How to plot upper and lower bounds in graph with 95% confidence.

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AL
AL 2023-4-21
回答： Walter Roberson 2023-4-21
% preallocate output variables
n_files = 2;
Time = cell(n_files, 1);
Veloc = cell(n_files, 1);
Ypk_plot = cell(n_files, 1);
Xpk_plot = cell(n_files, 1);
Y = cell(n_files, 1);
X = cell(n_files, 1);
P = cell(n_files, 1);
damp_ratio = zeros(1, n_files);
wd = zeros(1, n_files);
wn = zeros(1, n_files);
K_ex = zeros(1, n_files);
% read Data from files and process each file
for j = 1:n_files
% read Data from file
z1 = importdata("Xxsv0000"+num2str(j)+".txt");
% extract time and velocity Data
Time{j} = z1.data(:,1);
Veloc{j} = z1.data(:,2);
% find local maxima in velocity Data within the range of indices
[Ypk, Xpk] = findpeaks(Veloc{j}(1:550));
Ypk_plot{j} = Ypk(11:35);
Xpk_plot{j} = Xpk(11:35);
Y{j} = Ypk;
X{j} = Xpk;
P{j} = zeros(size(Ypk));
% plot Data against time Data and mark the locations of the peaks found
figure
plot(Time{j}, Veloc{j}, 'DisplayName', 'Data')
hold on
plot(Time{j}(Xpk_plot{j}), Ypk_plot{j}, 'dr', 'DisplayName', 'Pick points')
grid on
legend('Data','Pick Points','FontSize',12)
xlabel('Time','FontSize',12)
ylabel("Voltage (V/V)",'FontSize',12)
sgtitle(['K', num2str(j)])
% calculate logarithmic decrement, damping ratio, and natural frequency
t_new = Time{j}(X{j});
y_new = Y{j};
Log_Dec = abs(log(y_new(1:end-1) ./ y_new(2:end)));
Mean_dec = mean(Log_Dec);
Damp_period = (t_new(end) - t_new(1)) / length(t_new);
wd(j) = 2*pi / Damp_period;
damp_ratio(j) = Mean_dec / sqrt((2*pi)^2 + Mean_dec^2);
wn(j) = wd(j) * sqrt(1 - damp_ratio(j)^2);
% calculate spring constant
K_ex(1,j) = m_for_k(1,j) * wn(1,j)^2;
end
clear j n_files t_new Time Veloc X Xpk Xpk_plot Y;
clear y_new Ypk_plot z1 Damp_period Log_Dec Mean_dec Ypk P;

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回答（1 个）

Walter Roberson
Walter Roberson 2023-4-21
For this type of task, plotting 95% confidence, a common technique is to take the standard deviation std and use norminv to find the 2.5% and 97.5% probability levels for that mean and standard deviation, and plot those

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