2020年小美赛题目B题翻译（参考就行，我没参加比赛，纯属兴趣使然）

数学建模真的不适合我啊，劝退了，继续搞电路去了，这样一对比通信原理简单多了，这本书不错

我同学他们已经做完了，哈哈！

The of

氧饱和度的变异性

Pulse is used for ’ .

脉搏血氧仪是监测病人血氧饱和度的常规方法。

, we to be able to the of using a model.

在连续监测期间，我们希望能够使用一个模型来描述氧饱和度的模式。

We have the data of 36 , each was the for 1 hour at a of 1 Hz.

我们有36个人的数据，每个受试者在1hz的频率下连续测试了大约1小时的氧饱和度。（大约一个小时说明采样数据点在3600左右）

We also the about the , age, BMI, , and/or , and any that could .

我们还记录了参与者的以下信息，包括年龄、BMI、性别、吸烟史和/或当前吸烟状况，以及任何可能影响阅读的任何重要医学状况。（利用那个excel文件去数据挖掘，找到各个量和含氧量的关系）

We want to use these data to find of in so that we could use to an .

我们想用这些数据来找到氧饱和度变化的典型模式，这样我们就可以用几个参数来表征一个人。

We would also like to see the of to age, i.e., which in older .

我们还想知道氧饱和度系列的模式是否与年龄有关，也就是说，与年轻人相比，老年人的哪些特征会发生变化。

These be of or .

理想情况下，这些特征应该具有生物学或医学意义。

%处理氧含量数据的代码：
clc
close all
clear all
tic
load '010217B.txt';% input name of text file with appropriate extension
A = X010217B ;% for data such as 111213A add X at the beginning => i.e X111213A
m=mean(A)%数组均值
std = std(A)%数组标准差
[S,V]=dfa(A);
subplot (2,1,1)
title (['time-series'])
hold on
plot (A)
subplot (2,1,2)
scatter (S,V)
[r,a,b]=regression (S,V,'one'); % a = slope, b = intercept, r: correlation coefficnet (Pearson)
[r1,a1,b1]=regression (S(1:24),V(1:24),'one'); % a1 = slope, b1 = intercept, r1: correlation coefficnet (Pearson)
[r2,a2,b2]=regression (S(25:end),V(25:end),'one'); % a2 = slope, b2 = intercept, r2: correlation coefficnet (Pearson)alpha = a(1,1)
title (['slope =',num2str(alpha),])
r
[se]=sampen(A,2,0.2)[mse,sc]=msentropy(A);
toc

(S,V)=dfa(A);%dfa是去趋势波动分析法，
我之前理解为了有限状态自动机，唉，浪费了好长时间，  %下面是一个例程，可以参考参考，这个数据咋用，可以给我提供一下思路
clc
clear all
close all%创建一个模拟数据集并计算其平均值。 sdata表示股票的每日价格变化。
t = 0:300;
dailyFluct = gallery('normaldata',size(t),2);
sdata = cumsum(dailyFluct) + 20 + t/100;
%计算均值
mean(sdata)figure
plot(t,sdata);
legend('Original Data','Location','northwest');
xlabel('Time (days)');
ylabel('Stock Price (dollars)');%计算去趋势数据，并且从原始数据中移除
detrend_sdata = detrend(sdata);
trend = sdata - detrend_sdata;
mean(detrend_sdata)hold on
plot(t,trend,':r')
plot(t,detrend_sdata,'m')
plot(t,zeros(size(t)),':k')
legend('Original Data','Trend','Detrended Data',...'Mean of Detrended Data','Location','northwest')
xlabel('Time (days)');
ylabel('Stock Price (dollars)');

function SampEnVal = sampen(data, m, r)
% SampEn  计算时间序列data的样本熵
% 输入：data是数据一维行向量
%      m重构维数，一般选择1或2，优先选择2，一般不取m>2
%      r 阈值大小，一般选择r=0.1~0.25*Std(data)
% 输出：SampEnVal样本熵值大小data = data(:)';
N = length(data);
Nkx1 = 0;
Nkx2 = 0;for k = N - m:-1:1x1(k, :) = data(k:k + m - 1);x2(k, :) = data(k:k + m);
endfor k = N - m:-1:1x1temprow = x1(k, :);x1temp    = ones(N - m, 1)*x1temprow;   dx1(k, :) = max(abs(x1temp - x1), [], 2)';   Nkx1 = Nkx1 + (sum(dx1(k, :) < r) - 1)/(N - m - 1);    x2temprow = x2(k, :);x2temp    = ones(N - m, 1)*x2temprow;dx2(k, :) = max(abs(x2temp - x2), [], 2)';Nkx2      = Nkx2 + (sum(dx2(k, :) < r) - 1)/(N - m - 1);
end
Bmx1 = Nkx1/(N - m);
Bmx2 = Nkx2/(N - m);
SampEnVal = -log(Bmx2/Bmx1);
end