# -*- coding: utf-8 -*-
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from scipy import stats
import sys
import os
# ===== 中文字体支持 =====
plt.rcParams['font.sans-serif'] = ['SimHei', 'Microsoft YaHei'] # 解决中文显示问题
plt.rcParams['axes.unicode_minus'] = False # 修复负号显示
# ===== 数据预处理 =====
def preprocess_data(data):
"""
预处理近6年月度水沙通量数据
输入:DataFrame格式原始数据(需包含日期、月均流量、月均含沙量)
输出:处理后的月度时间序列(月流量均值、月排沙量均值)
"""
# 修复链式赋值警告(直接赋值替代inplace)
data = data.copy()
data['月均流量'] = data['月均流量'].fillna(data['月均流量'].mean())
data['月均含沙量'] = data['月均含沙量'].fillna(data['月均含沙量'].mean())
# 计算月排沙量(亿吨)[1](@ref)
data['日期'] = pd.to_datetime(data['日期']) # 确保日期格式正确
days_in_month = data['日期'].dt.days_in_month
data['月排沙量'] = data['月均流量'] * data['月均含沙量'] * days_in_month * 86400 * 1e-9
# 按月聚合(使用'ME'替代弃用的'M')[1,9](@ref)
monthly_data = data.groupby(pd.Grouper(key='日期', freq='ME')).agg({
'月均流量': 'mean',
'月排沙量': 'sum'
}).reset_index()
return monthly_data
# ===== 累积距平法 =====
def cumulative_anomaly(series):
"""
计算累积距平序列
输入:时间序列(月流量均值或月排沙量)
输出:累积距平序列、突变点索引
"""
try:
if series.size == 0 or series.isnull().all():
raise ValueError("输入序列为空或全为NaN值")
mean_val = series.mean()
anomalies = series - mean_val
cum_anomaly = anomalies.cumsum()
# 检测突变点(累积距平曲线一阶差分变号点)[5](@ref)
diff_sign = np.sign(np.diff(cum_anomaly))
turning_points = np.where(np.diff(diff_sign) != 0)[0] + 1
return cum_anomaly, turning_points
except Exception as e:
print(f"累积距平计算错误: {str(e)}")
return pd.Series(dtype=float), np.array([])
# ===== Mann-Kendall突变检验 =====
def mk_test(series, alpha=0.05):
"""
Mann-Kendall突变检验
输入:时间序列、显著性水平alpha
输出:UF统计量序列、UB统计量序列、突变点位置
"""
n = len(series)
UF = np.zeros(n)
s = 0
# 计算UF统计量(修正索引范围)[1,9](@ref)
for i in range(1, n):
for j in range(i):
if series[i] > series[j]:
s += 1
elif series[i] < series[j]:
s -= 1
E = i * (i - 1) / 4
Var = i * (i - 1) * (2 * i + 5) / 72
UF[i] = (s - E) / np.sqrt(Var) if Var > 0 else 0
# 计算UB统计量(确保与UF等长)[5](@ref)
UB = -UF[::-1] # 关键修复:直接反向取负
# 检测显著突变点(UF与UB在置信区间内的交点)[1](@ref)
critical_value = stats.norm.ppf(1 - alpha / 2)
cross_points = []
for i in range(1, n):
if (UF[i] * UB[i] < 0) and (abs(UF[i]) > critical_value):
cross_points.append(i)
return UF, UB, np.array(cross_points)
# ===== 主程序 =====
if __name__ == "__main__":
try:
print("=" * 60)
print("水沙通量突变性分析程序启动...")
print("=" * 60)
# 1. 数据加载(替换为实际数据路径)[1](@ref)
# 模拟数据(实际使用时替换此部分)
dates = pd.date_range('2016-01-01', '2021-12-31', freq='ME')
np.random.seed(42)
flow = np.random.normal(loc=1000, scale=200, size=len(dates))
sand = np.random.normal(loc=2.5, scale=0.8, size=len(dates))
raw_data = pd.DataFrame({
'日期': dates,
'月均流量': flow,
'月均含沙量': sand
})
print("✅ 模拟数据生成完成(共{}条记录)".format(len(raw_data)))
# 2. 数据预处理
processed_data = preprocess_data(raw_data)
print("✅ 数据预处理完成(含排沙量计算)")
# 3. 突变性分析(以月流量为例)
flow_series = processed_data['月均流量'].dropna()
if flow_series.size == 0:
raise ValueError("流量序列为空,请检查数据!")
# 3.1 累积距平法
cum_anomaly, turning_points = cumulative_anomaly(flow_series)
print("📊 累积距平法检测到{}个突变点".format(len(turning_points)))
# 3.2 M-K检验
UF, UB, cross_points = mk_test(flow_series.values)
print("📈 MK检验检测到{}个显著突变点".format(len(cross_points)))
# 4. 可视化
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10), dpi=100)
# 4.1 累积距平曲线
ax1.set_title('月流量累积距平曲线', fontsize=14)
ax1.plot(processed_data['日期'], cum_anomaly, 'b-', label='累积距平')
ax1.set_ylabel('累积距平值', fontsize=12)
ax1.grid(True, linestyle='--', alpha=0.7)
# 标记突变点
if len(turning_points) > 0:
ax1.scatter(
processed_data['日期'].iloc[turning_points],
cum_anomaly.iloc[turning_points],
c='red', s=80, label='突变点'
)
for idx in turning_points:
ax1.annotate(
processed_data['日期'].dt.strftime('%Y-%m').iloc[idx],
(processed_data['日期'].iloc[idx], cum_anomaly.iloc[idx]),
xytext=(0, 15), textcoords='offset points',
ha='center', fontsize=9
)
ax1.legend()
# 4.2 M-K检验曲线
ax2.set_title('Mann-Kendall突变检验', fontsize=14)
ax2.plot(processed_data['日期'], UF, 'r-', label='UF统计量')
ax2.plot(processed_data['日期'], UB, 'b--', label='UB统计量')
ax2.axhline(y=1.96, color='gray', linestyle='--', label='95%置信区间')
ax2.axhline(y=-1.96, color='gray', linestyle='--')
ax2.axhline(y=0, color='black', linewidth=0.8)
ax2.set_ylabel('统计量值', fontsize=12)
ax2.set_xlabel('日期', fontsize=12)
ax2.grid(True, linestyle='--', alpha=0.7)
# 标记显著突变点
if len(cross_points) > 0:
ax2.scatter(
processed_data['日期'].iloc[cross_points],
UF[cross_points],
c='black', s=100, label='显著突变点'
)
for idx in cross_points:
ax2.annotate(
processed_data['日期'].dt.strftime('%Y-%m').iloc[idx],
(processed_data['日期'].iloc[idx], UF[idx]),
xytext=(0, 10), textcoords='offset points',
ha='center', fontsize=9
)
ax2.legend()
plt.tight_layout()
# 5. 保存结果
output_path = os.path.join(os.getcwd(), '水沙通量突变性分析结果.png')
plt.savefig(output_path, dpi=300, bbox_inches='tight')
print("=" * 60)
print(f"✅ 分析结果已保存至: {output_path}")
print("=" * 60)
# 6. 结果显示
plt.show()
except Exception as e:
exc_type, exc_obj, exc_tb = sys.exc_info()
print("❌" * 60)
print(f"程序异常终止 (行:{exc_tb.tb_lineno}): {str(e)}")
print("❌" * 60)
报错内容·如下E:\Anaconda\python.exe C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py
生成模拟数据...
开始数据预处理...
数据预处理完成
E:\Anaconda\Lib\site-packages\statsmodels\tsa\seasonal.py:360: UserWarning: Glyph 27969 (\N{CJK UNIFIED IDEOGRAPH-6D41}) missing from font(s) DejaVu Sans.
fig.tight_layout()
E:\Anaconda\Lib\site-packages\statsmodels\tsa\seasonal.py:360: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
fig.tight_layout()
E:\Anaconda\Lib\site-packages\statsmodels\tsa\seasonal.py:360: UserWarning: Glyph 21547 (\N{CJK UNIFIED IDEOGRAPH-542B}) missing from font(s) DejaVu Sans.
fig.tight_layout()
E:\Anaconda\Lib\site-packages\statsmodels\tsa\seasonal.py:360: UserWarning: Glyph 27801 (\N{CJK UNIFIED IDEOGRAPH-6C99}) missing from font(s) DejaVu Sans.
fig.tight_layout()
E:\Anaconda\Lib\site-packages\statsmodels\tsa\seasonal.py:360: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
fig.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 21547 (\N{CJK UNIFIED IDEOGRAPH-542B}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 27801 (\N{CJK UNIFIED IDEOGRAPH-6C99}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 23395 (\N{CJK UNIFIED IDEOGRAPH-5B63}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 33410 (\N{CJK UNIFIED IDEOGRAPH-8282}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 24615 (\N{CJK UNIFIED IDEOGRAPH-6027}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 20998 (\N{CJK UNIFIED IDEOGRAPH-5206}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:149: UserWarning: Glyph 35299 (\N{CJK UNIFIED IDEOGRAPH-89E3}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 21547 (\N{CJK UNIFIED IDEOGRAPH-542B}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 27801 (\N{CJK UNIFIED IDEOGRAPH-6C99}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 23395 (\N{CJK UNIFIED IDEOGRAPH-5B63}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 33410 (\N{CJK UNIFIED IDEOGRAPH-8282}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 24615 (\N{CJK UNIFIED IDEOGRAPH-6027}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 20998 (\N{CJK UNIFIED IDEOGRAPH-5206}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:150: UserWarning: Glyph 35299 (\N{CJK UNIFIED IDEOGRAPH-89E3}) missing from font(s) DejaVu Sans.
plt.savefig('季节性分解.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 27969 (\N{CJK UNIFIED IDEOGRAPH-6D41}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 23395 (\N{CJK UNIFIED IDEOGRAPH-5B63}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 33410 (\N{CJK UNIFIED IDEOGRAPH-8282}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 24615 (\N{CJK UNIFIED IDEOGRAPH-6027}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 20998 (\N{CJK UNIFIED IDEOGRAPH-5206}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 35299 (\N{CJK UNIFIED IDEOGRAPH-89E3}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 21547 (\N{CJK UNIFIED IDEOGRAPH-542B}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:151: UserWarning: Glyph 27801 (\N{CJK UNIFIED IDEOGRAPH-6C99}) missing from font(s) DejaVu Sans.
plt.show()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 26085 (\N{CJK UNIFIED IDEOGRAPH-65E5}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 26399 (\N{CJK UNIFIED IDEOGRAPH-671F}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 25968 (\N{CJK UNIFIED IDEOGRAPH-6570}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 20540 (\N{CJK UNIFIED IDEOGRAPH-503C}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 27969 (\N{CJK UNIFIED IDEOGRAPH-6D41}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 21407 (\N{CJK UNIFIED IDEOGRAPH-539F}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 22987 (\N{CJK UNIFIED IDEOGRAPH-59CB}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 26102 (\N{CJK UNIFIED IDEOGRAPH-65F6}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 38388 (\N{CJK UNIFIED IDEOGRAPH-95F4}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 24207 (\N{CJK UNIFIED IDEOGRAPH-5E8F}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 21015 (\N{CJK UNIFIED IDEOGRAPH-5217}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 23610 (\N{CJK UNIFIED IDEOGRAPH-5C3A}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 24230 (\N{CJK UNIFIED IDEOGRAPH-5EA6}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 22825 (\N{CJK UNIFIED IDEOGRAPH-5929}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 23567 (\N{CJK UNIFIED IDEOGRAPH-5C0F}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 27874 (\N{CJK UNIFIED IDEOGRAPH-6CE2}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 31995 (\N{CJK UNIFIED IDEOGRAPH-7CFB}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 23454 (\N{CJK UNIFIED IDEOGRAPH-5B9E}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 37096 (\N{CJK UNIFIED IDEOGRAPH-90E8}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 31561 (\N{CJK UNIFIED IDEOGRAPH-7B49}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 32447 (\N{CJK UNIFIED IDEOGRAPH-7EBF}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 22270 (\N{CJK UNIFIED IDEOGRAPH-56FE}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 26041 (\N{CJK UNIFIED IDEOGRAPH-65B9}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 24046 (\N{CJK UNIFIED IDEOGRAPH-5DEE}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 20998 (\N{CJK UNIFIED IDEOGRAPH-5206}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 26512 (\N{CJK UNIFIED IDEOGRAPH-6790}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 20027 (\N{CJK UNIFIED IDEOGRAPH-4E3B}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:129: UserWarning: Glyph 21608 (\N{CJK UNIFIED IDEOGRAPH-5468}) missing from font(s) DejaVu Sans.
plt.tight_layout()
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 25968 (\N{CJK UNIFIED IDEOGRAPH-6570}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 20540 (\N{CJK UNIFIED IDEOGRAPH-503C}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 27969 (\N{CJK UNIFIED IDEOGRAPH-6D41}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 37327 (\N{CJK UNIFIED IDEOGRAPH-91CF}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 21407 (\N{CJK UNIFIED IDEOGRAPH-539F}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 22987 (\N{CJK UNIFIED IDEOGRAPH-59CB}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
C:\Users\cheny\Desktop\PythonProject2\水沙通量周期性模型.py:130: UserWarning: Glyph 26102 (\N{CJK UNIFIED IDEOGRAPH-65F6}) missing from font(s) DejaVu Sans.
plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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plt.savefig(f'{title}_小波分析.png', dpi=300)
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