如何在Matlab或其他绘图软件中根据数据确定阻尼系数

o2g1uqev  于 2022-12-13  发布在  Matlab
关注(0)|答案(2)|浏览(381)

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
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  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
matlab

2条答案

按热度按时间
e4eetjau

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：

f(x) = A * exp(-b*(x-x0)) * sin(2*pi*(x-x0)/T) + y0

现在，获得良好的初始值非常重要。

  • y0：y偏移很容易，数据趋向于y=0.5
  • x0：x偏移也很容易，从数据中读取第一个y=0.5交叉点，大约在x0=22040处
  • A：约为0.8（0.5至第一个最大值，约为1.3）
  • T：在22040和大约23480之间，您计算10个周期，因此大约T = (23480-22040)/10 = 144
  • B：对于最大值，您有：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：

### fitting damped oscillating data
reset session

FILE = "SO74694089.dat"

f(x) = A * exp(-b*(x-x0)) * sin(2*pi*(x-x0)/T) + y0

# starting values estimates
A  = 0.8
b  = 0.0027
x0 = 22040
T  = 144
y0 = 0.5

set yrange[-0.6:1.4]
set xrange[22000:]
set grid
set samples 1000

set fit brief nolog
fit f(x) FILE u 1:3 via A,b,T,y0

plot FILE u 1:3 w l, \
     f(x) lc "red"
### end of script

结果：

Final set of parameters            Asymptotic Standard Error
=======================            ==========================
A               = 0.882658         +/- 0.002062     (0.2336%)
b               = 0.00278188       +/- 1.023e-05    (0.3679%)
T               = 144.17           +/- 0.02687      (0.01864%)
y0              = 0.508991         +/- 0.0003925    (0.07712%)

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6tdlim6h

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。

Vi = V - mean(V);   %remove the mean of the signal
[OPTIONAL]...Vi = filter(B,1,Vi);  %apply low pass filter (B) 
[Pks,Locs] = findpeaks(Vi,'MinPeakDistance',D) %assuming you have an estimate of the frequency, set the value of D to something like 75% of the expected period so that you only detect peaks that are separated by the expected amount

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。

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