2025年泰迪杯B题详细解题思路

初步分析整理了B题的赛题分析与解题思路，后面还会更新详细的建模论文与解题代码，明天完成！

问题一

问题分析

需要从附件1的加速度数据中提取MET值，并按强度分类统计时长。核心在于正确处理时间戳间隔和MET区间分类。由于时间戳为毫秒级，需计算相邻时间差并累加至对应活动类别。需注意时间差计算的精度及MET区间的边界条件。

数学模型

Python代码

import pandas as pd
import re
import osdef process_volunteer(file_path):df = pd.read_csv(file_path)df['日期'] = pd.to_numeric(df['日期'])df = df.sort_values('日期')df['delta'] = df['日期'].diff().shift(-1) / (3600 * 1000)  # 转换为小时df = df.dropna(subset=['delta'])# 提取MET值df['MET'] = df['标签'].apply(lambda x: float(re.search(r'MET值\s*([0-9.]+)', x).group(1)))# 分类统计bins = [-float('inf'), 1, 1.6, 3, 6, float('inf')]labels = ['睡眠', '静态活动', '低等强度', '中等强度', '高等强度']df['category'] = pd.cut(df['MET'], bins=bins, labels=labels, right=False)result = df.groupby('category')['delta'].sum().to_dict()return {'志愿者ID': os.path.basename(file_path).split('.')[0],'记录总时长(小时)': round(df['delta'].sum(), 4),'睡眠总时长(小时)': round(result.get('睡眠', 0), 4),'高等强度运动总时长(小时)': round(result.get('高等强度', 0), 4),'中等强度运动总时长(小时)': round(result.get('中等强度', 0), 4),'低等强度运动总时长(小时)': round(result.get('低等强度', 0), 4),'静态活动总时长(小时)': round(result.get('静态活动', 0), 4)}# 主程序
metadata = pd.read_csv('Metadatal.csv')
results = []
for vid in metadata['志愿者ID']:file_path = f'附件1/P{vid}.csv'if os.path.exists(file_path):res = process_volunteer(file_path)results.append(res)pd.DataFrame(results).to_excel('result_1.xlsx', index=False)

Matlab代码

function B1()dataDir = '附件1/';meta = readtable('Metadatal.csv');results = cell(height(meta), 7);for i = 1:height(meta)vid = meta.志愿者ID{i};file = [dataDir 'P' vid '.csv'];if ~exist(file, 'file'), continue; end% 读取数据并排序tbl = readtable(file);tbl.日期 = str2double(tbl.日期);[~, idx] = sort(tbl.日期);tbl = tbl(idx, :);% 计算时间差delta = diff(tbl.日期) / (3600 * 1000); % 转换为小时met = zeros(length(delta), 1);for j = 1:length(delta)metStr = tbl.标签{j};metVal = regexp(metStr, 'MET值\s*([0-9.]+)', 'tokens', 'once');met(j) = str2double(metVal{1});end% 分类统计edges = [-inf, 1, 1.6, 3, 6, inf];[~, bin] = histc(met, edges);total = sum(delta);counts = accumarray(bin, delta, [5, 1], @sum, 0);% 保存结果results(i, :) = {vid, total, counts(1), counts(5), counts(4), counts(3), counts(2)};end% 输出到ExcelT = cell2table(results, 'VariableNames', {'志愿者ID', '总时长', '睡眠', '高等', '中等', '低等', '静态'});writetable(T, 'result_1.xlsx');
end

问题二

问题分析

需构建回归模型预测MET值。输入特征包括三轴加速度的时域、频域统计量及元数据（年龄、性别）。模型需捕捉加速度与MET值的非线性关系。

数学模型

Python代码

import numpy as np
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import cross_val_scoredef extract_features(data):x = data['X'].valuesy = data['Y'].valuesz = data['Z'].valuesvm = np.sqrt(x**2 + y**2 + z**2)# 时域特征features = {'x_mean': np.mean(x), 'x_std': np.std(x),'y_mean': np.mean(y), 'y_std': np.std(y),'z_mean': np.mean(z), 'z_std': np.std(z),'vm_mean': np.mean(vm), 'vm_std': np.std(vm),'vm_rms': np.sqrt(np.mean(vm**2))}# 频域特征for axis, sig in zip(['x', 'y', 'z'], [x, y, z]):fft = np.abs(np.fft.rfft(sig))features[f'{axis}_energy'] = np.sum(fft**2)return features# 训练数据准备
metadata = pd.read_csv('Metadatal.csv')
X, y = [], []
for vid in metadata['志愿者ID']:df = pd.read_csv(f'附件1/P{vid}.csv')df['MET'] = df['标签'].str.extract(r'MET值\s*([0-9.]+)').astype(float)# 滑动窗口处理（窗口5秒）window_size = 5for i in range(0, len(df
) - window_size, window_size):window = df.iloc[i:i+window_size]feat = extract_features(window)feat['age'] = metadata.loc[metadata['志愿者ID'] == vid, '年龄'].values[0]feat['gender'] = 1 if metadata.loc[metadata['志愿者ID'] == vid, '性别'].values[0] == '男' else 0X.append(feat)y.append(window['MET'].mean())# 训练模型
model = RandomForestRegressor(n_estimators=100)
scores = cross_val_score(model, pd.DataFrame(X), y, cv=5, scoring='r2')
print(f'交叉验证R²得分: {np.mean(scores):.4f}')
model.fit(pd.DataFrame(X), y)# 预测附件2数据

Matlab代码

function B2()% 特征提取函数function feat = extractFeatures(x, y, z)vm = sqrt(x.^2 + y.^2 + z.^2);feat = [mean(x), std(x), mean(y), std(y), mean(z), std(z), ...mean(vm), std(vm), rms(vm), sum(abs(fft(x)).^2), ...sum(abs(fft(y)).^2), sum(abs(fft(z)).^2)];end% 加载数据meta = readtable('Metadatal.csv');X = []; y = [];for i = 1:height(meta)file = ['附件1/P' meta.志愿者ID{i} '.csv'];tbl = readtable(file);met = cellfun(@(s) str2double(regexp(s, 'MET值\s*([0-9.]+)', 'tokens', 'once')), tbl.标签);% 滑动窗口处理winSize = 5;  % 5秒窗口for j = 1:winSize:height(tbl)-winSizex = tbl.X(j:j+winSize-1);y_axis = tbl.Y(j:j+winSize-1);z = tbl.Z(j:j+winSize-1);feat = extractFeatures(x, y_axis, z);X = [X; feat meta.年龄(i) strcmp(meta.性别{i}, '男')];y = [y; mean(met(j:j+winSize-1))];endend% 训练随机森林model = TreeBagger(100, X, y, 'Method', 'regression');% 预测附件2
end

问题三

问题分析

睡眠阶段通过低活动量时段检测。计算向量幅度（VM）的滑动窗口均值，低于阈值视为睡眠候选，进一步聚类划分模式。

数学模型

Python代码

from sklearn.cluster import KMeansdef detect_sleep(file_path):df = pd.read_csv(file_path)df['vm'] = np.sqrt(df['X']**2 + df['Y']**2 + df['Z']**2)# 滑动窗口检测低活动（30秒窗口）window_size = 30df['window'] = df.index // window_sizeactivity = df.groupby('window')['vm'].mean()sleep_windows = activity[activity < 0.1].index# 提取窗口特征features = []for win in sleep_windows:win_data = df[df['window'] == win]vm_mean = win_data['vm'].mean()vm_std = win_data['vm'].std()features.append([vm_mean, vm_std])# K-means聚类if len(features) == 0:return {'睡眠总时长': 0.0, '模式一': 0.0, '模式二': 0.0, '模式三': 0.0}kmeans = KMeans(n_clusters=3).fit(features)labels = kmeans.labels_counts = np.bincount(labels, minlength=3)hours = counts * window_size / 3600  # 转换为小时return {'睡眠总时长': round(np.sum(hours), 4),'模式一': round(hours[0], 4),'模式二': round(hours[1], 4),'模式三': round(hours[2], 4)}# 处理附件2并保存结果

Matlab代码

function B3()function [total, modes] = detectSleep(file)tbl = readtable(file);vm = sqrt(tbl.X.^2 + tbl.Y.^2 + tbl.Z.^2);% 检测低活动窗口（30秒窗口）winSize = 30;numWin = floor(height(tbl)/winSize);act = zeros(numWin, 1);for i = 1:numWinidx = (i-1)*winSize + 1 : i*winSize;act(i) = mean(vm(idx));endsleepWins = find(act < 0.1);% 提取特征并聚类features = zeros(length(sleepWins), 2);for j = 1:length(sleepWins)idx = (sleepWins(j)-1)*winSize + 1 : sleepWins(j)*winSize;vmWin = vm(idx);features(j, :) = [mean(vmWin), std(vmWin)];endif isempty(features)total = 0; modes = zeros(1,3);else[~, C] = kmeans(features, 3);counts = histcounts(C, 1:4);total = sum(counts) * winSize / 3600;modes = counts * winSize / 3600;endend% 应用至附件2（略）
end

问题四

问题分析

检测连续静态活动（MET<1.6）超过30分钟的时段。遍历预测的MET序列，记录连续满足条件的时段。

数学模型

设MET序列为 ( MET(t) )，窗口步长 ( \Delta t )（单位：分钟），久坐判定条件为：
[
\sum_{i=t}^{t+\Delta t} MET(i) < 1.6 \quad \text{且} \quad \Delta t \geq 30
]

Python代码

def sedentary_alert(met_series, window_min=5):delta = window_min / 60  # 转换为小时sedentary = []current_duration = 0.0start_idx = Nonefor i, met in enumerate(met_series):if met < 1.6:current_duration += deltaif start_idx is None:start_idx = ielse:if current_duration >= 0.5:  # 0.5小时=30分钟end_idx = i - 1sedentary.append((start_idx, end_idx, current_duration))current_duration = 0.0start_idx = Noneif current_duration >= 0.5:sedentary.append((start_idx, len(met_series)-1, current_duration))return sedentary# 应用至附件2预测结果

Matlab代码

function B4()function alerts = detectSedentary(met, winSize)delta = winSize / 60;  % 窗口分钟转小时alerts = [];start = 1; count = 0;for i = 1:length(met)if met(i) < 1.6count = count + delta;if isempty(start), start = i; endelseif count >= 0.5  % 0.5小时=30分钟alerts = [alerts; [start, i-1, count]];endcount = 0;start = [];endendif count >= 0.5alerts = [alerts; [start, length(met), count]];endend% 应用至附件2（略）
end

完整论文代码获取，请看下方~ 可直接指导比赛，冲国奖