RELIABILITY AND ITS RELATION
TO REGULATION AND DIAGNOSTICS IN THE
MACHINERY EXPLOITATION SYSTEMS
Lindstedt P.
Air Force Institute of Technology, Warsaw
Abstract: The paper presents a cybernetic system that describes the exploitation of technical
equipment. It is emphasized that basic parameters of the system include reliability, diagnostics and regulation, therefore mutual relationships between those three parameters are established and described. It is proved that the “map of defects” of the object (reliability) makes it possible to determine a set of diagnostic signals that represent the technical condition of the object and reflect possible alteration of the object status (diagnostics). Subsequently, detected alterations can serve as a background for necessary adjustment of technical equipment (regulation).
Keywords: exploitation system, reliability, technical diagnostics, regulations.
1. Introduction
Technical services of complex and expensive technical equipment (aircrafts, helicopters and avionic engines) understood as adjustment, diagnostics and reliability is the issue of increasing importance in the exploitation process thereof.
It was noticed that there exists a close relationship between the activities related to regulation and diagnostics of technical equipment and its reliability within its system of technical exploitation.
In practice of technical exploitation of equipment the following simple sequence of events can be noticed:
adjustment of various parts and module is usually caused by wear and tear of technical equipment components hence the need of adjustments is connected with diagnostic operations,
excessive wear of equipment leads to its damage thus diagnostic operations are connected with the reliability of the object,
reliability of the equipment and the developed map of defects leads to establishing an optimal set of diagnostic signals, thus reliability is connected with diagnostics.The above sequence confirms that alterations in the schemes of regulation, diagnostics and reliability must be considered concurrently within the frames of a unified cybernetic system for exploitation of technical equipment.
2. Cybernetic system for exploitation of technical equipment
The diagram of a model that reflects a cybernetic system for exploitation of technical equipment is presented in Fig. 1. The diagram shows that the object is subject to permanent deterioration during its entire lifetime, including the shelf life (readjustments, wear and tear, increase of defect rates). Therefore the deterioration process should determine the structure of the maintenance system aimed to sustain the performance of the equipment. Thus the maintenance scheme for any equipment should comprise systems for regulation, diagnostics and reliability [5, 7, 8].
Maintenance system to sustain the equipment performance System for equipment
exploitation System for equipmentstorage Cybernetic system for exploitation
of technical equipment
Deterioration De-adjustment
Wear and tear Defectiveness
Adjustment Diagnostics Reliability Operation purposes Deterioration Ageing Corrosion „t” „t” and „” „tE”
Fig. 1. Major components of the cybernetic system for exploitation of technical equipment:
t – dynamic time (Newton-type), – evolution time (Bergson-type), tE – exploitation time
The adjustments are aimed to maintain optimum performance quality of any technical equipment in accordance with the theory of automation. It is carried out in real time, i.e. dynamic time – “t” [8, 9, 11].
The main objective of diagnostics is to acquire information on alterations in the technical status of equipment which occur when it is exploited. The information is collected by means of indirect methods, without a need to dismantle the equipment [8, 10]. In diagnostic systems the two types of activities are distinguished: the first type of operation that is carried out in dynamic time – “t” and maintenance that is carried out during evolution time of the equipment – “”. Knowledge about alterations in technical status of the equipment provides the background for such exploitation of equipment that takes account of its technical condition. [1, 5, 12].
Reliability is aimed at specifying the reliability characteristics of the equipment on the background of information on defects that have occurred during the exploitation of the system. The reliability-related characteristics are defined as functions of the exploitation time “tE” [2, 3, 13].
According to the rules of cybernetics, any modifications in regulation, diagnostics and reliability of technical equipment are observed and recorded in a system log [1, 12]. These modifications are described in the exploitation time “tE” and serve as a background
for th planning of anticipated changes in operation of the equipment.
Diagnostics is a component that plays an essential role in maintaining sound operational conditions of the equipment as it is directly connected with the systems of regulation and reliability [8. 9].
3. Diagnostics in the cybernetic system for exploitation of technical
equipment
The diagram of a diagnostic system for technical equipment and its connections with the systems for regulation and reliability of the equipment is presented in Fig.2.
The analysis of Fig. 2 shows that the diagnostics concerns the considered equipment equally as its environment [5, 7] and the diagnostic procedures are performed in two different time scales – “t” and „” but the two scales are closely connected by the diagnostic activities that comprise both diagnostic tests (performed in the time scale “t”) and diagnostic inference (performed in the time scale “”).
Diagnostic tests (Fig. 2) are the essential component of the diagnostic process and are decisive of the effectiveness of the entire process. They can be subdivided into several stages that include the following [5, 10]:
I. Getting familiar with the equipment . In this stage of diagnostic tests wide knowledge about the equipment and its environment should be acquired.
II. Measurements of diagnostic signals. Here the suitable measurement techniques are selected and an accurate and thorough instruction for measurements is elaborated. This instruction should be in force in unaltered form during the entire lifetime of the equipment.
III. Removing interferences from diagnostic signals. This process is carried out by applying adequate filters or correlators (which is a more universal and efficient solution) in measurement circuits,,. which transpose measured timings of diagnostic signals (in the dynamic time scale t) onto timings of correlated functions (in the scale of transformation time and than onto functions of power spectral density (functions vs. the independent variable ).
Diagnostic tests
– “t” inference – “”Diagnostic Diagnostic system for
technical equipment Description of equipment and its environment Knowledge base Diagnosis Map of defects Diagnostic signals Models and diagnostic hresholds Comparison of models – alterations System of reliability Diagnostic susceptibility Measurements database System of regulation
Fig. 2. The diagram of a diagnostic system and its interconnections with the systems for regulation and reliability
IV. Forming of diagnostic signals. This operation is aimed to transform all measured signals to the non-dimensional form. The calculation value of the specific signal that results from the equipment design serves as a reference value for rating. V. Development of a database. The database shall comprise tables of quality
factors for the formed (rated) signals, correlation functions and power spectral density of signals. The database may also include matrices of parameters related to mathematic models that describe the equipment by the methods of static and dynamic identification. Development of databases is the final stage of diagnostic tests.
Diagnostic inference (Fig. 2) is the subsequent stage of the diagnostic process. It consists in transformation of results from diagnostic tests (databases) and other information about the equipment and its environment (base of knowledge) onto diagnosis, genesis and prognosis. Diagnostic inference includes several different stages [1, 5, 10].
I. Development of a diagnostic model. It consists in establishing relationships (on the background of the acquired knowledge) between diagnostic signals and alterations in technical status (defects) of the equipment. Formal assignment of diagnostic signals to specific faults by means of a diagnostic model is absolutely indispensable in the diagnosis-making process. The diagnostic model makes it possible to take a “snapshot” of a continuously changing technical condition of the equipment at a specific moment 0 when the diagnosis is made and to keep the snapshot unaltered
until the subsequent moments of diagnosis-making 1, 2 etc. occur. Therefore no
diagnostic rules can be implemented without a diagnostic model.
II. Development of algorithms for comparison of diagnostic models. This stage involves rules for comparison of models from the current diagnosis-making process with preceding models from the history of the equipment operation life. The obtained alterations of the model along with its parameters are transformed into changes in technical condition of the equipment.
III. Computer-aided diagnostic inference. Deals with problems of efficient elimination of subjective operation of diagnostic personnel from the diagnostic inference process and substitute such subjective approach by an expert system that works identically and follows the same rules both now and in future. Theoretical investigations confirmed by practical expertise give the evidence that strict adhesion to identical rules of inference, which is typical for computer expert systems, is much
more efficient that personal intelligence of an individual diagnosis expert who evaluates the system in real-time mode and can come to the conclusions that differ from suppositions of other diagnosis experts.
4. Reliability in the systems for exploitation of technical equipment
and its relations with diagnostics
Any technical equipment should be reliable, i.e. capable to perform its required functions under stated exploitation conditions [2, 3, 4, 13]. Properties of the equipment that determine its suitability for specific applications can be described by means of measurable functions attributable to essential parameters of the equipment. Any alterations to essential parameters of the equipment result in change of its reliability status. Partial or entire loss of the equipment applicability as well as alterations in essential parameters of technical equipment are phenomena that in Polish Standards (PN) are referred to as “failures”. The following failure types can be distinguished (understood as alterations of measurable essential parameters of the equipment): catastrophic breakdowns, ageing degradation and temporary defects (Fig. 3).
Fig. 3. Diagrams for alteration of measurable essential parameters „U” during operation of the equipment over the time period tE:
a) catastrophic breakdown, b) ageing degradation c) temporary defects
tU – failure time for technical equipment, ug/d – upper and lower limit for the parameter
value
The stochastic process that governs the occurrence of technical equipment failures depends on initial conditions and alterations enforced by external factors. The process is described by probabilistic functions (indicators) of reliability. Selection of reliability indicators for technical equipment (binary – GO/NOGO) that is manufactured in large lots or series is carried out by the standard PN-77/N-04010.
U
ug tEU tE ud a) U
ug tEU tE ud b) U
ug tEU tE ud c)
The basic functions and indicators of reliability are the following: Function of reliability:
)
(
)
(
t
EP
T
t
ER
(1) where:T
– random variable that describes the survival (operating condition) of the equipment,Function of failures:
)
(
1
)
(
)
(
t
EP
T
t
ER
t
EF
(2)Function of density of probability of failures
E E E
dt
t
dF
t
f
(
)
(
)
(3)Function of failure intensity:
(
)
(
(
)
)
E E Et
R
t
f
t
(4)Expected value of the equipment survival (until the first failure) :
0 ) ( ) (T R tE dtE E (5)During the exploitation process, according to the standard PN-77/N-04005 the following reliability estimators are calculated:
n
t
n
t
R
E E)
(
)
(
*
(6)where:
n
(
t
E)
– number of units that survived the time period
0
t,
E
with nofailures, n – total number of units under test
n
t
m
t
F
E E)
(
)
(
*
(7)where:
m
(
t
E)
– number of units that experienced defects over the time period
0
t,
E E E E E E Et
t
n
t
t
n
t
n
t
)
(
)
(
)
(
)
(
*
(8)where:
n
(
t
E
t
E)
– number of units that survived the time period
0
t,
E
t
E
with no failures, tE – time interval for testing the equipment
n i it
n
T
E
1 * *1
)
(
(9)where: t – time that expires until failure of the ii th unit occur.
The above functions make it possible to select an appropriate mathematical form for the function of reliability R(t) and other ones that are the most suitable to describe the stream of faults that is observable during equipment exploitation, e.g. R(t)et
– exponential distribution, R(t)et – Weibull’s distribution, etc. [2, 3, 4]). Therefore, number of failures and their distribution in time serve as a background to determine reliability-related characteristics of technical equipment. It should be mentioned here that an equipment defect is understood as such an undesired status of an object when the value of its essential parameter U (Fig. 3) exceeds permitted thresholds
ug or ud and the object itself changes its status from operable to inoperable.
It is why the need of failure prediction has appeared, which, in turn, implies the need to trace variations of unavailable and measurable essential parameters of equipment. This will be feasible after the use of the following diagnostic rules:
1. Every change in the parameters of the technical status is a source of measurable and available diagnostic signals.
2. Diagnostic signals enable indirect monitoring of unavailable and essential parameters of technical status.
3. Diagnostic signals make it possible to predict that any essential parameter is about to reach it threshold limit ug or ud.
US
OT
w u x y n
z
Application of diagnostic rules to prediction of possible defects enables the verification of required reliability characteristics during the exploitation process without having to wait for the actual failures of the equipment.
5. Regulation in the systems for exploitation of technical equipment
and its relations with diagnostics
The technical equipment should be properly adjusted. It means that adequate interrelationships between signals related to equipment operation should be assured [5, 11].
According to the rules of automatic control, the equipment must be tolerant to interferences that originate from the outside and should be adaptable, i.e. must keep pace with control signals determined by the equipment user.
In the exploitation process it was noticed that the equipment is subject to wear and tear during its operation and this causes, inter alia, its deregulation. Thus the equipment must be tuned up to sound operating condition by adjustment of the settings of the equipment. Therefore any adjustment of required settings aimed to ensure meeting of the requirements to operation quality of the equipment (equipment regulation) has its reasons in spontaneous alterations of design parameters of the equipment i.e. its technical status (equipment diagnostic).
The scale of dependence between the status of equipment settings and its technical condition is subject to variations. In extreme cases an object that is functionally inoperable can be technically correct and on the other hand, technical incorrectness may be combined with functional operability [5, 6, 9].
The degree of influence of individual components of the equipment and its parameters on its operational quality can be evaluated by analyzing the function of structural, parametric and interference sensitivity [6,11].
A technical object with a control system that operates in an open control loop is shown in Fig. 4.
Fig. 4. Technical object with an open-loop control system: OT – controlled unit,
US – control unit,
w – adjustable operation signal, n – settings for the control unit, u – signal by which the US affects
z – interference, y – usable signal, x – input signal
A technical object with a control system that operates in a closed control loop is shown in Fig. 5.
Fig. 5. Technical object with an closed-loop control system
OT – controlled unit, US – control unit,
w – adjustable operation signal n – settings for the control unit, u – signal by which the US affects the
OT,
z – interference, y – usable signal, x – input signal,
Components of the diagrams from Fig. 4 and Fig. 5 can be described by the transmittance function GUS whereas the controlled unit is characterized by the transmittance function
GOT.
Therefore the operation of the circuit from Fig. 4 is described by the following transmittance functions: forz 0 w GUSGOT s W s Y H ) ( ) ( , (10) for w = 0 z GOT s Z s Y H ) ( ) ( (11) Operation of the circuit from Fig. 5 can be described by the following transmittance functions for
z = 0
OT US OT US wG
G
G
G
s
W
s
Y
H
1
)
(
)
(
(12) forw = 0
OT US OT zG
G
G
s
Z
s
Y
H
1
)
(
)
(
(13) where: Y(s), W(s), Z(s) – stand for transform of the signalsy(t), w(t)
andz(t); s –
complex variable.US
OT
e w n u z x yThe above description serves as a background for determining the function of circuit sensitivity to alterations in its design, parameters of its components and environmental factors, which are represented here by the signals “w” and “z”,
Sensitivity of a system to alterations in its design is described by the following functions of design sensitivity: US W W US US US W W H G
dG
dH
H
G
G
dG
H
dH
W
W US
, (14) OT W W OT OT OT W W H GdG
dH
H
G
G
dG
H
dH
W
W OT
, (15) OT Z Z OT OT OT Z Z H GdG
dH
H
G
G
dG
H
dH
W
Z OT?
. (16)Based on the sensitivity functions (14) (16) one can establish how the design solutions of the system components affect its the static and dynamic quality, thus the interrelations between technical status of the technical equipment (diagnostics) and its operation status (automatic control and regulation) can be established.
Sensitivity of a system to alteration of parameters related to transmittances of its components can be described by means of the following functions of parametrical sensitivity: i W W i H k dk dH H k W W i , (17) i Z Z i H k dk dH H k W Z i , (18) i W W i H T dT dH H T W W i , (19)
i Z W i H T dT dH H T W Z i , (20)
where additional factors are used, namely: k – consecutive parameters of i
H
W andH
Ztransmittances and
T
i - consecutive time-constants ofH
W andH
Z transmittances.Based on functions of parametrical sensitivity described by the equations (17)(20), the impact of transmittance parameters (technical condition) on the dynamic quality of the equipment (operational status) can be established.
Sensitivity of the system to its environment in the time space can be described by the following functions of sensitivity to external signals:
z y y z dz dy y z Wy z , (21) w y y w dw dy y w Wy w , (22)
where additionally: y ,
z
, w – derivatives of they
,z
,w
signals.Therefore the function of sensitivity to external signals provides information how the operation mode (w) and operation conditions (z) affect the operation results (y).
To recapitulate, one can state that the determined functions of sensitivity to alterations of its design, parameters and external signal establish interrelationships between regulation actions and diagnostic ones.
Conclusions
Changes of technical conditions of equipment (status-related parameters) as are shown in Fig. 4 and Fig. 5 result in alteration of its operation mode as quality factors of equipment operation are subject to amendments. Because the operational quality of equipment should be continuously maintained at appropriate level, settings of control units should be tuned up according to the equipment needs (Fig. 4 and 5). Therefore the required alterations of settings of a control unit (performed during maintenance operations) serve as an evidence of changes in technical status. However, the extreme situation can be alleged that tuning up of settings to excessively worn and torn equipment may prove to be infeasible. This fact (preferably it should be predictable) serves as a background for anticipation of reliability-related characteristics.
The final conclusion can be made that regulation, diagnostics and reliability of technical objects stay in close relationships that can be optimally implemented within the cybernetic system for exploitation of technical equipment.
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