基于MATLAB的滚动轴承信号Paul谱（功率谱密度）分析实现

一、系统架构设计

matlab 复制代码

% 主程序流程
信号生成 --> 预处理 --> 功率谱分析 --> 包络解调 --> 特征提取 --> 故障诊断

二、核心代码实现

1. 轴承信号生成模块

matlab 复制代码

function [s, params] = generate_bearing_signal(fs, duration, fault_type)
    % 参数设置
    f_r = 1797;      % 转速(rpm)
    Z = 9;           % 滚动体数量
    d = 0.3126e-3;   % 滚动体直径(mm)
    D = 1.537e-3;    % 节径(mm)
    alpha = 0;       % 接触角(°)
    
    % 理论故障频率计算
    f_bpfi = f_r/60 * Z/2 * (1 + d/D*cosd(alpha));  % 内圈故障频率
    f_bpfo = f_r/60 * Z/2 * (1 - d/D*cosd(alpha));  % 外圈故障频率
    f_bsf = (D/(2*d)) * f_r/60 * (1 - (d/D*cosd(alpha))^2);  % 滚动体故障频率
    
    % 生成基础信号
    t = 0:1/fs:duration-1/fs;
    s = sin(2*pi*f_r/60*t);  % 轴承旋转基频
    
    % 添加故障特征
    switch fault_type
        case 'inner'
            s = s + 0.5*sin(2*pi*f_bpfi*t);
        case 'outer'
            s = s + 0.5*sin(2*pi*f_bpfo*t);
        case 'ball'
            s = s + 0.5*sin(2*pi*f_bsf*t);
    end
    
    % 添加噪声
    s = awgn(s, 20, 'measured');
    params = struct('fs',fs, 'f_bpfi',f_bpfi, 'f_bpfo',f_bpfo, 'f_bsf',f_bsf);
end

2. 信号预处理模块

matlab 复制代码

function clean_signal = preprocess(s, fs)
    % 小波去噪（db4小波，4层分解）
    wname = 'db4';
    level = 4;
    [c,l] = wavedec(s, level, wname);
    thr = wdcbm2(c,l,'sqtwolog');
    denoised = wdencmp('lvd',c,l,wname,thr,'s',0);
    
    % 去除直流分量
    clean_signal = denoised - mean(denoised);
    
    % 归一化处理
    clean_signal = (clean_signal - min(clean_signal)) / (max(clean_signal) - min(clean_signal));
end

3. 功率谱分析模块

matlab 复制代码

function [Pxx,f] = power_spectrum(s, fs)
    % 参数设置
    nfft = 2^nextpow2(length(s));
    window = hamming(1024);
    noverlap = 512;
    
    % 计算功率谱密度
    [Pxx,f] = pwelch(s,window,noverlap,nfft,fs);
    
    % 峰值检测
    [peaks,locs] = findpeaks(Pxx);
    [~,max_idx] = max(peaks);
    dominant_freq = f(locs(max_idx));
end

4. Hilbert包络解调模块

matlab 复制代码

function [env_spectrum] = envelope_spectrum(s, fs)
    % Hilbert变换
    y = hilbert(s);
    envelope = abs(y);
    
    % 包络谱分析
    N = length(envelope);
    P = fft(envelope);
    env_spectrum = abs(P(1:N/2)).^2 / N;
    f_env = (0:N/2-1)*fs/N;
end

5. 故障特征提取模块

matlab 复制代码

function features = extract_features(s, fs)
    % 时域特征
    features.rms = rms(s);
    features.peak = max(abs(s));
    features.kurt = kurtosis(s);
    
    % 频域特征
    [Pxx,f] = power_spectrum(s,fs);
    [~,idx] = max(Pxx);
    features.dominant_freq = f(idx);
    
    % 包络谱特征
    env_spectrum = envelope_spectrum(s,fs);
    [~,env_idx] = max(env_spectrum);
    features.env_freq = f_env(env_idx);
end

三、完整仿真流程

matlab 复制代码

%% 参数设置
fs = 12000;        % 采样频率(Hz)
duration = 2;      % 信号时长(s)
fault_type = 'outer'; % 故障类型：inner/outer/ball/normal

%% 信号生成与预处理
[s, params] = generate_bearing_signal(fs, duration, fault_type);
clean_signal = preprocess(s, fs);

%% 谱分析
[Pxx,f] = power_spectrum(clean_signal, fs);
[env_spectrum, f_env] = envelope_spectrum(clean_signal, fs);

%% 特征提取
features = extract_features(clean_signal, fs);

%% 可视化
figure;
subplot(3,1,1);
plot((0:length(clean_signal)-1)/fs, clean_signal);
title('预处理后信号时域波形');
xlabel('时间(s)'); ylabel('幅值');

subplot(3,1,2);
plot(f,10*log10(Pxx));
title('功率谱密度分析');
xlabel('频率(Hz)'); ylabel('功率谱密度(dB/Hz)');
xlim([0 5000]);

subplot(3,1,3);
plot(f_env, env_spectrum);
title('Hilbert包络谱分析');
xlabel('频率(Hz)'); ylabel('包络幅值');
xlim([0 5000]);

%% 结果验证
disp(['理论外圈频率: ', num2str(params.f_bpfo), ' Hz']);
disp(['检测到主频: ', num2str(features.dominant_freq), ' Hz']);
disp(['包络谱主频: ', num2str(features.env_freq), ' Hz']);

四、扩展应用

1. 故障分类器集成

matlab 复制代码

% 使用SVM进行分类
load('bearing_dataset.mat'); % 加载预处理数据集
model = fitcsvm(X_train, y_train, 'KernelFunction', 'rbf', 'Standardize', true);
predicted = predict(model, X_test);
accuracy = sum(predicted == y_test)/length(y_test);

2. 实时监测系统

matlab 复制代码

% 基于App Designer的实时监控界面
app = uifigure('Name', '轴承健康监测系统');
ax1 = uiaxes(app); plot(app, t, s); title('实时波形');
ax2 = uiaxes(app); plot(app, f, 10*log10(Pxx)); title('实时功率谱');

参考代码滚动轴承信号的保罗谱分析 www.youwenfan.com/contentcss/59579.html

五、常见问题处理

频谱泄漏
- 解决方案：使用加窗（汉宁窗）和重叠处理
matlab 复制代码
```
window = hanning(2048);
noverlap = 1024;
[Pxx,f] = pwelch(s,window,noverlap);
```
噪声干扰
- 解决方案：改进小波去噪参数
matlab 复制代码
```
thr = wdcbm2(c,l,'minimaxi');  % 改进阈值选择
```
特征频率偏移
- 解决方案：动态基频跟踪
matlab 复制代码
```
f_r = mean(peak_detect(s, fs, [10, 200]));  // 自动检测基频
```

六、参考文献

3GPP TS 38.901 V17.0.0 (2023-06) - 5G NR; Radio propagation model
《轴承故障诊断技术》（机械工业出版社）
IEEE Transactions on Industrial Electronics, "Deep Learning for Bearing Fault Diagnosis"