r - 对正弦模型进行非线性最小二乘 (nls) 拟合

Question

我想将以下函数拟合到我的数据中：

f(x) = 偏移+幅度sin(频率T+相位),

或根据维基百科： f(x) = C+alpha sin(omega T+phi)

我的数据存储在两列的文件中，我通过以下方式导入它们：

data<-read.table("C:/PATH/data.txt", header = FALSE, sep = "\t")

并通过以下方式转换它们：

minV<-data[3]
cV<-data[1]
values<-as.numeric(unlist(minV))
T<-as.numeric(unlist(cV))

因此，我得到了两个 double 类型的变量，一个称为“T”（相当于上面等式中的时间 T）和一个称为“值”（相当于上面等式中函数 f(x) 的值）。到目前为止，一切正常！但是，当我想将 f(x) 拟合到我的数据时，我会得到不好的结果（如果有的话）。这是我的代码：

r<-nls(values~C+alpha*sin(W*T+phi), start=list(C=8958.34, alpha=115.886, W=0.0652, phi=14.9286),

我现在的问题是，在这个简单的四行示例中（至少据我所知）唯一可能出错的是起始值。但是，它们是 Gnuplot 拟合的结果（它使用最小二乘法）并且它们看起来非常好（因为我没有“10 声望”，所以我无法附上图，抱歉）。{edit1: plot attach} 上面代码的结果：

C: 8950.06571617  alpha: -23.58439668    W: 0.06416806   phi: 16.46585060

我的后续步骤是改变起始值以获得合理的结果（也许起始值太好了......） - 没有成功！所以我现在的问题是：问题出在哪里？我想使用 R，因为我希望我可以产生一个合适的结果，即 a) 更好的 b) 比 Gnuplot 更差的起始值（至少 b）对我来说是一个非常重要的标准，这就是我不想要的原因使用 Gnuplot）。

Ps.：是的，这是我使用 R 的第一天。因此，如果您对我有解决方案/理由，如果我能理解它会很好。

PPs.：对于那些想要获得相关信息的人：我已经收集了很多链接，所以如果我得到至少“10名声望”，我可以在这里发布。{edit2：附加链接}

[R] 拟合周期性“正弦波”模型

非线性回归和非线性最小二乘

R中的非线性回归和非线性最小二乘

Nichtlineare 回归（德语）

R：非线性最小二乘

如何将曲线拟合到正弦波

官方文档 -> 手册

链接罗兰在他的回答中提供

PPs.：这里是我使用的数据（由制表符分隔，仅使用第一列（“计数器”）和第三列（“最小值”）；由于最大字符数/帖子，我删除了最后一列的一些值{edit3 ：由于附加链接而删除了其他条目}）{edit4：从“第二列（“角度”）”更改为“第一列（“计数器”）”。在代码和答案中，它的第一列也是如此。}：

#Counter    angle   min value   EV-min value    max value   EV_max-value
1   0,703125    9033    -81,990234375   9043    -82,556640625
2   1,40625 9033    -81,990234375   9042    -81,556640625
3   2,109375    9027    -75,990234375   9042    -81,556640625
4   2,8125  9025    -73,990234375   9038    -77,556640625
5   3,515625    9018    -66,990234375   9031    -70,556640625
6   4,21875 9013    -61,990234375   9025    -64,556640625
7   4,921875    9009    -57,990234375   9020    -59,556640625
8   5,625   9011    -59,990234375   9017    -56,556640625
9   6,328125    9000    -48,990234375   9009    -48,556640625
10  7,03125 8996    -44,990234375   9004    -43,556640625
11  7,734375    8989    -37,990234375   9004    -43,556640625
12  8,4375  8983    -31,990234375   8993    -32,556640625
13  9,140625    8983    -31,990234375   8991    -30,556640625
14  9,84375 8982    -30,990234375   8991    -30,556640625
15  10,546875   8975    -23,990234375   8983    -22,556640625
16  11,25   8964    -12,990234375   8978    -17,556640625
17  11,953125   8967    -15,990234375   8977    -16,556640625
18  12,65625    8958    -6,990234375    8967    -6,556640625
19  13,359375   8951    0,009765625 8960    0,443359375
20  14,0625 8947    4,009765625 8954    6,443359375
21  14,765625   8938    13,009765625    8951    9,443359375
22  15,46875    8933    18,009765625    8940    20,443359375
23  16,171875   8929    22,009765625    8941    19,443359375
24  16,875  8925    26,009765625    8933    27,443359375
25  17,578125   8923    28,009765625    8929    31,443359375
26  18,28125    8920    31,009765625    8927    33,443359375
27  18,984375   8912    39,009765625    8921    39,443359375
28  19,6875 8899    52,009765625    8916    44,443359375
29  20,390625   8899    52,009765625    8907    53,443359375
30  21,09375    8894    57,009765625    8901    59,443359375
31  21,796875   8892    59,009765625    8896    64,443359375
32  22,5    8886    65,009765625    8896    64,443359375
33  23,203125   8881    70,009765625    8892    68,443359375
34  23,90625    8879    72,009765625    8886    74,443359375
35  24,609375   8884    67,009765625    8888    72,443359375
36  25,3125 8875    76,009765625    8886    74,443359375
37  26,015625   8864    87,009765625    8881    79,443359375
38  26,71875    8860    91,009765625    8870    90,443359375
39  27,421875   8864    87,009765625    8872    88,443359375
40  28,125  8862    89,009765625    8872    88,443359375
41  28,828125   8859    92,009765625    8868    92,443359375
42  29,53125    8857    94,009765625    8864    96,443359375
43  30,234375   8852    99,009765625    8860    100,443359375
44  30,9375 8852    99,009765625    8855    105,443359375
45  31,640625   8847    104,009765625   8857    103,443359375
46  32,34375    8844    107,009765625   8853    107,443359375
47  33,046875   8842    109,009765625   8849    111,443359375
48  33,75   8844    107,009765625   8855    105,443359375
49  34,453125   8846    105,009765625   8852    108,443359375
50  35,15625    8846    105,009765625   8853    107,443359375
51  35,859375   8839    112,009765625   8849    111,443359375
52  36,5625 8841    110,009765625   8849    111,443359375
53  37,265625   8841    110,009765625   8846    114,443359375
54  37,96875    8844    107,009765625   8852    108,443359375
55  38,671875   8841    110,009765625   8852    108,443359375
56  39,375  8835    116,009765625   8846    114,443359375
57  40,078125   8839    112,009765625   8847    113,443359375
58  40,78125    8839    112,009765625   8847    113,443359375
59  41,484375   8846    105,009765625   8857    103,443359375
60  42,1875 8849    102,009765625   8860    100,443359375
61  42,890625   8852    99,009765625    8860    100,443359375
62  43,59375    8852    99,009765625    8860    100,443359375
63  44,296875   8853    98,009765625    8866    94,443359375
64  45  8857    94,009765625    8864    96,443359375
65  45,703125   8860    91,009765625    8864    96,443359375
66  46,40625    8860    91,009765625    8870    90,443359375
67  47,109375   8866    85,009765625    8875    85,443359375
68  47,8125 8868    83,009765625    8878    82,443359375
69  48,515625   8875    76,009765625    8884    76,443359375
70  49,21875    8884    67,009765625    8892    68,443359375
71  49,921875   8883    68,009765625    8894    66,443359375
72  50,625  8888    63,009765625    8897    63,443359375
73  51,328125   8892    59,009765625    8899    61,443359375
74  52,03125    8897    54,009765625    8909    51,443359375
75  52,734375   8903    48,009765625    8910    50,443359375
76  53,4375 8910    41,009765625    8921    39,443359375
77  54,140625   8916    35,009765625    8923    37,443359375
78  54,84375    8923    28,009765625    8929    31,443359375
79  55,546875   8925    26,009765625    8936    24,443359375
80  56,25   8930    21,009765625    8938    22,443359375
81  56,953125   8929    22,009765625    8938    22,443359375
82  57,65625    8936    15,009765625    8947    13,443359375
83  58,359375   8943    8,009765625 8954    6,443359375
84  59,0625 8947    4,009765625 8960    0,443359375
85  59,765625   8960    -8,990234375    8965    -4,556640625
86  60,46875    8965    -13,990234375   8973    -12,556640625
87  61,171875   8964    -12,990234375   8973    -12,556640625
88  61,875  8969    -17,990234375   8980    -19,556640625
89  62,578125   8967    -15,990234375   8980    -19,556640625
90  63,28125    8969    -17,990234375   8975    -14,556640625
91  63,984375   8975    -23,990234375   8983    -22,556640625
92  64,6875 8978    -26,990234375   8991    -30,556640625
93  65,390625   8985    -33,990234375   8998    -37,556640625
94  66,09375    8991    -39,990234375   9000    -39,556640625
95  66,796875   9000    -48,990234375   9006    -45,556640625
96  67,5    9004    -52,990234375   9013    -52,556640625
97  68,203125   9009    -57,990234375   9017    -56,556640625
98  68,90625    9013    -61,990234375   9022    -61,556640625
99  69,609375   9017    -65,990234375   9027    -66,556640625
100 70,3125 9024    -72,990234375   9033    -72,556640625
101 71,015625   9029    -77,990234375   9037    -76,556640625
102 71,71875    9031    -79,990234375   9042    -81,556640625
103 72,421875   9035    -83,990234375   9043    -82,556640625
104 73,125  9040    -88,990234375   9048    -87,556640625
105 73,828125   9048    -96,990234375   9054    -93,556640625
106 74,53125    9049    -97,990234375   9060    -99,556640625
107 75,234375   9051    -99,990234375   9064    -103,556640625
108 75,9375 9061    -109,990234375  9072    -111,556640625
109 76,640625   9060    -108,990234375  9069    -108,556640625
110 77,34375    9066    -114,990234375  9072    -111,556640625
111 78,046875   9064    -112,990234375  9072    -111,556640625
112 78,75   9067    -115,990234375  9071    -110,556640625
113 79,453125   9072    -120,990234375  9082    -121,556640625
114 80,15625    9069    -117,990234375  9080    -119,556640625
115 80,859375   9072    -120,990234375  9082    -121,556640625
116 81,5625 9074    -122,990234375  9083    -122,556640625
117 82,265625   9078    -126,990234375  9089    -128,556640625
118 82,96875    9082    -130,990234375  9090    -129,556640625
119 83,671875   9085    -133,990234375  9090    -129,556640625
120 84,375  9078    -126,990234375  9089    -128,556640625
121 85,078125   9072    -120,990234375  9083    -122,556640625
122 85,78125    9072    -120,990234375  9080    -119,556640625
123 86,484375   9076    -124,990234375  9085    -124,556640625
124 87,1875 9071    -119,990234375  9076    -115,556640625
125 87,890625   9067    -115,990234375  9074    -113,556640625
126 88,59375    9066    -114,990234375  9078    -117,556640625
127 89,296875   9066    -114,990234375  9078    -117,556640625
128 90  9066    -114,990234375  9076    -115,556640625
129 90,703125   9066    -114,990234375  9072    -111,556640625
130 91,40625    9061    -109,990234375  9071    -110,556640625
131 92,109375   9058    -106,990234375  9069    -108,556640625
132 92,8125 9061    -109,990234375  9069    -108,556640625
133 93,515625   9054    -102,990234375  9069    -108,556640625
134 94,21875    9053    -101,990234375  9056    -95,556640625
135 94,921875   9053    -101,990234375  9060    -99,556640625
136 95,625  9048    -96,990234375   9056    -95,556640625
137 96,328125   9042    -90,990234375   9051    -90,556640625
138 97,03125    9042    -90,990234375   9045    -84,556640625
139 97,734375   9035    -83,990234375   9043    -82,556640625
140 98,4375 9033    -81,990234375   9043    -82,556640625
141 99,140625   9024    -72,990234375   9031    -70,556640625
142 99,84375    9027    -75,990234375   9037    -76,556640625
143 100,546875  9018    -66,990234375   9031    -70,556640625
144 101,25  9011    -59,990234375   9020    -59,556640625
145 101,953125  9011    -59,990234375   9018    -57,556640625
146 102,65625   9006    -54,990234375   9011    -50,556640625
147 103,359375  9000    -48,990234375   9006    -45,556640625
148 104,0625    8993    -41,990234375   9004    -43,556640625
149 104,765625  8985    -33,990234375   8998    -37,556640625
150 105,46875   8987    -35,990234375   8994    -33,556640625
151 106,171875  8982    -30,990234375   8987    -26,556640625
152 106,875 8973    -21,990234375   8983    -22,556640625
153 107,578125  8965    -13,990234375   8977    -16,556640625
154 108,28125   8969    -17,990234375   8977    -16,556640625
155 108,984375  8965    -13,990234375   8971    -10,556640625
156 109,6875    8953    -1,990234375    8965    -4,556640625
157 110,390625  8951    0,009765625 8962    -1,556640625
158 111,09375   8943    8,009765625 8951    9,443359375
159 111,796875  8938    13,009765625    8951    9,443359375
160 112,5   8930    21,009765625    8941    19,443359375
161 113,203125  8927    24,009765625    8940    20,443359375
162 113,90625   8923    28,009765625    8930    30,443359375
163 114,609375  8923    28,009765625    8930    30,443359375
164 115,3125    8914    37,009765625    8929    31,443359375
165 116,015625  8909    42,009765625    8920    40,443359375
166 116,71875   8901    50,009765625    8914    46,443359375
167 117,421875  8899    52,009765625    8910    50,443359375
168 118,125 8890    61,009765625    8896    64,443359375
169 118,828125  8886    65,009765625    8896    64,443359375
170 119,53125   8884    67,009765625    8896    64,443359375
171 120,234375  8881    70,009765625    8890    70,443359375
172 120,9375    8883    68,009765625    8890    70,443359375
173 121,640625  8878    73,009765625    8886    74,443359375
174 122,34375   8875    76,009765625    8883    77,443359375
175 123,046875  8862    89,009765625    8875    85,443359375
176 123,75  8866    85,009765625    8878    82,443359375
177 124,453125  8866    85,009765625    8875    85,443359375
178 125,15625   8864    87,009765625    8875    85,443359375
179 125,859375  8860    91,009765625    8868    92,443359375
180 126,5625    8857    94,009765625    8870    90,443359375
181 127,265625  8853    98,009765625    8857    103,443359375
182 127,96875   8847    104,009765625   8859    101,443359375
183 128,671875  8847    104,009765625   8857    103,443359375
184 129,375 8844    107,009765625   8849    111,443359375
185 130,078125  8844    107,009765625   8855    105,443359375
186 130,78125   8844    107,009765625   8853    107,443359375
187 131,484375  8841    110,009765625   8852    108,443359375
188 132,1875    8839    112,009765625   8849    111,443359375
189 132,890625  8841    110,009765625   8849    111,443359375
190 133,59375   8841    110,009765625   8847    113,443359375
191 134,296875  8841    110,009765625   8846    114,443359375
192 135 8839    112,009765625   8847    113,443359375
193 135,703125  8836    115,009765625   8844    116,443359375
194 136,40625   8836    115,009765625   8844    116,443359375
195 137,109375  8841    110,009765625   8849    111,443359375
196 137,8125    8844    107,009765625   8855    105,443359375
197 138,515625  8844    107,009765625   8857    103,443359375
198 139,21875   8853    98,009765625    8862    98,443359375
199 139,921875  8852    99,009765625    8860    100,443359375
200 140,625 8853    98,009765625    8862    98,443359375
201 141,328125  8855    96,009765625    8864    96,443359375
202 142,03125   8859    92,009765625    8862    98,443359375
203 142,734375  8859    92,009765625    8866    94,443359375
204 143,4375    8868    83,009765625    8878    82,443359375
205 144,140625  8870    81,009765625    8883    77,443359375
206 144,84375   8875    76,009765625    8884    76,443359375
207 145,546875  8881    70,009765625    8890    70,443359375
208 146,25  8886    65,009765625    8894    66,443359375
209 146,953125  8888    63,009765625    8897    63,443359375
210 147,65625   8890    61,009765625    8903    57,443359375
211 148,359375  8903    48,009765625    8910    50,443359375
212 149,0625    8903    48,009765625    8916    44,443359375
213 149,765625  8907    44,009765625    8920    40,443359375
214 150,46875   8918    33,009765625    8925    35,443359375
215 151,171875  8921    30,009765625    8929    31,443359375
216 151,875 8927    24,009765625    8936    24,443359375
217 152,578125  8929    22,009765625    8940    20,443359375
218 153,28125   8933    18,009765625    8943    17,443359375
219 153,984375  8940    11,009765625    8947    13,443359375
220 154,6875    8943    8,009765625 8954    6,443359375
221 155,390625  8954    -2,990234375    8964    -3,556640625
222 156,09375   8956    -4,990234375    8967    -6,556640625
223 156,796875  8960    -8,990234375    8980    -19,556640625
224 157,5   8971    -19,990234375   8977    -16,556640625
225 158,203125  8973    -21,990234375   8980    -19,556640625
226 158,90625   8973    -21,990234375   8983    -22,556640625
227 159,609375  8969    -17,990234375   8980    -19,556640625
228 160,3125    8971    -19,990234375   8987    -26,556640625
229 161,015625  8978    -26,990234375   8989    -28,556640625
230 161,71875   8987    -35,990234375   8998    -37,556640625
231 162,421875  8994    -42,990234375   9004    -43,556640625
232 163,125 9000    -48,990234375   9006    -45,556640625
233 163,828125  9006    -54,990234375   9013    -52,556640625
234 164,53125   9009    -57,990234375   9020    -59,556640625
235 165,234375  9014    -62,990234375   9024    -63,556640625
236 165,9375    9020    -68,990234375   9029    -68,556640625
237 166,640625  9025    -73,990234375   9035    -74,556640625
238 167,34375   9027    -75,990234375   9038    -77,556640625
239 168,046875  9033    -81,990234375   9042    -81,556640625
240 168,75  9033    -81,990234375   9043    -82,556640625
241 169,453125  9040    -88,990234375   9049    -88,556640625
242 170,15625   9045    -93,990234375   9054    -93,556640625
243 170,859375  9048    -96,990234375   9060    -99,556640625
244 171,5625    9056    -104,990234375  9064    -103,556640625
245 172,265625  9058    -106,990234375  9067    -106,556640625
246 172,96875   9060    -108,990234375  9071    -110,556640625
247 173,671875  9061    -109,990234375  9071    -110,556640625
248 174,375 9067    -115,990234375  9076    -115,556640625
249 175,078125  9067    -115,990234375  9078    -117,556640625
250 175,78125   9067    -115,990234375  9078    -117,556640625
251 176,484375  9071    -119,990234375  9082    -121,556640625
252 177,1875    9069    -117,990234375  9082    -121,556640625
253 177,890625  9072    -120,990234375  9085    -124,556640625
254 178,59375   9082    -130,990234375  9089    -128,556640625
255 179,296875  9080    -128,990234375  9092    -131,556640625
256 180 9080    -128,990234375  9092    -131,556640625
257 180,703125  9078    -126,990234375  9089    -128,556640625
258 181,40625   9076    -124,990234375  9083    -122,556640625
259 182,109375  9074    -122,990234375  9085    -124,556640625
260 182,8125    9076    -124,990234375  9082    -121,556640625
261 183,515625  9071    -119,990234375  9078    -117,556640625
262 184,21875   9067    -115,990234375  9078    -117,556640625
263 184,921875  9071    -119,990234375  9078    -117,556640625
264 185,625 9067    -115,990234375  9076    -115,556640625
265 186,328125  9069    -117,990234375  9078    -117,556640625
266 187,03125   9064    -112,990234375  9074    -113,556640625
267 187,734375  9064    -112,990234375  9074    -113,556640625
268 188,4375    9061    -109,990234375  9071    -110,556640625
269 189,140625  9058    -106,990234375  9066    -105,556640625
270 189,84375   9056    -104,990234375  9066    -105,556640625
271 190,546875  9053    -101,990234375  9056    -95,556640625
272 191,25  9051    -99,990234375   9061    -100,556640625
273 191,953125  9048    -96,990234375   9058    -97,556640625
274 192,65625   9040    -88,990234375   9054    -93,556640625
275 193,359375  9042    -90,990234375   9048    -87,556640625
276 194,0625    9037    -85,990234375   9045    -84,556640625
277 194,765625  9033    -81,990234375   9045    -84,556640625
278 195,46875   9029    -77,990234375   9043    -82,556640625
279 196,171875  9027    -75,990234375   9040    -79,556640625
280 196,875 9020    -68,990234375   9038    -77,556640625
281 197,578125  9011    -59,990234375   9029    -68,556640625
282 198,28125   9009    -57,990234375   9020    -59,556640625
283 198,984375  9002    -50,990234375   9013    -52,556640625
284 199,6875    8996    -44,990234375   9009    -48,556640625
285 200,390625  8993    -41,990234375   9004    -43,556640625
286 201,09375   8989    -37,990234375   8996    -35,556640625
287 201,796875  8983    -31,990234375   8991    -30,556640625
288 202,5   8985    -33,990234375   8991    -30,556640625
289 203,203125  8978    -26,990234375   8989    -28,556640625
290 203,90625   8977    -25,990234375   8983    -22,556640625
291 204,609375  8971    -19,990234375   8982    -21,556640625
292 205,3125    8958    -6,990234375    8971    -10,556640625
293 206,015625  8958    -6,990234375    8965    -4,556640625
294 206,71875   8947    4,009765625 8958    2,443359375
295 207,421875  8941    10,009765625    8954    6,443359375
296 208,125 8934    17,009765625    8951    9,443359375
297 208,828125  8933    18,009765625    8940    20,443359375
298 209,53125   8929    22,009765625    8938    22,443359375
299 210,234375  8927    24,009765625    8934    26,443359375
300 210,9375    8920    31,009765625    8930    30,443359375
301 211,640625  8916    35,009765625    8921    39,443359375
302 212,34375   8909    42,009765625    8921    39,443359375
303 213,046875  8903    48,009765625    8910    50,443359375
304 213,75  8894    57,009765625    8905    55,443359375
305 214,453125  8894    57,009765625    8899    61,443359375
306 215,15625   8883    68,009765625    8897    63,443359375
307 215,859375  8881    70,009765625    8890    70,443359375
308 216,5625    8886    65,009765625    8894    66,443359375
309 217,265625  8879    72,009765625    8888    72,443359375
310 217,96875   8878    73,009765625    8886    74,443359375
311 218,671875  8873    78,009765625    8883    77,443359375
312 219,375 8862    89,009765625    8878    82,443359375
313 220,078125  8866    85,009765625    8878    82,443359375
314 220,78125   8862    89,009765625    8870    90,443359375
315 221,484375  8857    94,009765625    8862    98,443359375
316 222,1875    8859    92,009765625    8864    96,443359375
317 222,890625  8859    92,009765625    8870    90,443359375
318 223,59375   8857    94,009765625    8868    92,443359375
319 224,296875  8852    99,009765625    8860    100,443359375
320 225 8847    104,009765625   8857    103,443359375
321 225,703125  8842    109,009765625   8853    107,443359375
322 226,40625   8844    107,009765625   8855    
323 227,109375  8849    102,009765625   8857    
324 227,8125    8839    112,009765625   8849    
325 228,515625  8842    109,009765625   8849    
326 229,21875   8841    110,009765625   8849    
327 229,921875  8842    109,009765625   8852    
328 230,625 8836    115,009765625   8855    
329 231,328125  8839    112,009765625   8846    
330 232,03125   8836    115,009765625   8844    
331 232,734375  8839    112,009765625   8846    
332 233,4375    8842    109,009765625   8852    
333 234,140625  8846    105,009765625   8857    
334 234,84375   8852    99,009765625    8857    
335 235,546875  8857    94,009765625    8862    
336 236,25  8855    96,009765625    8862    
337 236,953125  8857    94,009765625    8864    
338 237,65625   8857    94,009765625    8864    
339 238,359375  8857    94,009765625    8866    
340 239,0625    8857    94,009765625    8872    
341 239,765625  8866    85,009765625    8878    
342 240,46875   8873    78,009765625    8881    
343 241,171875  8878    73,009765625    8886    
344 241,875 8883    68,009765625    8892    
345 242,578125  8886    65,009765625    8896    
346 243,28125   8892    59,009765625    8899    
347 243,984375  8896    55,009765625    8905    
348 244,6875    8903    48,009765625    8909    
349 245,390625  8907    44,009765625    8916    
350 246,09375   8912    39,009765625    8920    
351 246,796875  8914    37,009765625    8929    
352 247,5   8927    24,009765625    8934    
353 248,203125  8925    26,009765625    8936    
354 248,90625   8929    22,009765625    8938    
355 249,609375  8933    18,009765625    8940    
356 250,3125    8940    11,009765625    8951    
357 251,015625  8949    2,009765625 8958    
358 251,71875   8958    -6,990234375    8964    
359 252,421875  8962    -10,990234375   8973    
360 253,125 8965    -13,990234375   8973    
361 253,828125  8967    -15,990234375   8980    
362 254,53125   8971    -19,990234375   8980    
363 255,234375  8967    -15,990234375   8982    
364 255,9375    8975    -23,990234375   8982    
365 256,640625  8975    -23,990234375   8983    
366 257,34375   8977    -25,990234375   8991    
367 258,046875  8989    -37,990234375   8994    
368 258,75  8989    -37,990234375   9000    
369 259,453125  8996    -44,990234375   9007    
370 260,15625   9004    -52,990234375   9013    
371 260,859375  9007    -55,990234375   9018    
372 261,5625    9014    -62,990234375   9022    
373 262,265625  9017    -65,990234375   9025    
374 262,96875   9025    -73,990234375   9037    
375 263,671875  9029    -77,990234375   9042    
376 264,375 9033    -81,990234375   9042    
377 265,078125  9031    -79,990234375   9043    
378 265,78125   9042    -90,990234375   9051    
379 266,484375  9043    -91,990234375   9054    
380 267,1875    9048    -96,990234375   9058    
381 267,890625  9048    -96,990234375   9061    
382 268,59375   9056    -104,990234375  9060    
383 269,296875  9060    -108,990234375  9067    
384 270 9064    -112,990234375  9071    
385 270,703125  9064    -112,990234375  9072    
386 271,40625   9069    -117,990234375  9074    
387 272,109375  9071    -119,990234375  9080    
388 272,8125    9072    -120,990234375  9082    
389 273,515625  9071    -119,990234375  9083    
390 274,21875   9078    -126,990234375  9083    
391 274,921875  9080    -128,990234375  9087    
392 275,625 9082    -130,990234375  9085    
393 276,328125  9083    -131,990234375  9090    
394 277,03125   9072    -120,990234375  9087    
395 277,734375  9071    -119,990234375  9078    
396 278,4375    9072    -120,990234375  9082    
397 279,140625  9076    -124,990234375  9085    
398 279,84375   9074    -122,990234375  9082    
399 280,546875  9069    -117,990234375  9074    
400 281,25  9066    -114,990234375  9076    
401 281,953125  9069    -117,990234375  9076    
402 282,65625   9064    -112,990234375  9072    
403 283,359375  9066    -114,990234375  9074    
404 284,0625    9064    -112,990234375  9069    
405 284,765625  9064    -112,990234375  9071    
406 285,46875   9056    -104,990234375  9067    
407 286,171875  9056    -104,990234375  9066    
408 286,875 9056    -104,990234375  9061    
409 287,578125  9051    -99,990234375   9060    
410 288,28125   9042    -90,990234375   9058    
411 288,984375  9040    -88,990234375   9051    
412 289,6875    9038    -86,990234375   9048    
413 290,390625  9035    -83,990234375   9043    
414 291,09375   9033    -81,990234375   9042    
415 291,796875  9027    -75,990234375   9038    
416 292,5   9027    -75,990234375   9038    
417 293,203125  9020    -68,990234375   9029    
418 293,90625   9013    -61,990234375   9022    
419 294,609375  9011    -59,990234375   9024    
420 295,3125    9004    -52,990234375   9013    
421 296,015625  9000    -48,990234375   9004    
422 296,71875   8994    -42,990234375   9004    
423 297,421875  8983    -31,990234375   8998    
424 298,125 8978    -26,990234375   8989    
425 298,828125  8982    -30,990234375   8989    
426 299,53125   8978    -26,990234375   8983    
427 300,234375  8973    -21,990234375   8982    
428 300,9375    8969    -17,990234375   8982    
429 301,640625  8960    -8,990234375    8975    
430 302,34375   8953    -1,990234375    8965    
431 303,046875  8949    2,009765625 8954    
432 303,75  8947    4,009765625 8954    
433 304,453125  8936    15,009765625    8949    
434 305,15625   8930    21,009765625    8941    
435 305,859375  8925    26,009765625    8936    
436 306,5625    8925    26,009765625    8934    
437 307,265625  8918    33,009765625    8927    
438 307,96875   8916    35,009765625    8921    
439 308,671875  8905    46,009765625    8920    
440 309,375 8899    52,009765625    8910    
441 310,078125  8892    59,009765625    8905    
442 310,78125   8890    61,009765625    8897    
443 311,484375  8886    65,009765625    8896    
444 312,1875    8886    65,009765625    8894    
445 312,890625  8879    72,009765625    8892    
446 313,59375   8879    72,009765625    8888    
447 314,296875  8878    73,009765625    8886    
448 315 8873    78,009765625    8883    
449 315,703125  8866    85,009765625    8878    
450 316,40625   8866    85,009765625    8875    
451 317,109375  8866    85,009765625    8873    
452 317,8125    8860    91,009765625    8872    
453 318,515625  8859    92,009765625    8868    
454 319,21875   8857    94,009765625    8868    
455 319,921875  8857    94,009765625    8864    
456 320,625 8847    104,009765625   8860    
457 321,328125  8847    104,009765625   8857    
458 322,03125   8842    109,009765625   8852    
459 322,734375  8841    110,009765625   8852    
460 323,4375    8844    107,009765625   8853    
461 324,140625  8846    105,009765625   8857    
462 324,84375   8841    110,009765625   8853    
463 325,546875  8836    115,009765625   8846    
464 326,25  8839    112,009765625   8844    
465 326,953125  8841    110,009765625   8846    
466 327,65625   8839    112,009765625   8847    
467 328,359375  8842    109,009765625   8852    
468 329,0625    8836    115,009765625   8844    
469 329,765625  8842    109,009765625   8847    
470 330,46875   8842    109,009765625   8849    
471 331,171875  8849    102,009765625   8860    
472 331,875 8857    94,009765625    8864    
473 332,578125  8852    99,009765625    8859    
474 333,28125   8852    99,009765625    8862    
475 333,984375  8855    96,009765625    8862    
476 334,6875    8857    94,009765625    8866    
477 335,390625  8862    89,009765625    8870    
478 336,09375   8864    87,009765625    8875    
479 336,796875  8868    83,009765625    8878    
480 337,5   8872    79,009765625    8884    
481 338,203125  8881    70,009765625    8888    
482 338,90625   8886    65,009765625    8894    
483 339,609375  8884    67,009765625    8899    
484 340,3125    8886    65,009765625    8899    
485 341,015625  8897    54,009765625    8909    
486 341,71875   8901    50,009765625    8910    
487 342,421875  8903    48,009765625    8916    
488 343,125 8914    37,009765625    8923    
489 343,828125  8925    26,009765625    8929    
490 344,53125   8929    22,009765625    8934    
491 345,234375  8927    24,009765625    8938    
492 345,9375    8927    24,009765625    8936    
493 346,640625  8930    21,009765625    8941    
494 347,34375   8947    4,009765625 8954    
495 348,046875  8947    4,009765625 8960    
496 348,75  8958    -6,990234375    8967    
497 349,453125  8960    -8,990234375    8973    
498 350,15625   8965    -13,990234375   8977    
499 350,859375  8967    -15,990234375   8978    
500 351,5625    8964    -12,990234375   8971    
501 352,265625  8962    -10,990234375   8973    
502 352,96875   8971    -19,990234375   8983    
503 353,671875  8977    -25,990234375   8985    
504 354,375 8983    -31,990234375   8994    
505 355,078125  8989    -37,990234375   8998    
506 355,78125   8994    -42,990234375   9007    
507 356,484375  9004    -52,990234375   9009    
508 357,1875    9002    -50,990234375   9020    
509 357,890625  9011    -59,990234375   9025    
510 358,59375   9017    -65,990234375   9027    
511 359,296875  9022    -70,990234375   9027    
512 360 9022    -70,990234375   9038    

Answer 1

这种问题受到局部极值的困扰。通过扩展正弦，您可以将模型重写为

C + alpha * sin(omega*T) + beta * cos(omega*T)

只剩下一个非线性参数，您可以对该参数使用网格搜索（或一些稳健的优化算法）（其他参数使用线性回归）。

d <- read.table( "tmp.csv", dec=",", header=TRUE, nrows=400)
x <- d[,1]
y <- d[,3]

f <- function( omega ) { 
  x1 <- sin( omega * x )
  x2 <- cos( omega * x )
  r <- lm( y ~ x1 + x2 )
  res <- mean( residuals(r)^2 )
  attr( res, "coef" ) <- coef(r)
  res
}
omegas <- seq( .001, .2, length=1000 )
res <- sapply(omegas, f)
plot( 
  omegas, res,
  las=1, 
  ylab = "Residuals", xlab = "Omega",
  main = "Objective function: multiple local minima" 
)

i <- which.min( res )
omega0 <- optimize(f, interval = c(omegas[i-1], omegas[i+1]))$minimum
p <- c( attr( f(omega0), "coef" ), omega0 )
plot( x, y )
lines( 
  x, 
  p[1] + p[2] * sin( p[4] * x ) + p[3] * cos( p[4] * x ),
  col = "orange", lwd=3 
)

Answer 2

首先，我用“。”替换了您数据中的所有“，”。（或者您可以使用 的dec参数read.table），然后我删除了元素较少的行（最后的那些）并创建了一个适当的标题。

然后我使用data <- read.table(text="<paste the cleaned data here>", header=TRUE).

然后我这样做了：

values<-data[,3]
T <-data[,1]

r<-nls(values~C+alpha*sin(W*T+phi), 
       start=list(C=8958.34, alpha=115.886, W=0.0652, phi=14.9286))
summary(r) 

得到了这个：

Formula: values ~ C + alpha * sin(W * T + phi)

Parameters:
       Estimate Std. Error  t value Pr(>|t|)    
C     8.959e+03  3.892e+00 2302.173  < 2e-16 ***
alpha 2.214e+01  5.470e+00    4.047 6.16e-05 ***
W     6.714e-02  2.031e-03   33.065  < 2e-16 ***
phi   1.334e+01  5.113e-01   26.092  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 80.02 on 423 degrees of freedom

Number of iterations to convergence: 21 
Achieved convergence tolerance: 5.952e-06

然后我绘制：

plot(values~T)
lines(predict(r)~T)

得到了这个：

然后我读到这个：https ://stats.stackexchange.com/a/60997/11849

并做到了这一点：

raw.fft = fft(values)
truncated.fft = raw.fft[seq(1, length(values)/2 - 1)]
truncated.fft[1] = 0
W = which.max(abs(truncated.fft)) * 2 * pi / length(values)

r2<-nls(values~C+alpha*sin(W*T+phi), start=list(C=8958.34, alpha=115.886, W=W, phi=0))

lines(predict(r2)~T, col="red")  

summary(r2)

得到了这个：

和这个：

Formula: values ~ C + alpha * sin(W * T + phi)

Parameters:
       Estimate Std. Error t value Pr(>|t|)    
C     8.958e+03  2.045e-01 43804.2   <2e-16 ***
alpha 1.160e+02  2.913e-01   398.0   <2e-16 ***
W     4.584e-02  1.954e-05  2345.6   <2e-16 ***
phi   2.325e+00  4.760e-03   488.5   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.204 on 423 degrees of freedom

Number of iterations to convergence: 9 
Achieved convergence tolerance: 1.07e-06

PS：请注意，调用变量是一个非常糟糕的主意T。T是TRUER中的别名。