www.gusucode.com > ident_featured 案例代码 matlab源码程序 > ident_featured/iddemo8.m
%% Dealing with Multi-Experiment Data and Merging Models
% This example shows how to deal with multiple experiments and merging
% models when working with System Identification Toolbox(TM) for estimating
% and refining models.
% Copyright 1986-2011 The MathWorks, Inc.
%% Introduction
% The analysis and estimation functions in System Identification Toolbox
% let you work with multiple batches of data. Essentially, if you have
% performed multiple experiments and recorded several input-output
% datasets, you can group them up into a single IDDATA object and use them
% with any estimation routine.
%
% In some cases, you may want to "split up" your (single) measurement
% dataset to remove portions where the data quality is not good. For
% example, portion of data may be unusable due to external disturbance or a
% sensor failure. In those cases, each good portion of data may be
% separated out and then combined into a single multi-experiment IDDATA
% object.
%
% For example, let us look at the dataset iddemo8.mat:
load iddemo8
%%
% The name of the data object is |dat|, and let us view it.
dat
plot(dat)
%%
% We see that there are some problems with the output around
% sample 250-280 and around samples 600 to 650. These might have been
% sensor failures.
%
% Therefore split the data into three separate experiments and
% put then into a multi-experiment data object:
d1 = dat(1:250);
d2 = dat(281:600);
d3 = dat(651:1000);
d = merge(d1,d2,d3) % merge lets you create multi-exp IDDATA object
%%
% The different experiments can be given other names, for example:
d.exp = {'Period 1';'Day 2';'Phase 3'}
%%
% To examine it, use plot, as in |plot(d)|.
%% Performing Estimation Using Multi-Experiment Data
% As mentioned before, all model estimation routines accept
% multi-experiment data and take into account that they are recorded at
% different periods. Let us use the two first experiments for estimation
% and the third one for validation:
de = getexp(d,[1,2]); % subselection is done using the command GETEXP
dv = getexp(d,'Phase 3'); % using numbers or names.
m1 = arx(de,[2 2 1]);
m2 = n4sid(de,2);
m3 = armax(de,[2 2 2 1]);
compare(dv,m1,m2,m3)
%%
% The |compare| command also accepts multiple experiments. Use the right
% click menu to pick the experiment to use, one at a time.
compare(d,m1,m2,m3)
%%
% Also, |spa|, |etfe|, |resid|, |predict|, |sim| operate in the same way
% for multi-experiment data, as they do for single experiment data.
%% Merging Models After Estimation
% There is another way to deal with separate data sets: a model can be
% computed for each set, and then the models can be merged:
m4 = armax(getexp(de,1),[2 2 2 1]);
m5 = armax(getexp(de,2),[2 2 2 1]);
m6 = merge(m4,m5); % m4 and m5 are merged into m6
%%
% This is conceptually the same as computing |m| from the merged set |de|,
% but it is not numerically the same. Working on |de| assumes that the
% signal-to-noise ratios are (about) the same in the different experiments,
% while merging separate models makes independent estimates of the noise
% levels. If the conditions are about the same for the different
% experiments, it is more efficient to estimate directly on the
% multi-experiment data.
%%
% We can check the models |m3| and |m6| that are both ARMAX models obtained
% on the same data in two different ways:
[m3.a;m6.a]
[m3.b;m6.b]
[m3.c;m6.c]
compare(dv,m3,m6)
%% Case Study: Concatenating Vs. Merging Independent Datasets
% We now turn to another situation. Let us consider two data sets generated
% by the system m0. The system is given by:
m0
%%
% The data sets that have been collected are |z1| and |z2|, obtained from
% m0 with different inputs, noise and initial conditions. These datasets
% are obtained from iddemo8.mat that was loaded earlier.
pause off
%%
% First data set:
plot(z1) %generates a separate plot for each I/O pair if pause is on; showing only the last one here
%%
% The second set:
plot(z2) %generates a separate plot for each I/O pair if pause is on; showing only the last one here
%%
% If we just concatenate the data we obtained:
zzl = [z1;z2]
plot(zzl)
pause on
%%
% A discrete-time state-space model can be obtained by using |ssest|:
ml = ssest(zzl,3,'Ts',1, 'Feedthrough', [true, false]);
%%
% Compare the bode response for models m0 and ml:
clf
bode(m0,ml)
legend('show')
%%
% This is not a very good model, as observed from the four Bode plots
% above.
%%
% Now, instead treat the two data sets as different experiments:
zzm = merge(z1,z2)
% The model for this data can be estimated as before (watching progress this time)
mm = ssest(zzm,3,'Ts',1,'Feedthrough',[true, false], ssestOptions('Display', 'on'));
%%
% Let us compare the Bode plots of the true system (blue)
% the model from concatenated data (green) and the model from the
% merged data set (red):
clf
bode(m0,'b',ml,'g',mm,'r')
legend('show')
%%
% The merged data give a better model, as observed from the plot above.
%% Conclusions
% In this example we analyzed how to use multiple data sets together for
% estimation of one model. This technique is useful when you have multiple
% datasets from independent experiment runs or when you segment data into
% multiple sets to remove bad segments. Multiple experiments can be
% packaged into a single IDDATA object, which is then usable for all
% estimation and analysis requirements. This technique works for both time
% and frequency domain iddata.
%
% It is also possible to merge models after estimation. This technique can
% be used to "average out" independently estimated models. If the noise
% characteristics on multiple datasets are different, merging models after
% estimation works better than merging the datasets themselves before
% estimation.
%% Additional Information
% For more information on identification of dynamic systems with System
% Identification Toolbox visit the
% <http://www.mathworks.com/products/sysid/ System Identification Toolbox>
% product information page.