【故障诊断】用于轴承故障诊断的性能增强时变形态滤波方法及用于轴承断层特征提取的增强数学形态算子研究(Matlab代码实现）

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📋 📋 📋 本文目录如下： 🎁 🎁 🎁
目录
💥1 概述
📚2 运行结果
🎉3 参考文献
🌈4 Matlab代码实现

💥1 概述

形态学滤波是从集合论推导出的典型非线性信号处理方法。在这种方法中，可以通过与指定的结构元件（SE）相互作用来挖掘信号中的脉冲特征。SE的参数（即形状、高度和长度）选择对形态过滤结果有重要影响。针对该问题，该文提出一种自适应时变形态滤波（ATVMF）方法。ATVMF可以根据待分析信号的固有特性自适应地确定SE的形状和尺度，有效提高瞬态特征提取能力和计算效率。此外，还提出了广义形态产物算子（GMPO）的定义，可以构造新的形态积算子进行特征提取。

📚2 运行结果

部分代码：

function [ y ] = ATVMF( x, interp_method, operator )

% Algorithm name: Adaptive Time-Varying Morphological Filtering (ATVMF)

%

% Algorithm description: This method can achieve adaptive morphological filtering,

% in which a time-varying structure element (TVSE) is adaptively designed

% based on the characteristics of a signal and is no longer fixed.

%

% Input:

% x: signal to be analyzed (a vector)

% interp_method: selected interpllation method, such as 'spline', 'pchip',

% 'linear' and 'nearest', in which 'spline' is recommended.

% 'spline' -- cubic spline interpolation

% 'pchip' -- cubic Hermitian interpolation

% 'linear' -- piecewise linear interpolation

% 'nearest' -- nearest neighbor interpolation

% operator: selected morphological operator, see sub-function 'MF_operator'

%

% Output:

% y: morphological filtered signal

x = x(:)-mean(x); % a vector

N = length(x);

[indmin, indmax] = extreme_points(x); % Determine the location of local minima and maxima

% indmin -- the position of the local minimum point in the sequence x

% indmax -- the position of the local maximum point in the sequence x

tmin = indmin;

tmax = indmax;

xmin = x(tmin); % The magnitude of the local minimum point

xmax = x(tmax); % The magnitude of the local maximum point

% Sorting of local minimum and maximum points

textra = zeros(1,length(tmin)+length(tmax));

xextra = zeros(1,length(xmin)+length(xmax));

if tmin(1) < tmax(1) % The first extreme point is the minimum point

if tmin(end) > tmax(end) % The last extreme point is the minimum point

textra(1) = tmin(1);

xextra(1) = xmin(1);

for i = 1:length(tmax)

textra(2*i) = tmax(i);

textra(2*i+1) = tmin(i+1);

xextra(2*i) = xmax(i);

xextra(2*i+1) = xmin(i+1);

end

else % The last extreme point is the maximum point

for i = 1:length(tmax)

textra(2*i-1) = tmin(i);

textra(2*i) = tmax(i);

xextra(2*i-1) = xmin(i);

xextra(2*i) = xmax(i);

end

end

else % The first extreme point is the maximum point

if tmin(end) < tmax(end) % The last extreme point is the maximum point

textra(1) = tmax(1);

xextra(1) = xmax(1);

for i = 1:length(tmin)

textra(2*i) = tmin(i);

textra(2*i+1) = tmax(i+1);

xextra(2*i) = xmin(i);

xextra(2*i+1) = xmax(i+1);

end

else % The last extreme point is the minimum point

for i = 1:length(tmin)

textra(2*i-1) = tmax(i);

textra(2*i) = tmin(i);

xextra(2*i-1) = xmax(i);

xextra(2*i) = xmin(i);

end

end

end

% Selection of 'interp_method'

env = interp1(textra,xextra,textra(1):textra(end),interp_method);

delta = textra(1)-1;

S = length(indmin)-1; % number of SE

y = []; % output initialization

for s = 1:S

xnew = x(indmin(s)+1:indmin(s+1));

g = env(indmin(s)+1-delta:indmin(s+1)-delta);

g = g-min(g);

% the morphological filtering result

ynew = MF_operator( xnew, g, operator );

y = [y; ynew];

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% sub-function

function d = dilation(f,g)

% Morphological dilation operation

N = length(f);

M = length(g);

dtmp = f;

for i = 1:N

for j = 1:M

if (i-j) >= 1 && (i-j) <= N

tmp = f(i-j) + g(j);

if tmp > dtmp(i)

dtmp(i) = tmp;

end

end

end

end

d = dtmp;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% sub-function

function e = erosion(f,g)

% Morphological erosion operation

N = length(f);

M = length(g);

dtmp = f;

for i = 1:N

for j = 1:M

if (i+j) >= 1 && (i+j) <= N

tmp = f(i+j) - g(j);

if tmp < dtmp(i)

dtmp(i) = tmp;

end

end

end

end

e = dtmp;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% sub-function

function y = MF_operator( x, g, operator )

% Morphological operators

%

a1 = dilation(x,g); % dilation

a2 = erosion(a1,g); % closing

a3 = erosion(a2,g);

a4 = dilation(a3,g); % closing-opening

%

b1 = erosion(x,g); % erosion

b2 = dilation(b1,g); % opening

b3 = dilation(b2,g);

b4 = erosion(b3,g); % opening-closing

if strcmp(operator,'Gde') == 1

y = a1-b1;

elseif strcmp(operator,'Gco') == 1

y = a2-b2;

elseif strcmp(operator,'Gcooc') == 1

y = a4-b4;

elseif strcmp(operator,'AHde') == 1

y = x-(a1+b1)/2;

elseif strcmp(operator,'AHco') == 1

y = x-(a2+b2)/2;

elseif strcmp(operator,'AHcooc') == 1

y = x-(a4+b4)/2;

elseif strcmp(operator,'MGPO1') == 1

y = (a1-b1).*(a2-b2);

elseif strcmp(operator,'MGPO2') == 1

y = (a1-b1).*(a4-b4);

elseif strcmp(operator,'MGPO3') == 1

🎉3 参考文献

部分理论来源于网络，如有侵权请联系删除。

[1]陈斌， 宋大鹏， 张伟， 程彦， 王志， 一种用于轴承故障诊断的性能增强时变形态滤波方法， 测量学报 （2021） 109163.

[2]陈斌， 程彦， 张文， 梅国， 用于轴承断层特征提取的增强数学形态算子研究， ISA Trans. （2021）

[3]B. Chen, D. Song, W. Zhang, Y. Cheng, Z. Wang, A performance enhanced time-varying morphological filtering method for bearing fault diagnosis, Meas. J. Int. Meas. Confed. 176 (2021) 109163.

[4]B. Chen, Y. Cheng, W. Zhang, G. Mei, Investigation on enhanced mathematical morphological operators for bearing fault feature extraction, ISA Trans. (2021). https://doi.org/10.1016/j.isatra.2021.07.027.

🌈4 Matlab代码实现