Sie eine nicht-lineare kleinsten Quadrate (nls) fit für ein sinusförmigen Modell

Question

ich die folgende Funktion, um meine Daten passen will:

f (x) = Offset + Amplitude sin (Frequency T + Phase),

oder nach Wikipedia: f (x) = C + alpha sin (omega T + phi)

meine Daten in zwei Spalten in einer Datei gespeichert wird, und I die Daten werden durch die folgende:

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

und wandeln sie durch die folgende:

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

So bekommen I zwei Variable vom Typ double, sogenannte „T“ (entspricht der Zeit T in der obigen Gleichung) und sogenannte „Werte“ (äquivalent auf den Wert der Funktion f (x) in der obigen Gleichung). Bis jetzt funktioniert alles sehr gut! Wenn ich jedoch f (x) an meine Daten anpassen möchte, bekomme ich (wenn überhaupt) schlechte Ergebnisse. Hier ist mein Code:

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

Mein Problem ist jetzt, dass das einzige, was in diesem einfachen Vier-Linien-Beispiel (zumindest soweit ich weiß) falsch sein könnte, sind die Startwerte. Sie sind jedoch ein Ergebnis einer Gnuplot-Anpassung (sie verwendet die Methode der kleinsten Quadrate) und sie sehen ziemlich gut aus (da ich keine "10 Reputation" habe, kann ich keine Zeichnung anhängen, sry). {Edit1: Grundstück angebracht} Ergebnis des Codes von oben:

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

Mein nachfolgenden Schritt der Startwerte zu variieren war ein vernünftiges Ergebnis zu erhalten (vielleicht die Startwerte sind auch gut ...) - nein Erfolg! Also meine Frage ist jetzt: Wo ist das Problem? Ich wollte R verwenden, weil ich gehofft habe, dass ich eine Passform erzeugen kann, die a) besser ist mit b) schlechteren Startwerten als Gnuplot (t mindestens b) ist ein sehr wichtiges Kriterium für mich, deshalb möchte ich nicht Gnuplot verwenden).

Ps .: Ja, das ist mein erster Tag der Verwendung von R. Also, wenn Sie eine Lösung/Grund für mich haben, wäre es schön, wenn ich es verstehen könnte.

PPs .: Für diejenigen, die verwandte Informationen erhalten möchten: Ich habe eine Menge Links gesammelt, also wenn ich mindestens "10 Ruf" bekomme, kann ich sie hier posten. {Edit2: links angebracht}

[R] fitting periodic 'sine wave' model

Nonlinear Regression and Nonlinear Least Squares

Nonlinear Regression and Nonlinear Least Squares in R

Nichtlineare Regression (German)

R: Nonlinear Least Squares

How to fit a curve to a sinusoidal wave

official Documentation -> Manuals

Link Roland provided in his answer

PPs.: Hier wurden die von mir verwendeten Daten (getrennt durch Tabstop, nur Spalte eins ("counter") und drei ("min value") verwendet, einige Werte der letzten Spalte löschte ich aufgrund der maximalen Anzahl Zeichen/post {edit3: deleted zusätzliche Einträge aufgrund der angehängten Links}) {edit4: geändert von "Spalte zwei (" angle ")" in "Spalte eins (" counter ")". In dem Code und die Antworten seine Spalte ein, auch}.

#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

Zuerst ersetzen ich alle „“ in Ihren Daten mit „“ (alternativ könnten Sie das dec Argument von verwenden), dann habe ich Zeilen mit weniger Elementen (die am Ende) entfernt und einen richtigen Header erstellt.

Dann lese ich Ihre Daten mit data <- read.table(text="<paste the cleaned data here>", header=TRUE).

Dann habe ich dies:

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) 

Und bekam dies:

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 

Dann aufgetragen I:

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

Und erhielt diese:

Dann las ich das: https://stats.stackexchange.com/a/60997/11849

Und tat dies:

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) 

Und bekam dies:

Und:

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: Bitte beachten Sie, dass es eine extrem schlechte Idee ist, eine Variable T aufzurufen. T ist ein Alias ​​für TRUE in R.

Answer 2

Diese Art von Problem wird von lokalen Extrema geplagt. Durch den Sinus erweitern, können Sie das Modell neu zu schreiben als

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

Es gibt nur einen nicht-lineare Parameter links und Sie können eine Rastersuche (oder etwas robusten Optimierungsalgorithmus) auf diesem Parameter (verwenden und lineare Regression für die anderen).

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 
)