М.Г.Гоман и другие, краткое описание пакета программ интерактивной идентификации PII, 1998 г., Центральный Аэрогидродинамический институт, г. Жуковский, 1998 г. M.G.Goman et al, "PII - Programs of Interactive Identification. Brief description", Central Aerohydrodynamics Institute (TsAGI), Zhukovsky, Russia, 1998.

1. PII - Programs of Interactive
Identification
( brief description ).
© Central Aerohydrodynamics Institute (TsAGI),
Flight Dynamics and Control Department.
Zhukovsky, Moscow region, 140160, Russia.
e-mail: krit@tsagi.rssi.ru

2. PII is designed for:
u
u
determination of the relationships between the
dependent variable and some independent ones
identification of dynamic system parameters
PII consists of two parts:
• PIIREGR - linear regression
• PIIMTM - nonlinear dynamic system identification

3. System requirements
The program uses reliable mathematical techniques and
has user-friendly interface based on menu, hot-keys,
dialogue, graphic and hint windows. It works properly
on any IBM PC computers with the processor from 286
up to modern ones. To increase speed it works directly
with video-memory. That is why we recommend to use
it in DOS mode.

4. Program for linear
regression PIIREGR
PIIREGR uses method of linear regression to:
u estimate parameters of the given model parameters identification
u exclude statistically insignificant regressors from
the model - structure identification
This program is used in TsAGI during 5 years mainly for creating
the mathematical models of the aerodynamic forces and moments
coefficients based on wind-tunnel or flight test data. It is necessary to
create the data base for simulation of aircraft flight dynamics.

5. Stages of working with
PIIREGR
reading or creating (by built-in or external
editor) the file with the mathematical model
description
u reading file or group of files containing
experimental data on processes realizations
u performing regression in interactive manner
u keeping the results of regression
u

6. Reading or creating the
mathematical model and data
u
u
If the model already exists, read it using menu
model|read. In order to create model choose
model|edit or press <F4> to call built-in editor
and then create it following the rules of the special
language. You should use cursor keys to move
selected bar along line and pop-up menus and
<Enter> to execute the marked menu command.
To read file with the experimental data choose the
menu data|read data file or press <F3>.

7. Performing the regression
u
u
u
u
Select menu window to choose windows to be
shown or window|all to see all the windows
To start regression procedure choose run|regression
or press <F5>
To make one step of regression choose run|step of
regression or press <F6>
To identify the model choose run|identification or
press <F7>

8. Starting the regressionCoefficients of
Regressors
(screen view)
Menu
Process
the regression

9. After the first step of the
regression
model

10. The regression is completed
Process
(white)
Model
(yellow)

11. Statistical criteria
Fisher’s
criterion
R2 criterion

12. Saving the results
u
u
To save resulting coefficients choose data|wright
coefficients and then input the file name where
coefficients to be saved
To create the full protocol ( file name.log ) choose
options|auto log record before the start of the
regression procedure. You can see this file with
any text editor or viewer

13. PIIREGR demo version
The simplest example is supplied to evaluate
PIIREGR:
u
process y ( x ) = sin x - 0.5 sin 2 x + 0.3 cos 5 x - 0.1 sin 7 x + 0.5r
with the noise r £ 1 is expanded into Fourier series (
model is in the file ..regrmodel1.mod, process is in
the file ..regrprocess1.dat )

14. Program for identification of
dynamic systems - PIIMTM
PIIMTM is used to estimate parameters of the given
model presented in the general nonlinear form
ì dx = F( x,p ), x Î R n , p Î R k
ï dt
ï
íG mod = G( x,p),
ïa £ p £ b , i Î[1, k ]
i
i
ï i
î
p is the vector of system parameters identified with the
objective function minimization
F(p ) = {G mod ( x, p ) - G exp ( x, p )} 2 ® min
p

15. Application field
This program is used in TsAGI during 5 years for creating the
mathematical models of the unsteady aerodynamic forces and
moments coefficients based on wind-tunnel or flight test data in a
wide range of motion parameters. It is necessary to create the data
base for simulation of aircraft flight dynamics at high incidences.
A great number of interesting results was obtained with the aid of
this program. Some of them were reported on 10th and 11th IFAC
Symposium:
•Goman, M., A.Khrabrov and S.Usoltsev. Identification of Unsteady Aerodynamic
Model of a Delta Wing at High Angles of Attack. 10th IFAC Symposium on
System Identification, SYSID’94, p.p. 3.073-3.078
•Goman, M., A.Khrabrov and S.Usoltsev. Unsteady Aerodynamic Model for Large
Amplitude Maneuvers and its Parameter Identification, 11th IFAC Symposium on
System Identification, SYSID’97.

16. Stages of working with
PIIMTM
Dynamic system identification consists of two steps:
• search of the objective function F(p) minimum - external task
• system modelling at fixed parameters p - internal task
To solve these tasks for an acceptable time the program must have
the high computation speed. That is why the model presentation as
in the PIIREGR (run-time) is not acceptable here.
The following steps are necessary to identify a model:
u describe model with the C++ language using some macros
u create an executable unit (with the aid of PIIMTM, C++
compiler and linker)
u perform the identification (working with the executable unit)

17. Working with executable unit
At first you should:
u
u
u
u
read process or group of processes (menu input|read data)
set sensors and fixed values (menus parameters|sensors and
fixed|set fixed).
set parameters at which the model to be minimized (menu
parameters|variables) and press F9 (run|evaluate) to see the
results of modelling.
choose the method of minimization (menu parameters|method)
Now one can start identification.

18. Setting the guesses for the
unknown parameters
Constraints
Unknown
parameters
and their values
Experimental
process (z)
These parameters
are excluded from
identification

19. Choosing the method of
minimization

20. Starting identification
y = z’ - phase
variable - speed
(model)
Experimental
process (z - deflection)

21. Identification is being
performed

22. Identification has been
performed
Model
(white)
Experimental
process (grey)

23. Objective function profile

24. Saving the results
If the objective function minimum hasn’t been
reached, repeat identification procedure one more
( if it is necessary choose new guesses for the
unknown parameters). To see the obtained values of
the unknown parameters press <F4>. If the results
of identification are acceptable one can save them
(menu results).

25. Demo version
To evaluate this program two examples in model description text
and corresponding executable units are supplied:
u
The simplest dynamic system - the stone on the spring ( two
unknown parameters) (..mtmexample1model1.exe )
d 2x
dx
+ 2a + b 2 x = 0
dt 2
dt
u
You have the set of experimental data: ti , x (ti ), i = 1... N . Task is
to find a and b.
More complicated model( 38 unknown parameters). Mathematical
model of C L (a ( t ), q ( t )) at high angles of attack
(..mtmexample2model2.exe ) (for full description of the model
look at Proceedings of the 10th and 11th IFAC Symposium on

26. Information about developers
Programs of Interactive Identification
were developed in Flight Dynamics and Control Department
of Central Aerohydrodynamics Institute (TsAGI),
The leader of project is Dr. Mikhail Goman.
There is a possibility of development PII for Windows 95/NT
Our official address:
TsAGI, Zhukovsky, Moscow region, 140160, Russia.
e-mail: krit@tsagi.rssi.ru
(official)
sspchram@aha.ru
(Dr. Andrew Khramtsovskiy)

27. Thank you for your attention
Now you have enough information to start demo versions of
PIIREGR ( piiregr.exe ) and PIIMTM ( model1.exe, model2.exe )
(which are in the directory piipresregr) in order to assure that
these programs are excellent tools to perform linear regression and
dynamic systems identification for any your purposes.
Warning! Demo version will works only with data sets and models
which are supplied.