linear interpolation for the curves

I have 2 curves of pressure. Pressure represents y-axis and x-axis is the time. There is some difference between the 2 curves. First i have to interpolate to find the pressure for the missing time and secondly I have to find the relative error between the two existing curves using RMS.

Please help me in writing the codes for finding the pressure for the missing time considered as a target time using linear interpolation and for finding the relative error using RMS.

I have attached the excel sheet for better understanding

Answer 1

[Star Strider]

There are missing data, however they are all at the end of the first -time-pressure values. Filling them would require extrapolation, and that is to be strictly avoided here because that would require creating data where not previously existed, rather than interpolating intermediate missing values.

One approach —

% C1 = readcell('DENSITY_BASED_SOLVER.xlsx')
T1 = readtable('DENSITY_BASED_SOLVER.xlsx', 'VariableNamingRule','preserve', 'HeaderLines',1)

T1 = 5000×8 table
    Flow time (milli-seconds)    Pressure (MPa)     Var3      Var4    flow-time (Seconds)    Flow time(ms)    Pressure (Pascals)    Pressure (Mpa)
    _________________________    ______________    _______    ____    ___________________    _____________    __________________    ______________

            0.0038394               0.10773            NaN    NaN             1e-07             0.0001            1.0133e+05           0.10133    
             0.011518               0.10175            NaN    NaN             2e-07             0.0002            1.0133e+05           0.10133    
             0.017277               0.10474            NaN    NaN             3e-07             0.0003            1.0133e+05           0.10133    
             0.024956               0.10773        0.64816    NaN             4e-07             0.0004            1.0133e+05           0.10133    
             0.030716               0.10175            NaN    NaN             5e-07             0.0005            1.0133e+05           0.10133    
             0.034555               0.10175            NaN    NaN             6e-07             0.0006            1.0133e+05           0.10133    
             0.042234               0.10773            NaN    NaN             7e-07             0.0007            1.0133e+05           0.10133    
             0.046073               0.11372            NaN    NaN             8e-07             0.0008            1.0133e+05           0.10133    
             0.047993               0.13466            NaN    NaN             9e-07             0.0009            1.0133e+05           0.10133    
             0.047993               0.13466            NaN    NaN             1e-06              0.001            1.0133e+05           0.10133    
             0.049913               0.14963            NaN    NaN           1.1e-06             0.0011            1.0133e+05           0.10133    
             0.049913               0.14963            NaN    NaN           1.2e-06             0.0012            1.0133e+05           0.10133    
             0.053752               0.14065            NaN    NaN           1.3e-06             0.0013            1.0133e+05           0.10133    
             0.053752               0.14065            NaN    NaN           1.4e-06             0.0014            1.0133e+05           0.10133    
             0.053752               0.17057            NaN    NaN           1.5e-06             0.0015            1.0133e+05           0.10133    
             0.054712               0.18554            NaN    NaN           1.6e-06             0.0016            1.0133e+05           0.10133    

VN = T1.Properties.VariableNames;
t{1} = T1{:,1};
p{1} = T1{:,2};
t{2} = T1{:,6};
p{2} = T1{:,8};

% Q1 = nnz(isnan([p{1}]))
% Q11 = nnz(isnan(t{1}))
% Q12 = find(isnan(p{1}))
% t{1}(Q12-1)
% find(diff(Q12)>1)
% Q2 = nnz(isnan([t{2},p{2}]))

figure
plot(t{1}, p{1}, 'DisplayName','First Set')
hold on
xline(t{1}(484), '--r', 'DisplayName','Finite Time Limit')
plot(t{2}, p{2}, 'DisplayName','Second Set')
hold off
grid
xlabel('Time (ms)')
ylabel('Pressure (MPa)')
title('Original')
legend('Location','best')

[min_time_ends,idx] = min([t{1}(end) t{2}(end)])                % Shortest Time Vector & Set Number ('idx')

min_time_ends = 0.5000

idx = 2

tq{1} = t{1}(~isnan(t{1}));                                     % Eliminiate the 'NaN' Values So The Interpolation Will Work
[tq{1},idx] = unique(tq{1});                                    % Eliminate Duplicate Time Values, Return Unique Time Values & Associated Index
pq{1} = p{1}(idx);                                              % Pressure Values At Unique Time Values
pq{1} = interp1(tq{1}, pq{1}, t{2});                            % Interpolate Longer Pressure (p{2}) To Shorter Time Vector (t{1})

pdif = p{2} - pq{1};                                            % Pressure Difference

figure
plot(t{2}, pq{1}, 'DisplayName','First Set (Interpolated)')
hold on
plot(t{2}, p{2}, 'DisplayName','Second Set')
plot(t{2}, pdif, ':k', 'DisplayName','Pressure Difference')
hold off
grid
xlabel('Time (ms)')
ylabel('Pressure (MPa)')
title('Processed')
legend('Location','best')

Processing these data are not straightforward.

Now, use the rms function to find the RMS value of the difference between the two curves.

.

Answer 2

[Chhayank Srivastava]

I included the data with some cleaning to be imported by MATLAB and named the sheet "Data".

Few assumptions were made, as I didnt which pressure input you wanted to consider MPa or Pascals but nonetheless the code's logic will be similar.

clear; clc;
data = readtable('DENSITY_BASED_SOLVER.xlsx',"Sheet","Data");

%Pressure data 1 (pascals)
p_1(:,1) = data{:,1};
p_1(:,2) = data{:,2};
%Pressure data 2 (pascals)
p_2(:,1) = data{:,9};
p_2(:,2) = data{:,10};

%missing time ... Random points in time for 1D interpolation
time = rand(1,15);

%Interpolation .. I included all the data points but you can reduce data points closer to the relevant area for interpolation 
% This can be done by changing interp1(p_1(:,1),p_1(:,2),time) to interp1(p_1(st_intv:end_intv,1),p_1(st_intv:end_intv,2),time)
val_1 = interp1(p_1(:,1),p_1(:,2),time);
val_2 = interp1(p_2(:,1),p_2(:,2),time);

%RMSE
error = rmse(val_1,val_2)