如何将静音的正弦曲线拟合到数据python？

Question

我有一个静音振荡的数据集，想要适合它并找出Ae^-(kt)*sin(cx+phase)+d形式的值。

有什么想法可以做到吗？

这是我的数据

t = np.array([0.0, 0.2, 0.4, 0.6000000000000001, 0.8, 1.0, 1.2, 1.4, 1.5999999999999999, 1.7999999999999998, 1.9999999999999998, 2.1999999999999997, 2.4, 2.6, 2.8000000000000003, 3.0000000000000004, 3.2000000000000006, 3.400000000000001, 3.600000000000001, 3.800000000000001, 4.000000000000001, 4.200000000000001, 4.400000000000001, 4.600000000000001, 4.800000000000002, 5.000000000000002, 5.200000000000002, 5.400000000000002, 5.600000000000002, 5.8000000000000025, 6.000000000000003, 6.200000000000003, 6.400000000000003, 6.600000000000003, 6.800000000000003, 7.0000000000000036, 7.200000000000004, 7.400000000000004, 7.600000000000004, 7.800000000000004, 8.000000000000004, 8.200000000000003, 8.400000000000002, 8.600000000000001, 8.8, 9.0, 9.2, 9.399999999999999, 9.599999999999998, 9.799999999999997, 9.999999999999996, 10.199999999999996, 10.399999999999995, 10.599999999999994, 10.799999999999994, 10.999999999999993, 11.199999999999992, 11.399999999999991, 11.59999999999999, 11.79999999999999, 11.99999999999999, 12.199999999999989, 12.399999999999988, 12.599999999999987, 12.799999999999986, 12.999999999999986, 13.199999999999985, 13.399999999999984, 13.599999999999984, 13.799999999999983, 13.999999999999982, 14.199999999999982, 14.39999999999998, 14.59999999999998, 14.79999999999998, 14.999999999999979, 15.199999999999978, 15.399999999999977, 15.599999999999977, 15.799999999999976, 15.999999999999975, 16.199999999999974, 16.399999999999974, 16.599999999999973, 16.799999999999972, 16.99999999999997, 17.19999999999997, 17.39999999999997, 17.59999999999997, 17.79999999999997, 17.999999999999968, 18.199999999999967, 18.399999999999967, 18.599999999999966, 18.799999999999965, 18.999999999999964, 19.199999999999964, 19.399999999999963, 19.599999999999962, 19.79999999999996, 19.99999999999996, 20.19999999999996, 20.39999999999996, 20.59999999999996, 20.799999999999958, 20.999999999999957, 21.199999999999957, 21.399999999999956, 21.599999999999955, 21.799999999999955, 21.999999999999954, 22.199999999999953, 22.399999999999952, 22.59999999999995, 22.79999999999995, 22.99999999999995, 23.19999999999995, 23.39999999999995, 23.599999999999948, 23.799999999999947, 23.999999999999947, 24.199999999999946, 24.399999999999945, 24.599999999999945, 24.799999999999944, 24.999999999999943, 25.199999999999942, 25.39999999999994, 25.59999999999994, 25.79999999999994, 25.99999999999994, 26.19999999999994, 26.399999999999938, 26.599999999999937, 26.799999999999937, 26.999999999999936, 27.199999999999935, 27.399999999999935, 27.599999999999934, 27.799999999999933, 27.999999999999932, 28.199999999999932, 28.39999999999993, 28.59999999999993, 28.79999999999993, 28.99999999999993, 29.19999999999993, 29.399999999999928, 29.599999999999927, 29.799999999999926, 29.999999999999925, 30.199999999999925, 30.399999999999924, 30.599999999999923, 30.799999999999923, 30.999999999999922, 31.19999999999992, 31.39999999999992, 31.59999999999992, 31.79999999999992, 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data = np.array([-17.895166829633922, -7.850310582296288, -10.400080032016035, -12.555264688814987, -14.875887137689688, -17.403405204309593, -9.384189611217494, -4.8134501496749635, -11.288830542083133, -11.008508544742426, -11.008508544742426, -24.399675324728832, -11.801622922577621, -11.553206224788369, -6.85295195569654, 7.054570807289565, 59.28761332019553, 294.39871205088207, 238.80102498356405, 107.75489263075929, 56.92080305897116, -17.532368285997904, -134.43846589745613, -223.57517841817833, -278.0, -323.0007278024234, -321.8488538118969, -307.68383188196503, -254.07407770337704, -164.82546181276848, -80.251646949563, 130.4490343719881, 212.22747473618847, 274.903109187615, 306.2431386335884, 335.63590915224904, 314.16917348199877, 200.52715789444392, 113.2666646883099, 24.431244694397265, -75.25725464168488, -162.69840080405845, -224.60328495721353, -332.20357038414545, -337.45260390066187, -320.4436208691852, -266.3334080382526, -205.55236341947034, -112.4210341145465, 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Answer 1

当我查看前30个数据点时，就会看到：

所以我删除了数据的非正弦波部分。我还意识到，在前几个周期中拟合一个正弦波给我一些参数要容易得多，例如：

y = amplitude * sin(pi * (x - center) / width) + Offset

amplitude =  3.3098923173806202E+02
center =  2.1702445745645457E+02
width =  1.8508302910055434E+00
Offset = -9.6083629945476581E+00

而不是整个数据集。现在，我可以将这些参数作为常数（或初始参数估计值）重新插入到指数衰减方程中，并使用所有数据求解指数衰减。