The reduction of diagnostic information In the evolution investigation of state machines

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University of Technology and Life Science

Summary

Automation of the investigation system of evolution of the technical system con-dition (machines) in which diagnosing distinguishes itself from concon-dition prognosing and genesis requires qualifications to gather diagnostic parameters describing the change of machine condition during exploitation. The notion used above joins with suitable criteria and investigation of these problems in the search for the solution. The achievement of this aim requires studying the methodology of reduction of diag-nostic parameter gathering, including optimization and performance of the solution pattern. The implementation of settlements and proposals included in the study should enlarge the effectiveness and efficiency of diagnosing machines, and at the same time contribute to rationalizing their exploitation. The results of investigations connected with the implementation of procedures of monitoring the technical condi-tion of machine engines and the investigacondi-tion of chosen arrangements of mechanical vehicles were introduced. Examples of the rule of diagnostic inference were pre-sented for the gathering of diagnostic parameters and opinion on the condition. Keywords: machine state evolution, reduction diagnostic information, diagnostic procedure 1. Introduction

Diagnostic parameters are gathered from exit parameters. On the basis of investigation results and settlements in the works [13,17, 20,22, 23], with the aim of confirming some proposals con-tained in the works relating to reductions of diagnostic information [1,2,3,4,6,8,12], marking the gathering of diagnostic parameters in the process of diagnosing should include taking into account the prognosis and genesis of the condition of machines:

a) the ability to imitate the changes of the condition of a machine during exploitation; b) the quantity of information about the condition of a machine;

c) suitable changeability of the value of diagnostic parameters during the exploitation of a machine.

Suitable methods, procedures and algorithms taking into account these postulates were introduced below.

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2. The choice of diagnostic parameters in the process of diagnosing

Technical condition parameters of a machine change in time because they depend on the course of processes extorting aging. It was settled [5,6,16] that diagnostic parameters can reflect the condition of machines and they depend on changes of the parameters of state and time:

(

)

Y

₌

Y W

,

_Θ

(1) Their qualification makes the recognition of the technical condition of a machine possible.

The gathering of diagnostic parameters Y distinguishes itself from the gathering of exit pa-rameters YWY which describe the course of the exit processes (working processes and concurrent)

dependent on the condition of a technical object:

(

)

Y

_WY

=

Y

_WY

W

,

Θ

(2) Mutual relationship of state and exit parameters fulfils the following conditions below:

a) Condition of a unit – only one determined value of an exit parameter answers every value of the parameter of state;

b) The width condition of the field of changes – the largest relative change of the value of an exit parameter for a fixed value of the parameter of state;

c) The accessibility condition of the measurement of an exit parameter – it is characterized by the coefficient of the cost of measurement cj or the time of measurement tj;

d) The condition of measurability forms for the function. The function is measurable if there is a gathering for every k [22]:

{ : ( )

W Y W

₁ _j ₁

<

K

}

(3) The fulfilment of conditions 1 ∧ 2 ∧ 3 ∧ 4 favour from YWY the gathering of diagnostic

pa-rameters initially Y. A more exact distinction of gatherings applies most often the criterion of the minimum mistake of diagnosis. It distinguishes itself from the parameters which are characterized by the minimum mistake of diagnosis and the procedure of the choice of diagnostic parameters according to the minimum mistake of diagnosis.

The qualification of the mistake of diagnosis D is the essence of this method, i.e. the area of „cover” thickness of the conditional probabilities of the parameter was defined by Serdakow in the function [2,3] of the following dependence:

D

P

S

y

Q

P

S

y

Q

j j

=

§

©

¨¨

· _¹

¸¸ ⋅

+

§

©

¨¨

· _¹

¸¸ ⋅

1 1 2 2 (4)

Meanwhile, the probability of mistake and kind Q1 consists in the credit of machine in the

condi-tion of fitness S1 to condition of unfitness S2:

Q

f

y

S

dy

j j ygr 1 1

=

§

©

¨

· ¹

¸

+∞

³

(5)

(3)

and the probability of the mistake II kind Q2 consists in the credit of machine in condition of

unfitness S2to condition of fitness S1:

Q

f

y

S

dy

j j y_gr 2 2

=

§

©

¨

· ¹

¸

−∞

³

(6) Then, the choice of the „best” parameter through the minimization of the mistake of diagnosis is

as follows:

( )

y

j

D

j *

₌

_min

(7) The choice of diagnostic parameters according to the introduced method moves then to:

1. The analysis of parameters, depending on:

a) the investigation of the significance of the changes of diagnostic parameters value nearing the change of the technical condition of a machine;

b) marking and estimating the value border ygr according to the criterion of the smallest

Bayesa risk near the foundation of the value of the costs of mistakes and II kind.

2. The quantitative analysis which consists in the choice of parameters with regards to the criterion of the minimum mistake of diagnosis.

The gathering of diagnostic parameters whose elements are characterized according to good distributive properties and compartments of their changes are qualified near the change of the condition of a technical object and value border ygrj(ygrd, ygrg), together with the mistakes of the

diagnosis as a result of the realization of the procedure.

3. The choice of diagnostic parameters in the process of prognosis and genesis Gathering diagnostic parameters from gathering exit parameters.

On the basis of conducted investigations [13,14,15,16,18], with the aim of confirmation of some contained proposals in works related to reductions of diagnostic information in the process of prognoses [1,2,4,6,7,9,12], marking the gathering of diagnostic parameters and generating the condition of machines should be performed while taking into account the following issues:

a) the ability of the imitation of the changes of machine condition during exploitation; b) the quantity of information about the condition of a machine;

c) suitable changeability of the value of diagnostic parameters during the exploitation of a machine.

Suitable algorithms taking into account these postulates were presented as methods below. 3.1. The method of the maximum relative change of diagnostic parameter

In this method, a diagnostic parameter which possesses the largest value of the coefficient kj is

the most important. It takes into account an average speed of the change of parameters in a compartment of time (Θ1, Θb). It defines itself according to the following dependence:

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kj =

b

j j j m =1

¦

, bj =

¦

−

Θ

−

Θ

−

Θ

+ K i i i j jg i j i j

y

K

=1 1 1 , 1 +

)

(

)

(

)

(

)

(

1

₍₈₎

where: K – the number of elements of a temporary row in a compartment (Θ1, Θb).

3.2. The method of correlation of the value of diagnostic parameters with the condition of the machine

The method consists in the investigation of the correlation of the value of diagnostic parame-ters with the condition of the machine rj= r(W, yj) (alternatively from the exploitation, (rj = r((Θ,

yj)): rj =

¦

= = =

−

Θ

−

Θ

−

Θ

−

Θ

K k K k jk j k K k k jk j

y

1 1 2 , 2 1 ,

)

(

)

(

)

)(

(

(9)

¦

=

Θ

=

Θ

K k k

K

1

,

¦

=

K k k j j

y

K

y

1 ,

1

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where: rj = r(In, yj); j = 1,..., m – the coefficient of the correlation between variables In

(condi-tion

of a machine) and yj,

rjn = r(yj, yn); j, n = 1,..., m; j ≠ n – the coefficient of the correlation between changing yj and yn.

In case of the lack of data from the gathering in, they are replaced near the foundation, and the delimitation of the procedures of recognizing machine condition is realized in the compartment of normal waste, sometimes machine exploitation. Then, rj = r(Θ, yj); j = 1,..., m; k = 1,..., K (rj –

the coefficient of the correlation between changing Θk∈(Θ1, Θb) (Θk – the time of machine

exploi-tation ) and yj).

3.3. The method of the maximum informative capacity of a diagnostic parameter

The creation of the method consists in the choice of a parameter delivering the largest quantity of information about the condition of a machine. The diagnostic parameter has the largest meaning in the qualification of the change of the state, is correlated with it more strongly and correlated with different diagnostic parameters more faintly.

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This dependence introduces a figure of a coefficient of informative capacity – a diagnostic pa-rameter hj which is the modification of a coefficient treating to the gathering of variables as an

explanatory econometric model [21]:

hj =

¦

≠ =

+

m n j n j n j j

r

, 1 , , 2

1

(11) rj, n =

¦

= = =

−

K k K k n k n j k j K k jk j nk n

y

1 1 2 , 2 , 1 , ,

)

(

)

(

)

)(

(

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¦

=

K k k j j

y

K

y

1 ,

1

;

¦

=

K k k n n

y

K

y

1 ,

1

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In case of the lack of data from the gathering in, they are replaced near the foundation, and the delimitation of the procedures of recognizing machine condition is realized in the compartment of normal waste, sometimes machine exploitation. The advantage of the methods introduced above is that one-element is let choose from the gathering of exit parameters. The one-element gathering applies to the case when a machine is decomposited on teams, and the choice of one diagnostic parameter is necessary. One receives a poly unit gathering, when one complies with introduced procedures, and sharp limitation depends on the gathering of diagnostic parameters, whose values of coefficients are larger (smaller) from, received for method, small (large) positive numbers suitably.

The considerations introduced above formulated in the figure of algorithms of marking the gathering of diagnostic parameters.

4. Algorithm of the reduction of machine parameter gathering

Recognizing the condition of machines introduced in the study proposed not a very numerous gathering of admissible solutions (the gathering of the methods of diagnostic parameter choice in individual areas of recognizing the state) and cannot formulate the conclusion. Because of this, the worked out methodology of the optimization of the gathering of diagnostic parameters has the final character, and the element of the project of a system of recognizing machines can make up for it. The possibility of its application in all the stages of the existence of machines, however, can make up for the basis of more works in area software and hardware.

An algorithm of the reduction of the gathering of parameters of diagnostic machines contains the following stages:

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a) the gathering of the value of diagnostic parameters in the function of the time of machine exploitation { yj(Θk)}, the received implementation of passive - active experiment, where

Θk∈(Θ1, Θb);

b) the gathering of the value of diagnostic parameters:{ yj(Θ1)} – nominal values, { yjg }–

border values, j = 1, …, m;

c) the gathering of the conditions of a machine { Θk: { si}, k = 1, …, K; and = 1, …, And }

definite in the time of the implementation of passive – active experiment, where Θk∈(Θ1,

Θb);

d) the cost of diagnostic parameters c(yj) = const.

2. The optimization of the gathering of the value of diagnostic parameters (only in case of a large number of the gathering Y, e.g. m > 5). One marks the gathering of diagnostic parameters for help:

a) the method of correlation of the value of diagnostic parameters with the condition of a machine (sometimes from the exploitation, rj = r(In, yj), (rj = r((Θ, yj));

b) the method of quantity of the information of diagnostic parameters about machine condi-tion hj one uses the values of weights.

The aim of the choice of gathering diagnostic parameters [5,11, 4,23]: a) standard computational weights w1j:

w1j =

¦

= m j j j

w

1 (15) wj = j

d

1

, dj =

(

1 −

r

_j*

)

2

+

(

1 −

h

*_j

)

2 (16) j j j

r

max

*

₌

_, j j j

h

max

*

₌

₍₁₇₎

b) the maximization of the value of weights w1j and the choice of diagnostic parameters

ac-cording to the above-mentioned criterion were accepted as a criterion of the choice of a diagnostic parameter (diagnostic parameters).

c) there should be possible introduction weights w2j (standard values) from the compartment

(0,1) considering user preference and the choice of diagnostic parameters according to the above-mentioned criterion.

5. Conclusions

Recapitulating the questions relating to theoretical bases of the methodology of the reduction of diagnostic information considered above, that the following conclusions could be drawn: 1. The process of recognizing the condition of machines embraces the following kinds of diagnos-tic investigations: the opinion of the state, genesis and prognosis.

2. Delimitation of the gathering of diagnostic parameters is a basic question in the process of recognizing the condition of machines:

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a) in the process of the opinion of the condition of machines –criterion difference of the conditions of a machine;

b) in the process of prognosis and genesis with the utilization of the methods: the correlation of the value of a diagnostic parameter with the state and sometimes machine exploitation and informative capacity of a diagnostic parameter.

Now, one can formulate results of the diagnostic investigation of the evolution of the con-dition of machines, that is:

a) the change of the condition of a machine during exploitation;

b) the description of the condition of a machine with the help of features of the state and de-pendence among the features of the state and diagnostic parameters.

The main problems appear near the solution, so the choice of the „best” diagnostic parame-ters describing the current state and their change during the exploitation of the machine are crucial. The „best”, the notion used above, joins with suitable criteria and investigation of these problems in the categories of the search for an optimum solution; meanwhile, the investigation of these problems in the categories of a multi-criterion solution requires many criteria of opinion, e.g. for individual tasks (local optimum), or for the task of a general investigation of the evolution of the condition of a machine (global criterion).

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REDUKCJA INFORMACJI DIAGNOSTYCZNEJ W BADANIACH EWOLUCJI STANU MASZYN

Streszczenie

Automatyzacja systemu badania ewolucji stanu systemów technicznych (ma-szyn), w którym wyróĪnia siĊ diagnozowanie, prognozowania stanu i genezowanie stanu wymaga okreĞlenia zbioru parametrów diagnostycznych opisujących zmianĊ stanu maszyny w czasie eksploatacji. Problemy wystĊpujące w procesie redukcji in-formacji diagnostycznej sprowadzają siĊ do:

a) analizy procesu pogarszania siĊ stanu technicznego maszyn, okreĞlenia sta-nów maszyny, okreĞlenia tendencji i dynamiki zmian wartoĞci parametrów stanu;

b) wyboru „najlepszych” parametrów diagnostycznych opisujących ewolucjĊ stanu maszyny;

c) wykorzystania informacji diagnostycznej w badaniu ewolucji stanu w celu podjĊcia odpowiedniej decyzji eksploatacyjnej, np. w zakresie minimalizacji zagroĪeĔ bezpieczeĔstwa o Ğrodowiska eksploatowanych maszyn.

UĪyte powyĪej pojĊcie „najlepsze” wiąĪe siĊ z przyjĊciem odpowiednich kryte-riów i rozpatrzenie tych problemów w kategoriach poszukiwania rozwiązania poliop-tymalnego. OsiągniĊcie tego celu wymaga opracowania metodyki redukcji zbioru parametrów diagnostycznych, w tym sformułowania zadania optymalizacji wielokry-terialnej oraz przedstawienia schematu jego rozwiązania.

Realizacja ustaleĔ i propozycji zawartych w opracowaniu powinna zwiĊkszyü skutecznoĞü i efektywnoĞü diagnozowania maszyn, a tym samym przyczyniü siĊ do działaĔ racjonalizujących ich eksploatacjĊ.

Słowa kluczowe: ewolucja stanu maszyn, redukcja informacji diagnostycznej, procedury diagno-styczne

This paper is a part of WND-POIG.01.03.01-00-212/09 project. Henryk Tylicki