振动信号常用的时域和频域指标

matlab的旋律

通常振动信号为一时间序列，衡量振动信号的指标包括时域指标和频域指标，网上分享计算公式和源程序的比较少，本文给出了公式定义以及matlab/python源码。常见时域指标包括：

对应的Matlab程序如下：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%matlab程序
close all
clear
clc

st = 0.01;
data = sin(0:st:10);
Xr = mean(sqrt(abs(data)))*mean(sqrt(abs(data)));
Xmean = mean(abs(data));
Xrms = rms(data);
Xp=max(max(data), -min(data));

disp(['均方根值：',num2str(Xrms)]);
disp(['峰值指标：',num2str(max(max(data), -min(data)))]);
disp(['峰值因子：',num2str(Xp/Xrms)]);
disp(['峭度因子：',num2str(kurtosis(data))]);
disp(['峰度因子：',num2str(skewness(data))]);
disp(['方根幅度：',num2str(Xr)]);
disp(['裕度系数：',num2str(Xp/Xr)]);
disp(['绝对平均值：',num2str(Xmean)]);
disp(['脉冲因子：',num2str(Xp/mean(abs(data)))]);
disp(['波形指标：',num2str(Xrms/Xmean)]);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


########################################################################################
###python程序
import numpy as np
from scipy import stats

st = 0.01
data = np.sin(np.array([st*i for i in range(1001)]))
Xr = np.mean(np.sqrt(abs(data)))*np.mean(np.sqrt(abs(data)))
Xmean = np.mean(abs(data))
Xrms = np.sqrt(np.dot(data,data)/len(data))
Xp = max(max(data), -min(data))

print('均方根值：',Xrms)
print('峰值指标：',Xp);
print('峰值因子：',Xp/Xrms)
print('峭度因子：',stats.kurtosis(data))
print('峰度因子：',stats.skew(data))
print('方根幅度：',Xr)
print('裕度系数：',Xp/Xr)
print('绝对平均值：',Xmean)
print('脉冲因子：',Xp/np.mean(abs(data)))
print('波形指标：',Xrms/Xmean)
print('方差为：',np.var(data))
print('标准差为：',np.std(data))
########################################################################################


对应的Matlab程序如下：
close all
clear
clc

st = 0.01;
data = sin(0:st:10);

fs = 1/st;
N = length(data);
y = 2*abs(fft(data))/N;
f = fs*[1:N]/N;

FC = sum(f.*y)/sum(y);
MSF = sum(f.^2.*y)/sum(y);
RMSF = sqrt(MSF);
VF = sum((f-FC).^2.*y)/sum(y);
RVF = sqrt(VF);

disp(['重心频率：',num2str(FC)]);
disp(['均方频率：',num2str(MSF)]);
disp(['均方根频率：',num2str(RMSF)]);
disp(['频率方差：',num2str(VF)]);
disp(['频率标准差：',num2str(RVF)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


########################################################################################
###python程序
fs = 1/st
N = len(data)
y = 2*abs(fft(data))/N
f = np.array([(i+1)*fs/N for i in range(N)])
FC = np.dot(f,y)/np.sum(y)
MSF = np.dot(np.multiply(f,f),y)/np.sum(y)
RMSF = np.sqrt(MSF)
VF = np.dot(np.multiply(f-FC,f-FC),y)/np.sum(y);
RVF = np.sqrt(VF)

print('重心频率：',FC)
print('均方频率：',MSF)
print('均方根频率：',RMSF)
print('频率方差：',VF)
print('频率标准差：',RVF)
########################################################################################

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