包装盒网站模板下载折扣手游平台app排行榜

包装盒网站模板下载,折扣手游平台app排行榜,乐清高端网站建设,flashfxp上传网站模板如何对信号进行经验模态分解(EMD)#xff0c;然后对各个本征模态函数(IMF)进行希尔伯特变换#xff0c;最终获得能量谱的完整MATLAB实现。 算法原理概述 EMD Hilbert变换流程 原始信号 → EMD分解 → 多个IMF分量 残差→ 对每个IMF进行Hilbert变换 → 解析信号→ 计算瞬时频…如何对信号进行经验模态分解(EMD)然后对各个本征模态函数(IMF)进行希尔伯特变换最终获得能量谱的完整MATLAB实现。算法原理概述EMD Hilbert变换流程原始信号 → EMD分解 → 多个IMF分量 残差 → 对每个IMF进行Hilbert变换 → 解析信号 → 计算瞬时频率和瞬时幅度 → 构建Hilbert谱 → 计算能量谱密度MATLAB完整实现1. 主程序EMD-Hilbert能量谱分析function[hht_spectrum,energy_density,imfs]emd_hilbert_energy_analysis(signal,fs,varargin)% EMD分解与希尔伯特变换能量谱分析% 输入:% signal - 输入信号% fs - 采样频率% varargin - 可选参数% 输出:% hht_spectrum - Hilbert谱% energy_density - 能量谱密度% imfs - IMF分量%% 参数设置pinputParser;addParameter(p,num_imfs,10,isnumeric);% 最大IMF数量addParameter(p,max_iterations,1000,isnumeric);% 最大迭代次数addParameter(p,stop_threshold,0.05,isnumeric);% 停止阈值addParameter(p,plot_results,true,islogical);% 是否绘图addParameter(p,energy_band,[0,fs/2],isnumeric);% 能量谱频带parse(p,varargin{:});paramsp.Results;fprintf(开始EMD-Hilbert能量谱分析...\n);fprintf(信号长度: %d, 采样率: %.1f Hz\n,length(signal),fs);%% 步骤1: EMD分解tic;fprintf(正在进行EMD分解...\n);imfsemd_decomposition(signal,...max_imfs,params.num_imfs,...max_iterations,params.max_iterations,...stop_threshold,params.stop_threshold);decomposition_timetoc;fprintf(EMD分解完成! 得到 %d 个IMF分量, 耗时: %.2f 秒\n,size(imfs,1),decomposition_time);%% 步骤2: 希尔伯特变换与能量计算fprintf(正在进行希尔伯特变换...\n);[hht_spectrum,instantaneous_freq,instantaneous_amp]...hilbert_spectrum_analysis(imfs,fs);%% 步骤3: 能量谱计算fprintf(计算能量谱密度...\n);energy_densitycalculate_energy_spectrum(hht_spectrum,...instantaneous_freq,fs,params.energy_band);%% 步骤4: 结果显示ifparams.plot_resultsplot_emd_hilbert_results(signal,fs,imfs,hht_spectrum,...instantaneous_freq,energy_density);endfprintf(EMD-Hilbert能量谱分析完成!\n);end2. EMD分解核心函数functionimfsemd_decomposition(signal,varargin)% EMD经验模态分解% 实现经典的EMD算法将信号分解为IMF分量% 参数解析pinputParser;addParameter(p,max_imfs,10,isnumeric);addParameter(p,max_iterations,1000,isnumeric);addParameter(p,stop_threshold,0.05,isnumeric);parse(p,varargin{:});max_imfsp.Results.max_imfs;max_iterationsp.Results.max_iterations;stop_thresholdp.Results.stop_threshold;signalsignal(:);% 确保列向量Nlength(signal);residualsignal;imfs[];forimf_idx1:max_imfsfprintf( 提取IMF %d...,imf_idx);hresidual;% 当前待提取的IMFiteration_count0;whileiteration_countmax_iterations iteration_countiteration_count1;% 寻找局部极值点[max_locs,min_locs]find_local_extrema(h);% 检查是否满足IMF条件iflength(max_locs)2||length(min_locs)2fprintf(极值点不足停止分解\n);break;end% 计算上下包络线upper_envcompute_envelope(h,max_locs,spline);lower_envcompute_envelope(h,min_locs,spline);% 计算均值包络线mean_env(upper_envlower_env)/2;% 更新hh_prevh;hh-mean_env;% 检查停止条件stop_valuecompute_stop_criteria(h_prev,h,mean_env);ifstop_valuestop_thresholdbreak;endend% 保存IMFimfs[imfs;h];residualresidual-h;fprintf(完成 (迭代次数: %d)\n,iteration_count);% 检查残差是否足够小ifsum(residual.^2)1e-10*sum(signal.^2)||...length(find_local_extrema(residual))2fprintf(残差已足够小分解完成\n);break;endend% 添加残差作为最后一个分量if~isempty(residual)imfs[imfs;residual];endendfunction[max_locs,min_locs]find_local_extrema(x)% 寻找局部极值点diff_xdiff(x);sign_changesdiff(sign(diff_x));% 极大值点 (二阶导数为负)max_locsfind(sign_changes0)1;% 极小值点 (二阶导数为正)min_locsfind(sign_changes0)1;% 确保端点被正确处理ifx(1)x(2)max_locs[1;max_locs];elsemin_locs[1;min_locs];endifx(end)x(end-1)max_locs[max_locs;length(x)];elsemin_locs[min_locs;length(x)];endendfunctionenvelopecompute_envelope(x,extr_locs,method)% 计算包络线t1:length(x);ifstrcmpi(method,spline)% 三次样条插值iflength(extr_locs)4envelopespline(extr_locs,x(extr_locs),t);else% 极值点太少使用线性插值envelopeinterp1(extr_locs,x(extr_locs),t,linear,extrap);endelse% 线性插值envelopeinterp1(extr_locs,x(extr_locs),t,linear,extrap);endendfunctionstop_valuecompute_stop_criteria(h_prev,h,mean_env)% 计算停止准则% 使用基于标准差的方法numeratorsum((h_prev-h).^2);denominatorsum(h_prev.^2);ifdenominator0stop_value0;elsestop_valuenumerator/denominator;endend3. 希尔伯特变换与谱分析function[hht_spectrum,instantaneous_freq,instantaneous_amp]...hilbert_spectrum_analysis(imfs,fs)% 希尔伯特谱分析% 对每个IMF进行希尔伯特变换计算瞬时频率和幅度[num_imfs,N]size(imfs);t(0:N-1)/fs;% 初始化输出变量instantaneous_freqzeros(num_imfs,N);instantaneous_ampzeros(num_imfs,N);hht_spectrumzeros(num_imfs,N);fori1:num_imfsfprintf( 处理IMF %d 的希尔伯特变换...\n,i);current_imfimfs(i,:);% 希尔伯特变换获得解析信号analytic_signalhilbert(current_imf);% 计算瞬时幅度instantaneous_amp(i,:)abs(analytic_signal);% 计算瞬时相位解卷绕instantaneous_phaseunwrap(angle(analytic_signal));% 计算瞬时频率 (导数方法)instantaneous_freq(i,:)diff([instantaneous_phase(1),instantaneous_phase])*fs/(2*pi);% 限制频率范围为正值instantaneous_freq(i,instantaneous_freq(i,:)0)0;instantaneous_freq(i,instantaneous_freq(i,:)fs/2)fs/2;% 构建Hilbert谱 (幅度平方表示能量)hht_spectrum(i,:)instantaneous_amp(i,:).^2;endend4. 能量谱计算函数functionenergy_densitycalculate_energy_spectrum(hht_spectrum,...instantaneous_freq,fs,energy_band)% 计算能量谱密度[num_imfs,N]size(hht_spectrum);% 频率分辨率设置freq_resolution1;% Hzfreq_binsenergy_band(1):freq_resolution:energy_band(2);% 初始化能量谱矩阵energy_densityzeros(num_imfs,length(freq_bins)-1);fori1:num_imfsfprintf( 计算IMF %d 的能量谱...\n,i);fort1:N current_freqinstantaneous_freq(i,t);current_energyhht_spectrum(i,t);% 找到对应的频率区间freq_bin_idxfind(freq_binscurrent_freq,1,last);if~isempty(freq_bin_idx)freq_bin_idxlength(freq_bins)energy_density(i,freq_bin_idx)energy_density(i,freq_bin_idx)current_energy;endend% 归一化能量谱ifsum(energy_density(i,:))0energy_density(i,:)energy_density(i,:)/sum(energy_density(i,:));endend% 计算总能量谱total_energy_densitysum(energy_density,1);ifsum(total_energy_density)0total_energy_densitytotal_energy_density/sum(total_energy_density);endenergy_density[energy_density;total_energy_density];end5. 结果可视化函数functionplot_emd_hilbert_results(signal,fs,imfs,hht_spectrum,...instantaneous_freq,energy_density)% 绘制EMD-Hilbert分析结果Nlength(signal);t(0:N-1)/fs;num_imfssize(imfs,1);% 创建图形窗口figure(Position,[100,100,1400,1000]);%% 子图1: 原始信号subplot(4,3,1);plot(t,signal,b,LineWidth,1.5);title(原始信号,FontSize,12,FontWeight,bold);xlabel(时间 (s));ylabel(幅值);grid on;%% 子图2: EMD分解结果subplot(4,3,[2,3]);plot_offset0;colorsparula(num_imfs);fori1:num_imfsplot(t,imfs(i,:)plot_offset,Color,colors(i,:),LineWidth,1.2);hold on;text(t(end)0.02,plot_offset,sprintf(IMF%d,i),...FontSize,10,HorizontalAlignment,left);ifinum_imfs plot_offsetplot_offsetmax(abs(imfs(i,:)))*1.5;endendtitle(EMD分解结果,FontSize,12,FontWeight,bold);xlabel(时间 (s));ylabel(IMF分量);grid on;xlim([t(1),t(end)]);%% 子图3: Hilbert谱 (时频谱)subplot(4,3,[4,5]);[T,F]meshgrid(t,1:num_imfs);surf(T,F,hht_spectrum,EdgeColor,none);view(2);colormap(jet);colorbar;title(Hilbert谱 (时频分布),FontSize,12,FontWeight,bold);xlabel(时间 (s));ylabel(IMF序号);%% 子图4: 瞬时频率subplot(4,3,6);hold on;fori1:num_imfsplot(t,instantaneous_freq(i,:),Color,colors(i,:),LineWidth,1);endtitle(瞬时频率,FontSize,12,FontWeight,bold);xlabel(时间 (s));ylabel(频率 (Hz));grid on;legend(arrayfun((x)sprintf(IMF%d,x),1:num_imfs,UniformOutput,false),...Location,best,FontSize,8);%% 子图5: 各IMF能量谱subplot(4,3,[7,8]);freq_bins1:size(energy_density,2);bar_dataenergy_density(1:end-1,:);h_barbar(freq_bins,bar_data,stacked);title(各IMF分量能量谱分布,FontSize,12,FontWeight,bold);xlabel(频率区间);ylabel(归一化能量);legend(arrayfun((x)sprintf(IMF%d,x),1:num_imfs,UniformOutput,false),...Location,best,FontSize,8);grid on;%% 子图6: 总能量谱subplot(4,3,[9,10]);total_energyenergy_density(end,:);stem(freq_bins,total_energy,filled,LineWidth,1.5,MarkerSize,4);title(总能量谱密度,FontSize,12,FontWeight,bold);xlabel(频率区间);ylabel(能量密度);grid on;%% 子图7: 能量分布统计subplot(4,3,[11,12]);% 计算各IMF能量贡献imf_energy_contributionzeros(1,num_imfs);fori1:num_imfsimf_energy_contribution(i)sum(hht_spectrum(i,:));endtotal_energysum(imf_energy_contribution);imf_energy_contributionimf_energy_contribution/total_energy*100;pie(imf_energy_contribution,arrayfun((x)sprintf(IMF%d\n%.1f%%,x,...imf_energy_contribution(x)),1:num_imfs,UniformOutput,false));title(各IMF能量贡献比例,FontSize,12,FontWeight,bold);sgtitle(EMD分解与希尔伯特能量谱分析,FontSize,14,FontWeight,bold);end6. 测试用例与演示%% 测试函数模拟信号分析functiontest_emd_hilbert_analysis()% 测试EMD-Hilbert能量谱分析fprintf( EMD-Hilbert能量谱分析测试 \n\n);% 生成测试信号fs1000;% 采样频率 1000 Hzt0:1/fs:2;% 2秒信号% 多分量测试信号signal2*sin(2*pi*50*t).*(10.5*sin(2*pi*5*t))...% 调幅信号1.5*sin(2*pi*120*t)...% 高频分量0.8*chirp(t,80,2,20)...% 扫频信号0.3*randn(size(t));% 噪声fprintf(生成测试信号:\n);fprintf( - 50Hz调幅信号\n);fprintf( - 120Hz正弦信号\n);fprintf( - 80-20Hz扫频信号\n);fprintf( - 高斯白噪声\n\n);% 执行EMD-Hilbert分析[hht_spectrum,energy_density,imfs]emd_hilbert_energy_analysis(...signal,fs,...num_imfs,8,...max_iterations,500,...plot_results,true,...energy_band,[0,200]);% 显示能量分析结果display_energy_analysis(imfs,hht_spectrum);endfunctiondisplay_energy_analysis(imfs,hht_spectrum)% 显示能量分析结果fprintf(\n 能量分析结果 \n\n);num_imfssize(imfs,1);total_energysum(hht_spectrum(:));fprintf(%-8s %-12s %-12s %-15s\n,...IMF,能量,能量百分比,累计百分比);fprintf(%s\n,repmat(-,1,50));cumulative_percentage0;fori1:num_imfs imf_energysum(hht_spectrum(i,:));percentageimf_energy/total_energy*100;cumulative_percentagecumulative_percentagepercentage;fprintf(IMF%-5d %-12.4e %-11.2f%% %-14.2f%%\n,...i,imf_energy,percentage,cumulative_percentage);endfprintf(%s\n,repmat(-,1,50));fprintf(总计 %-12.4e %-11.2f%%\n,total_energy,100.0);% 显示主要能量集中区域fprintf(\n主要能量集中分析:\n);energy_threshold0.05;% 5%能量阈值significant_imfs[];fori1:num_imfs imf_energysum(hht_spectrum(i,:))/total_energy;ifimf_energyenergy_threshold significant_imfs[significant_imfs,i];endendif~isempty(significant_imfs)fprintf(主要能量集中在: IMF%s\n,mat2str(significant_imfs));fprintf(这些IMF包含了 %.2f%% 的总能量\n,...sum(hht_spectrum(significant_imfs,:),all)/total_energy*100);elsefprintf(能量分布较为均匀无明显主导IMF\n);endend%% 实际应用示例故障诊断信号分析functionbearing_fault_analysis()% 轴承故障信号分析示例fprintf( 轴承故障诊断信号分析 \n\n);% 模拟轴承故障信号 (简化模型)fs12000;% 12 kHz采样频率t0:1/fs:1;% 1秒信号% 轴承故障特征频率 (示例)bpfo120;% 外圈故障频率 120 Hzbpfi145;% 内圈故障频率 145 Hzbsf65;% 滚动体故障频率 65 Hzftf15;% 保持架故障频率 15 Hz% 生成故障信号fundamental0.8*sin(2*pi*30*t);% 转频 30 Hz% 故障冲击序列fault_impactszeros(size(t));impact_intervalround(fs/bpfo);% 外圈故障冲击间隔impact_locations1:impact_interval:length(t);fault_impacts(impact_locations)1.5;% 共振响应resonance_freq3000;% 3 kHz 共振频率resonance_signalfilter([1,-1.8*cos(2*pi*resonance_freq/fs),0.81],...[1,-1.2*cos(2*pi*resonance_freq/fs),0.25],fault_impacts);% 合成信号signalfundamentalresonance_signal0.1*randn(size(t));fprintf(轴承故障信号特征:\n);fprintf( 转频: 30 Hz\n);fprintf( 外圈故障频率: 120 Hz\n);fprintf( 系统共振频率: 3000 Hz\n\n);% 执行EMD-Hilbert分析[hht_spectrum,energy_density,imfs]emd_hilbert_energy_analysis(...signal,fs,...num_imfs,6,...energy_band,[0,5000],...plot_results,true);% 故障特征提取extract_fault_features(imfs,hht_spectrum,fs,[bpfo,bpfi,bsf,ftf]);endfunctionextract_fault_features(imfs,hht_spectrum,fs,fault_freqs)% 提取故障特征fprintf(\n 故障特征分析 \n\n);% 计算各IMF的频谱num_imfssize(imfs,1);fori1:num_imfs% FFT分析imf_fftfft(imfs(i,:));Nlength(imf_fft);f(0:N-1)*fs/N;% 寻找主要频率成分[~,dominant_freq_idx]max(abs(imf_fft(1:floor(N/2))));dominant_freqf(dominant_freq_idx);fprintf(IMF%d 主要频率成分: %.2f Hz\n,i,dominant_freq);% 检查是否接近已知故障频率forj1:length(fault_freqs)ifabs(dominant_freq-fault_freqs(j))10% 10 Hz容差switchjcase1fprintf( → 检测到外圈故障特征!\n);case2fprintf( → 检测到内圈故障特征!\n);case3fprintf( → 检测到滚动体故障特征!\n);case4fprintf( → 检测到保持架故障特征!\n);endendendendend参考代码 emd分解之后再进行希尔伯特变换获得能量谱www.3dddown.com/csa/77762.html算法特点与优势EMD-Hilbert方法的优势自适应分解- EMD根据信号特性自动分解局部特征提取- 能够捕捉非平稳信号的时变特性能量定位- 精确确定能量在时频域的分布物理意义明确- 每个IMF代表特定的振动模式应用场景机械故障诊断- 轴承、齿轮箱故障检测生物信号处理- EEG、ECG信号分析地震信号分析- 地层结构识别语音信号处理- 语音特征提取