【数字信号分析】基于奇异谱齿轮箱振动信号分析附Matlab代码

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本文探讨了奇异谱分析在齿轮箱振动信号中的重要性，如何通过MATLAB工具进行信号采集、数字化处理和特征提取，以诊断齿轮箱的健康状态。作者还提到了结合其他信号分析方法以提高诊断准确性。

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🔥 内容介绍

数字信号分析是一种用于研究和理解信号特性的重要工具。在工程和科学领域中，数字信号分析被广泛应用于振动信号的研究和分析。本文将重点讨论基于奇异谱的数字信号分析在齿轮箱振动信号中的应用。

齿轮箱是许多机械系统中至关重要的组成部分，它们转换和传递动力以驱动机械设备。然而，齿轮箱在运行过程中会产生振动信号，这些振动信号可以包含有用的信息，例如齿轮的健康状态和系统的运行状况。因此，对齿轮箱振动信号进行分析和诊断是非常重要的。

奇异谱分析是一种常用的信号分析方法，它可以有效地揭示信号中的非线性和非平稳特性。在齿轮箱振动信号分析中，奇异谱可以帮助工程师和研究人员识别齿轮箱中的故障和异常。通过对振动信号进行奇异谱分析，可以提取出信号中的频率成分和振幅变化，从而帮助诊断齿轮箱的健康状况。

在进行奇异谱齿轮箱振动信号分析时，首先需要采集振动信号数据。这些数据可以通过加速度传感器或振动传感器来获取。接下来，将采集到的振动信号数据进行数字化处理，然后应用奇异谱分析方法进行频谱分析和特征提取。最后，通过对奇异谱结果的解释和分析，可以得出关于齿轮箱健康状态的结论。

除了奇异谱分析外，还可以结合其他数字信号分析方法，例如小波分析和频谱分析，来对齿轮箱振动信号进行综合分析。这些方法的综合应用可以提高对齿轮箱振动信号的理解和诊断能力，从而更好地保障机械系统的安全和可靠运行。

总之，数字信号分析在齿轮箱振动信号分析中发挥着重要作用。奇异谱分析作为其中的一种方法，可以帮助工程师和研究人员深入了解齿轮箱的振动特性，并对齿轮箱的健康状态进行准确诊断。随着数字信号分析技术的不断发展和完善，相信在未来会有更多的创新方法和工具应用于齿轮箱振动信号分析中，为机械系统的运行和维护提供更有效的支持。

📣 部分代码

function [SSDcomponents]=SSD(v,Fs,th,maxNumberofComponents)% Function to decompose a given signal by means of Singular Value Decomposition.% Refactored and optimized by Fabian Fraenz% INPUTS:% v: mono-variate input signal to decompose% Fs: sampling frequency% th: threshold which defines the variance of the residual (default 0.01),% at which the decomposition stops. A threshold of 0.01 means that when the% residual reaches 1% or less of the variance of the original signal v, the% algorithm stops decomposing that residual.% maxNumberofComponents: stops the decomposition after% maxNumberofComponents have been retrieved% OUTPUTS:% SSDcomponents: SSD components of the original signal v. Components are % ordered in decreasing order of frequency content.% EXAMPLE:% Creation of some simple timeserie% y  = sin(2*pi*5*(0:999)/1000);% y2 = 0.1*sin(2*pi*15*(0:999)/1000);% y3 = y+y2;% y3(500:999) = y3(500:999)+sin(2*pi*75*(500:999)/1000);%% x1 = sin(2*pi*5*(0:999)/1000);% x2 = [zeros(1,500) sin(2*pi*75*(501:1000)/1000)];% x3 = 0.1*sin(2*pi*15*(0:999)/1000);%% v  = y3;%% Sampling frequency 1000 and threshold of 0.005%% SSDcomponents = SSD(v,1000,0.005);%warning off;if nargin < 3 || isempty(th)    th = 0.01;endif nargin < 4 || isempty(maxNumberofComponents)    maxNumberofComponents = 1000;endv=v(:)';L=length(v);v = v-mean(v);orig = v;RR1=zeros(size(v));k1 = 0;if Fs/L <= 0.5    lf = L;else    lf = 2*Fs;endremen = 1;testcond = 0;while (remen > th) && (k1 < maxNumberofComponents)    k1 = k1+1;    v = v-mean(v);    v2 = v;        clear nmmt    [nmmt,ff] = pwelch(v2,[],[],4096,Fs);    [~,in3] = max(nmmt);    nmmt = nmmt';        if ((k1 == 1) && (ff(in3)/Fs < 1e-3)) % trend detection at first iteration        l = floor(L/3);        M = zeros(L-(l-1), l);        for k=1:L-(l-1),            M(k,:) = v2(k:k+(l-1));        end        [U,S,V] = svd(M);        U(:,l+1:end) = [];        S(l+1:end,:) = [];        V(:,l+1:end) = [];                rM = rot90(U(:,1)*S(1,:)*V');        r = zeros(1,L);        [~,m] = size(rM);        for k=-(l-1):L-(l),            r(k+l) = sum(diag(rM,k))/m;          end    else % if no trend detected, or after trend removal        for cont = 1:2            v2 = v2-mean(v2);            [deltaf] = gaussfitSSD(ff,nmmt'); % Gaussian fit of spectral components            % estimation of the bandwidth            [~,iiii1] = min(abs(ff-(ff(in3)-deltaf)));            [~,iiii2] = min(abs(ff-(ff(in3)+deltaf)));            l = floor(Fs/ff(in3)*1.2);                        if l <= 2 || l > floor(L/3)                l = floor(L/3);            end                        M=zeros(L, l);            % M built with wrap-around            for k=1:l,                M(:,k)=[v2(end-k+2:end)'; v2(1:end-k+1)'];            end                        [U,S,V] = svd(M,0);                        %% Selection of all principal components with a dominant frequency            % inside the estimated band-width            if size(U,2)>l                yy = abs(fft(U(:,1:l),lf));            else                yy = abs(fft(U,lf));            end            yy_n = size(yy,1);            ff2 = (0:yy_n-1)*Fs/yy_n;            yy(floor(yy_n/2)+1:end,:) = [];            ff2(floor(length(ff2)/2)+1:end) = [];            % %            if size(U,2)>l                [~,ind1] = max(yy(:,1:l));            else                [~,ind1] = max(yy);            end                        ii2 = find(ff2(ind1)>ff(iiii1) & ff2(ind1)<ff(iiii2)); %0.31            [~,indom] = min(abs(ff2-ff(in3)));            [~, maxindom] = max(yy(indom,:));            if isempty(ii2)                rM=U(:,1)*S(1,:)*V';            else                if ii2(ii2==maxindom)                    rM = U(:,ii2)*S(ii2,:)*V';                else                    ii2 = [maxindom,ii2];                    rM = U(:,ii2)*S(ii2,:)*V';                end            end                        %%            if cont == 2                vr = r;            end                       [~,m] = size(rM);             for k=-(L-1):0,                kl = k+L;                if kl >= m                    r(kl) = sum(diag(rM,k))/m;                    else                    r(kl) = (sum(diag(rM,k))+sum(diag(rM,kl)))/m;                end            end            r = fliplr(r);                        if cont == 2 && r*(v-r)'<0 % check condition for convergence                r = vr;            end            v2 = r;        end    end    RR1(k1,:) = (v*r'/(r*r'))*r;    v=v-RR1(k1,:);    remenold = remen;    if testcond        remen = sum((sum(RR1(stept:end,:),1)-orig2).^2)/(sum(orig2.^2));        if k1 == stept+3;            break        end    else        remen = sum((sum(RR1(1:end,:),1)-orig).^2)/(sum(orig.^2));    end    % in rare cases, convergence becomes very slow; the algorithm is then    % stopped if no real improvement in decomposition is detected (this is     % something to fix in future versions of SSD)    if abs(remenold - remen)< 1e-5         testcond = 1;        stept = k1+1;        orig2 = v;    endend% Notify the user that the there is to much noise in the signal to% accurately decompose it.if testcond    fprintf('warning: noise level affecting decomposition, total energy described by SSD components is: %3.1f\n %',(1-sum((sum(RR1(1:end,:),1)-orig).^2)/(sum(orig.^2)))*100);endftemp = (0:size(RR1,2)-1)*Fs/size(RR1,2);sprr = abs(fft(RR1'));[~,isprr] = max(sprr);fsprr = ftemp(isprr);[~,iord] = sort(fsprr,'descend');RR1 = RR1(iord,:);SSDcomponents = RR1;