我最近做了一个实验,测量了一个RLC电路的输出信号,该电路的行为完全类似于阻尼自由谐振子。我想从数据中确定阻尼比。我的第一个想法是对包络使用衰减指数拟合,如下图所示。
经过几个小时的绝望,我设法使用Matlab提供的曲线拟合工具添加指数拟合,但我不得不手动选择要考虑的峰值。有什么方法可以实现同样的结果,但要用代码吗?
我的意思是,我知道一定有办法,但我已经挣扎了太多的时间,超过了法律允许的时间,所以如果有任何好心的人能帮我写一个脚本,我会热情地欢迎它。我可以用Gnuplot,python或Matlab。
先谢了
这里有一个完整数据文件的链接,因为SO不允许我在这里转储整个内容data file link
time[0] Y[0] time[1] Y[1]
747979 -4.694474E-1 -5.114054E-1
747979 -4.267468E-1 -4.689731E-1
747979 -4.694474E-1 -4.689731E-1
747979 -4.694474E-1 -5.114054E-1
747979 -4.267468E-1 -4.689731E-1
747980 -4.267468E-1 -5.114054E-1
747980 -4.694474E-1 -5.114054E-1
747980 -4.694474E-1 -4.689731E-1
747980 -4.694474E-1 -5.114054E-1
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747981 -4.694474E-1 -4.689731E-1
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748005 5.553671E-1 -3.416763E-1
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748005 5.126665E-1 -3.416763E-1
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748014 5.126665E-1 -8.708270E-2
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748014 4.699659E-1 -1.295150E-1
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748019 5.553671E-1 8.264637E-2
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748021 5.553671E-1 1.250786E-1
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748026 5.126665E-1 2.523754E-1
748026 5.126665E-1 3.372400E-1
748026 4.699659E-1 2.948077E-1
748027 5.126665E-1 3.372400E-1
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748027 5.126665E-1 3.372400E-1
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748028 5.126665E-1 3.372400E-1
748028 5.126665E-1 3.796722E-1
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748028 5.126665E-1 3.796722E-1
748028 5.126665E-1 4.221045E-1
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748049 5.126665E-1 1.101021E+0
748049 5.126665E-1 1.058589E+0
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748050 5.553671E-1 1.101021E+0
748050 5.126665E-1 1.101021E+0
748050 5.126665E-1 1.101021E+0
748051 5.126665E-1 1.143453E+0
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748051 5.126665E-1 1.101021E+0
748051 5.553671E-1 1.101021E+0
748051 5.126665E-1 1.101021E+0
748052 5.126665E-1 1.101021E+0
748052 5.553671E-1 1.101021E+0
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748086 5.553671E-1 9.737240E-1
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748087 5.553671E-1 9.312917E-1
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748088 5.553671E-1 9.312917E-1
748088 5.553671E-1 9.312917E-1
748088 5.553671E-1 9.312917E-1
748089 5.553671E-1 9.312917E-1
748089 5.553671E-1 8.888594E-1
748089 5.553671E-1 9.312917E-1
748089 5.553671E-1 9.312917E-1
748089 5.553671E-1 9.312917E-1
748090 5.553671E-1 9.312917E-1
748090 5.553671E-1 8.888594E-1
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748090 5.553671E-1 8.888594E-1
748090 5.553671E-1 8.888594E-1
748091 5.553671E-1 8.888594E-1
748091 5.553671E-1 8.888594E-1
748091 5.553671E-1 8.464272E-1
748091 5.553671E-1 8.888594E-1
748091 5.553671E-1 8.888594E-1
748092 5.553671E-1 8.464272E-1
748092 5.553671E-1 8.464272E-1
748092 5.553671E-1 8.464272E-1
748092 5.126665E-1 8.464272E-1
748092 5.553671E-1 8.464272E-1
748093 5.553671E-1 8.039949E-1
748093 5.553671E-1 8.039949E-1
748093 5.126665E-1 7.615626E-1
748093 5.126665E-1 7.615626E-1
748093 5.126665E-1 8.039949E-1
748094 5.126665E-1 8.039949E-1
748094 5.126665E-1 7.615626E-1
748094 5.126665E-1 7.615626E-1
748094 5.553671E-1 7.615626E-1
748094 5.553671E-1 7.615626E-1
748095 5.126665E-1 7.615626E-1
748095 5.553671E-1 7.615626E-1
748095 5.553671E-1 7.615626E-1
748095 5.553671E-1 7.615626E-1
748095 5.126665E-1 7.615626E-1
748096 5.553671E-1 7.615626E-1
748096 5.553671E-1 7.191304E-1
748096 5.553671E-1 7.191304E-1
748096 5.553671E-1 7.191304E-1
748096 5.553671E-1 7.191304E-1
748097 5.553671E-1 7.191304E-1
748097 5.126665E-1 6.766981E-1
748097 5.553671E-1 6.766981E-1
748097 5.553671E-1 6.766981E-1
748097 5.553671E-1 6.766981E-1
748098 5.553671E-1 6.766981E-1
748098 5.553671E-1 6.766981E-1
748098 5.553671E-1 6.766981E-1
748098 5.553671E-1 6.766981E-1
748098 5.553671E-1 6.766981E-1
748099 5.553671E-1 6.342658E-1
748099 5.553671E-1 6.342658E-1
748099 5.553671E-1 6.342658E-1
748099 5.553671E-1 6.342658E-1
748099 5.553671E-1 6.342658E-1
748100 5.553671E-1 5.918336E-1
748100 5.553671E-1 5.918336E-1
748100 5.553671E-1 5.918336E-1
748100 5.553671E-1 5.918336E-1
748100 5.553671E-1 5.918336E-1
748101 5.553671E-1 5.918336E-1
748101 5.553671E-1 5.918336E-1
748101 5.553671E-1 5.918336E-1
748101 5.553671E-1 5.494013E-1
748101 5.553671E-1 5.918336E-1
748102 5.553671E-1 5.069690E-1
748102 5.553671E-1 5.494013E-1
748102 5.553671E-1 5.494013E-1
748102 5.553671E-1 5.494013E-1
748102 5.553671E-1 5.494013E-1
748103 5.553671E-1 5.494013E-1
748103 5.553671E-1 5.069690E-1
748103 5.553671E-1 5.069690E-1
748103 5.553671E-1 5.069690E-1
748103 5.553671E-1 5.069690E-1
748104 5.553671E-1 4.645368E-1
748104 5.553671E-1 4.645368E-1
748104 5.553671E-1 4.645368E-1
748104 5.553671E-1 4.645368E-1
748104 5.553671E-1 4.645368E-1
748105 5.553671E-1 4.221045E-1
748105 5.553671E-1 4.645368E-1
748105 5.553671E-1 4.221045E-1
748105 5.553671E-1 4.221045E-1
748105 5.553671E-1 4.221045E-1
748106 5.126665E-1 4.221045E-1
748106 5.553671E-1 4.221045E-1
748106 5.553671E-1 4.221045E-1
748106 5.553671E-1 4.221045E-1
748106 5.553671E-1 4.221045E-1
748107 5.553671E-1 4.221045E-1
748107 5.553671E-1 4.221045E-1
748107 5.553671E-1 3.796722E-1
748107 5.553671E-1 4.221045E-1
748107 5.553671E-1 3.796722E-1
748108 5.553671E-1 3.796722E-1
748108 5.553671E-1 3.796722E-1
748108 5.553671E-1 3.796722E-1
748108 5.553671E-1 3.796722E-1
748108 5.553671E-1 3.796722E-1
748109 5.553671E-1 3.796722E-1
748109 5.553671E-1 3.372400E-1
748109 5.553671E-1 3.796722E-1
748109 5.553671E-1 3.372400E-1
748109 5.553671E-1 3.372400E-1
748110 5.553671E-1 3.372400E-1
748110 5.553671E-1 3.372400E-1
748110 5.553671E-1 3.372400E-1
748110 5.553671E-1 3.372400E-1
748110 5.553671E-1 2.948077E-1
748111 5.553671E-1 2.523754E-1
748111 5.553671E-1 2.523754E-1
748111 5.553671E-1 2.523754E-1
748111 5.553671E-1 2.948077E-1
748111 5.553671E-1 2.523754E-1
748112 5.553671E-1 2.523754E-1
748112 5.553671E-1 2.523754E-1
748112 5.553671E-1 2.523754E-1
748112 5.553671E-1 2.523754E-1
748112 5.553671E-1 2.523754E-1
748113 5.553671E-1 2.099432E-1
748113 5.553671E-1 2.523754E-1
748113 5.553671E-1 2.099432E-1
748113 5.553671E-1 2.523754E-1
748113 5.553671E-1 2.099432E-1
748114 5.553671E-1 2.099432E-1
748114 5.553671E-1 2.099432E-1
748114 5.553671E-1 2.099432E-1
748114 5.553671E-1 2.099432E-1
748114 5.553671E-1 2.099432E-1
748115 5.553671E-1 2.099432E-1
748115 5.553671E-1 1.675109E-1
748115 5.553671E-1 2.099432E-1
748115 5.553671E-1 2.099432E-1
748115 5.553671E-1 1.675109E-1
748116 5.553671E-1 1.675109E-1
748116 5.553671E-1 1.675109E-1
748116 5.126665E-1 1.675109E-1
748116 5.553671E-1 1.675109E-1
748116 5.553671E-1 1.675109E-1
748117 5.553671E-1 1.250786E-1
748117 5.553671E-1 1.250786E-1
2条答案
按热度按时间e4eetjau1#
拟合一个振荡函数可以工作,但也可能变得困难。
首先,你需要一个你认为你的数据遵循的函数。在你的例子中,这可能是:
现在,获得良好的初始值非常重要。
T = (23480-22040)/10 = 144
A_n = A_0 * exp(-b *(xmn-xm0)
。因此,得到b = -ln(A_n/A_0)/(xmn-xm0)
。因此,取第一最大值A_0
的振幅和例如A_4
的振幅(当然,减去偏移y0)。得到大约b = -ln(0.8/0.17)/(22650-22075) = 0.0027
如果你有一个交互式终端,例如wxt,你可以很容易地用鼠标光标读出这些值。
一般来说,如果你在gnuplot控制台中运行拟合,它要么a)收敛,要么B)“永远”运行,要么c)因错误而停止。在b)的情况下,你可以至少在gnuplot 5.4.1中中断(按Ctrl+C),让你显示当前值。如果它们相当好,你可以停止并使用这些值作为初始值。
如果你有一个很好的初始值,例如上面的过程,拟合可能会收敛得相对较快。实际上,在下面的例子中,参数
x0
在拟合过程中并不用于变化,但它也可以变化。脚本:
结果:
6tdlim6h2#
指数模型方法在我看来是合理的。如果你有一个算法来自动找到峰值,你可以把它们放入你的指数衰减模型,而不必手动选择它们。有多种方法来做这件事,我不得不根据复杂性用不同的方法来“解决”这个问题(噪声,周期性等)的输入数据。如果你的信号是相当干净的,我会去与以下方法。
此时,您可以对Pks和Locs做一些进一步的检查以限定它们,但除此之外,这些都是指数模型的输入。