基于Python的信号处理（包络谱，低通、高通、带通滤波，初级特征提取，机器学习，短时傅里叶变换）及轴承故障诊断探索

Python是一种广泛使用的解释型、高级和通用的编程语言，众多的开源科学计算软件包都提供了Python接口，如计算机视觉库OpenCV、可视化工具库VTK等。Python专用计算扩展库，如NumPy、SciPy、matplotlab、Pandas、scikit-learn等。

开发工具上可用Spyder，在安装Anaconda时已经安装好，可以从开始菜单或者使用命令行spyder启动。Spyder是一个免费、开源的集成开发环境，用Python编写，用于Python程序的开发，由科学家、工程师和数据分析师设计。它综合开发工具的高级编辑、分析、调试和分析功能与科学软件包的数据探索、交互执行、深入检查和漂亮的可视化功能独特地结合在一起。可以单步执行，查看运行后的各变量的值，查看序列数据线图等，非常方便。其他的集成开发工具（IDE）还包括：

VisualStudioCode（简称VSCode）是一款由微软开发且跨平台的免费源代码编辑器。该软件支持语法高亮、代码自动补全（又称IntelliSense）、代码重构功能，并且内置了命令行工具和Git版本控制系统。用户可以更改主题和键盘快捷方式实现个性化设置，也可以通过内置的扩展程序商店安装扩展以拓展软件功能。VisualStudioCode默认支持非常多的编程语言，要使用Python进行开发，需要先安装相应的Python扩展（PythonextensionforVisualStudioCode）。

PyCharm，主要用于Python语言开发，由捷克公司JetBrains开发，提供代码分析、图形化调试器，集成测试器、集成版本控制系统，并支持使用Django进行网页开发。PyCharm是一个跨平台开发环境，拥有MicrosoftWindows、macOS和Linux版本。社区版在Apache许可证下发布，另外还有专业版在专用许可证下发布，其拥有许多额外功能。

本项目采用Python语言进行简单的信号处理（包络谱，低通、高通、带通滤波，初级特征提取，机器学习，短时傅里叶变换）及轴承故障诊断探索。

n_win_numb = 128;n_win = np.hamming(n_win_numb);n_overlap = 127;nfft = n_win_numb;pad_to = nfft*10;
plt.figure(figsize=(8,6))plt.specgram(y, NFFT = nfft, Fs = fs, window = n_win, noverlap = n_overlap, pad_to=pad_to);plt.title(['Increasing Win Overlap: win=',n_win_numb,' / overlap=',n_overlap, ' / nfft=',nfft, 'pad_to=',pad_to]);plt.xlabel('time(s)');plt.ylabel('freq(Hz)')

n_win_numb = 32;n_win = np.hamming(n_win_numb);n_overlap = 0;nfft = n_win_numb;
plt.figure(figsize=(8,6))plt.specgram(y, NFFT = nfft, Fs = fs, window = n_win, noverlap = n_overlap);plt.title(['Increasing Win Overlap: win=',n_win_numb,' / overlap=',n_overlap, ' / nfft=',nfft]);plt.xlabel('time(s)');plt.ylabel('freq(Hz)')

n_win_numb = 32;n_win = np.hamming(n_win_numb);n_overlap = 30;nfft = n_win_numb;pad_to = nfft*10;
plt.figure(figsize=(8,6))plt.specgram(y, NFFT = nfft, Fs = fs, window = n_win, noverlap = n_overlap, pad_to=pad_to);plt.title(['Increasing Win Overlap: win=',n_win_numb,' / overlap=',n_overlap, ' / nfft=',nfft, 'pad_to=',pad_to]);plt.xlabel('time(s)');plt.ylabel('freq(Hz)')

n_win_numb = 256;n_win = np.hamming(n_win_numb);n_overlap = 250;nfft = n_win_numb;
plt.figure(figsize=(8,6))plt.specgram(y, NFFT = nfft, Fs = fs, window = n_win, noverlap = n_overlap);plt.title(['Increasing Win Overlap: win=',n_win_numb,' / overlap=',n_overlap, ' / nfft=',nfft]);plt.xlabel('time(s)');plt.ylabel('freq(Hz)')

fig = plt.figure(figsize=(12,8))ax = Axes3D(fig,azim=-0.001,elev=80)plt.ylabel('Frequency');plt.xlabel('Div #')for x, y, z, c in zip(plot_x.T, plot_y.T, A_div.T, colors):    ax.plot3D(y,x,z,color=c, linewidth=0.5)plt.gca().invert_xaxis()

colors = cm.rainbow(np.linspace(0, 1, len(plot_y)))
fig = plt.figure(figsize=(12,8))ax = Axes3D(fig,azim=-0.001,elev=85)plt.ylabel('Time (s)');plt.xlabel('Div #')for x, y, z, c in zip(plot_x.T, plot_y.T, y_div.T, colors):    ax.plot3D(y,x,z,color=c, linewidth=0.7)plt.gca().invert_xaxis()

feature_n_mean = np.mean(feature_n,axis=0)feature_f_mean = np.mean(feature_f,axis=0plt.figure(figsize=(8,6))plt.plot(feature_n_mean,'-bo')plt.plot(feature_f_mean,'-rx')plt.title('Average of Features')plt.xticks(np.arange(0,np.size(feature_name)),feature_name,rotation='vertical');plt.show()

from lightgbm import LGBMClassifier, plot_importance
n_estimator = 100
colsample_bytree = 0.1model = LGBMClassifier(n_estimator=n_estimator,colsample_bytree = colsample_bytree)
model.fit(x_train, y_train)
y_test_pred = model.predict(x_test)
importance = model.feature_importances_plt.figure(figsize=(4,4))
cm = pd.DataFrame(confusion_matrix(y_test, y_test_pred))
sns.heatmap(cm, annot=True)plt.figure(figsize=(8,6))
plt.plot(importance,'-ko')
plt.xticks(np.arange(0,np.size(feature_name)),feature_name,rotation='vertical');fig,ax = plt.subplots()
plot_importance(model,ax=ax)print(model.score(x_test, y_test))
# print(metrics(y_test,y_test_pred))
plt.figure(figsize=(8,6))
plt.figure(figsize=(8,6))
z_ML_utils.plot_decision_boundaries(x,y,XGBClassifier, idx1=idx1, idx2=idx2, n_estimator=n_estimator,colsample_bytree = colsample_bytree)
完整的项目代码：https://mbd.pub/o/bread/Y5yXmJtt

工学博士，担任《Mechanical System and Signal Processing》《中国电机工程学报》《控制与决策》等期刊审稿专家，擅长领域：现代信号处理，机器学习，深度学习，数字孪生，时间序列分析，设备缺陷检测、设备异常检测、设备智能故障诊断与健康管理PHM等。