.719	6998.633	6772.434	6885.967	6947.574	减增
6.00E-05	#NUM!	#NUM!	#NUM!	7649.098	7556.86	7536.495	7032.077	7121.659	7167.24	7121.904	减增
5.00E-05	#NUM!	#NUM!	#NUM!	7799.96	7854.842	7778.486	7605.823	7314.084	7427.332	7478.419	减增
4.00E-05	#NUM!	#NUM!	#NUM!	8286.757	8739.181	8479.45	7991.8	7783.22	7787.638	8109.28	减增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	9431.867	9068.759	8492.333	8670.079	8626.428	8942.089	减增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	10874.67	10603.9	9917.007	9715.8	9760.119	10192.09	减增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	11748.41	11655.1	10691.97	10538.41	10392.46	11170.86	减增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	12143.8	11778.9	11092.84	10585.31	10290.51	10105	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	13221.49	12421.91	12423.99	11173.28	10615.21	11765.07	减增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	13118.74	13267.88	12067.15	11283.51	11328.94	11175.66	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	14152.05	12949.28	12552.78	12575.63	12096.29	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	13712.14	14297.72	12806.92	11903.02	12119.57	减增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	15312.7	14960.49	12806.81	12726.17	12626.69	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	18203.4	16270.77	15243.97	13836.1	14477.19	减增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	19136.19	17267.23	14914.66	14819.74	14294.52	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	23396.82	20689.23	18621.47	17131.7	17840.11	减增

当δ<0.01随着d的增大ω1有多个拐点

第四组数据m0

m0
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	0.505334	0.62826	0.73608	0.955393	1.17095	1.610242	1.904568	2.421481	3.007772	3.533921	减
0.01	0.737741	0.96924	1.090497	1.172706	1.225872	1.470611	1.851868	2.3459	3.024788	2.815485	减
0.001	1.817987	1.881834	1.880771	1.765998	1.671179	1.591591	1.737443	1.684421	1.957375	1.861023	减
1.00E-04	#NUM!	#NUM!	34.64811	7.066283	3.911752	2.006463	1.776902	1.494733	1.443229	1.461345	增
9.00E-05	#NUM!	#NUM!	183.5996	7.930429	4.235918	2.475097	1.916435	1.52014	1.422273	1.427881	增
8.00E-05	#NUM!	#NUM!	#NUM!	10.53942	3.6174	2.460676	1.724788	1.372848	1.29334	1.449545	增
7.00E-05	#NUM!	#NUM!	#NUM!	19.67389	7.023086	2.63957	1.96893	1.634651	1.483292	1.526612	增
6.00E-05	#NUM!	#NUM!	#NUM!	21.05908	4.44258	2.71271	1.618676	1.484458	1.271116	1.368663	增
5.00E-05	#NUM!	#NUM!	#NUM!	36.54869	5.555361	2.700215	1.723862	1.391659	1.264312	1.326313	增
4.00E-05	#NUM!	#NUM!	#NUM!	182.501	5.1142	2.502504	1.469764	1.202912	1.129142	1.14833	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	5.189184	2.665425	1.473377	1.198799	1.025559	1.089616	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	4.308048	2.119596	1.272601	0.971976	0.840208	0.939283	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	32.63614	3.561189	1.50874	0.983697	0.821927	0.895049	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	34.50727	4.293304	1.666944	1.01752	0.842583	0.782787	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	14.37644	3.409635	1.592611	0.885052	0.707495	0.836023	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	32.86958	3.943944	1.464832	0.952661	0.777486	0.762104	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.218137	1.377416	0.87326	0.749858	0.782384	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.961576	1.528698	0.967993	0.71802	0.671713	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.860658	1.661222	0.806434	0.64483	0.628879	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.461257	1.335311	0.850284	0.596096	0.610854	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	5.02562	1.867248	0.790027	0.623905	0.556138	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	7.466932	1.575092	0.720749	0.454135	0.504466	增

 

 

当δ<0.001随着d的增加m0急剧增加

第五组数据m1

m1
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	0.588446	0.616395	0.809073	1.010402	1.002715	1.307629	1.49206	1.368575	1.900003	2.120443	减
0.01	0.65697	0.75939	0.935947	1.047341	1.196221	1.229894	1.452489	1.646385	2.020372	1.682979	减
0.001	1.140369	1.240927	1.128779	1.065801	1.101887	0.918593	1.057979	1.009053	1.170221	0.862861	增
1.00E-04	#NUM!	#NUM!	17.7641	3.984766	2.334848	1.301857	1.190342	1.050619	0.92598	0.937585	增
9.00E-05	#NUM!	#NUM!	107.5379	4.080537	2.502425	1.485332	1.210099	1.137352	0.833757	0.858811	增
8.00E-05	#NUM!	#NUM!	#NUM!	5.279121	2.134754	1.462137	1.153108	0.983808	0.868943	0.843855	增
7.00E-05	#NUM!	#NUM!	#NUM!	11.02128	3.757741	1.631517	1.261218	1.169066	1.002674	1.00178	增
6.00E-05	#NUM!	#NUM!	#NUM!	11.72802	2.570039	1.582754	1.187766	1.042916	0.873924	0.961451	增
5.00E-05	#NUM!	#NUM!	#NUM!	21.23098	3.156614	1.582298	1.085766	0.999047	0.861446	0.883192	增
4.00E-05	#NUM!	#NUM!	#NUM!	108.7124	2.58393	1.386599	0.985459	0.882484	0.826737	0.733645	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	2.60511	1.509307	1.033553	0.784482	0.682455	0.645024	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	2.057884	1.091841	0.809239	0.661543	0.563204	0.546956	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	17.88548	2.000626	1.126295	0.772837	0.679098	0.576027	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	17.43058	2.380779	1.121562	0.805022	0.739354	0.736275	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	6.804228	1.950875	0.910758	0.723606	0.702869	0.570727	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	16.76111	1.94401	0.973069	0.800193	0.643498	0.663353	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	1.549521	0.873949	0.61465	0.524536	0.62697	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	2.315456	0.78499	0.70925	0.688564	0.600932	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	2.451981	0.899551	0.742505	0.60838	0.61185	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	1.78701	0.744542	0.585587	0.584398	0.504193	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	2.081313	1.048887	0.735424	0.59537	0.614286	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.178909	0.973091	0.64274	0.570869	0.532656	增

 

当δ<0.001随着d的增加m1急剧增加

第六组数据mx0

mx0
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	1.505334	1.62826	1.73608	1.955393	2.17095	2.610242	2.904568	3.421481	4.007772	4.533921	减
0.01	1.737741	1.96924	2.090497	2.172706	2.225872	2.470611	2.851868	3.3459	4.024788	3.815485	减
0.001	2.817987	2.881834	2.880771	2.765998	2.671179	2.591591	2.737443	2.684421	2.957375	2.861023	减
1.00E-04	#NUM!	#NUM!	35.64811	8.066283	4.911752	3.006463	2.776902	2.494733	2.443229	2.461345	增
9.00E-05	#NUM!	#NUM!	184.5996	8.930429	5.235918	3.475097	2.916435	2.52014	2.422273	2.427881	增
8.00E-05	#NUM!	#NUM!	#NUM!	11.53942	4.6174	3.460676	2.724788	2.372848	2.29334	2.449545	增
7.00E-05	#NUM!	#NUM!	#NUM!	20.67389	8.023086	3.63957	2.96893	2.634651	2.483292	2.526612	增
6.00E-05	#NUM!	#NUM!	#NUM!	22.05908	5.44258	3.71271	2.618676	2.484458	2.271116	2.368663	增
5.00E-05	#NUM!	#NUM!	#NUM!	37.54869	6.555361	3.700215	2.723862	2.391659	2.264312	2.326313	增
4.00E-05	#NUM!	#NUM!	#NUM!	183.501	6.1142	3.502504	2.469764	2.202912	2.129142	2.14833	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	6.189184	3.665425	2.473377	2.198799	2.025559	2.089616	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	5.308048	3.119596	2.272601	1.971976	1.840208	1.939283	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	33.63614	4.561189	2.50874	1.983697	1.821927	1.895049	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	35.50727	5.293304	2.666944	2.01752	1.842583	1.782787	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	15.37644	4.409635	2.592611	1.885052	1.707495	1.836023	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	33.86958	4.943944	2.464832	1.952661	1.777486	1.762104	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.218137	2.377416	1.87326	1.749858	1.782384	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.961576	2.528698	1.967993	1.71802	1.671713	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	5.860658	2.661222	1.806434	1.64483	1.628879	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	5.461257	2.335311	1.850284	1.596096	1.610854	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	6.02562	2.867248	1.790027	1.623905	1.556138	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	8.466932	2.575092	1.720749	1.454135	1.504466	增

 

当δ<0.001随着d的增加mx0急剧增加

第七组数据mx1

mx1
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	1.588446	1.616395	1.809073	2.010402	2.002715	2.307629	2.49206	2.368575	2.900003	3.120443	减
0.01	1.65697	1.75939	1.935947	2.047341	2.196221	2.229894	2.452489	2.646385	3.020372	2.682979	减
0.001	2.140369	2.240927	2.128779	2.065801	2.101887	1.918593	2.057979	2.009053	2.170221	1.862861	增
1.00E-04	#NUM!	#NUM!	18.7641	4.984766	3.334848	2.301857	2.190342	2.050619	1.92598	1.937585	增
9.00E-05	#NUM!	#NUM!	108.5379	5.080537	3.502425	2.485332	2.210099	2.137352	1.833757	1.858811	增
8.00E-05	#NUM!	#NUM!	#NUM!	6.279121	3.134754	2.462137	2.153108	1.983808	1.868943	1.843855	增
7.00E-05	#NUM!	#NUM!	#NUM!	12.02128	4.757741	2.631517	2.261218	2.169066	2.002674	2.00178	增
6.00E-05	#NUM!	#NUM!	#NUM!	12.72802	3.570039	2.582754	2.187766	2.042916	1.873924	1.961451	增
5.00E-05	#NUM!	#NUM!	#NUM!	22.23098	4.156614	2.582298	2.085766	1.999047	1.861446	1.883192	增
4.00E-05	#NUM!	#NUM!	#NUM!	109.7124	3.58393	2.386599	1.985459	1.882484	1.826737	1.733645	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	3.60511	2.509307	2.033553	1.784482	1.682455	1.645024	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	3.057884	2.091841	1.809239	1.661543	1.563204	1.546956	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	18.88548	3.000626	2.126295	1.772837	1.679098	1.576027	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	18.43058	3.380779	2.121562	1.805022	1.739354	1.736275	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	7.804228	2.950875	1.910758	1.723606	1.702869	1.570727	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	17.76111	2.94401	1.973069	1.800193	1.643498	1.663353	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	2.549521	1.873949	1.61465	1.524536	1.62697	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.315456	1.78499	1.70925	1.688564	1.600932	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.451981	1.899551	1.742505	1.60838	1.61185	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	2.78701	1.744542	1.585587	1.584398	1.504193	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.081313	2.048887	1.735424	1.59537	1.614286	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.178909	1.973091	1.64274	1.570869	1.532656	增

 

当δ<0.001随着d的增加mx1急剧增加

第八组数据m01

m01
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	1.09378	1.244655	1.545153	1.965795	2.173665	2.917871	3.396628	3.790055	4.907775	5.654364	减
0.01	1.394711	1.72863	2.026444	2.220046	2.422093	2.700505	3.304357	3.992285	5.04516	4.498464	减
0.001	2.958356	3.122761	3.00955	2.831799	2.773067	2.510184	2.795422	2.693475	3.127596	2.723884	增
1.00E-04	#NUM!	#NUM!	52.41221	11.05105	6.2466	3.308319	2.967244	2.545352	2.369209	2.39893	增
9.00E-05	#NUM!	#NUM!	291.1375	12.01097	6.738342	3.960429	3.126534	2.657492	2.25603	2.286692	增
8.00E-05	#NUM!	#NUM!	#NUM!	15.81854	5.752154	3.922813	2.877896	2.356656	2.162283	2.2934	增
7.00E-05	#NUM!	#NUM!	#NUM!	30.69517	10.78083	4.271088	3.230148	2.803717	2.485965	2.528391	增
6.00E-05	#NUM!	#NUM!	#NUM!	32.78711	7.012619	4.295463	2.806442	2.527374	2.145041	2.330114	增
5.00E-05	#NUM!	#NUM!	#NUM!	57.77967	8.711975	4.282513	2.809628	2.390706	2.125758	2.209505	增
4.00E-05	#NUM!	#NUM!	#NUM!	291.2134	7.69813	3.889104	2.455223	2.085396	1.95588	1.881975	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	7.794294	4.174732	2.50693	1.983281	1.708014	1.73464	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	6.365932	3.211437	2.081841	1.633519	1.403412	1.486239	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	50.52162	5.561816	2.635035	1.756534	1.501025	1.471077	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	51.93785	6.674083	2.788506	1.822542	1.581936	1.519062	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	21.18067	5.36051	2.503369	1.608658	1.410364	1.406749	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	49.6307	5.887954	2.437901	1.752853	1.420984	1.425457	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.767659	2.251365	1.48791	1.274394	1.409355	增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	6.277032	2.313687	1.677243	1.406584	1.272645	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	7.312639	2.560774	1.548939	1.25321	1.240729	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	6.248267	2.079853	1.435871	1.180494	1.115047	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	7.106934	2.916135	1.525451	1.219274	1.170424	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	10.64584	2.548183	1.363489	1.025004	1.037122	增

 

当δ<0.001随着d的增加m01急剧增加

第九组数据k

k
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.1	2368637	2695366	3346110	4257033	4707185	6318802	7355577	8207564	10628043	12244822	减
0.01	5665208	7021562	8231262	9017658	9838357	10969246	13422046	16216355	20493052	18272415	减
0.001	25192443	26592471	25628401	24114723	23614579	21375954	23804952	22936800	26633642	23195754	增
1.00E-04	#NUM!	#NUM!	9.08E+08	1.92E+08	1.08E+08	57341629	51429929	44117451	41064451	41579580	增
9.00E-05	#NUM!	#NUM!	5.23E+09	2.16E+08	1.21E+08	71208447	56215038	47781673	40563381	41114685	增
8.00E-05	#NUM!	#NUM!	#NUM!	3.01E+08	1.09E+08	74652540	54767383	44848004	41149027	43644225	增
7.00E-05	#NUM!	#NUM!	#NUM!	5.87E+08	2.06E+08	81683219	61775572	53620223	47543314	48354698	增
6.00E-05	#NUM!	#NUM!	#NUM!	6.86E+08	1.47E+08	89898441	58735172	52894648	44892898	48766241	增
5.00E-05	#NUM!	#NUM!	#NUM!	1.29E+09	1.95E+08	95736707	62809972	53444859	47521873	49394056	增
4.00E-05	#NUM!	#NUM!	#NUM!	7.47E+09	1.97E+08	99697996	62940166	53459570	50139383	48244826	增
3.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	2.32E+08	1.24E+08	74539562	58969695	50785075	51576753	增
2.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	2.43E+08	1.23E+08	79586295	62447491	53650769	56817164	增
1.00E-05	#NUM!	#NUM!	#NUM!	#NUM!	2.47E+09	2.72E+08	1.29E+08	85829735	73344771	71881399	增
9.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	2.57E+09	3.3E+08	1.38E+08	90201726	78293589	75181795	增
8.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	1.19E+09	3.01E+08	1.41E+08	90336596	79201117	78998135	增
7.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	2.88E+09	3.42E+08	1.42E+08	1.02E+08	82589774	82849766	增
6.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	3.1E+08	1.47E+08	96851854	82953568	91738495	减增
5.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	4.35E+08	1.6E+08	1.16E+08	97557003	88267339	增
4.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	5.75E+08	2.01E+08	1.22E+08	98530420	97549166	增
3.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	5.92E+08	1.97E+08	1.36E+08	1.12E+08	1.06E+08	增
2.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	7.62E+08	3.13E+08	1.64E+08	1.31E+08	1.26E+08	增
1.00E-06	#NUM!	#NUM!	#NUM!	#NUM!	#NUM!	1.74E+09	4.17E+08	2.23E+08	1.68E+08	1.7E+08	增

 

 

当δ<0.001随着d的增加k增加

数据综合

	计算ωx	计算ω0	计算ω1	m0	m1	mx0	mx1	m01	k
δ>0.001	减小	增加	减小	减小	减小	减小	减小	减小	减小
δ<=0.001	7个拐点	9个拐点	9个拐点	增加	增加	增加	增加	增加	增加

 

 

可以明显观察到所有9个量在δ=0.001附近的变化趋势都是相反的，

ω0和ω1的变化规律是相反的，但是波动要比较其他的量要平稳的多，这个现象可以用频率与点的分布有关的假设去解释，

所有9个量只有ω0是先增加再减小的。

实验数据

学习率 0.1

权重初始化方式

Random rand1 =new Random();

int ti1=rand1.nextInt(98)+1;

int xx=1;

if(ti1%2==0)

{ xx=-1;}

tw[a][b]=xx*((double)ti1/x);

第一层第二层和卷积核的权重的初始化的x分别为1000,1000,200

d2（mnistx,0）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

 

	最大准确率p-max
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	0.787707	0.926241	0.884634	0.399817	0.967376	0.870922	0.913948	0.828369	0.953191	0.905437
0.4	0.611348	0.783452	0.957447	0.921525	0.860047	0.919622	0.979669	0.976832	0.976832	0.982979
0.3	0.873286	0.922459	0.987707	0.928874	0.976832	0.987707	0.992908	0.997636	0.998109	0.997163
0.2	0.949409	0.988652	0.991017	0.92746	0.990544	0.994326	0.995745	0.997163	0.997163	0.997636
0.1	0.989598	0.958865	0.983924	0.925488	0.993853	0.994799	0.998582	0.997163	0.996217	0.998109
0.01	0.931915	0.982033	0.987234	0.923461	0.991962	0.993853	0.996217	0.997636	0.997163	0.998109
0.001	0.982033	0.978723	0.980142	0.92071	0.982979	0.995272	0.997636	0.997163	0.997163	0.99669
1.00E-04	0.865721	0.941371	0.965957	0.921147	0.991017	0.996217	0.994799	0.99669	0.997163	0.998109
9.00E-05	0.926714	0.946572	0.976359	0.917812	0.989598	0.990071	0.995272	0.997636	0.997163	0.997163
8.00E-05	0.956028	0.983452	0.973995	0.918451	0.982506	0.983924	0.995745	0.998109	0.99669	0.997163
7.00E-05	0.968322	0.956501	0.976359	0.918929	0.984397	0.995745	0.995745	0.996217	0.995272	0.997636
6.00E-05	0.914421	0.896927	0.979196	0.918557	0.983924	0.995272	0.997163	0.997163	0.997636	0.997636
5.00E-05	0.900236	0.963593	0.956028	0.919095	0.995272	0.993853	0.995272	0.997636	0.997163	0.998109
4.00E-05	0.904965	0.982506	0.960757	0.91999	0.972104	0.987707	0.995745	0.99669	0.99669	0.997163
3.00E-05	0.945154	0.921513	0.970213	0.919492	0.987707	0.995745	0.995272	0.997163	0.997163	0.997163
2.00E-05	0.888416	0.972577	0.948936	0.921213	0.983924	0.996217	0.992908	0.998582	0.999054	0.998109
1.00E-05	0.952719	0.948936	0.974941	0.920212	0.982506	0.992435	0.995272	0.995745	0.996217	0.998109
9.00E-06	0.987707	0.956974	0.979196	0.919281	0.992908	0.990071	0.997163	0.996217	0.997636	0.998582
8.00E-06	0.819385	0.972577	0.964066	0.920896	0.976359	0.98156	0.99669	0.996217	0.997163	0.998109
7.00E-06	0.869976	0.929078	0.93617	0.922108	0.98156	0.975414	0.992908	0.995745	0.99669	0.997636
6.00E-06	0.893144	0.852482	0.926714	0.920141	0.948936	0.984397	0.99669	0.997163	0.997636	0.997636
5.00E-06	0.89409	0.889835	0.960757	0.920539	0.966903	0.986288	0.995745	0.994326	0.997636	0.997163
4.00E-06	0.914421	0.920095	0.9513	0.920916	0.983452	0.977305	0.992435	0.99669	0.996217	0.99669
3.00E-06	0.943262	0.84539	0.919622	0.922098	0.95792	0.983452	0.991017	0.996217	0.996217	0.99669
2.00E-06	0.778251	0.910638	0.917258	0.921464	0.992908	0.988652	0.983452	0.99669	0.997636	0.99669
1.00E-06	0.910638	0.932861	0.906856	0.92246	0.973522	0.974941	0.995272	0.99669	0.99669	0.998109

 

	耗时 min/199
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	4.445717	3.361217	4.853283	3.406	3.4847	3.458233	3.58405	3.316667	5.41685	3.722733
0.4	3.163933	4.2936	6.098017	4.4017	4.552417	4.593867	4.8079	4.498533	6.949167	4.998317
0.3	5.8274	4.495267	4.778983	4.6172	4.767067	4.884867	4.571567	4.706633	7.1075	5.301083
0.2	5.9865	4.663783	6.597683	5.83685	4.9215	5.015717	5.144817	4.876633	7.786967	5.439433
0.1	6.1934	4.850433	7.2629	6.933783	5.175167	5.184033	5.405133	5.02295	7.796967	5.799317
0.01	6.895617	5.63085	8.64815	7.957717	5.96095	5.793883	6.09255	5.772883	8.758017	6.484483
0.001	8.632433	6.884817	9.1431	9.311233	6.986017	4.525033	7.05725	6.587233	10.0382	7.310267
1.00E-04	12.24895	9.52915	12.1106	10.91075	6.6905	9.654	8.636183	8.027767	11.85452	8.90695
9.00E-05	12.39028	9.8186	12.5024	12.0775	9.082133	8.743633	8.672533	8.197933	11.82882	8.995983
8.00E-05	11.94238	10.12003	9.643733	12.4507	9.248483	8.824167	7.93385	8.202283	12.05707	9.722083
7.00E-05	13.26953	10.53675	12.84552	12.79737	9.48825	9.035233	9.023367	7.46655	12.28057	9.805383
6.00E-05	13.92442	10.04992	13.33407	13.14648	9.543667	9.471267	9.227017	8.513233	12.4136	10.00677
5.00E-05	14.86603	11.6692	13.8548	10.78533	9.878967	9.756467	9.4494	8.646383	12.61033	10.22158
4.00E-05	11.97173	12.48775	13.422	14.20235	7.94835	7.896767	10.32367	8.83835	13.04053	10.39577
3.00E-05	16.50817	13.2259	14.83683	14.55913	10.4121	10.64587	10.20427	9.144983	13.279	9.43595
2.00E-05	19.00735	13.78183	17.18997	15.72455	11.15398	11.00283	7.299033	9.667	13.89445	10.84797
1.00E-05	24.54688	16.20098	20.48065	16.59888	13.25457	12.27335	12.2597	10.75145	11.05777	11.62145
9.00E-06	24.97243	17.90365	19.66688	19.40655	13.15702	12.50143	12.31818	10.85813	11.25468	11.91007
8.00E-06	25.2692	17.9942	21.54817	20.55805	13.49947	11.54188	12.82097	11.089	11.63953	12.00235
7.00E-06	27.48128	19.79193	21.73178	20.09165	13.99622	12.94402	12.42	11.43927	11.66117	11.46962
6.00E-06	28.32122	24.37823	23.4247	19.95688	14.77345	13.23173	10.04913	11.41863	10.23712	14.46183
5.00E-06	30.18652	26.20527	18.95425	21.78292	15.6476	14.62495	12.6482	11.9469	13.18252	16.55975
4.00E-06	34.12605	29.92287	20.53998	21.32082	14.7863	14.35922	13.50825	11.73323	13.47633	17.29183
3.00E-06	40.64245	32.4776	22.858	24.42958	17.59202	15.59048	14.06647	12.9705	12.55687	17.83875
2.00E-06	36.80765	35.65485	23.67747	27.71418	18.94678	16.97027	15.58413	14.46345	13.27635	19.1907
1.00E-06	48.57048	46.97597	31.47465	34.03535	23.12363	19.71553	18.36043	16.6463	15.34665	21.71437

 

d2（mnistx,1）81-con（3*3）49-30-2-（2*k） ,k∈{0,1}

	最大准确率p-max
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	0.978723	0.982506	0.976359	0.844917	0.942317	0.96643	0.954137	0.980615	0.961229	0.877541
0.4	0.984397	0.980615	0.98487	0.986761	0.978723	0.98487	0.982506	0.980142	0.978723	0.970213
0.3	0.982979	0.982979	0.982506	0.98818	0.98487	0.979669	0.987707	0.981087	0.976359	0.974941
0.2	0.98487	0.986761	0.983452	0.979669	0.98156	0.982033	0.98156	0.980142	0.984397	0.979669
0.1	0.979669	0.980615	0.98487	0.984397	0.985343	0.981087	0.985816	0.981087	0.980615	0.978251
0.01	0.973995	0.979669	0.985343	0.988652	0.984397	0.990071	0.986288	0.987707	0.986288	0.983452
0.001	0.977778	0.980142	0.987707	0.980142	0.987234	0.991489	0.988652	0.990071	0.989598	0.990071
1.00E-04	0.986288	0.969267	0.987707	0.98818	0.990071	0.986761	0.991962	0.986288	0.990071	0.989598
9.00E-05	0.947991	0.977778	0.979669	0.987707	0.978723	0.991962	0.991489	0.989125	0.990071	0.98818
8.00E-05	0.964539	0.983452	0.964066	0.983452	0.977305	0.992435	0.98487	0.990071	0.990544	0.990071
7.00E-05	0.980615	0.972577	0.985816	0.991489	0.986288	0.993381	0.988652	0.990071	0.991962	0.990071
6.00E-05	0.961229	0.96643	0.962175	0.98156	0.98818	0.994326	0.990071	0.988652	0.992435	0.989125
5.00E-05	0.938534	0.949882	0.985816	0.98487	0.982033	0.989598	0.990071	0.993853	0.991962	0.990544
4.00E-05	0.977778	0.960757	0.972577	0.980142	0.990544	0.983452	0.990071	0.991489	0.989598	0.991489
3.00E-05	0.981087	0.970213	0.984397	0.983452	0.989125	0.982506	0.989125	0.988652	0.990071	0.990544
2.00E-05	0.975414	0.942317	0.955083	0.983452	0.98818	0.982506	0.988652	0.991962	0.990544	0.987234
1.00E-05	0.987707	0.939007	0.98818	0.991489	0.987707	0.986288	0.992435	0.990544	0.990071	0.989598
9.00E-06	0.970213	0.974941	0.965485	0.974941	0.974941	0.986761	0.989125	0.990544	0.991017	0.990071
8.00E-06	0.956974	0.953664	0.989598	0.975887	0.992435	0.982506	0.98818	0.987707	0.991489	0.990544
7.00E-06	0.955556	0.989598	0.993381	0.977778	0.989598	0.98487	0.990544	0.990544	0.991489	0.991017
6.00E-06	0.933333	0.952719	0.977778	0.985816	0.987234	0.978251	0.991017	0.993381	0.989598	0.991017
5.00E-06	0.933806	0.965012	0.959811	0.979196	0.98156	0.989598	0.989125	0.994326	0.98818	0.991962
4.00E-06	0.964066	0.98818	0.983452	0.980615	0.98818	0.989598	0.98818	0.992435	0.992435	0.991017
3.00E-06	0.966903	0.966903	0.979669	0.980615	0.982506	0.991962	0.98487	0.987707	0.989598	0.987707
2.00E-06	0.929078	0.95461	0.989125	0.989598	0.985816	0.991489	0.988652	0.992435	0.992435	0.991489
1.00E-06	0.919622	0.977305	0.991962	0.983924	0.973522	0.983924	0.992435	0.986761	0.991962	0.990544

 

 

	耗时 min/199
δ	1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
0.5	1.422333	3.894683	4.94805	3.436117	4.308133	3.520417	3.557617	3.3832	1.314617	3.661117
0.4	4.9125	4.895983	6.289583	4.534033	5.5548	6.32855	6.516533	4.770717	5.046167	5.3677
0.3	5.025633	5.087283	6.566433	4.748633	5.798317	6.636283	6.751417	4.997483	5.375733	5.655567
0.2	5.209883	5.251767	6.787783	4.8946	5.962	6.840617	6.993117	5.2482	5.600433	0.840983
0.1	5.443217	5.470083	7.014233	5.200683	6.22895	6.53675	7.2	5.580383	5.7937	5.64565
0.01	6.19535	6.41825	5.576817	5.940117	7.637817	7.136883	8.0642	6.294817	6.8284	6.3787
0.001	8.228167	8.290567	10.07687	7.4839	9.394483	8.736217	9.565083	7.35155	7.947683	7.489583
1.00E-04	14.32538	11.07957	15.31927	9.32535	12.63123	10.96525	11.59315	8.728033	9.3754	8.813833
9.00E-05	14.73663	13.9446	14.85418	11.30035	12.74145	11.8233	11.8336	8.936533	9.704467	8.986367
8.00E-05	15.501	14.81533	13.45057	11.6163	12.79292	11.70238	12.32752	8.99575	8.7208	9.293967
7.00E-05	15.87958	14.8351	15.65873	11.7507	13.73462	11.95635	12.08393	9.280733	9.865183	9.2639
6.00E-05	15.36885	15.48042	16.55792	12.19285	13.50033	12.81625	12.05205	9.55095	9.9049	8.402267
5.00E-05	16.80617	14.42467	17.3282	11.7784	14.10828	13.32352	10.38122	9.691467	10.09893	9.48175
4.00E-05	17.2757	18.41705	18.21748	13.35283	14.98195	9.745533	10.48705	9.02525	10.71492	9.5762
3.00E-05	18.28852	19.38785	19.89542	15.33597	15.86695	13.89655	10.414	10.65882	6.55155	9.962833
2.00E-05	22.94062	22.366	22.59092	16.22	17.06837	14.4598	11.36835	11.13865	12.04705	10.44915
1.00E-05	29.61708	29.4258	29.10293	18.65833	20.46935	16.81587	11.91942	12.0111	12.26727	10.42728
9.00E-06	31.64762	30.18498	30.4366	19.91692	21.16757	15.83328	12.98652	12.18153	12.30075	11.03838
8.00E-06	33.7263	31.05033	30.38265	25.73568	21.83735	18.01983	13.59408	11.48607	12.27552	11.66977
7.00E-06	36.5358	33.34162	31.80323	28.13275	22.46492	18.77172	16.54392	12.71963	7.34375	11.59743
6.00E-06	38.27928	35.7317	34.83445	29.25468	24.30003	17.63537	15.40202	13.06252	12.94153	12.13977
5.00E-06	41.5101	38.83813	32.29933	29.84257	26.60728	19.68347	18.59375	13.63908	12.31923	10.61688
4.00E-06	45.5644	43.93442	33.879	32.9055	27.73898	23.18125	19.72765	12.87817	12.50212	13.03635
3.00E-06	55.64228	52.89503	40.25887	37.23753	30.99052	21.91538	19.30377	14.7379	13.16163	13.23238
2.00E-06	76.9769	54.82058	48.90273	42.34932	29.33985	26.40945	22.72518	15.18567	13.90563	14.09025
1.00E-06	120.068	88.98115	62.04817	58.25057	36.11708	29.29723	25.21703	19.66868	15.39393	15.97267